Strategies - Risksubscriptions.risk.net/wp-content/uploads/2016/03/JOIS.pdf · Strategies The...

Volume 5 Number 1December 2015

The Jo

urn

al of In

vestmen

t Strategies

Volume 5 N

umber 1 D

ecember 2015

Incisive Media, Haymarket House, 28-29 Haymarket, London SW1Y 4RX

The Journal of

■ Diffusing explosive portfolio performance evaluation of high frequency traders G. Charles-Cadogan

■ The dynamics of energy futures and equity sectors: evidence from the United States and Canada K. Smimou

■ Under the radar: structural alpha in the small-cap equity market Elena Ranguelova, Jonathan Feeney and Yi Lu

PEFC Certified

This book has been produced entirely from sustainable papers that are accredited as PEFC compliant.

www.pefc.org

StrategiesInvestment

JoIS_5_1_Dec15.indd 1 25/11/2015 09:21

Tria

l Cop

y For all subscription queries, please call:

UK/Europe: +44 (0) 207 316 9300

USA: +1 646 736 1850 ROW: +852 3411 4828

in numbers

140,000

Users

Page views

19,400+ on Regulation

6,900+ on Commodities

19,600+ on Risk Management

6,500+ on Asset Management

58,000+ articles stretching back 20 years

200+

New articles & technical papers

370,000

21,000+ on Derivatives £

Visit the world’s leading source of exclusive in-depth news & analysis on risk management, derivatives and complex fi nance now.

(each month)

(each month)

See what you’re missing

(each month)

RNET16-AD156x234-numbers.indd 1 21/03/2016 09:44

The Journal of Investment StrategiesEDITORIAL BOARD

Editor-in-ChiefArthur M. Berd General Quantitative LLC

Advisory BoardRobert Engle NYU Stern School of BusinessKenneth A. Froot Harvard Business SchoolRobert Jarrow Cornell University, Johnson School of Business

Editorial BoardJesper Andreasen Danske Bank Chris Limbach PGGMMarco Avellaneda NYU Courant Institute Alex Lipton Bank of AmericaVineer Bhansali PIMCO Merrill LynchJean-Philippe Bouchaud Capital Fund Marcos Lopez de Prado Guggenheim

Management Partners and Lawrence BerkeleyPeter Carr Morgan Stanley National LaboratoryJohn Chisholm Acadian Asset Management Dilip Madan University of MarylandDean Curnutt Macro Risk Advisors Attilio Meucci SYMMYSVladimir Finkelstein Blue Mountain Capital Jacques Pezier University of SussexRoss Garon Cubist Systematic Strategies Vladimir Piterbarg Barclays CapitalLisa Goldberg UC Berkeley Jeffrey Rosenberg BlackrockPhilippe Gougenheim Gougenheim Investments Pierre Sarrau BlackrockAli Hirsa Sauma Capital LLC Euan Sinclair Bluefin TradingPhilippe Ithurbide Amundi Asset Didier Sornette ETH Zurich

Management Cyrille Urfer Gonet & CiePetter Kolm NYU Courant Institute Peter Zangari MSCI Barra

SUBSCRIPTIONSThe Journal of Investment Strategies (Print ISSN 2047-1238 j Online ISSN 2047-1246) is publishedquarterly by Incisive Risk Information Limited, Haymarket House, 28–29 Haymarket, LondonSW1Y 4RX, UK. Subscriptions are available on an annual basis, and the rates are set out in thetable below.

UK Europe USRisk.net Journals £1945 €2795 $3095Print only £735 €1035 $1215Risk.net Premium £2750 €3995 $4400

Academic discounts are available. Please enquire by using one of the contact methods below.

All prices include postage.All subscription orders, single/back issues orders, and changes of addressshould be sent to:

UK & Europe Office: Incisive Media (c/o CDS Global), Tower House, Sovereign Park,Market Harborough, Leicestershire, LE16 9EF, UK. Tel: 0870 787 6822 (UK),+44 (0)1858 438 421 (ROW); fax: +44 (0)1858 434958

US & Canada Office: Incisive Media, 55 Broad Street, 22nd Floor, New York, NY 10004, USA.Tel: +1 646 736 1888; fax: +1 646 390 6612

Asia & Pacific Office: Incisive Media, 20th Floor, Admiralty Centre, Tower 2,18 Harcourt Road, Admiralty, Hong Kong. Tel: +852 3411 4888; fax: +852 3411 4811

Website: www.risk.net/journal E-mail: [email protected]

To subscribe to a Risk Journal visit Risk.net/subscribe or email [email protected]

http://subscriptions.risk.net/subscribe/

mailto:corpsubs%40risk.net?subject=

The Journal of Investment StrategiesGENERAL SUBMISSION GUIDELINES

Manuscripts and research papers submitted for consideration must be original workthat is not simultaneously under review for publication in another journal or otherpublication outlets. All articles submitted for consideration should follow strict aca-demic standards in both theoretical content and empirical results. Articles should beof interest to a broad audience of sophisticated practitioners and academics.

Submitted papers should follow Webster’s New Collegiate Dictionary for spelling,and The Chicago Manual of Style for punctuation and other points of style, apart froma few minor exceptions that can be found at www.risk.net/journal. Papers should besubmitted electronically via email to: [email protected]. Please clearlyindicate which journal you are submitting to.

You must submit two versions of your paper; a single LATEX version and a PDFfile. LATEX files need to have an explicitly coded bibliography included. All files mustbe clearly named and saved by author name and date of submission. All figures andtables must be included in the main PDF document and also submitted as separateeditable files and be clearly numbered.

All papers should include a title page as a separate document, and the full names,affiliations and email addresses of all authors should be included. A concise andfactual abstract of between 150 and 200 words is required and it should be includedin the main document. Five or six keywords should be included after the abstract.Submitted papers must also include an Acknowledgements section and a Declarationof Interest section. Authors should declare any funding for the article or conflicts ofinterest. Citations in the text must be written as (John 1999; Paul 2003; Peter and Paul2000) or (John et al 1993; Peter 2000).

The number of figures and tables included in a paper should be kept to a minimum.Figures and tables must be included in the main PDF document and also submittedas separate individual editable files. Figures will appear in color online, but willbe printed in black and white. Footnotes should be used sparingly. If footnotes arerequired then these should be included at the end of the page and should be no morethan two sentences. Appendixes will be published online as supplementary material.

Before submitting a paper, authors should consult the full author guidelines at:

http://www.risk.net/static/risk-journals-submission-guidelines

Queries may also be sent to:The Journal of Investment Strategies, Incisive Media,Haymarket House, 28–29 Haymarket, London SW1Y 4RX, UKTel: +44 (0)20 7004 7531; Fax: +44 (0)20 7484 9758E-mail: [email protected]




The Journal of

InvestmentStrategies

The journalThe Journal of Investment Strategies is an international refereed journal focusing onthe rigorous treatment of modern investment strategies.

Investment strategy research is a distinct subject matter, combining insights fromvarious areas of financial economics and utilizing techniques from econometrics andstatistics, among other fields. As an applied field of research, it directly impacts thepractice of asset management, a large and diverse industry with many constituents,including traditional and alternative buy-side investment managers as well as thesell-side and independent advisors. As an academic topic, it presents unique andinteresting challenges for understanding the sources of investment returns and forformulating consistent and systematic methodologies for portfolio management in adynamic context.

Much research in this area, particularly the studies going beyond classical portfoliotheory, is not currently accessible to a wider audience. In particular, many researchpapers originating from the industry are not well distributed. The Journal of InvestmentStrategies, therefore, has three fundamental aims:

(1) to foster high-quality, original and innovative work on investment strategies;

(2) to provide practitioners and academics with access to the resulting technicalresearch; and

(3) to serve as an educational forum on timely issues concerning investmentstrategies.

Content GuidelinesTopics considered for publication in the journal include:

� Fundamental strategies;

� Relative value strategies;




� Tactical strategies;

� Event-driven strategies;

� Algorithmic trading strategies;

� Principal investment strategies;

� Portfolio management and asset allocation;

� Econometric and statistical methods.

The Editorial Board will consider two types of submission:

� Full-length original papers covering both theory and practice; and

� Short expository or discussion papers for publication in the Investment StrategyForum.

Research Papers

Research papers are typically full-length academic papers of between 8,000 and10,000 words in length. Topics for research can be of interest to both academic andindustry professionals. Papers submitted for publication must be original and shouldnot have been published or considered for publication elsewhere.

Investment Strategy Forum

The Forum is intended to provide rapid communication on findings and ideas aboutinvestment strategies that are topical, expository and educational in nature. The mis-sion of the Forum is to promote active discussions of current issues. Articles shouldnot exceed 6,000 words. The main goal of these submitted papers is to educate a wideraudience and to increase understanding of the issues and topics that may not be easilyaccessible to either academics or practitioners.




The Journal of Investment Strategies Volume 5/Number 1

CONTENTS

Letter from the Editor-in-Chief vii

RESEARCH PAPERSDiffusing explosive portfolio performance evaluation of high frequencytraders 1G. Charles-Cadogan

The dynamics of energy futures and equity sectors: evidence fromthe United States and Canada 29K. Smimou

Under the radar: structural alpha in the small-cap equity market 101Elena Ranguelova, Jonathan Feeney and Yi Lu

Editor-in-Chief: Arthur M. Berd Subscription Sales Manager: Aaraa JavedPublisher: Nick Carver Global Head of Sales: Michael LloydJournals Manager: Dawn Hunter Information and Delegate Sales Director: Michelle GodwinEditorial Assistant: Carolyn Moclair Composition and copyediting: T&T Productions LtdMarketing Executive: Giulia Modeo Printed in UK by Printondemand-Worldwide

©Copyright Incisive Risk Information (IP) Limited, 2015. All rights reserved. No parts of this publicationmay be reproduced, stored in or introduced into any retrieval system, or transmitted, in any form or by anymeans, electronic, mechanical, photocopying, recording or otherwise without the prior written permission of thecopyright owners.

Marketing Manager: Rainy Gill




LETTER FROM THE EDITOR-IN-CHIEF

Arthur M. BerdGeneral Quantitative LLC

Welcome to the first issue of the fifth volume ofThe Journal of Investment Strategies. Inthis issue, we present you with three papers: one on robust investment strategy design,one on performance evaluation of high frequency strategies, and one on assessmentof structural alphas in the small cap market.

In the first paper in the issue, G. Charles-Cadogan investigates in detail the per-formance of high frequency traders and algo strategies, which in some cases reportstratospheric Sharpe ratios on an annualized basis, sometimes as high as 10, or evenhigher. Such a big difference between the performance of high-frequency trading(HFT) and non-HFT investment managers has puzzled many industry experts, but itis usually just attributed to a claim that HFT strategies are often performing a quasi-market-making service and therefore their compensation must be more akin to analmost sure fee than to uncertain risky return. The author, however, diagnoses theproblem differently – as a misspecification of the annualized Sharpe ratio metric inthe case of the HFT strategy – and introduces an “effective Sharpe ratio” that correctsthis misspecification. The resulting corrected Sharpe ratio numbers are a lot closerto those of other investment strategies, and one is led to think that, if measured onan apples-to-apples basis, there is a broad correspondence between all these differentpockets of the investment management industry.

I am very intrigued by this novel interpretation and believe that the author may justhave found the answer to the question that many hedge fund managers have askedthemselves: “Should I also be doing high frequency trading, if it is so much moreprofitable than what I do currently?” I have asked myself this question as well, butmy answer was based on a slightly different logic.

While I contend that HFT strategies are often far more profitable than “normal”ones, I think that the competitive landscape in the HFT world is dramatically different.Unlike in conventional investment management, the total amount of profit is limitedby the overall volumes traded in the market, and this creates a “winner-takes-all”(or the top few winners take all) structure for participants in HFT. Of course, at anygiven point in time the winners do get exceptional returns. But since it is difficult tomaintain the competitive edge so that one is always not just better than average butis actually in the top few winning spots, then the true nature of the business returnswill be intermittent, and the profits will immediately vanish (or even become losses)as soon as someone else edges just past you to be above the cutoff of the winners’circle.

www.risk.net/journal




For me, then, betting on an HFT strategy is akin to betting on a poker player to wina World Series title. Sure, if the player in question is a top pro, perhaps it is not sucha bad bet, but if only the winner takes home the prize and the rest do not get paidanything, then even for such top players professional poker becomes a rather difficultprofession. And for the rest of us, it is not even worth trying.

Charles-Cadogan’s findings therefore make a lot of sense to me, as they mean that,after adjusting for the difficulty of being among the top winners, the average resultsof HFT traders would be in line with what other professional investors can achieve.This would mean that the trading ecosystem might actually be sustainable, and theoften-heard fears that HFT will somehow displace traditional traders and investorsare exaggerated.

In the issue’s second paper, K. Smimou presents an extensive study of the depend-ence of the performance of the major equity sectors on energy markets. By settingthe problem in a practical manner, as a task of finding an optimal addition of energyfutures contracts to sector exposures in order to improve a sector rotation strategy, theauthor is able not only to demonstrate the importance of the energy exposure overallbut also to calculate the differential impact of its inclusion on various sectors.

The question of macroeconomic dependencies in equity sectors is not a new one, butmost of the studies that I know focus on bottom-up computations, which are difficultto carry through even though they might be important for the understanding of theoverall picture. For me, empirical/phenomenological studies like this one carry a lotof weight because they allow us to let the data tell us the true story, and then see if thatstory is actually consistent with our intuition or if it requires changing our point ofview. And the major added benefit of such a line of attack is that the result is not onlyilluminating but is actually directly applicable, ie, one gets a recipe for improvinga long-standing trading strategy such as sector rotation in a nontrivial manner. Tomy mind, this makes Smimou’s paper an ideal example of what we always strive topresent in The Journal of Investment Strategies: an academically rigorous study anda methodology that has practical novelty and significance. I hope many readers willagree with me.

In our third paper, Elena Ranguelova, Jonathan Feeney and Yi Lu investigate theattractiveness of small cap equity strategies from an investor’s perspective. They findthat as an asset (sub)class, small caps offer unique features that make them more fertileground than large caps for finding truly alpha generating investment managers. Theydemonstrate that there are structural reasons for this, including insufficient coverageby research, lack of focus by large investors, liquidity premium, etc.All of this makes alot of sense, and I agree completely that, as long as those structural differences persist,the small cap sector is likely to continue to offer alpha generating opportunities formanagers and their investors.

Journal of Investment Strategies 5(1)




I would like to thank our readers for their continued support and interest. I hopethat they will find something useful in this issue of The Journal of Investment Strate-gies and that we will be able to continue to offer equally interesting issues in thefuture.

www.risk.net/journal




Journal of Investment Strategies 5(1), 1–27

Research Paper

Diffusing explosive portfolio performanceevaluation of high frequency traders

G. Charles-Cadogan1,2

1University of Johannesburg, Faculty of Economic and Financial Sciences, Department ofEconomics and Econometrics, Auckland Park 2600, Johannesburg, South Africa2Institute for Innovation and Technology Management (IITM), Ted Rogers School of Management,Ryerson University, 575 Bay, Toronto, ON M5G 2C5, Canada; email: [email protected]

(Received March 31, 2015; revised September 21, 2015; accepted October 20, 2015)

ABSTRACT

Several analysts report explosive annualized Sharpe ratios (ASRs) for investmentportfolio performance evaluation of high frequency traders (HFTers) ranging from4.3 to 5000. This suggests that the profitability of high frequency trading (HFT) ismuch higher than that of other actively managed portfolios. In highly competitivefinancial markets where ASRs for experienced traders are often much less than 2,those numbers imply that the ASR for HFT is misspecified. Thus, HFT performanceis incomparable to the performance of experienced traders, hedge funds and otheractively managed portfolios. This paper addresses the misspecification problem byintroducing an efficient Sharpe ratio (ESR) that diffuses explosive ASRs for HFTso that they are comparable to SRs for other actively managed funds. We derive asubordinate stochastic process for HFT strategy that jumps positively only when thetrader executes a successful trade and otherwise stays flat. And we use that processto construct an SR deflator for ESR. We apply the ESR formula to a sample of riskand return data on HFT strategy, and find that the ESR for aggressive HFT is 1.15,medium HFT is 2.88, and passive HFT is 1.43. For the HFT industry as a whole theESR is between 1.07 and 1.87. Those ESRs for HFT are equivalent to SRs reported

Print ISSN 2047-1238 j Online ISSN 2047-1246Copyright © 2015 Incisive Risk Information (IP) Limited

1




2 G. Charles-Cadogan

for experienced traders, hedge funds multistrategy, convertible option arbitrage, andfund-of-fund strategies. Thus, contrary to reports, the profitability of HFT is in linewith industry norms for active portfolio management.

Keywords: Sharpe ratio; portfolio performance evaluation; high frequency trading; subordinateprocess; stock price dynamics; active portfolio management.

1 INTRODUCTION

Computers enact code that might have some strategic reasoning built into it but theyare basically just running hard-wired rules. High frequency traders have pressure tokeep their code short, there’s a limit to how much they can process, and all they cando is give a quick response to a stimulus. That changes how we should perceive themarket and makes dealing with rules of thumb and evolutionary knowledge a moresuitable model for information processing by computers in markets than de novoreasoning. HFT in particular works that way. Stimulus–response means somethinghappens, you look it up in a table and then you act on it.

Professor Doyne Farmer, interview in Treadwell (2013)

This paper introduces a statistical test that corrects for highly inflated annualizedSharpe ratios (ASRs) (Sharpe 1966, 1994) reported in the empirical literature onhigh frequency trading (HFT). By its very nature HFT is based on a high numberof trades and statistical arbitrage of asset prices in which volatility plays a key role(Avellaneda and Lee 2010; Moosa and Ramiah 2015). Thus, a coherent statisticaltest should take the number of trades into account. Our test accounts for those factorswith the introduction of a subordinate stochastic process1 for HFT strategy that jumpspositively only when the trader executes a successful trade and otherwise stays flat. Weidentify a simple intuitively appealing summary statistic that can be extrapolated frompublicly available data, and which serves as the single correction factor for modifyingASR to get an efficient SR (ESR).Application of the ESR correction factor to a sampleof risk and return data on HFT strategy finds that the ESR for aggressive HFT is 1.15,medium HFT is 2.88, and passive HFT is 1.43.2 Those ESRs for HFT are equivalentto SRs reported for experienced traders, hedge funds multistrategy, convertible optionarbitrage, and fund-of-fund strategies (Coates and Page 2009; Gregoriou and Gueyie2003). The intuition behind the test is illustrated in the following example.

1 Roughly, if f .t; !/I t > 0g is a stochastic process and � is a monotone function, thenf�. .t; !/I t > 0g is a subordinate stochastic process. See Bochner (1955, p. 92) for technicaldetails.2 According to Aldridge and Krawciw (2015) aggressive HFT strategies “rely on ultra fastinfrastructure and market orders to take advantage of news, predictive analytics or short livedinformational asymmetries”. Whereas passive HFT tends to provide market making services.

Journal of Investment Strategies www.risk.net/journal




Diffusing explosive portfolio performance evaluation of high frequency traders 3

1.1 Heuristic example

Consider two traders,A and B, whose performances are evaluated for returns measuredover a given period, say, monthly. Let SRA

p .12/ D SRAp

p12 and SRB

p.12/ D SRBp

p12

be the annualized Sharpe ratio (ASR) and �Ap and �B

p be the volatility of the portfoliosmanaged by A and B, respectively. Suppose that SRA

p D SRBp and �A

p D �Bp . Other

things being equal, extant portfolio performance evaluation theory, based on thosestatistics, concludes that the performance of each trader is the same. However, supposetrader A traded for nine months of the year while trader B traded for four months ofthe year. If each trader is in the same style class, faces the same universe of assets andtransaction costs, then trader B is more efficient and consequently better than trader Abecause she attains the same SR at lower cost when her trading time is compared withthat of trader A. Specifically, the ratio

SRBp=

p4

SRAp=

p9

D 1:5

implies that trader B is 1.5 times more efficient than trader A because her tradingtimes are lower than those of trader A, even though the annualized clock time is 12for each trader. Replacing SRA

p and SRBp by

fSRAp D SRA

p=p9 and fSRB

p D SRBp=

p4

provides a more accurate assessment of the traders’ performance. In which case,

fSRAp .12/ D fSRA

p

p12 D SRA

p

p12=9 and fSRB

p.12/ D fSRBp

p12 D SRB

p

p12=4:

This is functionally equivalent to replacing the volatility of the respective portfoliosby Q�A

p D �Ap

p9 and Q�B

p D �Bp

p4. So Q�A

p and Q�Bp are subordinate to � i

p

p12, i D A;B.

The example above shows that trading times (ie, number of trades) should beincluded as an adjustment factor in volatility estimates for portfolio performanceevaluation.3 This paper generalizes the heuristic example in the context of an SRadapted to HFT stock price. It extends the literature on subordinated asset pricing(see, for example, Ané and Geman 2000; Clark 1973; Easley et al 2012; Mandelbrotand Taylor 1967) with a novel application of the partial sums of positive returns as anadmissible subordinator for SR deflation. Specifically, we prove that

ESR D ASRqOT .r/

;

3 This example implies a 100% hit rate for A and B. In practice, the hit rate is lower so the SR willhave to be adjusted to account for that.

www.risk.net/journal Journal of Investment Strategies





where OT .r/ D ��Nrannp is an instrumental variable for partial sums of positive returns,�

is volume of trades executed by traders in the selected class, and Nrannp is the annualized

return on the HFT portfolio.The rest of the paper proceeds as follows. In Section 2 we provide a brief review of

the use of Sharpe ratios in the HFT literature. In Section 3 we develop the ESR teststatistic, and in Section 4 we apply it to a sample of risk and return data for HFT. InSection 5 we conclude the paper.

2 POSITIONING OF THE PAPER IN THE CONTEXT OF RELATEDLITERATURE

2.1 The literature on Sharpe ratios for HFT

The significance of our proposed innovation for HFT lies in the fact that portfolioperformance evaluation is one of the most actively researched areas in financial eco-nomics. For instance Elton et al (2014, Chapter 26, pp. 693–698) reference 141articles – spanning six pages – on the topic. In Aldridge (2013, Table 6.1, pp. 106–108) the tabulation of the pantheon of modified SRs in the literature spans two pages.However, much of the portfolio performance evaluation literature is based on equi-librium asset pricing models and factor models developed in static or low frequencyenvironments. Recently, some analysts extended portfolio performance evaluation toHFT by using performance evaluation metrics like the annualized Sharpe ratio (Sharpe1966) – initially designed to evaluate single-period mutual fund performance. Notableexceptions are Kumiega et al (2014) and Cooper et al (2015) who introduce robustperformance based measures for algorithmic and high frequency trading adapted tostatistical process control concepts such as “process capability”. Their model takesthe cost of research and development and capital expenditure into consideration indeveloping hurdle rates instead of assuming a risk-free rate of zero as is commonpractice in HFT literature.

Coates and Page (2009) conducted a study on the SR for traders on the DAX(German Stock Exchange) and found that experienced traders had an SR of 1.01 witha high of 1.539 in a subsample. Papers by Aldridge (2010, 2013), Baron et al (2014),Clark-Joseph (2014) and Menkveld (2013) report average ASR numbers for highfrequency traders (HFTers) ranging from 4.3 to 5000.4 Moosa and Ramiah (2015)challenged the 37.3 to 5000 SR numbers reported inAldridge (2010) by demonstratingthat there is no relation between profitability and the length of holding period and

4 According to the Credit Suisse hedge index Sharpe ratios are typically less than 2. Refer to www.hedgeindex.com/hedgeindex/en/indexoverview.aspx?indexname=HEDG&cy=USD.






frequency of trading.5 None of the aforementioned papers used trading time as adirecting process (eg, a subordinator) to compute the ASRs used to evaluate HFT.However, Baron et al (2014, p. 20) report that the ASR for passive HFTers (5.85) intheir sample is higher than that for aggressive HFTers (4.29) who trade more. In thecontext of our example, this implies that passive HFT is more efficient than aggressiveHFT. We show later in the paper that those rankings and conclusions change oncethey are calibrated with our efficient SR.

An important paper by Lo (2002) used the delta method and generalized methodof moments (GMM) to illustrate how Sharpe ratios (SRs) are biased by violation ofnormality and serial correlation in returns. While the former may not be as severefor observations that are not in the tail, the latter is more severe–especially for HFT.For instance, Aldridge (2014) studies runs in HFT data as predictors of flash crasheswhile Egginton et al (2014) study quote stuffing as a source of these runs. Accordingto Egginton et al (2014, p. 1), “quote stuffing is a practice where a large number oforders to buy or sell securities are placed and then canceled almost immediately”.This practice may be related to the concept of pinging.6 Thus, serial correlation ischaracterized by runs and quote stuffing.

Clark-Joseph (2014) studies how exploratory trading by HFTers segments the mar-ket into aggressive and passive traders that induce runs in HFT data. Baron et al(2014) study the distribution of ASRs across trader types. In fact, in Figure 1 on thenext page Jonathan Mackinlay demonstrates how spectral analysis of alpha signalsdetermines trading cycles that HFTers use to trade. Mackinlay describes the plot as:

The spectral density of the combined alpha signals across twelve pairs of stocks....It is clear that the strongest signals occur in the shorter frequencies with cycles of upto several hundred seconds.

So, by definition, HFT is based on exploiting market microstructure with low latencytrades where trading rules, not fundamentals, are the order or the day (Mackinlay2014; Treadwell 2013). Bailey and Lopez de Prado (2012) introduced a time invariantprobabilistic Sharpe ratio (PSR) concept, with an SR deflator, that depends on the trackrecord of the portfolio manager over a select number n of returns, skewness �3, andkurtosis �4. The PSR estimates the probability that a portfolio manager’s realized SR

5 The astronomical ASRs are belied by the rapid shrinkage of HFT profits (Popper 2012), whichraises the question of whether those numbers are actually measuring HFT performance.6 “Ping” is a computer network utility that measures the round trip time for a host to receiveand respond to a message. If the host is flooded with such requests then the host system may beoverwhelmed so it diverts resources to respond to the ping requests. See Zubulake and Lee (2011,pp. 42–43) for its strategic use by HFTers to detect dark pool trades.






FIGURE 1 Alpha spectral density.

1.3

1.5

1.4

1.6

1.7

1.9

1.8

2.0

2.1

2.2

50 100 150 300200 250

Freq

uenc

y (s

econ

ds)

×103

Spectral decomposition of HFT alpha signals. Source: Jonathan Mackinlay (May 22, 2011) “Alpha spectral analysis”,available at http://jonathankinlay.com/index.php/2011/05/alpha-spectral-analysis/.

exceeds a given threshold. In that inverse SR approach, the probability estimates forrealized SRs are used to rank portfolio managers.7

An earlier paper by Gregoriou and Gueyie (2003, p. 79) addressed issues like theone presented in the introduction. However, they were concerned with extreme valuesthat affect portfolio returns but which may not be captured by ASR. They proposeda modified value-at-risk (MVAR) factor in lieu of the standard deviation to accountfor skewness and kurtosis in hedge fund returns. In contrast, our model identifiesa subordinator induced by HFTers trading strategy as a deflator. Ironically, Sharpe

7 Bailey and Lopez de Prado (2014) and Goetzmann et al (2007, p. 1507) also introduced an SRdeflator for portfolio performance evaluation.






FIGURE 2 Net position of HFT in large stock by time.

0 10 20 30 40 50 60

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5

Minutes since market opening for January 30, 2008

Hours since market opening for January 30, 2008

Days from January 28 to February 1, 2008

–200

–100

0

100

–200

–100

0

100

400

200

200

–200

0

Net

pos

ition

"U

nile

ver"

(th

ousa

nd e

uros

)

Source: Menkveld (2013, Figure 3).

(1994) states that:

the Sharpe ratio is not independent of the time period over which it is measured. Thisis true for both ex ante and ex post measures.

The heuristic example in Section 1.1 suggests that using ASR to evaluate HFT isbiased and inefficient because the clock time used for reporting data is different fromthe trading times of HFTers (Easley et al 2012). Specifically, a trading time variableshould be used to compute an efficient standard deviation for HFT. To do so, one hasto identify high frequency stock price dynamics in order to derive a suitable metricfor HFT portfolio performance evaluation. Figure 2, taken from Menkveld (2013,Figure 3, p. 721), is:

[a] raw data plot [of] high frequency trader net position by frequency. This figureplots, for the median week in the sample, the high frequency trader’s net position inUnilever, the median stock in the large stock group. It plots the series for essentiallythree frequencies: minutes, hours, and days.






The plots show that the patterns of HFT positions change dramatically when theunderlying frequency is changed from minutes to hours to days.

2.2 Volume, volatility, transactions and HFT stock price formulation

It is well understood that the number of trades is a significant explanatory factor inasset price volatility (Ané and Geman 2000; Jones et al 1994; Ling 2015; McInishand Wood 1991; Türkoglu 2015). For instance, seminal papers by Clark (1973, The-orem 4, pp. 139–140) and more recently Carr and Wu (2004, pp. 113–114) provideevidence that clock time and trading times differ and matter for asset pricing and riskmanagement. Clark argued in favor of replacing clock time with volume as a subor-dinator or directing process.8 Ané and Geman (2000) and Jones et al (1994) extendedthat argument and find that number of trades is a more informative subordinator thanvolume, which is comprised of number of trades and size of trade.

Carr and Wu (2004) claim that a time-changed Levy process addresses: (1) assetprice jumps, leading to nonnormal return innovations; (2) stochastic volatility; and (3)correlation of returns and their volatilities. However, those papers were not applied toHFT environments. Easley et al (2012) present a detailed analysis and argue forcefullyin favor of event times, ie, volume or number of trades, as a subordinator for HFTasset pricing. Each of the authors above used subordinate processes in their analyses,and we do the same in this paper. Thus, to the extent that volatility plays a key role inex ante SR formulas, we expect the cumulative number of trades to play a key role aswell – as shown in the example in Section 1.1.

Somewhat surprisingly, the literature is silent on mathematical models of underly-ing high frequency stock price formulas. Refer to Jones (2013) and O’Hara (2015) fora recent review of the literature. To be sure, continuous asset pricing models (Merton1992) proliferate the mathematical finance and financial economics literature. Morerecently, Ling (2015, p. 6) extended the classic geometric Brownian model for assetprices by substituting number of trades as a subordinator for clock time. However,those models are normative. They are not adapted to market microstructure. To thebest of our knowledge, the HFT stock price formula proposed by Charles-Cadogan(2012) is the only high frequency stock price formula derived from an asymptotictheory of a trading rule. A notable exception is Cartea and Jaimungal (2013, p. 518)who used a hidden Markov model and marked point process (Jacobsen 2006) for HFTstock price. Thus, we will employ analytics from Cadogan’s HFT stock price formulato model HFT returns and derive a suitable metric for HFT portfolio performanceevaluation.

8 Refer to Definition 3.4 below for a subordinate process.






3 THE MODEL

In this section we present a few technical preliminaries in Section 3.1, and furthermotivation for the use of subordinate time instead of clock time in Section 3.2. Weintroduce the SR for HFT based on Charles-Cadogan (2012) HFT stock price formula,and the main results of the paper in Proposition 3.9 in Section 3.4.

3.1 Preliminaries

The following technical primitives are taken from Karatzas and Shreve (1991) andtheir use is implicit below. We assume the existence of a sample space ˝ and a� -field F of Borel measurable subsets of ˝. Thus, .˝;F / is a measurable space.That space is equipped with a nondecreasing filtration of sub-� fields of F givenby fFt I t > 0g. We endow .˝;F / with a complete probability measure P so that.˝;F ; fFtg; P / is the underlying probability space in our analysis. We assume thatt > 0 and that Ft� , �.

Ss<t Fs/ represents the set of events strictly prior to t

and that FtC , �.T

�>0 FtC�/ represents the events strictly after t . A real-valuedstochastic process is a collection of random variablesX D fXt I 0 6 t < 1g definedon .˝;F / and taking values in a state space .S;S/, where S is the � -field for S .

The Sharpe ratio is a summary statistic based on the mean and standard deviationof the difference between portfolio returns .Rp/ and returns on a benchmark usuallytaken as the risk-free rateRf . Sharpe (1994) emphasized two important characteristicsof the ratio, which we summarize as follows.

Assumption 3.1 The Sharpe ratio is not independent of the time period over whichit is measured.

Assumption 3.2 The differential return on the portfolio is based on a zeroinvestment strategy.

In this paper we assume that Assumption 3.2 holds and examine the implicationsof Assumption 3.1 for Sharpe ratio computation.

Assumption 3.3 Sample paths of stochastic processes are right continuous withleft-hand limit.

Let �p be the volatility, ie, standard deviation, of a portfolio and EŒRp� be theexpected return. The ex ante Sharpe ratio SRp for returns computed for a given singleperiod, ie, daily, monthly or annual is represented by the formula

SRp D EŒRp� �Rf

�p

: (3.1)






Sharpe (1994) provides a heuristic example in which he extended the “one periodmean and standard deviation of the differential mean” to T periods by assuming that�p.T / D �p

pT so that the “T -period” Sharpe ratio SRp.T / is now represented by

SRp.T / D EŒRp� �Rf

�p

pT D SRp

pT : (3.2)

As already mentioned in the introduction, and presented with more details here, sev-eral analysts have used that formula to annualize SR computed for daily returns bymultiplying by the factor

p252 based on the assumption of 252 trading days in a

year. For example, the Baron et al (2014, p. 3) study of HFT returns report that “themedian HFT firm demonstrates unusually high and persistent risk-adjusted perfor-mance with an annualized Sharpe ratio of 4.3”. They used a formula like the one in(3.2) for SRi D SRp

p252. Clark-Joseph (2014, p. 19) study reports that 30 HFT

firms he studied:

earned a combined average of 1:51million per trading day during the sample period.Individual HFTs’ annualized Sharpe ratios are in the neighborhood of 10 to 11.

Menkveld (2013, Table 2, p. 727) reports an ASR of 7.6 for the anonymous HFTersengaged in cross-market trading in his study.Aldridge (2010) reportedASRs for which“the maximum possible annualized Sharpe ratio for EUR/USD trading strategies withdaily position rebalancing was 37.3, while EUR/USD trading strategies that heldpositions for 10 seconds could potentially score Sharpe ratios well over [the] 5000(five thousand) mark”.

3.2 Market microstructure of HFT asset prices

The heuristic example in Section 1.1 calls for an efficient SR (ESR). It implies thatwe could modify Sharpe’s T period volatility adjustment in (1.2) with a volatilitymeasure of type Q�p.T .t// D �p

pT .t/, where T .t/ is a trading time. Below we show

that the latter is a random time or subordinator (defined next) for high frequencytrades.

Definition 3.4 (Subordinate process) Let S.t; !/ be a Markov process with con-tinuous transition probabilities Qt and let T .t; !/ be a process with nonnegativeindependent increments. Then S.T .t/; !/ is a Markovian process with transitionprobabilities Pt , given by a linear combination of Qt . The process S.T .t/; !/ issaid to be subordinate to S.t; !/ using the random or operational time T .t; !/. Theprocess T .t; !/ is called a subordinator or directing process.






FIGURE 3 Oscillating prices and trading times.

According to Nanex, this figure shows that “on January 14, 2008, in the early hours of trading, prices of the March2008 eMini S&P 500 (ES) futures contract began oscillating rapidly. After about 4 seconds and 100 oscillations, theprice swings widened to the equivalent of about 400 points on the Dow Jones Industrial Average. The oscillationsthen abruptly stopped and in less than 2 seconds, the price collapsed 5.3% from its peak: the equivalent of a 760point drop in the Dow. After reaching bottom, the market was halted for 10 seconds. Prices returned to normal levelswithin the next few minutes. Between 5:30am and 8:00am that morning, the exchange canceled most of the trades.”Source: Nanex LLC.

Figure 3 depicts oscillating price patterns for a pathological case of HFT in theeMini S&P 500 futures.9 According to our model, only the jumps in returns arerecorded during the four-second interval where the algo presumably went berserk.Figure 4 on the next page provides a striking depiction of our heuristic example.Prices and volume were relatively flat and then they jumped as the trader executed apresumably profitable trade. Thus, the number of trades is an instrument for tradingtime. Furthermore, the “jump times” are subordinate to the total time period duringwhich a trade could have been executed.

9 The eMini 500 is a stock market index futures contract traded on the Chicago MercantileExchange’s Globex electronic trading platform. The notional value of one contract is fifty times thevalue of the S&P 500 stock index.






FIGURE 4 Liquidity plot depicting trading times.

According to Nanex, this figure shows that “on September 13, 2012, at 12:25:27, the December 2012 eMini contractexperienced an evaporation of liquidity at such an alarming rate that it produced one of the most disturbing chartson market stability we have ever seen. Basically, about 80% of the orders resting in the book vanished in a second.To be sure, liquidity before major news events always dries up beginning 1 to 2 minutes before the scheduled time,but always at a gradual rate. This event tells us that either one firm controls 80% of this contract, or that algorithmshave become dangerously susceptible to herd behavior and can be triggered to stampede in a heartbeat.” Source:Nanex LLC.

3.3 Sufficient statistics for ESR

If returns are approximately normally generated, the mean and standard deviation ofa sample of returns generated by a portfolio manager are sufficient statistics (DeGroot1970, p. 156) for characterizing the sample distribution she induced by her decisionmaking. In other words, the portfolio manager generates a distribution of returns thatis subordinate to the underlying distribution for the universe of asset returns availableto her. Therefore, one might expect her trading time to be based on the sufficientstatistics as well. The intuition behind this argument is as follows.

3.3.1 Example: random times as sufficient statistics for ESR

Assume for the sake of argument that a stock price follows a Brownian motionBt .!/. Thus, .0; t/ are sufficient statistics since Brownian motion has a normal






FIGURE 5 Sample path for running maximum Mt .!/ for Brownian motion.

0.5

1.0

1.5

2000 4000 6000 10 0008000

Source: http://math.stackexchange.com/questions/109873/maximum-of-a-brownian-motion-and-its-integral.

distribution with mean 0 and variance t . Define the running maximum as Mt .!/ Dmaxf06s6tg Bt .!/. Let �b.!/ D infft > 0 j Bt .!/ > bg be the first time the stockprice exceeds the level b. Figure 5 depicts a typical sample path forMt .!/. For exam-ple, the horizontal axis could be measured in milliseconds (ms). Cursory inspectionshows that Mt .!/ jumps shortly after 0 at around 0.25 ms, then remains flat until itjumps again around 2 ms and so on. So the running total on the vertical axis is smallerthan that on the horizontal axis. It can be shown (Karatzas and Shreve 1991, p. 96)that

P f�b.!/ < tg D P fMt .!/ > bg D 2p2�

Z 1

b=p

t

e�x2

dx Dp2.1 � ˚.b

p2=t//;

(3.3)

where ˚.bp2=t/ is the cumulative normal distribution probability estimate in the

right (or left) tail starting at bp2=t . If either b is small or t is large or both, then

the probability in (1.3) is close to 1. In other words, the subordinate time �b.!/ Dinfft > 0 j Bt .!/ > bg when the stock price exceeds level b is less than the clocktime t at which the stock price movement is recorded almost surely. Moreover, itcan be shown that the subordinate (time-changed) processM�b.!/ is also a Brownianmotion characterized by sufficient statistics .0; �b.!// � .0; t/ (Karatzas and Shreve1991, Theorem 4.6, p. 174).

In the context of Figure 5,M�b.!/ would tend to lie aboveMt .!/ almost surely sinceit is a running maximum that only jumps for values greater than b. So the sufficient






statistics for the subordinate process is a subset of the sufficient statistics from thesupervening process. Specifically, the SR for evaluating the stock price performanceis based on the mean and standard deviation of the stock (Sharpe 1994). So the SR forthe subordinate process for the stock is based on a subset of the sufficient statisticsfor the stock. We summarize this argument with the following.

Proposition 3.5 (Sufficient statistics for ESR) The ESR for a portfolio dependson a subset of the sufficient statistics for the stocks that comprise that portfolio.

3.4 The Sharpe ratio and HFT stock price dynamics

Below, T .t; !/ is a subordinate trading time analogous to �b.!/ in the heuristicexample above. So the volatility for an underlying HFT portfolio Sp.t; !/ is givenby Q�p.t; !/ D �p

pT .t; !/, where �p is the corresponding single-period volatility.

We assume the stock price formula adapted to high frequency trading strategies is theone introduced in Charles-Cadogan (2012, p. 18) as follows:

Sp.t; !/ D Sp.t0/ exp

� Z t

t0

�X .u; !/„ ƒ‚ …volatility

ˇX .u; !/„ ƒ‚ …exposure

dBX .u; !/„ ƒ‚ …news

�; (3.4)

where X is a hedge factor, �X is its volatility, ˇX is exposure to the hedge factorandBX .u; !/ is a background driving Gaussian process motivated by news about thehedge factor. Cartea and Jaimungal (2013, p. 513) replaced the integrand in (3.4) witha sum of discrete marked point processes (Jacobsen 2006). This gives

Sp.t; !/ D Sp.t0/ exp

� NtXiD1

�.Zt�

i/

i

�;

where t�i is the number of trades or trading times,Zt�i

is the given state or “mark” ofthose trades, �Zt�

ii is independent and identically distributed (iid) price innovations,

andNt is a counting process for arrival of trades. After discretizing (3.4) over dyadicpartition ˘ .n/ for the interval Œ0; 1�, say, Charles-Cadogan (2012, p. 26) deriveddiagnostics for the SR for HFT which implies the following empirical SR processesfor HFT:

SRHFT.t; !/ D� NrHFT.t; !/ � rf

NsHFT.t; !/

�

„ ƒ‚ …ex post Sharpe ratio

; (3.5)

rHFT.t; !/ D �X .t; !/ˇX .t; !/Q�X .t; !/ exp.�t NrHFT.t; !//; (3.6)






NrHFT.T; !/ D T �1

T �1Xj D0

rHFT.tj ; !/; Ns2HFT.T; !/

D T �1

T �1Xj D0

.rHFT.tj ; !/ � NrHFT.T; !//2: (3.7)

The right-hand side of rHFT.t; !/ in (3.6) is a decomposition of HFT returns byhedge factor and news. Menkveld (2013, Table 3, p. 728) reports ASRs (with Lo(2002) serial correlation correction) that depend on CAPM betas. However, the SRformula above depends on the beta for HFTers hedge factor exposure. Furthermore,Menkveld’s estimated ASR jumps by a factor of about 3 from 7.62 for daily returnsto 23.43 for returns computed every half hour. So ASR is sensitive to the frequency ofmeasurement. In contrast, some of the past HFT returns in the summand in (3.7) arenegative. Moreover, the exponential term is positive but not monotonic so it cannotbe used in lieu of the correction factor T in (3.2). Thus, we need to construct asubordinator from HFT returns to supplant T .

3.5 Construction of subordinate trading time for HFT

Let � .n/j .!/ be a stopping time for HFTers over dyadic intervals for Œ0; 1� such that

�.n/j .!/ D infft .n/

j j rHFT.t.n/j ; !/ 2 Eg;

E D frHFT.t.n/j ; !/ j rHFT.t

.n/j ; !/ > rf g; (3.8)

where E is the set of all HFT returns that exceed the risk-free rate. So E 2 Ft.n/Cj

and � .n/j .!/ is Ft.n/C

j-measurable. In practice, rf is often taken as 0 in the HFT

literature (see, for example, Coates and Page (2009, p. 1); Aldridge (2013, p. 108)).Let T .t .n/

0 ; : : : ; t.n/2n�1; 1I!/ be a subordinator, ie, directing process, for HFT returns

adapted to the filtration fFt.n/

j

.!/I t .n/j > 0g and defined as follows:

T .t.n/0 ; : : : ; t

.n/2n�1; 1I!/ D

2n�1Xj D0

rHFT.t.n/j ; !/IfrHFT.t

.n/

j;!/2Eg; (3.9)

r�j.!/ D rHFT.t

.n/j ; !/IfrHFT.t

.n/

j;!/2Eg: (3.10)

We claim that T .�/ is an efficiency measure. It jumps only when the HFTer executesa successful trade in the set of returns E that exceeds the risk-free rate.10 That is,TC � T � D r�j

.!/ since Ft.n/�j

� Ft.n/Cj

. So T satisfies Assumption 3.3.

10 Charles-Cadogan (2015) also introduced a subordinate jump process that militates against viola-tion of Sharpe ratio based Hansen–Jagannathan bounds in consumption-based asset pricing models(CCAPMs). Charles-Cadogan and Mataramvura (2015) extend the information-based asset pricingmodels of Hoyle et al (2011) and Ikpe et al (2014) by proving that the partial sums of positivejumps in a Cauchy bridge information process is an admissible subordinator for asset pricing. Sosuccessful trades reflect traders’ superior information.






In the context of the heuristic example in Section 1.1, let TA.t.n/0 ; : : : ; t

.n/2n�1; 1I!/

and TB.t.n/0 ; : : : ; t

.n/2n�1; 1I!/ be the directing process for two HFTers, A and B, with

the same empirical Sharpe ratio SRHFT.T /, and let

TB.�/ > TA.�/ and SRHFT.T / D NrHFT.T; !/ � rfNsHFT.T; !/

: (3.11)

The efficient Sharpe ratio relationship is

ESRBHFT.T j TB.�// D SRHFT.T /

pTB.�/

> ESRAHFT.T j TA.�// D SRHFT.T /

pTA.�/: (3.12)

Thus, trader B is more efficient because she executes more successful trades in thesame window when compared with traderA. Under extant modifications of the Sharperatio there is no way to tell which of two traders is more efficient. According to(3.9) the subordinator is simply the sum of positive returns. Most importantly, in thecontext of Proposition 3.5 it is a subset of the sufficient statistics that characterize theunderlying stock price. This conveys information not only about how many successfultrades there were but also incorporates the cumulative returns for successful trades inthe SR formula. Since the returns will be less than 1 almost surely, the subordinatoris less than T . That is,

PrfT > T .t .n/0 ; : : : ; t

.n/2n�1; 1I!/g D 1 � � (3.13)

for some small 0 < � < 1. This scenario is depicted in Figure 6 on the facingpage and Figure 7 on page 18 using daily S&P 500 returns for illustrative purposeswhere the diagonal mimics T . If r�j

.!/ is independent for j D 0; : : : ; 2.n/ � 1,then Tn.r.�; !// is a Levy process characterized by the jumps r�j

.!/ (Karatzas andShreve 1991, p. 405). In other words, the joint distribution of r.�; !/ is in the classof Levy distributions, and Tn.r.�; !// is a type of Skorokhod embedding (Hall andHeyde 1980).

Assuming that r.t; !/ is drawn from a stable distribution with index ˛ so r.t; !/ Dt1=˛r.1; !/, the exponential term in rHFT.t; !/ in (3.4) implies that

SRHFT.T / � Op.exp.T �1C1=˛//; (3.14)

where Op.�/ means that the growth of the respective variable is bounded by the terminside the bracket. For internal consistency in our model, this requires that, for somefunction�.t/, the exponential growth of SRHFT.t/must be consistent withTn.r.�; !//

for given t . These artifacts of our model imply that trading times are drawn from astable distribution – call it G.






FIGURE 6 CUSUM returns and CUSUM positive returns.

SP500CARMAX252

Jan 2,1957

Jan 2,1963

Jan 2,1969

Jan 2,1975

Jan 2,1981

Jan 2,1987

Jan 2,1993

Jan 2,1999

Jan 2,2005

Jan 2,2011

SP500CAR

0

10

20

30

40

50

60

–10

Cumulative sum (CUSUM) of returns SP500CAR D PNj D1 rj , and subordinate CUSUM trading time for positive

returns SP500CARMAX252 D TN .r.�; !// D PNiD0 r�j

.!/. Schematically, the diagonal represents clock time T .Source: S&P 500 daily, January 1, 1957–December 31, 2012.

Lemma 3.6 (Stable trading time distribution) Let r�j .!/ be in the domain of attrac-tion of a stable law G. The empirical process

1

˛�.t/�1 lim

n!1r�0.!/Tn.t j �/.!/

D 1

˛�.t/�1 lim

n!1

� 2n�1Xj D1

r�j .!/�Œ�.n/

j; �

.n/

j C1/.t/

�)d G; (3.15)

where G is a stable law with index 0 < ˛ < 2.

Proof See Appendix A, available online. �

This lemma leads to an ancillary result.

Lemma 3.7 (HFT hurdle rate) HFT hurdle rate is a function of random tradingtime.

Proof See Appendix B, available online. �






FIGURE 7 Subordinator CUSUM positive returns.

SP500CARMAX252

Jan 2,1957

0

0.01

0.02

0.03

0.04

0.05

0.06

Jan 10,1957

Jan 18,1957

Jan 26,1957

Feb 3,1957

Feb11,1957

A magnification of a sample subordinator window for the first thirty periods in 1957. It remains flat and jumps onlywhen positive return is realized–similar to Mt .!/ in the Brownian motion example in Figure 5 on page 13. Source:S&P 500 daily, January 1, 1957–December 31, 2012.

HFT data is characterized by runs, so we would expect returns to be correlated.Even so, (Billingsley 1956, Theorem 5.2, p. 263) implies that if fr�j

.!/g2.n/�1j D0 is

an m-dependent sequence, ie, there are independent runs in the data separated byperiods of length greater than m, and if Tn.r.�; !// is suitably normed, then theinvariance principle holds. That is, Tn.r.�; !// will be an approximate Levy processwith positive jumps as indicated in Lemma 3.6. We summarize this with the followinglemma.

Lemma 3.8 (Subordinator) The subordinator Tn.r.�; !// is an approximate Levyprocess controlled by jumps in random trading times Tn.t j �/.!/.

Proof See (B.2) in the online appendix. �

Based on the foregoing arguments we proved the following proposition.

Proposition 3.9 (Efficient Sharpe ratio) Let SRp be the Sharpe ratio computedfor a given frequency for measuring portfolio returns, and SRp.T / D SRp

pT be the

corresponding “annualized” Sharpe ratio for the portfolio at frequency T differentfrom the underlying frequency of measurement. The efficient Sharpe ratio for the






portfolio is given by

ESRp.T j TN .r.�; !/// D SRp

sT

TN .r.�; !//

D SRp.T /pTN .r.�; !//

; TN .r.�; !// > 0; (3.16)

almost surely, where the subset of cumulative returns for N successful trades,TN .r.�; !// D

PNiD0 r�j

.!/, is a sufficient statistic for ESR, and PrfT >

TN .r.�; !//g D 1 � � for some small � > 0.

Remark 3.10 The inclusion of TN .r.�; !// in the denominator in (3.16) mitigatesagainst the exponential growth of SRHFT.T / in (3.14).

4 APPLICATION OF ESR TO A SAMPLE OF HFT RISK AND RETURNDATA

In this section we apply the formula in Proposition 3.9 to published data on risk andreturn for the sample of HFT firms in Baron et al (2014), hereinafter referred to asBBK. Since we do not have granular data we resort to identifying suitable instrumentsfor the subordinate process TN .r.�; !// in Proposition 3.9, defined in the appendix in(A.3).According to that equation, a suitable instrument should include average returnsand a time dependent factor for �.t/ that accounts for exponential growth in ASR.

Figure 8 on the next page depicts the exponential growth in the volume of stockstraded for the S&P 500. Therefore, “volume growth” may be a suitable instrumentfor �.t/ in Lemma 3.6. Figure 9 on page 21 is a replica of the distribution of changesin prices for E-mini S&P 500 futures depicted in Easley et al (2012). It plainly showshigh excess kurtosis for price changes measured in clock time. Whereas, price changesmeasured relative to volume are approximately normally distributed with no excesskurtosis.

4.1 Instrumental variables for HFT returns subordination

Kyle and Obizhaeva (2013, Equation (5), p. 6) provide theoretical justification for a“business time”, ie, trading time, and volume relationship. Specifically, their tradingtime relationship is

� D� NWEŒj QI j�

�2=3

D� N�P NVEŒj QI �j

�2=3

; (4.1)

where � (not to be confused with �.t/ in Lemma 3.6) is a proxy for “business time”,QI is a risk transfer random variable with an invariant, ie, stable, distribution, NW is






FIGURE 8 Daily closing price and trading volume in S&P 500 Index, January 1, 1950–September 15.

Vol

ume

×109

0

2

4

6

8

10

12

14

Jan 3,1950

Jan 3,1956

Jan 3,1962

Jan 3,1968

Jan 3,1974

Jan 3,1980

Jan 3,1986

Jan 3,1992

Jan 3,1998

Jan 3,2004

Jan 3,2010

Clo

sing

pric

e

2500

2000

1500

1000

500

0

Volume Close Exponential volume growth

Exponential growth of daily price patterns is subordinate to exponential growth for daily volume almost surely in thesense of Bochner (1955, Theorem 4.3.2, p. 93). The notable exception is during the financial crisis between 2007and 2009 when price patterns were topsy-turvy and anomalous. Source: author’s compilation from publicly availabledata at https://finance.yahoo.com/q/hp?s=%5EGSPC+Historical+Prices.

average trading activity, N� is volatility adjusted for order flow imbalance, P is stockprice, and NV is average volume.

Below, our trading time is T .r/ and its relationship with volume � is as follows.We construct the instrumental variable OT .r/ D � � maxf0; Nrann

p g for use in our ESRformula where � D %Vol (represented as fractions), and Nrann

p is average annualizedreturns. Whereupon we derive the modified SRs

bESRp D ASRpqOT .r/

D SRp

sT

OT .r/D SRp

sT

� � Nrannp

; (4.2)

bESRHFT DNrannp

NsannHFT

sT

� � Nrannp

D 1

NsannHFT

sT � Nrann

p

�: (4.3)






FIGURE 9 HFT clock time versus volume time for price changes over sample periodJanuary 1, 2008–October 22, 2010.

0

0.05

0.15

0.10

0.20

0.25

0 1 2 3 4 5–1–2–3–4–5

Time clock Volume clock Normal distribution(same bins as time clock)

The red line is the distribution of standardized price changes for the E-mini S&P500 futures sampled every minute.The blue line is the equivalent sampled every 1/50 of the average daily volume.The black dashed line is the standardnormal distribution. This is a manifestation of Bochner (1955, Theorem 4.3.2) that the stable price change processis subordinate to the approximately Gaussian volume process. Source: Easley et al (2012).

Table 1 on the next page provides rough estimates for the ESR extrapolated fromBBK (2014, Tables 1 and 3).11 Our ESR numbers in column 10 are strikingly lowerthan the ASR numbers reported by BBK in column 9. For instance, in BBK thereported ASRs for aggressive, median, passive and all HFTs are 4.26, 5.26, 5.85 and5.25, respectively. Our corresponding ESR estimates are 1.15, 2.88, 1.43 and 1.87respectively. Since OT .r/ is additive by Lemma 3.6, the subordinator for “All HFT”should be 13:86 C 8:30 C 2:05 D 24:21 and the bESR D 5:25=

p24:21 D 1:07. In

Appendix C, available online, we estimated an ESR of 1.29 for median ASR (4.30) for“All HFT”. However, using the additive subordinator approach we get an ESR D 1:09.This implies that our instrumental variable approach overestimated bESRs for HFT.So the ESRs in Table 1 on the next page are actually much lower than estimated here.Aldridge (2013, p. 113) provides examples of SRs more in line with our numbers.

11 Baron et al (2014, p. 16) used the formula ..ri � rf /=�i /�p252 to compute their SR statistics

where ri is average daily returns, rf D 0 and �i is the standard deviation over the sample period.However, the SRs reported in their Table 3 is based on annualized terms.






TABLE 1 Efficient Sharpe ratio (ESR) estimates for HFT.

HFT N Nrannp � ann

p CS. Nrdp / �%Vol PS. Nrd

p ) OT .r/ ASR bESR

Aggressive 18 91.08 170.55 22 952.16 15.22 3493.32 13.86 4.29 1.15Median 39 27.42 45.61 6 909.84 30.28 2092.30 8.30 5.26 2.88Passive 28 23.13 22.24 5 828.76 8.87 517.01 2.05 5.85 1.43All 85 39.49 87.83 9 951.48 20.04 1994.09 7.91 5.25 1.87

Data on high frequency trader type (HFT), sample size N , average annualized returns Nrannp , average annualized

volatility � annp , daily percentage of market volume traded (%Vol) by traders in category and (mean) annualized

Sharpe ratio (ASR) are taken from Baron et al (2014, Tables 1 and 3). CS. Nrdp / is the cumulative average daily

returns maxf0,252 � Nrannp g assuming annualized returns were computed as in Campbell et al (1997, Equation (1.4.4),

p. 10), PS. Nrdp / D %Vol � CS. Nrd

p / is a partial sum and %Vol is in fractions, the subordinate trading time OT .r/ DPS. Nrd

p /=252 D %Vol � maxf0; Nrannp g and cESR D ASR=

pOT .r/ from (4.2).

FIGURE 10 Distribution of adjusted Sharpe ratios by fund type.

All HFTPassive HFTMedian HFT

Aggressive HFT

Funds of hedge fundsConvertible arbitrage hedge funds

Multistrategy hedge fundsMutual fund

Bottom ten funds of hedge fundsMiddle ten funds of hedge fundsBottom ten funds of hedge funds

Experienced traders*

0 0.5 1.0 1.5 2.0 2.5 3.0

Adjusted Sharpe ratio

�Unadjusted SR. Data for Bottom ten, middle ten and top ten funds of hedge funds are taken from Gregoriou andGueyie (2003, Exhibit 2, pp. 80-81) adjusted SR with modified value at risk (MVaR). Other hedge fund and mutualfund data are taken from Lo (2002, Table 4) adjusted SR with correlation correction. Data on experienced tradersare taken from Coates and Page (2009). The ESR data is taken from Table 1.

Avellaneda and Lee (2010) also provide a distribution of SRs for pairs trading thatare in line with our ESR for HFT.

Perhaps more important is the change in rank order of HFTs when the BBK statisticsare used compared with our ESR statistics. Our ESR ranks median HFTs above passiveand aggressive whereas BBK ranks median HFTers between passive and aggressive.






Lo (2002, p. 45) also found that after his serial correlation correction was applied toASR the ranking of hedge funds in his sample changed dramatically. According toour ESR for HFT numbers, in the context of Lo (2002, Table 4) correlation adjustedSR for hedge funds, ESRs for aggressive, median and passive HFTers are comparableto hedge funds that employ multistrategy (1.17, 2.18), convertible option arbitrage(1.43, 1.67, 2.99), and fund-of-fund strategies (1.39), respectively. Additionally, inthe context of Gregoriou and Gueyie (2003, Exhibit 2, pp. 80-81) our imputed ESRnumbers are consistent with the SRs for the top ten, middle ten and bottom ten hedgefunds in their samples even though the average SR for those funds were much lowerthan that for the HFT’s here.12 Figure 10 on the facing page displays the comparativedata.

One obvious shortcoming of our analysis is we do not have granular data that allowsus to compute the partial sum of positive returns on HFT trades.13 Furthermore, theinstrumental variable OT .r/ D �� maxf0; Nrann

p g, where � is %Vol in fractions in (4.3),only works for Nrann

p > 0 since we are interested in evaluating successful traders.However, we believe that given our data limitations, OT .r/ is a reasonable instrumen-tal variable for number of successful trades in Proposition 3.5. This conjecture issupported by Figure 4 on page 12 where the volume of trade intensifies when HFTsexecute trades. Ideally, scaling back the volume of trade with the size of trade wouldprovide a more accurate measure of number of trades. Furthermore, in (4.1) a tradingtime and volume relationship is supported by theory, and Carrion (2013, p. 689) usedvolume weighted average price (VWAP) to evaluate HFT performance. So volumeof executed trades is dispositive of HFT firm performance.

5 CONCLUSION

In this paper we introduce an intuitively appealing efficient Sharpe ratio formulaadapted to high frequency trading. It takes into account the number of successful tradesexecuted by a trader, which is a subset of the sufficient statistics used to compute SRs.Specifically, the correction factor is the cumulative total returns for successful trades.Other correction factors in the literature are based on extension of sample momentsthat invariably include at least a subset of our correction factor. The upshot of our effi-cient Sharpe ratio formula is it shows that the spectacular annualized Sharpe ratio esti-mates reported in the emerging literature on high frequency trading are functionally

12 In Gregoriou and Gueyie (2003) fund of hedge funds analysis, the distribution of SRs greater than1 are: “top ten funds” f1:07; 1:86; 2:29g; “middle ten funds” f1:03; 1:31; 2:14; 3:06g; and “bottomten funds” f1:65; 1:66g.13 David Bradfield noted that that variable may not pick up heterogeniety of traders, and GrahamBarr noted that risk may not be priced in our setup. However, given the rules-based nature of HFTactivity we believe that asset pricing fundamentals do not apply here.






equivalent to Sharpe ratios for hedge funds, or other traditional investment vehicles,after our single correction factor is applied. As the investment opportunity set for HFTextends to emerging markets (Jones 2014), our model warns against the use of naiveannualized SRs for performance evaluation of HFTers without correction factors ofthe type introduced here. Our ESR formula can be applied to publicly available dataon risk and return provided that suitable instruments for estimating the partial sumfor positive returns in the underlying portfolio can be identified.

DECLARATION OF INTEREST

The authors report no conflicts of interest. The authors alone are responsible for thecontent and writing of the paper.

ACKNOWLEDGEMENTS

I thank Arthur Berd (the editor-in-chief) and an anonymous referee for commentswhich greatly improved the paper. This paper benefited from several discussions withHaim Abraham. I am grateful to Greg Gregoriou, Oliver Martin, Freedom Gumedze,David Bradfield, Graham Barr and seminar participants at the Department of Statis-tical Sciences, University of Cape Town for their comments on earlier drafts of thepaper. I thank Ben Van Vliet for drawing my attention to nascent literature on perfor-mance review in algorithmic trading; and Eric Scott Hunsader from Nanex LLC, andJonathan MacKinlay for permission to use their charts.

REFERENCES

Aldridge, I. (2010). How profitable are high frequency strategies? Huffington Post Busi-ness, July 26. URL: www.huffingtonpost.com/irene-aldridge/how-profitable-are-high-f_b_659466.html

Aldridge, I. (2013). High Frequency Trading: A Practical Guide to Algorithmic Strategiesand Trading Systems, 2nd edn. Wiley.

Aldridge, I. (2014). High-frequency runs and flash-crash predictability. Journal of PortfolioManagement 40(3), 113–123.

Aldridge, I., and Krawciw, S. (2015). Aggressive high-frequency trading in equities.Huffington Post Business, February 18. URL: www.huffingtonpost.com/irene-aldridge/aggressive-highfrequency-_1_b_6698982.html?

Ané,T., and Geman, H. (2000).Order flow, transaction clock, and normality of asset returns.Journal of Finance 55(5), 2259–2284.

Avellaneda, M., and Lee, J.-H. (2010). Statistical arbitrage in the US equities market.Quantitative Finance 10(7), 761–782.

Bailey, D. H., and Lopez de Prado, M. (2012). The Sharpe ratio efficient frontier. Journal ofRisk 15(2), 3–44.






Bailey, D. H., and Lopez de Prado, M. (2014). The deflated Sharpe ratio: correcting forselection bias, backtest overfitting and non-normality. Journal of Portfolio Management40(5), 94–107.

Baron, M., Brogaard, J., and Kirilenko, A. A. (2014). Risk and return in high frequencytrading. Working Paper, May. URL: http://ssrn.com/abstract=2433118.

Billingsley, P. (1956).The invariance principle for dependent random variables.Transactionsof the American Mathematical Society 83(1), 250–268.

Bochner, S. (1955). Harmonic Analysis and the Theory of Probability. University ofCalifornia Press, Berkeley, CA.

Campbell, J. Y., Lo, A. W., and MacKinlay, A. C. (1997). The Econometrics of FinancialMarkets. Princeton University Press.

Carr, P., and Wu, L. (2004). Time-changed Lévy processes and option pricing. Journal ofFinancial Economics 71(1), 113–141.

Carrion, A. (2013). Very fast money: high-frequency trading on the NASDAQ. Journal ofFinancial Markets 16(4), 680–711.

Cartea, A., and Jaimungal, S. (2013). Modelling asset prices for algorithmic and highfrequency trading. Applied Mathematical Finance 20(6), 512–547.

Chan, N. H., and Tran, L. T. (1989). On the first-order autoregressive process with infinitevariance. Econometric Theory 5(3), 354–362.

Charles-Cadogan, G. (2012). Trading rules over fundamentals: a stock price formula forhigh frequency trading, bubbles and crashes. Working Paper, SSRN. URL: http://ssrn.com/abstract=1977561.

Charles-Cadogan, G. (2015). Asset pricing with alpha-stable myopic loss aversion andintolerance for decline in consumption. Paper presented at˙ RSA 3rd Economic TheoryWorkshop, Cape Town.

Charles-Cadogan, G., and Mataramvura, S. (2015).Asset pricing with myopic loss aversionto credit default. Working Paper, University of Johannesburg and University of CapeTown.

Clark, P. K. (1973). A subordinated stochastic process model with finite variance forspeculative prices. Econometrica 41(1), 135–155.

Clark-Joseph, A. D. (2014). Exploratory trading. Working Paper, Department of Finance,University of Illinois.

Coates, J. M., and Page, L. (2009). A note on trader Sharpe ratios. PLOS ONE 4(11),e8036.

Cooper, R., Ong, M., and Van Vliet, B. (2015). Multi-scale capability: a better approach toperformance measurement for algorithmic trading. Algorithmic Finance 4(1–2), 55–68.

DeGroot, M. (1970). Optimal Statistical Decisions. McGraw-Hill.Easley, D., Lopez de Prado, M. M., and O’Hara, M. (2012). The volume clock: insights into

the high-frequency paradigm. Journal of Portfolio Management 39(1), 19–29.Egginton, J., Van Ness, B. F., and Van Ness, R. A. (2014). Quote stuffing. Working Paper,

University of Mississippi. URL: http://ssrn.com/abstract=1958281.Elton, E. J., Gruber, M. J., Brown, S. J., and Goetzmann, W. N. (2014). Modern Portfolio

Theory and Investment Analysis, 9th edn. Wiley.Feller, W. (1970). An Introduction to Probability Theory and Its Applications, Volume 2.

Wiley.






Goetzmann, W., Ingersoll, J., Spiegel, M., and Welch, I. (2007). Portfolio performancemanipulation and manipulation-proof performance measures. Review of Financial Stud-ies 20(5), 1503–1546.

Gregoriou, G., and Gueyie, J. (2003). Risk-adjusted performance of funds of hedge fundsusing a modified Sharpe ratio. Journal of Wealth Management 6(3), 77–83.

Hall, P., and Heyde, C. C. (1980). Martingale Limit Theory and Its Applications. AcademicPress, New York.

Hoyle, E., Hughston, L. P., and Macrina, A. (2011). Lévy random bridges and the modellingof financial information. Stochastic Processes and Their Applications 121(4), 856–884.

Ikpe, D., Mataramvura, S., and Becker, R. (2014). Modelling financial information byconditioning. Communications on Stochastic Analysis 8(1), 99–110.

Jacobsen, M. (2006).Point ProcesssTheory and Applications: Marked Point and PiecewiseDetermiitic Processes. Probability and Its Applications. Birkhäuser, Boston, MA.

Jain, N. (1982). Donsker-Varadhan type of invariance principle. Zeitschrift für Wahrschein-lichkeitstheorie und verwandte Gebiete 59, 117–138.

Jones, C. M. (2013). What do we know about high frequency trading? Working Paper,Columbia Business School. URL: http://ssrn.com/abstract=2236201.

Jones, C.M., Kaul, G., and Lipson, M.L. (1994).Transactions, volume, and volatility.Reviewof Financial Studies 7(4), 631–651.

Jones, G. (2014). High frequency trading gives players the edge on JSE. BusinessDayBDlive, October 24. URL: www.bdlive.co.za/business/financial/2014/10/24/high-frequency-trading-gives-players-the-edge-on-jse.

Karatzas, I., and Shreve, S. E. (1991). Brownian Motion and Stochastic Calculus. GraduateTexts in Mathematics. Springer.

Kumiega, A., Neururer, T., and Van Vliet, B. (2014). Trading system capability. QuantitativeFinance 14(3), 383–392.

Kyle, A. S., and Obizhaeva, A. A. (2013). Market microstructure invariance: theory andempirical tests. Technical Report, Department of Finance, University of Maryland.

Ling, X. (2015). Normality of stock returns with event time clocks. Accounting and Finance,doi: 10.1111/acfi.12150.

Lo, A. W. (2002). The statistics of Sharpe ratios. Financial Analysts Journal 58(4), 36–52.

Mackinlay, J. (2014). Pattern trading. Quantitative research and trading blog, July. URL:http://jonathankinlay.com/index.php/2014/07/pattern-trading/.

Mandelbrot, B., and Taylor, H. M. (1967). On the distribution of stock price differences.Operations Research 15(6), 1057–1062.

McInish, T. H., and Wood, R. A. (1991). Hourly returns, volume, trade size, and number oftrades. Journal of Financial Research 14(4), 303–315.

Menkveld, A. J. (2013). High frequency trading and the new market makers. Journal ofFinancial Markets 16(4), 712–740.

Merton, R. C. (1992). Continuous-Time Finance. Blackwell, Boston, MA.

Moosa, I., and Ramiah, V. (2015). The profitability of high frequency trading: is it real? InHandbook of High Frequency Trading, Gregoriou, G. N. (ed), Chapter 2. Elsevier.

O’Hara, M. (2015). High frequency market microstructure. Journal of Financial Economics116(2), 257–270.






Popper, N. (2012).High-speed trading no longer hurtling forward.NewYorkTimes, BusinessDay, October. URL: www.nytimes.com/2012/10/15/business/with-profits-dropping-high-speed-trading-cools-down.html.

Sharpe, W. F. (1966). Mutual fund performance. Journal of Business 39(1), 119–138.Sharpe, W. F. (1994). The Sharpe ratio. Journal of Portfolio Management 21(1), 49–58.Treadwell, R. (2013).Beyond economics:Prof.Doyne Farmer on how computers are chang-

ing the way trading is analyzed. Trading Mesh. URL: www.thetradingmesh.com/pg/blog/mike/read/72400/.

Türkoglu, A. (2015).Normally distributed high-frequency returns: a subordination approach.Quantitative Finance, DOI: 10.1080/14697688.2015.1023335.

Urstadt, B. (2010). Trading shares in milliseconds. Technology Review, January/February.URL: www.technologyreview.com/computing/24167/.

Zubulake, P., and Lee, S. (2011). The High Frequency Game Changer: How AutomatedTrading Strategies Have Revolutionized the Markets. Wiley.






Research Paper

The dynamics of energy futures and equitysectors: evidence from the United Statesand Canada

K. Smimou

Faculty of Business, University of Ontario Institute of Technology, 2000 Simcoe Street North,Oshawa, ON L1H 7K4, Canada; email: [email protected]

(Received April 1, 2015; revised August 4, 2015; accepted September 28, 2015)

ABSTRACT

This paper investigates a sector-rotation strategy that includes energy futures withina particular economic cycle in order to elucidate two congruent objectives. The firstobjective is to examine the dynamic relationship between various major equity sectorsand energy futures, while endogenously controlling for US dollar movement andmonetary policy shocks. The second objective is to assess the benefits of includingenergy contracts (equally weighted or optimally weighted energy futures portfolios)to enhance the performance and sturdiness of an equity-sector rotation strategy. Thefindings pinpoint the predictive role and the higher, positive effect of energy futuresportfolios on some American and Canadian equity sectors, as well as their negative(or nonexistent) effect on other equity sectors. We find that during periods of highexchange rate, the US dollar has an additional (all direct and interaction) effect onsome equity sectors: negative in the case of Canadian basic materials and Americanenergy sectors, and positive in the Canadian financial sector. Further, evidence lendssupport (through a dynamic assessment of the sector-rotation strategy) to arguments

Print ISSN 2047-1238 j Online ISSN 2047-1246Copyright © 2015 Incisive Risk Information (IP) Limited

29




30 K. Smimou

in favor of diversification benefitting overall portfolio performance via the additionof energy futures, a gain that is more pronounced when using an optimally than anequally weighted (or individual futures contracts) energy futures portfolio.

Keywords: energy futures markets; commodity; sector-rotation strategy; tactical asset allocation;sector-class diversification; cross-market linkages.

1 INTRODUCTION

Equity-sector rotation is one of the most effective “active” investment strategies usedby portfolio managers. An asset-class rotation strategy requires shifts of funds inand out of (or underweighting) a sector; this may depend on the perception andjudgment of the manager with regard to how the stock market or a specific sector isvalued compared with an alternative asset class. Meanwhile, the manager must also betaking advantage of the market’s next move by emphasizing certain equity sectors inresponse to the next expected phase of the business cycle. In that direction, the sector-rotation strategy consists of diversifying holdings over the life of an investment byshifting (or underweighting) investment assets from one sector of the economy toanother (eg, financial, utility, consumer staples, health care, materials, etc). Not allsectors of the economy perform well at the same time, thus the need for an optimallyeffective method to preserve gain and reduce overall risk.

Our empirical examination here is built on the premise that markets, notably energymarkets, are leading indicators of the economy and are following the business cyclein tandem. For example, commodities tend to boom when inflationary pressures startto develop, and to peak when they become unsustainable. This was suggested byMurphy (2004), who noted that market-group rotation is a dynamic process, whichis required to take advantage of these interrelations when they are available. It is welldocumented that the prices of some key industrial commodities serve as price signalsfor the strength of global and developed countries’ economies. For instance, Hu andXiong (2013) provided evidence that stock prices across East Asian economies haveshown significant, positive reactions to the changes in futures prices of commoditiestraded in the United States; these serve as barometers of the global economy (see, forexample, Kilian and Murphy 2014; Kilian 2009; Singleton 2014). This directs ourattention to the expectations and decisions of bankers in many financial institutionswith regard to the effect of commodity behavior, notably the European Central Bank(ECB), which considered the high prices of commodities such as oil to be a key factorin raising key interest rates in March 2008.

This sector-rotation strategy, including, as we maintain in this paper, the holdingof energy futures (either individually or as a portfolio of energy futures), can helpmanagers obtain the benefits of commodity diversification. To show this, we attempt





The dynamics of energy futures and equity sectors 31

to accurately time a particular economic cycle while utilizing this strategy to elucidatetwo congruent objectives. The first objective is to examine the dynamic relationshipbetween various major equity sectors (in the United States and Canada) and energyfutures (crude oil, natural gas, gasoline, heating oil and electricity) while endoge-nously controlling for US dollar movement and monetary policy shocks. That is, weintend to determine whether selected energy futures move equity-sector indexes, usingUS and Canadian evidence. Subsequently, the second objective is to assess and illus-trate the benefits of including individual futures contracts in either an equally weightedor optimally weighted energy futures portfolio in order to enhance the performanceand sturdiness of an equity-sector rotation strategy (DuBois 1992).

Erb and Harvey (2006), Gorton and Rouwenhorst (2006) and Smimou (2010) havepresented strong evidence in support of the addition of commodity futures contractsto a diversified stock portfolio in order to lower the risk of equity portfolios. Gor-ton and Rouwenhorst (2006), while attempting to provide various conventional factsabout commodity futures, revealed that the negative correlation of commodity futuresreturns with both equity returns and bond returns is the result of different commodityfutures’ behavior over a business cycle. Thus, commodity futures serve to diversifycyclical variation in stock and bond returns. Therefore, commodity portfolio diver-sification has been advocated as a way of enhancing average returns while reducingportfolio risk for an investor who may consider holding equity domestic or foreignsecurities. We improve upon this initial conjecture by adding energy futures to thesector-rotation strategy, thereby augmenting the diversification gain by reducing theoverall risk of equity-sector portfolios. We anticipate integrating the energy futuresin this exercise as a logical response to the clear argument presented in past studies,which states that the gain of some commodity futures is foreseeable but related to thebehavior of the business cycle.1

During a period of crisis, the equity-sector rotation strategy may not prove to beeffective, as many or all fundamental (and psychological) factors are shifted, and allsectors, including those that may be considered “recession-proof”, may be affectedby those changes and thus become more correlated (see Bartram and Bodnar 2009;Kaminsky et al 2003; Kaminsky and Reinhart 2000). Fabozzi et al (2010) advancedsome crucial explanations and recommendations after the 2008 global financial cri-sis (GFC). They also strengthened the argument for the necessary consideration ofmacroeconomic factors in asset management and the timing of asset allocation deci-sions. Our investigation in this paper is in accord with that line of reasoning and servesas a response to that consideration. First, we try to analyze the relevant intermarketrelationships between equity sectors and energy futures and understand how these

1 For example, sectors (and industries) whose sales rise and fall along with general economic activityare attractive investments during the early stages of an economic recovery.





32 K. Smimou

relationships can enhance asset allocation and investment decisions (see Fabozzi et al2010).

Moreover, as discussed in some recently published articles, during the 2008 finan-cial crisis, “traditional” diversification benefits were limited, given the fact thatinvestors had narrow options to choose from when attempting to protect the capi-tal appreciation of their investments while avoiding the adverse outcome of the crisis.This paper is not alone in noting that, during the crisis, diversification provided littlehelp to investors, as equity markets worldwide witnessed a serious decline in cycle(Bartram and Bodnar 2009; Horta et al 2010).2 Therefore, our present contributionindirectly examines in an ex post framework how an enhanced sector-rotation strategycould have avoided the worst of the crisis while positioning those portfolio invest-ments in a safer path. Through this paper, we conclude that such efforts are most likelyto succeed by including energy futures known to have (and capture) a great deal ofcyclical behavior over the business cycle.

Using the same reasoning, this paper further assesses any potential diversificationgains using various risk metrics by constructing optimal portfolios based on energyfutures and equity-sector indexes, while tracking their performance over various timeperiods. Thus, indirectly, this empirical investigation connects two strands of theliterature. The first focuses on the energy market literature, as we intend to showthe relevance of the behavior of futures markets and/or the relationship betweencommodities and equity, and how they are linked to macroeconomic understandings(see, for example, Olson et al 2014; Fishe and Smith 2012; Joy 2011; Smimou 2010;Gorton and Rouwenhorst 2006; Erb and Harvey 2006; Capie et al 2005; Harvey 1988).The second strand focuses on the commodity/currency futures and equity marketliterature, notably those studies related to oil, gold or commodity futures in generaland US equity markets (see, for example, Chang et al 2009; Marshall et al 2013;Brunnermeier and Pedersen 2009; Batten and Lucey 2007; Switzer and El-Khoury2007; Brennan and Subrahmanyam 1996; Bessembinder and Seguin 1992).

The rest of this paper is structured as follows. Section 2 discusses key relatedstudies to show the basis of our exploratory research questions. Section 3 looks atthe construction of energy futures portfolios, providing our data-collection methods,the outlines of the variables we use and relevant summary statistics. Section 4 detailsthe nature of the dynamics of the equity sector vis-à-vis that of the energy futures. It

2 Bartram and Bodnar (2009) cited two important observations about the financial crisis in terms ofvolatility and correlations. The volatility of all nations increased during the crisis, with a nontrivialincrease in the correlation among the returns of all nations in the crisis period but a less significantincrease in the post-crisis period.






also documents Granger causality between equity sectors and energy futures whilecontrolling for movement of the US dollar and monetary policy shock. Section 5presents empirical evidence by looking more closely at the portfolio holdings andsector-rotation strategy, and how they are enhanced by the inclusion of energy futuresfor both the United States and Canada. Finally, Section 6 presents our conclusions.

2 RELATED STUDIES AND CONTRIBUTION

The literature on the behavior of equity sectors and their interactions (within the sectoras well as in the overall equity market, both local and global) is immense; therefore,given space limitations, we present only a brief review of some of the most relevantstudies for our purposes. Research has long documented the importance of identifyingequity-sector returns with major factors behind their movements and behavior (see,for example, Balli et al 2013). Here, the authors examined the spillover effects of localand global shocks on Gulf Cooperation Council (GCC)-wide equity-sector returns;they found differences in behavior among GCC equity sectors in response to globalor regional shocks. For example, the impact of regional and global shocks was lowerfor basic materials, telecom and utility sectors than among other equity sectors in theGCC region. Most relevant to our study, this particular article documented the factthat portfolios diversified across GCC-wide sectors performed better than portfoliosdiversified across GCC national equity markets; this conclusion was obtained usingmean–variance frontiers in line with Markowitz (1952) and Moerman (2008). How-ever, Rouwenhorst (1998) noted that, sometimes, when there is a dominance of someequity sectors in the overall country equity index, a low correlation is observed amongcountry portfolio returns. This is because some of those indexes are imperfectly corre-lated due to the inherent sector dominance. Thus, we deem that equity sectors revealmore information about the diversification we have sought to achieve than does ameasurement of national or country indexes. To further support the importance of ourwell-timed examination of equity-sector diversification/rotation with energy futurescompared with other traditional country diversifications/effects that are likely to havelimitations, notably during crisis times, a Morgan Stanley Dean Witter report statesthat “while country influences will continue to be important, the intra-[Economic andMonetary Union]-Europe activity will likely over time shift away from country-leveldecisions, and more toward more ‘active’ stock and sector strategies” (Young et al1998).

In trying to examine the important linkages between equity sectors and energyfutures, the work of Soucek (2013) is relevant. More specifically, it examines theimpact of trading activity comovements on equity, and the relationship of this tocrude oil and gold futures proxied by open interest. The author found that the extentof market linkages is a result of changes in external market conditions, such as during





34 K. Smimou

periods of instability in financial markets, when the correlation between energy andequity futures open interest declines while the correlation between gold and stockmarket moves further in the negative direction (see also Büyüksahin and Robe 2014).

In the same vein, other studies have explored additional dimensions regarding thebehavior of stock market prices and oil prices. Filis et al (2011) examined time-varying correlations between stock market prices and oil prices using six countries,and they found that the correlation between markets exhibits a time-varying patternguided by external information shocks. Yet, they also revealed that, during the 2008GFC, the lagged oil prices exhibited a positive correlation with stock markets (seealso Narayan et al 2010; Olson et al 2014). In that context, market timing as a viablestrategy is widely discussed by researchers, who generally suggest that investors takeadvantage of the predictability of stock markets in their portfolio decisions (Glostenand Jagannathan 1994; Henriksson and Merton 1981). Jiang et al (2007) proposednew measures of market timing based on mutual-fund portfolio holdings (holdings-based measures). They found that actively managed US domestic funds have positivetiming ability. In addition, the authors illustrated that those managed funds with timingcapability use public information to predict market returns, and the funds show highindustry concentration and are active in industry rotation. In our paper, we respond tothis observation made by Jiang et al (ie, that there is a stronger market timing impactin the case of industry shifting than in the case of intra-industry portfolio allocations)by examining the portfolio holdings of investors who engage in an optimal portfolioselection process to complement sector rotation with the enhancement of an energyfutures portfolio (Avramov and Wermers 2006).

It is widely documented that energy commodities, notably crude oil, are some ofthe most influential physical commodities. This particular energy commodity playsa prominent role in all economies, affecting the world economy in many significantways, such that the examination of oil behavior and the linkage between this commod-ity and related oil firms is vital for investment decisions, policy-making processes,financial hedging and portfolio management and asset allocation (see, for example,Park and Ratti 2008; Cologni and Manera 2008; Cunado and Perez de Garcia 2005;Hamilton and Herrera 2004; Huang et al 1996; Mork 1994; Rzepczynski et al 2004).In line with Milonas (1991), we deem that examining energy futures and their impacton equity sectors by preventing potential bias involves studying their effects individ-ually rather than using existing commodity indexes. Yet, at the same time, we needto be able to reduce the idiosyncratic risk; therefore, we build two energy portfolios:one is an equally weighted portfolio, and the other is an optimally weighted energyfutures portfolio.

Our paper differs in various ways from past studies (see, for example, Malik andEwing 2009). We examine the impact of constructed diversified energy futures port-folios on equity sectors, while taking into account viable control variables in our






analysis. Further, we delve into the potential of augmenting portfolio holdings withthe equity-sector rotation strategy based on evidence from the United States andCanada to provide further insight and robust results. To build our empirical frame-work in line with the scope of our paper, we note that Chng (2009) presented evidenceof the economic and cross-market trading dynamics and linkages between commodityfutures, pinpointing the fact that fund managers usually integrate cross-border finan-cial market linkages to build investment strategies and portfolios (see, for example,German and Kharoubi 2008; Driesprong et al 2008). Therefore, it is beneficial torespond to existing cross-market linkages by examining the nature of interactionsbetween some of the most relevant and liquid energy futures and the behavior ofequity sectors in the United States and Canada.

This paper is motivated by the recent decline in performance of many equity mar-kets, even though these declines are global developments that began with the 2008worldwide financial crisis. In such an economic climate, effective and optimal invest-ment strategies can benefit from the existence of a number of commodity futures,which are known to offer a great deal of diversification and hedge against expectedinflation while preserving a positive return over the business cycle. Building on thetheoretical work of past literature, we argue that energy futures individually or withinenergy portfolios offer potential gains that clearly capture the evolving market andeconomic conditions. We outline ways that movements of energy futures exhibit aviable impact (positive or negative) on the returns of selected equity sectors, therebyoffering ample opportunity for active portfolio managers to take advantage of thatdynamic relationship and benefit while building their equity-sector strategies. Fur-ther, the appreciation of currency (US dollar index) has had a significant effect onsome equity sectors in the United States and Canada, but this is not consistent overtime. The nature of the relationship between commodities in general (notably oiland its refined fuels) and the dollar has changed over the past two decades due tobetter-anchored inflationary expectations.

Past studies examining the dynamic relationship between energy and equity marketsin isolation or in connection to the dollar have suffered from certain limitations thatthis paper aims to compensate for with four major contributions.

(1) The majority of past studies use spot data while ignoring the additional valuableinformation available via futures markets; trading in commodity is usuallyachieved through futures markets.

(2) No studies have included the liquidity property of energy futures (individuallyor collectively as a portfolio) in relation to the movement of other assets, suchas equity-sector returns.





36 K. Smimou

(3) Although some past research offered gains in understanding by highlightingcommodity behavior and its relation to other assets for diversification pur-poses and investment, the studies did not clearly address that connection whilecontrolling for some relevant macroeconomic control variables (eg, recession,market depth of energy commodity, term spread or market returns) known tomatter with regard to equity sector over the business cycle.

(4) Although some studies pointed out that commodity appreciation and its crucialrole as a diversifier were noticeable during the GFC, to our knowledge none ofthem have provided an empirical procedure with which to capture the effect ofthe recent financial crisis and measure its effect on the equity-sector rotationstrategy; thus, we attempt to examine dynamically how a portfolio holding willdiffer once it is fully enhanced with energy futures before and after a financialcrisis.3

The purpose of our paper is to expand previous research. First, by focusing onthe relationship between equity-sector returns and energy futures while using sam-ples from two countries (the United States and Canada) that differ economically inmany ways, especially when it comes to equity sectors and their interactions withthe global energy market. Second, by considering the dynamic relationship usingtwo portfolios (equally weighted and optimally weighted), we propose an optimalportfolio allocation using the selected equity sectors at different frequencies.

3 We note here that, given the scope and purpose of this paper, we are explicitly avoiding the use of acommodity index such as the Commodity Research Bureau (CRB) Index or similar, since our focusis also on illustrating the benefit of holding individual energy futures against optimally constructedenergy portfolios. Meanwhile, we are not concerned about the examination or the influence of othercommodities, such as agriculture, metals, etc; therefore, the use of the well-known commodityindexes that usually cover a wide range of commodities (agriculture, metals, energy and somesoft commodities) sorted into multiple groups, each with different weightings, will not allow us toachieve the objective of this paper. For example, the CRB Index has been subject to a continuousadjustment of the individual components used in calculating the index since its original twenty-eightwere chosen in 1957 (with nine revisions). In addition, the author is aware of the existence of othercommodities, but he is more concerned with examining the impact and role of energy commoditiesas given in this paper. Energy futures represent the most liquid commodities in the market, andthey have a great influence on the local and global economies; thus, the author argues that rotationstrategies including energy futures should reveal valuable insights for all concerned stakeholdersand investors.






3 DATA AND DESCRIPTIVE STATISTICS

3.1 Construction of energy futures portfolios

When building the optimally weighted energy futures portfolio (OWP), we are assum-ing that it will be fully invested; but it is not a long-only mean–variance portfolio.This is particularly relevant to the examination in this paper, because we allow for ashort sales condition that slightly differs from the portfolios used in past studies (see,for example, Andriosopoulos and Nomikos 2014). Yet, we incorporate electricity inour list of contracts, since we do not want our portfolio selection to be based onlyon crude oil and its refined fuels. Andriosopoulos and Nomikos (2014) examined theperformance of the energy-sector spot index (long-only index) versus a set of selectedstocks from the Dow Jones, FTSE 100, Bovespa, UK and the US index filters. Ourpaper goes a step beyond this by examining the equity rotation strategy (active strat-egy) together with energy futures portfolios. In addition, our energy portfolios arebased on futures contracts while following a specific rolling procedure suggested inpast studies. The potential benefit of using energy futures is one of enhancing theequity-sector rotation strategy by taking advantage of the cyclical market conditions,a relevant consideration since Gorton and Rouwenhorst (2006) found that, during lateexpansion and early recession periods of the business cycle, commodity returns areabove their average and outperform stocks and bonds. By attempting to build an opti-mally weighted (or equally weighted) energy futures portfolio, we are accumulatingbenefits and capturing three properties.

(1) Utilizing the property of timing strategies of rotation of equity sectors.

(2) Adding the forward property of the energy futures contracts, which are provento have a subsequent impact on the movement of a number of equity sectors. Forexample, Gorton and Rouwenhorst (2006) presented evidence that correlationbetween the equity index and commodity index futures varies over time (ie, itdepends on the economic cycle and holding period).

(3) Including the international diversification property by examining the US versusCanadian equity sectors to showcase a potentially higher portfolio return (gain)and lower portfolio risk.

Gorton and Rouwenhorst (2006) stressed that equity and commodities fluctuateover the business cycle, and Erb and Harvey (2006) pointed out that commoditycorrelations tend to be very low; hence, they recommended an equally weightedportfolio of commodities to provide better diversification gains for investors. Alongthese same lines, we construct an equally weighted energy futures portfolio (EWP)to showcase the gains of adding energy futures to equity-sector rotation (see, forexample, Fuertes et al 2010; Jensen et al 2002). Recently, Olson et al (2014) argued





38 K. Smimou

that past studies tend to ignore the importance of currency movements and their impacton the energy–equity relationship. In light of that suggestion, we include the USdollar index futures contract in our empirical study to control for its potential effectas we examine the energy–equity-sector relationship. (As mentioned above, somepast studies ignore crucial explanatory variables, and this is a prime example (see,for example, Mensi et al 2013; Frankel 2014).) Industrial structure explains little ofthe benefits and importance of international diversification. Heston and Rouwenhorst(1994) found that diversification across countries within an industry is a much moreeffective tool for risk reduction than industry diversification within a country.4

3.1.1 Equally weighted and optimally weighted energy futures portfolios

On the one hand, to build an equally weighted energy portfolio, we simply constructweekly equally weighted energy futures portfolios based on the concept of an investorcontinuously maintaining an equal weight on all selected contracts, such that they holda long position in each contract. As maturity approaches, investors roll over to thenearest contract and hold that contract up to one week before maturity; then, investorsroll their positions again to the following nearest contract. The use of this weightingscheme for customized portfolios is uncontroversial, as it has been used more thanonce in previous studies (see, for example, Miffre and Rallis 2007; Goetzmann andIbbotson 1990; Bodie and Rosansky 1980). For example, the PowerShares DB Agri-culture Fund, which is based on the Deutsche Bank Liquid Commodity Index, is anequally weighted portfolio of futures contracts. Erb and Harvey (2006) showed thata reliable source of returns for an equally weighted portfolio of diverse commod-ity futures contracts is the diversification return, which is the outcome of balancedvolatile instruments in a well-diversified portfolio with low correlation. Miffre andRallis (2007) used an equally weighted portfolio that consisted of thirty-one commod-ity futures. In the present study, despite the limited span of some energy futures, wecover five highly liquid energy contracts within a common time horizon. We do thisin order to have sufficient data as well as draw some valuable conclusions pertinentto the objective of this paper on the long-term historical risks and returns of energyfutures, and their relationship to the risks of other equity-sector assets.

4 Due to space limitations, in this paper we have not tackled the issue of international diversificationacross equity sectors (sector-based international diversification), while alternately including con-structed energy futures portfolios. An investigation of sector-based international diversification forthe purpose of making asset allocations within the US and Canadian equity sectors will be part ofa future research study (see, for example, He and Kryzanowski 2007).






On the other hand, to construct the optimally weighted energy futures portfolios, werely on the mean–variance framework of Markowitz (1952), such that the followingmodel is used to search for the optimal proportions Xj , which minimize the varianceof the portfolio for given expected rates of return. Thus,

model .1/ W

8ˆ<ˆ:

MinV.x/ D Varj QRPj D X0DX;

subject to AX D B;

Xj free j D 1; : : : ; N;

whereD is the variance–covariance matrix of the rates of return on investment in asseti; j .i; j D 1; : : : ; N / and is a symmetric positive semidefinite matrix of orderN�N ;A is the 2 �N matrix of coefficients of the linear constraints, where �P D EŒ QRP� isthe expected portfolio return. B D

��P1

�is a two-vector of the right-hand side, and

X is an N -vector of the decision variables. By means of quadratic programming, theoptimal solution is achieved for the subperiod or the full period for all energy futurescontracts while allowing short sales. Practically, we are aware that short selling maybe impossible for feasibility reasons (exchanges or brokers may not allow it for certaininstruments) or, more frequently, for regulatory reasons applying to specific types ofinvestors. Yet, for this study’s purpose of constructing an optimally weighted energyportfolio (to proxy the performance of the energy market in futures markets) basedon five highly liquid distinct energy contracts, we decided to provide investors witha potential gain once they relax the “long-only” constraint. In addition, we cannotignore the extra information that a short position on some futures may offer to investors(the avoid-wasted-information condition) when we eliminate the long-only constraint,since this will add to the overall performance of the portfolio. The potential gain andrisk reduction of the portfolios that allow short positions is prevalent, given that manysophisticated individual and institutional investors engage in short sales (eg, hedgefund managers).

3.2 Data and relevant variables

Adding the US dollar to our analysis is relevant, since past studies examining thelinkage between energy futures prices and exchange rates have documented that crudeoil, heating oil and unleaded gasoline are conintegrating with a trade-weighted indexof exchange rates, and exchange rates are known to have preceded the movement ofheating oil and crude oil futures prices (Sadorsky 2000; Basher et al 2012). To obtainenergy futures contracts, we use data collected from the primary exchanges, includingthe Intercontinental Exchange (ICE) and Chicago Mercantile Exchange (CME). Forexample, the ICE US dollar index (USDX) futures contract is a leading benchmark forthe international value of the US dollar, and it is the world’s most widely recognized





40 K. Smimou

traded currency index; this contract is traded twenty-two hours a day on the ICEplatform.5

In addition to the main variables (equity sectors from both countries), we usedmacroeconomic data from Thomson Reuters Datastream in order to be exhaustive inour sample selection and control variables. Following Bessembinder (1992), we usesome relevant macroeconomic variables: inflation, change in short-term treasury bill(t-bill) yields, change in term structure (term spread 1, TS1, 5Y-3M, and term spread 2,TS2, 10Y-3M) and growth of US GDP (US GDG) and Canadian GDP (CN GDG)(see also Chen et al 1986).6 In line with past studies, we chose to proxy monetarypolicy shocks based on term spreads collected from Datastream (Naes et al 2011).We used two term spreads for each country, calculated as the difference between theyield on a ten-year treasury bond and the yield on a three-month t-bill (term spread 1,TS1, based on third power (3PN), 10YR constant maturity rate; term spread 2, TS2,based on fifth power (5PN), 10YR constant maturity rate; see, for example, Estrellaand Mishkin (1998); Harvey (1988); Harvey (1989)).7

Our paper includes a set of energy futures and equity-sector indexes traded in theUnited States and Canada over the same time frame of April 14, 2003–January 27,2014.8 Equity sectors represent the major sectors in both countries. In the case ofthe United States, we selected eight equity sectors from either the New York StockExchange (NYSE) or the Standard & Poor’s 500 (S&P 500) Dow Jones indexesthat are classified as members of the designated sector. The eight equity sectors are

5 The USDX futures reveal the position of the US dollar against six component currencies (theeuro, Japanese yen, British pound, Canadian dollar, Swedish krona and Swiss franc) based on theirrespective percentage weights in the index. This contract does not have a price limit.6 Hirshleifer (1988) showed that a future pricing function contains a hedging-dependent and pos-sibly a market-specific premium for residual risk in addition to premiums for systematic risk. Yet,Bessembinder (1992) found that a hedging-conditioned residual risk on expected returns is strongestfor agricultural and foreign currency futures.7 Both term spreads were computed as the ten-year yield less the three-month t-bill rate of eachcountry (long-term yields less short-term rates). The constant maturity series simply pertains to anassumption of what the yield of a bond will be, using the desired term of derivation (either 3PN or5PN) for a specific maturity by interpolating the data of the yield curve constituents.8 This data covers a period ending January 27, 2014, the latest available date at the time of down-loading. Further, we deem and assume that the starting date in 2003 to test our propositions willnot be adversely affected by the choice of our sample or time horizon. We confine the choice ofsectoral indexes to those capturing the economic characteristics of countries; while we could haveincluded additional sectors or energy commodities, eg, ethanol, in our analysis, the variables wouldhave substantially limited the coverage of our sample. We only cover the period for which all thevariables were available.






energy (NYSE), financials (NYSE), health care (NYSE), energy (S&P), industrials(S&P), health care (S&P), financials (S&P) and utilities (S&P). In addition, marketreturns are proxied using relevant market indexes pertinent to the equity sectors underexamination. Thus, we collect historical data of the NYSE (composite) and S&P 500(composite).9

For Canada, we collect the equity indexes among members of the eight designatedsectors within the Toronto Stock Exchange (TSX), which are energy (TSX), materials(TSX), industrials (TSX), transport (TSX), financials (TSX), utilities (TSX), healthcare (TSX) and consumer staples (TSX). In addition, for estimation purposes andto proxy Canadian market returns, we employ the S&P/TSX (composite) index. Wecompute the returns from the American perspective, so that all indexes have beencomputed in US dollars.

To capture the effect of the most recent financial crisis, we develop one dummyvariable for each country (the United States and Canada). We define a dummy variablefor two reasons:

(1) to make our result robust in this attempt to clearly ascertain the impact offinancial crisis on the behavior of selected equity sectors in each country inrelation to both energy futures and the US dollar;

(2) to examine changes in the behavior of futures contracts while interacting withthe state of the US dollar over the course of the business cycle (see Gorton andRouwenhorst 2006).

We define this dummy variable (DREC) solely based on US or Canadian economicgrowth (US GDG or CN GDG), which is a recession (business-cycle contraction)over the period t , generally defined as two successive quarters of negative growth.This dummy variable can be represented as follows:

DREC;t D(1 if GDGt < 0 and ŒGDGt�1 < 0 or GDGtC1 < 0�;

0 otherwise:

That is, if there is negative growth over periods t and t � 1, then we identify dummyvariables related to both periods as recession periods. Once we identify a period as arecession period, we expand the same dummy variable to create weekly data from itto match the frequency of other available data.

In the present study, since the focus is on the dynamic relation between equitysectors and energy futures, we include five futures via the CME Group but subjectto NYMEX rules and regulations: West Texas Intermediate (WTI) crude oil (CO),

9 Further details regarding the number of firms that are constituents of each equity index are givenin Table 1A in the online appendix.





42 K. Smimou

heating oil (HO), gasoline (RB), natural gas (NG) and electricity (PJM). For thelatter, we only used PJM on peak futures traded at NYMEX, a highly liquid contractthat matches the time horizon of other energy contracts, since PJM off-peak futureswere only available from November 19, 2007 and not from April 14, 2003.

3.2.1 Open interest and market depth

Institutional investors who implement various hedging strategies in futures marketsmay wonder about the size and market depth of the energy markets contracts requiredto achieve their objectives. Thus, we add the open interest of selected futures con-tracts to our list of control variables. This noteworthy feature of the energy futuresmarkets represents the total number of outstanding contracts; thus, a high open inter-est indicates that more trades will occur in the future and has a positive impact ontrading volume (see Cornell 1981; Wang and Yu 2004; Bhargava and Malhotra 2007;Aguenaou et al 2011).

Several authors considered the merit of studying the open interest in commodityfutures markets as a measure of market depth. Such studies of activities in futuresmarkets have examined only the total open interest or total volume, which representsthe aggregate participation of all traders (see, for example, Hong and Yogo 2012). Inthe futures markets, open interest is arguably a suitable measure of participant activity,as it represents the total demand for futures contracts. Bessembinder and Seguin (1992,p. 2016) noted that “futures-trading activities vary throughout the contract life cycle,with systematic increases in volume and open interest as the expiration date nears”.Therefore, if we want to understand the size and depth of the market, we may needto examine open interest, which is partly related to participation and partly relatedto the market size of the underlying product. Karpoff (1987) summarized the resultsof several studies on the relation between changes in price and trading volume. Itis documented that it is common to capture a positive relation between volume andthe size of price changes for commodity and currency futures. Chang et al (2000)examined the relation between stock market volatility and the demand for S&P 500stock index futures contracts using open interest as a proxy for hedging demand.

In futures markets, we need to be specific about the rolling procedure used to obtainour sample. We computed the returns for each individual energy future as follows.

3.2.2 Rollover procedure and return calculations

We used weekly frequency in various tests to match the frequencies of other availabledata. Therefore, what we observe here is partially in agreement with Grammatikosand Saunders (1986, p. 323), who noted, “it is observed that, in many futures as wemove into the delivery month, trading volume and open interest shift gradually to thecontract with the next nearest delivery date”.






The CME Group has specific rollover dates for equity index products. For example,it is generally defined as eight calendar days before a contract expires for most equityindex futures contracts.10 We note from a practical perspective that roll in commodityfutures is generally not as organized as in financial futures. We usually see a patternwhere most of the roll is spread over the entire month preceding the first delivery day,and sometimes longer. Participants who are trying to roll their positions will adjusttheir bids or offers in the spread market over time, based on the amount of open interestremaining in the expiring month, using their previous experience of spread-pricingpatterns during a roll. When there are large quantities of bid or offer in the spreadmarkets during a normal roll period, it is common to see large orders enter the marketon the opposite side; but large trade will not occur until the prices converge.

We note the merit of examining the research questions by using different frequencyseries to align those variables with the appropriate control variables, some of whichare only available on a quarterly frequency (eg, GDP growth). Following De VilleDe Goyet et al (2008), we construct continuous series of the selected contracts, suchthat a contract expiring in a given week w of the month m is replaced with the nextnearest-to-maturity contract on the last day of the previous week,w�1. We intend tomaintain the same practical intuition as maturity approaches (on delivery month) asinvestors who want to maintain a position in futures, who will simultaneously closetheir position and open the “nearest” identical position in the same contract. This isusually done with a spread trade instead of two separate trades, but the investor isbilled for each leg of the spread trade, just as if it were two separate trades. We use theclose prices such that the series roll to the same nearest contract; then, we computeweekly futures returns based on the weekly data as the change in the logarithms ofthe close prices. After applying the roll criteria set above, quarterly (monthly) data iscalculated as the average of the weekly returns of the quarter (the month).11

3.3 Descriptive statistics

The selected energy contracts differ in terms of statistics. Based on Table 1 on page 45,which provides the descriptive statistics of the relevant futures returns in addition to

10 See further details regarding the rollover of index futures at the CME Group site: www.cmegroup.com/.11 In general, the month when investors will roll a position depends on the purpose of holding theposition and on perceived advantages to rolling to one particular month over another. The monththey roll does matter, but it matters more in some situations than in others; for example, if theposition is for a near-term or long-term hedge, or for speculation on the direction of the market ingeneral. The spread relationship is very important in determining how some positions will be rolled.Most markets are affected by carrying costs, and some are affected by seasonal supply or demand.Further detail regarding timing and rolling procedure is provided in a working paper by the author(Smimou 2012).





44 K. Smimou

the energy futures portfolios using weekly data, we observe that, among the futurescontracts, crude oil, heating oil, OWP and gasoline have the highest average returns(0.22, 0.26, 0.203 and 0.199%, respectively, over the sample period April 2003–January 2014), while natural gas and PJM electricity have the lowest returns over thesame period (see Table 1). Results of the Jarque–Bera (J–B) test (Jarque and Bera1980) show that the null hypothesis of normal distribution is significantly rejectedfor all relevant variables. It is worth noting that the reward-to-risk (R-R) ratio is thehighest for heating oil futures, followed by the OWP, WTI crude oil contract.

Looking at Table 2 on page 46, which provides descriptive statistics of equity-sectorreturns as well as term spreads in the United States and Canada, we learn that overthe sample period the US sector returns in part (a) hover between �0.008% (S&Pfinancial sector) and 0.21% in the energy sector (S&P classification). It is logicalto observe that, during the same period, crude oil and heating oil futures were onaverage among the best performers compared with other selected energy futures. TheCanadian equity sectors in part (b) of Table 2 have a positive mean stock return thathovers between 0.31% (transport sector) and 0.14% (utilities) over the sample period.Moreover, the majority of both US and Canadian equity sectors are skewed to the right,meaning that there is a higher probability of investors in the United States and Canadagetting positive than negative returns. The market returns also have a kurtosis that issubstantially greater than 3, which exceeds that of the normal distribution (leptokurticdistribution). In addition, the skewness and kurtosis coefficients of the different seriesindicate a deviation from the normality assumption. The results of the J–B test showthat the null hypothesis of normal distribution is significantly rejected for all variablesin Table 2.

Although the main focus of this paper goes beyond simply measuring diversificationbenefits using correlation, we examine the correlations of selected variables, notablybetween energy futures (individually and portfolios) and equity-sector returns, togauge the degree of covariance between them.12 The results in Table 3 on page 48show that the benefit of diversification stems from the fact that the returns amongassets are highly uncorrelated or negatively correlated. It is worthwhile noting that,for the case of Canada (a commodity-energy economy), there is higher correlationbetween the returns of selected energy futures and those of equity sectors, thoughthey remain low and most of the time do not exceed 0.15.

In Table 3 on page 48, the selected energy futures prove to be quite effectiveat reducing risk through diversification when combined. At this stage, given EWPsand OWPs with negative, statistically insignificant correlation coefficients against USequity sectors, and very low correlation with Canadian equity sectors, we can conclude

12 We note that all of these measures have a strong time-varying component.






TAB

LE

1S

umm

ary

stat

istic

sof

wee

kly

retu

rns

ofen

ergy

futu

res

and

the

US

dolla

rin

dex

futu

res

cont

ract

over

the

sam

etim

efr

ame:

Apr

il14

,200

3–Ja

nuar

y27

,201

4(n

D56

4).

Var

iab

les

‚…„

ƒC

rud

eo

ilH

eati

ng

Gas

olin

eN

atu

ral

Ele

ctri

city

Do

llar

Sta

tist

ics

(CO

)o

il(H

O)

(RB

)g

as(N

G)

(PJM

)E

WP

OW

Pin

dex

Mea

n(%

)0.

220.

267

0.19

9�0

.016

0.00

340.

135

0.20

3�0

.037

Med

ian

(%)

0.64

40.

440.

50�0

.33

0.00

0.29

0.16

�0.1

1M

inim

um�0

.312

�0.1

86�0

.24

�0.2

38�2

.32

�0.4

65�0

.186

�0.0

42M

axim

um0.

241

0.17

30.

274

0.24

61.

275

0.27

30.

163

0.04

9S

D0.

051

0.04

570.

056

0.07

10.

192

0.05

60.

043

0.01

2S

K�0

.80

�0.2

3�0

.36

0.23

�2.1

8�0

.55

�0.2

90.

37R

-Rra

tio0.

0433

0.05

80.

036

�0.0

022

0.00

020.

024

0.04

73�0

.032

KR

5.57

1.21

3.19

0.79

41.9

99.

921.

367

0.90

J–B

775.

6��

38.7

3��

246.

5��

19.6

2��

4113

8.4��

�22

98.9

��

50.7

6��

31.1

7��

EW

Pis

calc

ulat

edus

ing

the

five

ener

gyfu

ture

s,w

hile

OW

Pis

base

don

the

mea

n–va

rianc

epo

rtfo

liose

lect

ion

amon

gth

efiv

een

ergy

futu

res.

The

sym

bols

��

,��an

d�

repr

esen

tst

atis

tical

sign

ifica

nce

atth

e1%

,5%

and

10%

leve

ls,r

espe

ctiv

ely.

SD

deno

tes

stan

dard

devi

atio

n,S

Kde

note

ssk

ewne

ssan

dK

Rde

note

sku

rtos

is.





46 K. Smimou

TAB

LE

2S

umm

ary

stat

istic

sof

wee

kly

retu

rns

ofch

osen

equi

tyse

ctor

san

deq

uity

mar

ket

inde

xes

(mar

ket

prox

ies)

and

othe

rm

acro

-ec

onom

icva

riabl

es(e

g,te

rmsp

read

s)in

the

Uni

ted

Sta

tes

and

Can

ada

over

the

sam

etim

efr

ame:

Apr

il14

,20

03–J

anua

ry27

,20

14(n

D56

4).[

Tabl

eco

ntin

ues

onne

xtpa

ge.]

(a)

US

equi

tyse

ctor

sba

sed

onth

eN

YS

Eor

the

S&

P

Var

iab

les

‚…„

ƒH

ealt

hH

ealt

hTe

rmTe

rmE

ner

gy

Fin

anci

alca

reE

ner

gy

Ind

ust

rial

sca

reF

inan

cial

sU

tilit

ies

NY

SE

S&

P50

0sp

read

spre

adS

tati

stic

s(N

YS

E)

(NY

SE

)(N

YS

E)

(S&

P)

(S&

P)

(S&

P)

(S&

P)

(S&

P)

(co

mp

osi

te)

(co

mp

osi

te)

(5Y

–3M

)(1

0Y–3

M)

Mea

n(%

)0.

184

0.03

70.

120.

210.

144

0.12

4�0

.008

0.12

60.

125

0.12

51.

202.

03M

edia

n(%

)0.

360.

210.

190.

360.

230.

210.

230.

240.

190.

241.

302.

16M

inim

um�0

.213

�0.2

34�0

.128

�0.1

9�0

.153

�0.1

38�0

.204

�0.1

2�0

.19

�0.1

49�0

.005

2�0

.005

Max

imum

0.18

70.

211

0.09

20.

160.

137

0.09

10.

260.

098

0.15

0.12

90.

028

0.03

8S

D0.

035

0.03

90.

021

0.03

50.

031

0.02

10.

045

0.02

30.

028

0.02

60.

008

0.01

1S

K�0

.66

�0.2

3�0

.8�0

.69

�0.3

3�0

.66

0.02

6�0

.54

�0.5

9�0

.37

�0.1

07�0

.50

R-R

ratio

0.05

10.

010.

058

0.06

10.

047

0.05

8�0

.002

0.05

50.

044

0.04

81.

477

1.73

KR

5.34

7.14

7.15

4.21

4.53

6.18

7.17

4.22

7.7

5.82

�0.9

2�0

.83

J–B

697.

1��

1179

.7��

�12

37.7

��

452.

4��

483.

6��

920.

2��

1184

.4��

�43

6.5��

�13

98.9

��

791.

8��

21.1

2��

40.1

2��






TAB

LE

2C

ontin

ued.

(b)

Can

adia

neq

uity

sect

ors

Var

iab

les

‚…„

ƒTe

rmTe

rmH

ealt

hC

on

sum

ersp

read

spre

adE

ner

gy

Mat

eria

lsIn

du

stri

als

Tran

spo

rtF

inan

cial

sU

tilit

ies

care

stap

les

S&

P/T

SX

TS

1T

S2

Sta

tist

ics

(TS

X)

(TS

X)

(TS

X)

(TS

X)

(TS

X)

(TS

X)

(TS

X)

(S&

P)

(co

mp

osi

te)

(5Y

–3M

)(1

0Y–3

M)

Mea

n(%

)0.

216

0.19

0.24

0.31

0.18

0.14

0.21

0.18

0.18

50.

987

1.57

Med

ian

(%)

0.31

0.67

0.38

0.32

0.32

0.25

0.38

0.27

0.42

0.90

1.54

Min

imum

�0.2

7�0

.38

�0.2

1�0

.17

�0.2

6�0

.19

�0.3

27�0

.156

�0.2

64�0

.004

�0.0

033

Max

imum

0.23

40.

270.

220.

190.

230.

167

0.15

80.

170.

211

0.02

60.

035

SD

0.04

60.

053

0.03

60.

036

0.03

60.

030.

040.

025

0.03

60.

0072

0.01

SK

�0.8

4�1

.08

�0.3

2�0

.07

�0.7

11�0

.69

�0.9

8�0

.38

�1.0

00.

370.

174

R-R

ratio

0.04

60.

036

0.06

60.

084

0.04

90.

048

0.05

30.

072

0.05

11.

381.

545

KR

5.92

7.86

6.26

3.81

11.7

57.

1110

.26

7.96

9.54

5�0

.602

�0.7

8J–

B87

2.6��

�15

34.3

��

911.

5��

334.

6��

3229

.9��

�12

10.6

��

2518

.1��

�14

75.7

��

2194

.1��

�21

.86��

�17

.55��

�

The

sym

bols

��

,��

and

�re

pres

ent

stat

istic

alsi

gnifi

canc

eat

the

1%,

5%an

d10

%le

vels

,re

spec

tivel

y.F

orth

eC

anad

ian

equi

tyse

ctor

s,w

eco

mpu

teth

ere

turn

sfr

omth

eA

mer

ican

pers

pect

ive,

soal

lin

dexe

sha

vebe

enco

mpu

ted

inU

Sdo

llars

.SD

deno

tes

stan

dard

devi

atio

n,S

Kde

note

ssk

ewne

ssan

dK

Rde

note

sku

rtos

is.





48 K. Smimou

TAB

LE

3C

orre

latio

nsbe

twee

nw

eekl

yen

ergy

futu

res

retu

rns,

incl

udin

gE

WP

and

OW

Ppo

rtfo

lios,

and

chos

eneq

uity

-sec

tor

retu

rns

inth

eU

nite

dS

tate

san

dC

anad

aov

erth

esa

me

time

fram

e:A

pril

14,2

003–

Janu

ary

27,2

014.

[Tab

leco

ntin

ues

onne

xtpa

ge.]

(a)

Uni

ted

Sta

tes

Eq

uit

yC

rud

eo

ilH

eati

ng

oil

Nat

ura

lgas

Gas

olin

eE

lect

rici

tyU

Sse

cto

rs(C

O)

(HO

)(N

G)

(RB

)(P

JM)

EW

PO

WP

do

llar

Ene

rgy

(NY

SE

)�0

.022

�0.0

230.

048

�0.0

610.

064

0.02

40.

006

�0.0

54F

inan

cial

�0.0

67�0

.076

�0.1

1�0

.16�

0.09

3�0

.051

�0.0

90.

20H

ealth

care

�0.0

68�0

.11

�0.0

99�0

.19��

0.04

3�0

.086

�0.1

10.

006

Ene

rgy

(S&

P)

�0.0

11�0

.026

0.03

4�0

.056

0.03

40.

007

�0.0

09�0

.12

Indu

stria

ls�0

.045

�0.0

15�0

.06

�0.1

6�0.

091

�0.0

2�0

.034

0.21

Hea

lthca

re�0

.08

�0.1

2�0

.12

�0.2

0��0.

07�0

.084

�0.1

240.

04F

inan

cial

�0.0

39�0

.08

�0.1

6��0

.14�

0.09

7�0

.052

�0.0

970.

21U

tiliti

es�0

.14

�0.1

1�0

.06

�0.2

3��

0.00

4�0

.118

�0.1

20.

022






TAB

LE

3C

ontin

ued.

(b)

Can

ada

Eq

uit

yC

rud

eo

ilH

eati

ng

oil

Nat

ura

lgas

Gas

olin

eE

lect

rici

tyU

Sse

cto

rs(C

O)

(HO

)(N

G)

(RB

)(P

JM)

EW

PO

WP

do

llar

Ene

rgy

(TS

X)

0.05

60.

152��

�0.

061

0.09

9��0.

092��

0.13

3��

0.13

2��

�0.0

94M

ater

ials

0.06

40.

14��

�0.

025

0.11

��

0.10

4��0.

134��

�0.

12��

��0

.11

Indu

stria

ls0.

057

0.15

��

0.06

40.

096��

0.09

1��0.

132��

�0.

132��

��0

.057

Tran

spor

t0.

049

0.15

2��

0.06

70.

085��

0.08

6��0.

127��

�0.

131��

��0

.03

Fin

anci

al0.

024

0.12

��

0.02

50.

082�

0.10

��0.

11��

�0.

098��

�0.0

6U

tiliti

es0.

005

0.08

�0.

016

0.04

0.09

��0.

093��

0.06

4��

�0.1

6�

Hea

lthca

re�0

.03

0.08

��0

.008

0.00

60.

14��

�0.

104��

0.04

60.

063

Con

sum

erst

aple

s0.

042

0.09

5��0.

043

0.04

70.

103��

0.11

��

0.08

�0.0

76

The

sym

bols

��

,��an

d�

repr

esen

tsta

tistic

alsi

gnifi

canc

eat

the

1%,5

%an

d10

%le

vels

,res

pect

ivel

y.





50 K. Smimou

TABLE 4 Correlations between quarterly energy futures returns of EWPs and OWPs andthe business cycle of the United States and Canada, proxied by quarterly economic growth(GDP growth, denoted by US GDG and CN GDG, respectively) and monthly inflation ratesover the same time frame (April 2003–January 2014). [Table continues on next page.]

(a) Quarterly data (n D 43)

US GDP Canadiangrowth GDP growth

(US GDG) (CN GDG) EWP OWP

US GDG 1.0 0.681�� 0.382�� 0.451��

CN GDG 1.0 0.45�� 0.521��

that energy futures portfolios offer better diversification than do some individualenergy futures contracts.13

Both energy futures portfolios exhibit a very important positive correlation withthe energy equity sectors of Canada, higher than those of the United States. Thisis not surprising, given Canada’s dependence on Alberta’s oil-rich economy to fuelprosperity, but the correlation is insignificant in relation to crude oil futures (0.056),as seen in Table 3 on page 48. In terms of their relation to US dollar returns, evidencein Table 3 shows statistically insignificant positive correlation coefficients against theUS equity sectors but negative correlation coefficients against the Canadian equitysectors. Only the utilities sector returns exhibit a statistically significant negativecorrelation coefficient against the US dollar. This points to the relevance of includingUS dollar movement among control variables to avoid spurious or biased results aswe estimate the energy futures’ impact on selected equity returns (see Section 4).

A crucial observation can be made in reference to the correlation between USeconomic growth and Canadian growth (which both proxy the business cycle). Inboth countries, a comparison of these numbers with the constructed energy futuresportfolios in part (a) of Table 4 confirms that there is a higher positive correlationbetween the behavior of the energy futures and the business cycle. This echoes theobservations of Gorton and Rouwenhorst (2006) and Erb and Harvey (2006), whoused US evidence that commodities fluctuate over the business cycle. Here, we clearlypinpoint a higher co-movement in Canada than in the United States. This result par-tially motivated our empirical examination in this paper, as investors are searching foropportunities to rotate their investment when market conditions change over a periodof time, favoring one sector over another.

13 Due to space limitations, further results for the other correlations among the rest of the selectedvariables are not reported but are available upon request from the author.






TAB

LE

4C

ontin

ued.

(b)

Mon

thly

data

(nD

127)

US

Can

adia

nIN

FIN

FE

WP

OW

PL

EW

P�

1L

OW

P�

1L

EW

P�

2L

OW

P�

2

US

INF

1.0

0.83

��

�0.1

24�0

.13

0.08

30.

106

0.17

3�0.

183��

CN

INF

1.0

�0.1

43�0

.127

0.03

0.06

0.05

0.06

EW

P1.

00.

855��

�0.

005

0.05

60.

014

0.08

OW

P1.

00.

126

0.10

90.

035

0.10

4L

EW

P�

11.

00.

856��

�0.

004

0.05

7L

OW

P�

11.

00.

118

0.10

8L

EW

P�

21.

00.

86��

�

LO

WP

�2

1.0

The

sym

bols

��

,��an

d�

repr

esen

tsta

tistic

alsi

gnifi

canc

eat

the

1%,5

%an

d10

%le

vels

,res

pect

ivel

y.To

mat

chth

efr

eque

ncy

ofre

alG

DP,

we

have

tous

equ

arte

rlyE

WP

and

OW

Pen

ergy

futu

res

port

folio

retu

rns,

whi

char

eca

lcul

ated

asth

eav

erag

eof

the

wee

kly

retu

rns

ofE

WP

and

OW

Pov

erth

atqu

arte

r(p

art(

a)).

Tom

atch

the

freq

uenc

yof

infla

tion

rate

s(I

NF

),w

eus

em

onth

lyE

WP

and

OW

Pen

ergy

futu

res

port

folio

retu

rns

calc

ulat

edba

sed

onth

ew

eekl

yda

taov

erth

em

onth

inpa

rt(b

).L

stan

dsfo

rla

g(e

ither

one

time

perio

d(�

1)or

two

time

perio

ds(�

2)).

Eve

nw

hen

we

choo

sea

thre

etim

epe

riod

(�3)

lag,

we

obse

rve

high

erpo

sitiv

eco

rrel

atio

nbe

twee

nth

ela

gof

OW

P(0

.21)

orE

WP

(0.1

9)an

dth

eU

Sin

flatio

nra

te,s

ugge

stin

gth

aten

ergy

futu

res

port

folio

sca

nhe

dge

agai

nste

xpec

ted

infla

tion

sinc

eth

eyha

vehi

gher

corr

elat

ion

coef

ficie

nts

with

the

expe

cted

infla

tion

(thr

ee-m

onth

forw

ard)

.Her

e,th

eco

rrel

atio

nis

betw

een

two

time

serie

ssh

ifted

rela

tive

toon

ean

othe

r;dy

nam

ical

ly,

the

US

infla

tion

attim

et

has

ahi

gher

posi

tive

corr

elat

ion

coef

ficie

ntw

ithth

een

ergy

futu

res

port

folio

sat

man

ypr

evio

ustim

es(t

�2;

t�

3;::

:).





52 K. Smimou

In addition, looking at the correlation between inflation and energy futures port-folios time series when they are shifted in time relative to one another, part (b) ofTable 4 on page 50 reveals a consistent and statistically significant positive correla-tion between energy futures portfolios (two-month lag) and US inflation rates. Thisis not the case with Canadian inflation rates, which show statistically insignificantpositive correlation coefficients. This result explains why energy futures portfoliosmay be used to hedge against expected inflation rates: inflation may have a delayedresponse to energy futures movement. This is in line with past literature that lookedat commodity diversification. We also notice that the gains of being a good hedgeagainst inflation are maintained given the correlation coefficients they exhibit (Elderet al 2012). Similarly, Greer (2000) looked at the rebalancing effect and showed theimportance of commodity benefits in a period of unexpected rises in inflation.

4 DYNAMIC ENERGY FUTURES–EQUITY SECTORS RELATION

4.1 Causality linkages among relevant variables

In this section, we carry out Granger causality tests between equity returns and energyfutures portfolios while conditioning for US dollar movement; thus, we need to use astationary time series. Hence, we first test for the unit root of each variable. To test forstationarity, we use the augmented Dickey–Fuller (ADF) and Phillips–Perron (PP)unit root tests with and without trend. Table 5 on the facing page (parts (a) and (b))reports the estimation results for all relevant equity and futures returns and the termspread for both countries. Our results indicate that all the variables are stationary, withthe exception of the US and Canadian term spreads, which are integrated of order 1.For these variables, we use log difference to preserve stationarity.

Next, we investigate the nature of causality linkages between sector returns and theconstructed energy futures portfolios, while allowing for reverse causality. To checkthe robustness of our results, we follow past studies that documented the impact ofthe US dollar on the movement of some energy contracts, including crude oil. Thus,we incorporate currency movement in the vector autoregression (VAR) estimation tocontrol for potential effects while testing for causality.

For illustrative purposes, we apply the Granger (1969) causality test followingLongstaff (2010) to investigate the emergence or changes in direction of causal-ity between sector returns and the constructed energy futures portfolios. Thus, weestimate the following multivariate VAR with k lag length:

Yit D ˛i CpX

kD1

ˇkYit�k CpX

kD1

�kXt�k C "t ;

where Yit is the returns of each chosen equity sector i , and Xt represents the returnof the constructed energy futures portfolio at time t ; ˇik contains the parameters of






TABLE 5 The unit root tests for the major variables (futures and equity-sector returns)and term spreads of the United States and Canada using ADF and PP unit root tests, withand without trend, based on weekly data.

(a) US data

ADF tests PP tests‚ …„ ƒ ‚ …„ ƒSeries Lag No trend Trend No trend Trend

NY energy 7 �7.9�� 7.97�� 26.81�� 26.9��

NY financials 7 �7.71�� 7.70�� 26.93�� 26.94��

NY health 7 �7.99�� 8.03�� 25.32�� 25.34��

S&P energy 7 �8.07�� 8.13�� 27.13�� 27.21��

S&P industrials 7 �7.80�� 7.81�� 24.67�� 24.67��

S&P health 7 �7.92�� 8.04�� 25.15�� 25.24��

S&P financials 7 �7.74�� 7.75�� 28.79�� 28.8��

S&P utilities 7 �8.86�� 8.88�� 26.35�� 26.42��

US TS1 7 �1.88 �1.87 �2.08 �2.05Crude oil 7 �6.99�� 7.02�� 25.81�� 25.84��

Heating oil 7 �7.68�� 7.72�� 24.62�� 24.65��

Natural gas 7 �8.48�� 8.84�� 24.94�� 24.95��

Gasoline 7 �7.26�� 7.28�� 25.31�� 25.33��

Electricity 7 �8.88�� 8.89�� 28.9�� 28.88��

EWP 7 �7.89�� 7.88�� 25.92�� 25.93��

OWP 7 �7.39�� 7.41�� 24.44�� 24.46��

(b) Canadian data

ADF tests PP tests‚ …„ ƒ ‚ …„ ƒSeries Lag No trend Trend No trend Trend

TSX energy 7 �7.52�� 7.64�� 27.29�� 27.47��

TSX materials 7 �7.81�� 8.0�� 26.59�� 26.82��

TSX industrials 7 �7.92�� 7.92�� 25.73�� 25.75��

TSX transport 7 �8.52�� 8.53�� 25.56�� 25.57��

TSX financials 7 �7.3�� 7.34�� 26.64�� 26.7��

TSX utilities 7 �7.79�� 7.9�� 27.91�� 28.09��

TSX health 7 �7.28�� 7.75�� 25.29�� 25.58��

TSX consumer 7 �8.26�� 8.25�� 26.74�� 26.75��staplesCN TS1 7 �1.73 �1.73 �2.07 �2.06

Following the null hypothesis, series are I.1/, and stationary under an alternative hypothesis. Results do not changewhen we apply the same test for the three variables using trend and for others lags. *** denotes significance at the1% level. Results for US TS1 (CN TS1) are comparable with those using US TS2 (CN TS2). After testing on the firstdifference of US TS1 and CN TS1, they are integrated of order 1, I.1/. We use the log difference for these variablesto preserve stationarity. Estimation covers April 2003–January 2014; sample size n D 564.





54 K. Smimou

TAB

LE

6G

rang

erca

usal

ityte

stre

sults

base

don

wee

kly

data

(usi

ngU

Sse

ctor

retu

rns

and

ener

gyfu

ture

sre

turn

sw

ithan

dw

ithou

ta

cont

rolv

aria

ble

(Wor

W/O

):th

eU

Sdo

llar

(cur

renc

ych

ange

)m

easu

rein

VaR

)ov

erth

efu

llsa

mpl

epe

riod

(Apr

il20

03to

Janu

ary

2014

).(a

)E

WP

port

folio

.[Ta

ble

cont

inue

son

next

page

.]

Fu

llsa

mp

leF

ull

sam

ple

per

iod

per

iod

US

do

llar

‚…„

ƒ‚

…„ƒ

On

e-w

ayin

dex

con

tro

lTe

stA

djR

-R

ever

seTe

stA

djR

-d

irec

tio

nva

riab

lest

atis

tic

squ

are

dir

ecti

on

stat

isti

csq

uar

e

EW

P¹

NY

ener

gyN

o15

.3��

�[0

.000

]0.

08N

Yen

ergy

¹E

WP

2.51

�[0

.058

]0.

03Ye

s10

.2�

[0.0

0]0.

212

2.90

[0.0

4]0.

03E

WP

¹N

Yfin

No

0.33

[0.8

0]0.

013

NY

fin¹

EW

P2.

36�

[0.0

7]0.

027

Yes

0.16

1[0

.93]

0.08

62.

55�

[0.0

5]0.

025

EW

P¹

NY

heal

thN

o0.

31[0

.82]

0.00

06N

Yhe

alth

¹E

WP

2.03

[0.1

1]0.

026

Yes

0.33

4[0

.8]

0.07

82.

18�

[0.0

9]0.

023

EW

P¹

SP

ener

gyN

o16

.8��

�[0

.00]

0.08

9S

&P

ener

gy¹

EW

P2.

01[0

.11]

0.02

5Ye

s12

.0��

�[0

.00]

0.17

92.

18�

[0.0

89]

0.02

3E

WP

¹S

Pin

dN

o0.

89[0

.44]

0.00

7S

Pin

d¹

EW

P2.

93��

[0.0

33]

0.03

0Ye

s0.

177

[0.9

1]0.

043

3.17

��[0

.024

]0.

028

EW

P¹

SP

heal

thN

o0.

266

[0.8

5]0.

01S

Phe

alth

¹E

WP

2.22

�[0

.085

]0.

03Ye

s0.

34[0

.79]

0.04

22.

38�

[0.0

7]0.

024

EW

P¹

SP

finN

o0.

11[0

.95]

0.03

1S

Pfin

¹E

WP

2.79

��[0

.04]

0.03

Yes

0.09

[0.9

6]0.

065

2.92

��[0

.034

]0.

027

EW

P¹

SP

utili

ties

No

5.62

��

[0.0

01]

0.03

3S

Put

ilitie

s¹

EW

P0.

32[0

.80]

0.01

7Ye

s2.

99��

[0.0

3]0.

094

0.31

[0.8

2]0.

013






TAB

LE

6(b

)O

WP

port

folio

.

Fu

llsa

mp

leF

ull

sam

ple

per

iod

per

iod

US

do

llar

‚…„

ƒ‚

…„ƒ

On

e-w

ayin

dex

con

tro

lTe

stA

djR

-R

ever

seTe

stA

djR

-d

irec

tio

nva

riab

lest

atis

tic

squ

are

dir

ecti

on

stat

isti

csq

uar

e

OW

P¹

NY

ener

gyN

o38

.1��

�[0

.00]

0.17

5N

Yen

ergy

¹O

WP

2.48

�[0

.06]

0.00

9Ye

s24

.2��

�[0

.00]

0.26

52.

34�

[0.0

7]0.

01O

WP

¹N

Yfin

No

2.50

�[0

.06]

0.02

4N

Yfin

¹O

WP

4.58

��

[0.0

04]

0.02

0Ye

s0.

51[0

.66]

0.08

74.

82��

�[0

.003

]0.

023

OW

P¹

NY

heal

thN

o0.

71[0

.54]

0.00

3N

Yhe

alth

¹O

WP

2.01

[0.1

1]0.

006

Yes

1.07

[0.3

6]0.

082

1.98

[0.1

1]0.

008

OW

P¹

S&

Pen

ergy

No

39.3

��

[0.0

0]0.

18S

&P

ener

gy¹

OW

P1.

60[0

.18]

0.00

4Ye

s26

.7��

[0.0

0]0.

231.

44[0

.23]

0.00

51O

WP

¹S

&P

ind

No

3.23

��[0

.022

]0.

009

S&

Pin

d¹

OW

P3.

07��

[0.0

3]0.

0122

Yes

0.82

[0.4

8]0.

047

3.07

��[0

.03]

0.01

4O

WP

¹S

&P

heal

thN

o0.

137

[0.9

3]0.

009

S&

Phe

alth

¹O

WP

2.21

�[0

.08]

0.00

7Ye

s0.

79[0

.49]

0.04

2.29

�[0

.078

]0.

009

OW

P¹

S&

Pfin

No

1.23

[0.2

9]0.

037

S&

Pfin

¹O

WP

6.05

��

[0.0

0]0.

027

Yes

0.26

[0.8

5]0.

066

6.20

��

[0.0

0]0.

03O

WP

¹S

&P

utili

ties

No

11.3

��

[0.0

0]0.

06S

&P

utili

ties

¹O

WP

0.09

[0.9

6]0.

007

Yes

5.43

��

[0.0

01]

0.10

50.

081

[0.9

7]0.

014

The

figur

esbe

twee

nbr

acke

ts[.]

are

p-v

alue

sof

the

F-t

ests

tatis

tic,r

evea

ling

that

ther

eis

noca

usal

ityfr

omon

eva

riabl

eto

the

othe

r.T

he*,

**an

d**

*in

dica

tesi

gnifi

canc

eat

the

10%

,5%

and

1%le

vels

,res

pect

ivel

y.N

ullh

ypot

hesi

s:¹

impl

ies

X“d

oes

notG

rang

erca

use”

Y.“

Adj

”den

otes

adju

sted

.





56 K. Smimou

TAB

LE

7G

rang

erca

usal

ityte

stre

sults

base

don

wee

kly

data

(usi

ngC

anad

ian

sect

orre

turn

san

den

ergy

futu

res

retu

rns

with

and

with

out

aco

ntro

lvar

iabl

e(W

orW

/O):

the

US

dolla

r(c

urre

ncy

chan

ge)

mea

sure

inV

AR

)ov

erth

efu

llsa

mpl

epe

riod

(Apr

il20

03to

Janu

ary

2014

).(a

)E

WP

port

folio

.[Ta

ble

cont

inue

son

next

page

.]

Fu

llsa

mp

leF

ull

sam

ple

per

iod

per

iod

US

do

llar

‚…„

ƒ‚

…„ƒ

On

e-w

ayin

dex

con

tro

lTe

stA

djR

-R

ever

seTe

stA

djR

-d

irec

tio

nva

riab

lest

atis

tic

squ

are

dir

ecti

on

stat

isti

csq

uar

e

EW

P¹

TS

Xen

ergy

No

24.3

��

[0.0

0]0.

125

TS

Xen

ergy

¹E

WP

3.42

��[0

.02]

0.03

3Ye

s17

.4��

�[0

.00]

0.29

3.78

��[0

.011

]0.

031

EW

P¹

TS

Xm

atN

o4.

32��

�[0

.005

]0.

043

TS

Xm

at¹

EW

P1.

31[0

.27]

0.02

2Ye

s1.

09[0

.35]

0.23

1.61

[0.1

8]0.

02E

WP

¹T

SX

ind

No

3.14

��[0

.02]

0.01

3T

SX

ind

¹E

WP

2.7��

[0.0

4]0.

03Ye

s1.

10[0

.34]

0.12

2.92

��[0

.03]

0.03

EW

P¹

TS

Xtr

ans

No

2.52

�[0

.06]

0.01

5T

SX

tran

s¹

EW

P1.

84[0

.14]

0.02

5Ye

s1.

17[0

.32]

0.08

61.

96[0

.11]

0.02

2E

WP

¹T

SX

finN

o2.

96��

[0.0

3]0.

02T

SX

fin¹

EW

P1.

67[0

.17]

0.02

4Ye

s0.

87[0

.45]

0.13

61.

80[0

.14]

0.02

1E

WP

¹T

SX

utili

ties

No

7.97

��

[0.0

0]0.

062

TS

Xut

ilitie

s¹

EW

P2.

20�

[0.0

8]0.

027

Yes

3.57

��[0

.014

]0.

232

2.08

[0.1

02]

0.02

2E

WP

¹T

SX

heal

thN

o3.

89��

�[0

.009

]0.

015

TS

Xhe

alth

¹E

WP

0.87

[0.4

5]0.

02Ye

s2.

13�

[0.0

9]0.

057

0.74

4[0

.52]

0.01

5E

WP

¹T

SX

Con

sst

No

2.97

��[0

.03]

0.02

2T

SX

cons

st¹

EW

P1.

07[0

.36]

0.02

Yes

1.10

[0.3

4]0.

154

1.13

[0.3

3]0.

017






TAB

LE

7(b

)O

WP

port

folio

.

Fu

llsa

mp

leF

ull

sam

ple

per

iod

per

iod

US

do

llar

‚…„

ƒ‚

…„ƒ

On

e-w

ayin

dex

con

tro

lTe

stA

djR

-R

ever

seTe

stA

djR

-d

irec

tio

nva

riab

lest

atis

tic

squ

are

dir

ecti

on

stat

isti

csq

uar

e

OW

P¹

TS

Xen

ergy

No

64.0

��

[0.0

0]0.

265

TS

Xen

ergy

¹O

WP

4.36

��

[0.0

05]

0.02

Yes

43.3

��

[0.0

0]0.

373.

67��

[0.0

12]

0.02

OW

P¹

TS

Xm

atN

o16

.5��

�[0

.00]

0.10

TS

Xm

at¹

OW

P1.

71[0

.16]

0.00

5Ye

s5.

33��

�[0

.001

]0.

251.

41[0

.23]

0.00

5O

WP

¹T

SX

ind

No

11.6

��

[0.0

0]0.

055

TS

Xin

d¹

OW

P3.

55��

[0.0

14]

0.01

5Ye

s4.

77��

�[0

.003

]0.

137

3.35

��[0

.02]

0.01

5O

WP

¹T

SX

tran

sN

o8.

20��

�[0

.00]

0.04

4T

SX

tran

s¹

OW

P2.

43�

[0.0

6]0.

008

Yes

3.52

��[0

.01]

0.09

72.

37�

[0.0

7]0.

01O

WP

¹T

SX

finN

o12

.9��

�[0

.00]

0.07

TS

Xfin

¹O

WP

3.12

��[0

.026

]0.

012

Yes

5.44

��

[0.0

01]

0.15

72.

85�

[0.0

4]0.

013

OW

P¹

TS

Xut

ilitie

sN

o26

.4��

�[0

.00]

0.14

4T

SX

utili

ties

¹O

WP

2.55

�[0

.055

]0.

009

Yes

12.8

��

[0.0

0]0.

271.

73[0

.16]

0.00

7O

WP

¹T

SX

heal

thN

o4.

94��

�[0

.002

]0.

02T

SX

heal

th¹

OW

P1.

40[0

.24]

0.00

3Ye

s2.

25�

[0.0

8]0.

058

1.10

[0.3

4]0.

003

OW

P¹

TS

Xco

nsst

No

11.7

��

[0.0

0]0.

065

TS

Xco

nsst

¹O

WP

1.22

[0.3

]0.

002

Yes

4.12

��

[0.0

07]

0.16

80.

78[0

.5]

0.00

2

The

figur

esbe

twee

nbr

acke

ts[.]

rela

teth

atth

ep

-val

ueof

the

F-t

ests

tatis

ticre

veal

sth

atth

ere

isno

caus

ality

from

one

varia

ble

toth

eot

her.

The

*,**

and

***

indi

cate

sign

ifica

nce

atth

e10

%,5

%an

d1%

leve

ls,r

espe

ctiv

ely.

Nul

lhyp

othe

sis:

¹im

plie

sX

“doe

sno

tGra

nger

caus

e”Y

.





58 K. Smimou

our VAR system, and k is the number of lags. Since the robustness of our resultsmay be sensitive to the lags, we estimate the VAR system assuming its lag length isbetween one and seven lags; we then choose the lag structure while minimizing theAkaike information criterion (AIC). Part (a) of Table 6 on page 54 reports the Grangercausality test results of EWPs. Part (b) reports our results using the OWPs.

The results show that when the EWP proxy is used to examine the interactionbetween energy futures markets and US equity sectors, there is only the followinginstance of a relation: the null hypothesis of EWP does not Granger cause the USenergy sector (either NY or S&P) or the US utilities sector to be rejected at the 1%or 10% levels. We note that the energy sector is Granger caused by energy futuresmarkets, and that causality gets stronger when we condition the movement of the USdollar index futures. Further, we witness a reverse causality between the US health(NY), industrials, financials, energy (S&P) and the equally weighted energy futuresportfolios, yet the explanatory power of those tests is weaker. It is not surprisingto observe one Granger causality between industrials and health sectors to energyfutures portfolios (EWP), since their products and services exhibit a demand pressure(hedging purpose) on the energy contracts, notably crude oil, heating oil and naturalgas. Yet, we note that the financial sector displays a crucial Granger causality on theEWP, though this result is stable even when we count on the fluctuation of the US dollarindex futures. This result may be explained by a new trend, the financialization ofcommodity markets, as financial investors start to have a great impact via risk-sharingand information discovery in commodity markets. We argue that financialization hassubstantially changed commodity markets through these mechanisms, as suggestedby Cheng and Xiong (2014) as well as Acharya et al (2013). Since our sample coverstrades from as far back as April 2003, we note that there is a great deal of one-wayinterconnection between selected individual commodities and the financial sectors(NY and S&P), which may be explained by the recent financial investors’ risk-sharingand information discovery in commodity markets.

In part (b) of Table 6 on page 54, we repeat Granger causality using the otherenergy futures portfolios (OWP). The same results are revealed, this time with a higherexplanatory power such that energy futures portfolios Granger cause the energy (NYand S&P) and utilities (S&P) sectors. When we account for the dollar index futuresmovement, the Granger causality between OWP and industrial sectors no longerpersists. Again, we note the same reverse Granger causality from energy, industrials,health and financials to the optimally weighted energy futures markets.

In Table 7 on page 56, using the Canadian equity-sector returns and same energyfutures portfolios EWP and OWP in parts (a) and (b), respectively, the same obser-vation concerning Granger causality pertains between EWP and all selected equityreturns; however, it is not supported once we condition for the movement of the USdollar index futures in our estimation, except in the case of energy. This result lends






support to the visible influence, from the Canadian perspective, of the US dollar cur-rency. Also, we note the reverse effect from industrials to EWP. Clearly, this result isstable even if we count on the fluctuation of the currency that supports and validatesthe previous observation in the case of the United States.

Similarly, the results in part (b) of Table 7 on page 56 (when we use OWP) rejectthe null hypothesis for the relationship between OWP and all Canadian sector returns,even after conditioning for movement of the US dollar index. We find one-way causal-ity with statistically significant reverse causality from energy, industrials, transportand financials to the optimally weighted energy futures portfolios. As mentionedabove, some of the reverse Granger causality may be anecdotally obvious (eg, thefact that industrials or transport exert an impact on and Granger cause the OWP viathe demand pressure on the energy futures for hedging purposes), yet the explanatorypower of the reverse direction in our data is always lower than that of the one-waydirection, which is from the energy contracts to the Canadian equity sectors. There-fore, we can conclude that, regardless of the fluctuation of the US dollar futures index(which may be due to many factors), the influence of the energy futures portfolioswill prevail. This investment proves to be a reliable factor relative to the state of theCanadian equity sectors.

To ensure the robustness of our estimations, we test out-of-sample predictive ability(Granger causality) using a sample period starting in the first week of April 2003 andending in the second week of June 2005.14 The remaining period then constitutesthe out-of-sample period. For this purpose, since we are interested in � -step-aheadforecasts, and in line with Clark and West (2007) and McCracken (2007), the restrictedmodel takes the form

YtC� D ˛1;1 C ˇ1;2Yt C u1;tC� ;

and the unrestricted model takes the form

YtC� D ˛2;1 C ˇ2;2Yt C ı2;1Xt C ı2;2Xt�1 C u2;tC�

by adding two lags of X to the restricted model, where YtC� is the realized returnof the variable Y over the week t C � , and X is the variable that potentially predictsthe (Granger-cause) return of variable Y .15 To test the predictive capacity for futurereturns at tC� of each indicator, the unrestricted model is compared with the restricted

14 Each total sample (T observation) is divided into in-sample (R observation) and out-of-sample(P observation) with P=R approximately equal to 4 (Chen 2009).15 We note that McCracken (2007) highlighted that his method is not applicable to tests of equalforecast accuracy for horizons greater than 1; therefore, given our purpose of examining more thanone period, in this test we rely on the method suggested by Clark and West (2007) as it was appliedin Chen (2009).





60 K. Smimou

TAB

LE

8T

here

sults

ofou

t-of

-sam

ple

test

sof

Gra

nger

caus

ality

base

don

wee

kly

data

over

the

full

sam

ple

perio

d(A

pril

2003

–Jan

uary

2014

).(a

)U

Sse

ctor

and

ener

gyfu

ture

spo

rtfo

lio(O

WP

port

folio

).[T

able

cont

inue

son

next

page

.]

On

e-w

ayR

ever

sed

irec

tio

n�

D1

�D

2�

D3

�D

4d

irec

tio

n�

D1

�D

2�

D3

�D

4

OW

P¹

NY

ener

gy1.

32�

1.53

��2.

03��

2.45

��N

Yen

ergy

¹O

WP

1.20

1.17

1.11

1.11

2O

WP

¹N

Yfin

1.03

1.14

1.54

�1.

71��

NY

fin¹

OW

P0.

230.

340.

570.

80O

WP

¹N

Yhe

alth

1.01

1.10

1.23

1.54

�N

Yhe

alth

¹O

WP

0.78

1.12

1.23

1.43

�

OW

P¹

SP

ener

gy1.

341.

43�

2.19

��2.

13��

SP

ener

gy¹

OW

P1.

36�

1.49

�1.

57�

1.80

��

OW

P¹

SP

ind

1.21

1.32

1.46

�1.

53�

SP

ind

¹O

WP

0.67

0.70

0.72

0.87

OW

P¹

SP

heal

th1.

091.

191.

241.

34�

SP

heal

th¹

OW

P0.

450.

570.

680.

85O

WP

¹S

Pfin

1.01

1.10

1.13

1.15

SP

fin¹

OW

P2.

13��

2.76

��2.

34��

1.52

�

OW

P¹

SP

utili

ties

1.11

1.29

�1.

37�

1.32

�S

Put

ilitie

s¹

OW

P1.

031.

221.

131.

25






TAB

LE

8(b

)C

anad

ian

sect

oran

den

ergy

futu

res

port

folio

(OW

Ppo

rtfo

lio).

On

e-w

ayR

ever

sed

irec

tio

n�

D1

�D

2�

D3

�D

4d

irec

tio

n�

D1

�D

2�

D3

�D

4

OW

P¹

TS

Xen

ergy

1.41

�1.

48�

2.01

��2.

23��

TS

Xen

ergy

¹O

WP

1.02

1.17

1.12

1.11

OW

P¹

TS

Xm

at1.

43�

1.73

��1.

98��

2.02

��T

SX

mat

¹O

WP

0.78

0.98

1.03

1.09

OW

P¹

TS

Xin

d1.

231.

34�

1.50

�1.

34T

SX

ind

¹O

WP

0.65

0.72

0.91

1.01

OW

P¹

TS

Xtr

ans

1.02

1.64

�1.

82��

1.94

��T

SX

tran

s¹

OW

P0.

450.

480.

490.

52O

WP

¹T

SX

fin1.

011.

111.

151.

36�

TS

Xfin

¹O

WP

0.12

0.33

0.46

0.50

OW

P¹

TS

Xut

ilitie

s1.

071.

43�

1.53

�1.

76��

TS

Xut

ilitie

s¹

OW

P0.

340.

340.

410.

47O

WP

¹T

SX

heal

th1.

181.

231.

40�

1.37

�T

SX

heal

th¹

OW

P0.

230.

710.

650.

81O

WP

¹T

SX

cons

st1.

091.

261.

30�

1.23

TS

Xco

nsst

¹O

WP

0.23

0.34

0.54

0.75

The

figur

esre

pres

ent

the

MS

PE

-adj

ofou

t-of

-sam

ple

test

sin

alig

nmen

tw

ithth

ew

ork

ofM

cCra

cken

(200

7),

Cla

rkan

dW

est

(200

7)an

dC

hen

(200

9).T

hepr

edic

tive

regr

essi

onm

odel

isth

eY

varia

ble

ofth

e�

thw

eek

ahea

d,an

dth

eX

varia

ble

isus

edas

apr

edic

tor.

The

null

hypo

thes

isfo

rth

eC

lark

and

Wes

t(2

007)

test

isth

atth

eM

SP

E-a

djof

the

pred

ictiv

ere

gres

sion

and

rest

ricte

dm

odel

s(a

mod

elth

atin

clud

esth

ela

gva

riabl

eof

the

depe

nden

tva

riabl

ean

da

cons

tant

term

)ar

eeq

uala

gain

stth

eal

tern

ativ

e(ie

,th

atth

eM

SP

E-a

djfo

rth

epr

edic

tive

mod

elis

less

than

that

ofth

ere

stric

ted

mod

el).

The

criti

calv

alue

sof

this

test

are

1.28

2(1

0%)

and

1.64

5(5

%).

The

*an

d**

indi

cate

sign

ifica

nce

atth

e10

%an

d5%

leve

ls,r

espe

ctiv

ely.

Nul

lhyp

othe

sis:

¹im

plie

sX

“doe

sno

tGra

nger

caus

e”Y

.





62 K. Smimou

model; we use the statistic of Clark and West (2007), which is named “MSPE-adj”and calculated as follows (see Chen 2009):

MSPE-adj DpP � Nfp

OV;

Nf D P�1X

t

OftC� ;

OftC� D . Ou1tC� /

2 � Œ. Ou2tC� /

2 � . OY 1tC� � OY 2

tC� /2�:

A recursive estimation scheme is used such that the size of the sample used to estimateeach parameter grows as one makes predictions for successive observations. Firstestimates are achieved using data from 1 to R, and we use those estimates to predictthe next estimates with data from 1 to RC 1, and so on.

Here, P is the out-of-sample portion used to compute the forecasts OY 1tC� and OY 2

tC�

from the restricted and unrestricted models, respectively. The Ou1tC� and Ou2

tC� are theforecasting errors from the two models. OV is the sample variance of . OftC� � Nf /. TheMSPE-adj statistic is compared with the critical values generated from an approxi-mately normal distribution in order to test the null hypothesis of no-predictability ofvariable X .16 The null hypothesis is rejected if the MSPE-adj statistic is higher thanthe critical value.

Results in Table 8 on page 60 show the MSPE-adj test for energy futures portfolioGranger-caused (or vice versa) US sector returns as well as energy futures portfolioGranger-caused (or in reverse) Canadian sector returns (see parts (a) and (b), respec-tively). In general, the results exhibit some patterns similar to the in-sample evidencein Table 6 on page 54 and Table 7 on page 56, such that the energy futures portfoliostill Granger causes some sectors, notably the US energy sectors and to some extentall Canadian sectors. We note that the longer the � -step-ahead forecasts (time hori-zon), the higher the significance of our results. That is, given our sample attributes inthis paper, we conjecture that the longer the time horizon (step-ahead forecasts), thehigher the level of predictability and influence of energy futures portfolios on somereturns’ equity sectors.

4.2 Impact of energy futures on equity sectors

4.2.1 Energy futures portfolios and selected US equity sectors

Following past studies (see, for example, Hearn and Piesse 2009; Malik and Ewing2009), the present examination of the dynamic relationship between energy futuresand US equity sectors is achieved by empirically gauging the predictive capability of

16 We use the same critical values as Clark and West (2007).






energy futures on equity sectors. We estimate the following full model A (see Table 9on the next page and Table 10 on page 70):

Yit D ˛0 C 'L ENGt�1 CmX

lD1

ılXit;l C !Dolt C �DREC;t C �Dol_Intt C �i ;

where Yit is the dependent variable that denotes the return of equity sector i over theweek t . Energy futures impact is proxied by a constructed EWP of the five selectedenergy futures and another constructed OWP. Independent variables were includedby taking one lag of the chosen EWP or OWP (L ENG is taking either L EWP orL OWP) and a set of m control variables, including the stock market return (MR)relevant to the market where the firms are listed (based on either the NYSE indexor S&P 500); a change of open interest of the EWP or OWP (denoted by OI andcalculated as an equally weighted or optimally weighted average of the change ofopen interest of each energy futures contract); and the term spread of each country,calculated as the difference between the yield on a ten-year treasury bond and the yieldon a three-month t-bill (term spread 1, TS1, based on 5Y-3M, while term spread 2 iscomputed using 10Y-3M). We include changes in the US dollar index futures contract(Dol), as well as the dummy GDG–Recession–DREC, and an interaction term betweenenergy futures proxy (EWP or OWP) and the change in the US dollar index is labeledDol_Int.17

The estimation process based on model (A) is completed by following two sequen-tial steps. The first step, as a sub-model of (A), is without Dol_Int (EQ-1), and thesecond step includes the Dol_Int (EQ-2) interaction term. The interaction term helpsus to establish the effect of the energy futures on the equity-sector return and to seeif the return of an equity sector is more or less sizable as the US dollar futures indexincreases; thus, it captures the marginal effect of energy futures conditional on theexistence of the higher movement of US currency. Along this same line of reasoning,we attempt to further enhance our estimation while ruling out the possibility of thesubstitution effect in relation to a direct US dollar effect on the equity-sector returns,which might be captured by a mistaken estimation that does not incorporate the inter-action between currency fluctuations (state of the US dollar) and energy market; ie,it could be possible that some equity-sector markets perform well when the US dol-lar is appreciating by contributing via interaction with the energy futures market. In

17 Based on the specification of model A, variance inflation factors (VIF) were checked for all theindependent variables including L EWP, and were found to be less than 2, with most values lessthan 1.03 (average value of all VIFs D 1:04; highest value D 1:07). Further, the VIF values ofall independent variables including L OWP were found to be less than 2, with most values lessthan 1.06 (average value of all VIFs D 1:08; highest value D 1:16); this suggests no problem ofmulticollinearity.





64 K. Smimou

TAB

LE

9(a

)The

US

equi

ty-s

ecto

rre

turn

san

deq

ually

wei

ghte

den

ergy

futu

res

port

folio

s,E

WP

;sam

ple

size

D56

4.[T

able

cont

inue

son

next

thre

epa

ges.

]

Dep

end

ent

Ad

jR-

vari

able

Co

nst

'L

EW

Pı

MR

ıO

IıT

S1

!D

ol

�D

RE

C�

Do

l_In

tsq

uar

e

NY

ener

gyE

Q-1

0.00

030.

12��

�1.

07��

�0.

03�0

.02

�0.0

90.

0001

0.87

6[0

.001

][0

.016

][0

.03]

[0.3

2][0

.08]

[0.0

8][0

.004

]E

Q-2

0.00

040.

123��

�1.

07��

�0.

03�0

.01

�0.0

911.

760.

787

[0.0

01]

[0.0

16]

[0.0

31]

[0.0

3][0

.08]

[0.0

7][1

.16]

NY

finE

Q-1

�0.0

02��

�0.0

46��

�1.

31��

��0

.002

0.03

0.04

60.

0009

0.86

3[0

.000

7][0

.013

][0

.04]

[0.0

22]

[0.0

5][0

.067

][0

.005

]E

Q-2

�0.0

02��

�0.0

51��

�1.

31��

��0

.004

0.02

40.

036

�3.1

3��

0.86

6[0

.000

7][0

.013

][0

.04]

[0.0

22]

[0.0

58]

[0.0

6][1

.19]

NY

heal

thE

Q-1

0.00

04�0

.024

��0.

612��

�0.

020.

001

0.01

20.

0007

0.67

0[0

.000

8][0

.009

][0

.024

][0

.022

][0

.06]

[0.0

5][0

.003

]E

Q-2

0.00

03�0

.025

��

0.61

2��

0.01

60.

004

0.01

1�0

.58

0.67

1[0

.000

8][0

.009

][0

.024

][0

.023

][0

.06]

[0.0

46]

[0.7

1]S

Pen

ergy

EQ

-10.

001

0.13

9��

1.04

80.

024

�0.0

4�0

.12

�0.0

020.

68[0

.001

][0

.02]

[0.0

38]

[0.0

4][0

.09]

[0.0

8][0

.005

]E

Q-2

0.00

10.

144��

�1.

05��

�0.

027

�0.0

43�0

.11

2.27

�0.

683

[0.0

01]

[0.0

18]

[0.0

4][0

.04]

[0.1

0][0

.07]

[1.3

6]






TAB

LE

9(a

)C

ontin

ued.

Dep

end

ent

Ad

jR-

vari

able

Co

nst

'L

EW

Pı

MR

ıO

IıT

S1

!D

ol

�D

RE

C�

Do

l_In

tsq

uar

e

SP

ind

EQ

-1�0

.000

7�0

.001

41.

11��

�0.

014

0.07

3�0

.007

�0.0

020.

90[0

.000

6][0

.008

][0

.022

][0

.015

][0

.047

][0

.04]

[0.0

02]

EQ

-2�0

.000

60.

0016

1.11

��

0.01

70.

061

�0.0

061.

190.

903

[0.0

006]

[0.0

08]

[0.0

22]

[0.0

15]

[0.0

48]

[0.0

38]

[0.7

7]S

Phe

alth

EQ

-10.

001

�0.0

2��0.

67��

�0.

011

�0.0

570.

020.

001

0.66

2[0

.000

8][0

.009

][0

.03]

[0.0

24]

[0.0

6][0

.044

][0

.003

]E

Q-2

0.00

1�0

.02��

0.67

��

0.01

�0.0

50.

022

0.15

60.

66[0

.000

8][0

.009

][0

.03]

[0.0

3][0

.06]

[0.0

44]

[0.6

7]S

Pfin

EQ

-1�0

.002

��0

.055

��

1.54

��

0.00

40.

024

0.04

40.

0005

0.78

2[0

.001

][0

.02]

[0.0

61]

[0.0

33]

[0.0

7][0

.09]

[0.0

07]

EQ

-2�0

.002

��0

.062

��

1.54

��

0.00

080.

011

0.03

�3.9

6��0.

786

[0.0

01]

[0.0

2][0

.06]

[0.0

3][0

.08]

[0.0

9][0

.001

]S

Put

ilitie

sE

Q-1

0.00

20.

043��

�0.

65��

��0

.06��

�0.0

850.

076

�0.0

003

0.55

8[0

.002

][0

.012

][0

.032

][0

.028

][0

.07]

[0.0

6][0

.004

]E

Q-2

0.00

20.

044��

�0.

65��

��0

.06��

�0.0

840.

080.

870.

559

[0.0

01]

[0.0

13]

[0.0

3][0

.03]

[0.0

8][0

.06]

[1.1

4]





66 K. Smimou

TAB

LE

9(b

)The

US

equi

ty-s

ecto

rre

turn

san

dop

timal

ly-w

eigh

ted

ener

gyfu

ture

spo

rtfo

lios,

OW

P;s

ampl

esi

zeD

564.

Dep

end

ent

Ad

jR-

vari

able

Co

nst

'L

OW

Pı

MR

ıO

IıT

S1

!D

ol

�D

RE

C�

Do

l_In

tsq

uar

e

NY

ener

gyE

Q-1

0.00

30.

19��

�1.

04��

��0

.00

�0.0

5�0

.10

0.00

10.

809

[0.0

03]

[0.0

2][0

.03]

[0.0

0][0

.08]

[0.0

6][0

.004

]E

Q-2

0.00

30.

198��

�1.

04��

��0

.00

�0.0

3�0

.09

1.5

0.81

[0.0

03]

[0.0

2][0

.02]

[0.0

0][0

.08]

[0.0

6][1

.52]

NY

finE

Q-1

�0.0

01�0

.068

��

1.32

��

�0.0

00.

031

0.05

0.00

060.

865

[0.0

01]

[0.0

2][0

.04]

[0.0

0][0

.05]

[0.0

6][0

.005

]E

Q-2

�0.0

02�0

.068

��

1.32

��

�0.0

00.

020.

03�3

.94��

0.86

9[0

.001

][0

.02]

[0.0

4][0

.00]

[0.0

6][0

.06]

[0.0

02]

NY

heal

thE

Q-1

�0.0

02�0

.061

��

0.62

5��

0.00

0.02

40.

014

�0.0

001

0.68

4[0

.002

][0

.014

][0

.02]

[0.0

0][0

.06]

[0.0

5][0

.003

]E

Q-2

�0.0

02�0

.06��

�0.

62��

�0.

000.

014

0.00

5�1

.82��

0.68

7[0

.002

][0

.013

][0

.024

][0

.00]

[0.6

][0

.042

][0

.75]

SP

ener

gyE

Q-1

0.00

50.

23��

�1.

02��

��0

.00

�0.0

8�0

.12�

�0.0

001

0.71

7[0

.003

][0

.02]

[0.0

4][0

.00]

[0.0

9][0

.07]

[0.0

05]

EQ

-20.

005�

0.23

3��

1.02

��

�0.0

0�0

.07

�0.1

12.

100.

719

[0.0

03]

[0.0

2][0

.03]

[0.0

0][0

.09]

[0.0

7][1

.73]






TAB

LE

9(b

)C

ontin

ued.

Dep

end

ent

Ad

jR-

vari

able

Co

nst

'L

OW

Pı

MR

ıO

IıT

S1

!D

ol

�D

RE

C�

Do

l_In

tsq

uar

e

SP

ind

EQ

-1�0

.001

�0.0

031.

11��

�0.

000.

074

�0.0

09�0

.002

0.90

2[0

.001

][0

.011

][0

.022

][0

.00]

[0.0

5][0

.04]

[0.0

02]

EQ

-2�0

.000

8�0

.002

1.11

��

0.00

0.06

1�0

.008

1.03

70.

902

[0.0

01]

[0.0

11]

[0.0

22]

[0.0

0][0

.05]

[0.0

4][1

.06]

SP

heal

thE

Q-1

�0.0

02�0

.053

��

0.68

��

0.00

��0

.03

0.02

0.00

040.

673

[0.0

02]

[0.0

14]

[0.0

3][0

.00]

[0.0

6][0

.04]

[0.0

03]

EQ

-2�0

.002

�0.0

53��

�0.

67��

�0.

00�

�0.0

30.

02�0

.63

0.67

3[0

.002

][0

.013

][0

.03]

[0.0

0][0

.06]

[0.0

4][0

.77]

SP

finE

Q-1

�0.0

01�0

.08��

�1.

55��

��0

.00

0.01

80.

044

0.00

010.

783

[0.0

02]

[0.0

3][0

.067

][0

.00]

[0.0

7][0

.09]

[0.0

07]

EQ

-2�0

.001

�0.0

8��

1.54

��

�0.0

0�0

.006

0.02

�5.3

��0.

789

[0.0

02]

[0.0

3][0

.06]

[0.0

0][0

.08]

[0.0

8][2

.15]

SP

utili

ties

EQ

-10.

005��

0.06

5��

0.64

��

�0.0

0�0

.088

0.09

�0.0

020.

565

[0.0

02]

[0.0

15]

[0.0

3][0

.00]

[0.0

78]

[0.0

6][0

.003

]E

Q-2

0.00

6��0.

067��

�0.

64��

��0

.00

�0.1

00.

090.

980.

565

[0.0

03]

[0.0

15]

[0.0

32]

[0.0

0][0

.08]

[0.0

6][1

.41]

In-s

ampl

epr

edic

tabi

lity

test

sof

US

equi

tyse

ctor

retu

rns

whi

leco

nditi

onin

gfo

ren

ergy

futu

res

port

folio

s,an

dot

her

rele

vant

cont

rolv

aria

bles

,ov

erth

esa

mpl

epe

riod.

(Wee

kly

data

;sam

ple

perio

d:A

pril

2003

–Jan

uary

2014

).R

esul

tsof

indi

vidu

alco

ntra

cts

and

thei

rim

pact

son

vario

useq

uity

sect

ors

are

notr

epor

ted

here

due

tosp

ace

limita

tion,

butt

hey

dono

tdiff

erqu

alita

tivel

yfr

omth

ose

pres

ente

din

part

s(a

)an

d(b

)ab

ove.

The

yar

eav

aila

ble

from

the

auth

orup

onre

ques

t.*,

**an

d**

*in

dica

tea

sign

ifica

ntdi

ffere

nce

from

zero

atth

e10

%,

5%an

d1%

leve

ls,

resp

ectiv

ely.

Rob

ust

stan

dard

erro

rsar

epr

ovid

edin

brac

kets

belo

wth

ees

timat

edco

effic

ient

san

dar

eco

rrec

ted

for

hete

rosc

edas

ticity

usin

ga

hete

rosc

edas

ticity

-con

sist

entc

ovar

ianc

em

atrix

ofth

epa

ram

eter

estim

ates

(Whi

te19

80;M

acK

inno

nan

dW

hite

1985

).A

llD

urbi

n–W

atso

nte

stst

atis

tics,

thou

ghno

trep

orte

dhe

re,

reje

ctth

ehy

poth

esis

ofra

ndom

resi

dual

sof

the

regr

essi

ons

atth

e0.

05le

vel.

“L”s

tand

sfo

rla

g.F

orfu

rthe

rde

tails

,see

Sec

tion

4.2.

1.





68 K. Smimou

particular, in the American context, Froot and Stein (1991) showed that asymmetricinformation could lead foreign firms to buy US firms in times when the value of theUS dollar is low relative to the foreign currency.

Table 9 on page 64 shows all the results for various specifications such that equity-sector returns of the week are regressed on the previous week’s energy futures port-folios (EWP (part (a)) or OWP (part (b))). In part (a), using EWP, we notice that theenergy futures portfolios (proxy performance energy futures market) factor shows astatistically and economically significant impact on the prediction of equity sectors,positive in the case of energy and utilities but negative in the case of financials andhealth sectors (using either those based on NY or S&P 500).18 An increase in theenergy futures market predicts an increase of some US equity-sector returns and adecline of others, or no impact at all (as in the case of the industrials sector). Here,we estimate in each regression whether or not the energy futures market at t �1 has apositive predictive ability on the future performance of equity sector i . The explana-tory power of the estimation is higher, with both statistically significant coefficients ofthe equity market (MR) and the lagged energy futures markets, and hovers between0.55 and 0.87 across various specifications. Qualitatively, the same observation ismaintained even when we use the other proxy of energy futures portfolios market(OWP), which consists of optimally weighted futures contracts. In part (b) of Table 9,we notice that the OWP proxy shows a higher significant predictive ability on energy,utilities, financials and health.

In addition, in the specification in which interaction terms were not considered,the coefficient of energy futures movement on the equity-sector returns using eitherproxy (EWP or OWP) hovers around 0.04 via 0.12 to 0.14 for those sectors withpositive impact, meaning that, during the sample period, about 4% or 12% of thefuture equity-sector return growth can be attributed to the energy futures market. Inthe case of those with negative impact, only �2.4% or �5.5% for health and financialsectors, respectively (part (a) of Table 9 on page 64), the effect can be attributed tothe movement of the energy futures markets.

Further, when we progressively add the interaction term Dol_Int, the specificationresults reveal that this term carries additional information about the future perfor-mance of some US equity sectors: negative in the case of financials (S&P or NY) andhealth (NY), and positive in the case of the energy (S&P) sector, regardless of theenergy futures market proxy employed (see parts (a) and (b) of Table 9 on page 64). A

18 Due to space limitations, we only consider predictability analysis in-sample. It is well known thatgood in-sample predictability does not necessarily translate into good out-of-sample predictability(see, for example, Goyal and Welch 2008). Yet, when we test out-of-sample predictive ability inline with Chen (2009), and the MSPE-adj statistic of Clark and West (2007), the main result holdsqualitatively.






period of greater appreciation of the US dollar index futures contracts accompaniedcontemporaneously by high energy futures markets will further suppress the perfor-mance of the financial sector. However, it will also generate a large surge in the energysector. Results show that during periods of high appreciation of the US dollar, someof the equity sectors gain (or lose) more than other sectors via (and conditional on thestate of) the energy channel, or in response to a high increase in the energy futuresmarket.

4.2.2 Energy futures portfolios and selected Canadian equity sectors

In this section, we extend our empirical examination by looking at the relationshipbetween energy futures markets and the Canadian equity sectors. This extension isnecessary because the Canadian equity sectors and rotation of market groups andsectors are usually built on the idea that markets are leading indicators of the econ-omy. Therefore, it is worth examining the interaction of the most relevant Canadiansectors with the most liquid energy futures markets. The financial market in Canada,given its size and commodity-driven features, is an ideal testing ground for empir-ical appraisal. The Canadian economy is considered to be commodity based, withboth the real economy and equity markets heavily influenced by commodities. Aswe re-examine that relationship, we seek to offer new support and explanations forthe results reviewed in Section 4.2.1 in relation to energy futures portfolios and theUS economy. In this section again, we estimate the following full model (A) usingCanadian equity sectors:

Yit D ˛0 C 'L ENGt�1 CmX

lD1

ılXit;l C !Dolt C �DREC;t C �Dol_Intt C �i ;

where Yit is the dependent variable i that denotes the return of equity sector i over theweek t . We intend to determine if this dynamic relationship between equity sectors andenergy futures markets is contingent on the nature of equity sectors, and if it will varyby country given its economic fundamentals and financial structures. In the process,we are indirectly examining if the predictive ability of energy futures movementis contingent upon the appropriate match between economic fundamentals (growthopportunities, exchange rates and interest rates) and factors specific to equity marketand firm (eg, institutional factors).

Second, this empirical examination has relevant policy implications that will provebeneficial to other nations with similar economic characteristics, as there are geo-graphical overlaps that will make this investigation of potential interest. Noticeabletrends characterizing the equity markets of many countries stem from a number offactors, including globalization, deregulation and a similarity of banking system.Although the methods of the present study depart from current knowledge in some





70 K. Smimou

TAB

LE

10(a

)T

heC

anad

ian

equi

ty-s

ecto

rre

turn

san

deq

ually

wei

ghte

den

ergy

futu

res

port

folio

sE

WP

;sa

mpl

esi

zeD

564.

[Tab

leco

ntin

ues

onne

xtth

ree

page

s.]

Dep

end

ent

Ad

jR-

vari

able

Co

nst

'L

EW

Pı

MR

ıO

IıT

S1

!D

ol

�D

RE

C�

Do

l_In

tsq

uar

e

TS

X-E

nerg

yE

Q-1

�0.0

003

0.11

9��

1.17

��

0.03

2�0

.02

0.05

30.

002

0.87

5[0

.001

][0

.015

][0

.03]

[0.0

3][0

.09]

[0.0

8][0

.004

]E

Q-2

�0.0

003

0.11

8��

1.17

��

0.03

1�0

.007

0.05

3�0

.20

0.87

5[0

.001

][0

.016

][0

.031

][0

.03]

[0.0

9][0

.08]

[1.3

4]T

SX

mat

EQ

-1�0

.000

1�0

.023

1.22

��

0.01

1�0

.06

�0.3

2��0.

004

0.68

2[0

.002

][0

.03]

[0.0

7][0

.042

][0

.15]

[0.1

6][0

.011

]E

Q-2

0.00

05�0

.014

1.21

��

0.01

5�0

.02

�0.3

1��6.

18��

0.68

8[0

.002

][0

.03]

[0.0

63]

[0.0

4][0

.16]

[0.1

4][2

.43]

TS

Xin

dE

Q-1

0.00

09�0

.051

��

0.93

��

0.02

0.00

30.

002

�0.0

020.

819

[0.0

01]

[0.0

14]

[0.0

24]

[0.0

3][0

.086

][0

.061

][0

.004

]E

Q-2

0.00

07�0

.052

��

0.93

3��

0.02

�0.0

15�0

.002

�0.9

10.

819

[0.0

01]

[0.0

14]

[0.0

3][0

.03]

[0.0

85]

[0.0

61]

[0.8

1]T

SX

tran

sE

Q-1

0.00

1�0

.054

��

0.86

3��

�0.0

430.

110.

014

�0.0

030.

684

[0.0

01]

[0.0

2][0

.036

][0

.04]

[0.1

1][0

.08]

[0.0

05]

EQ

-20.

0009

�0.0

54��

�0.

865��

��0

.043

0.08

90.

011

�0.5

00.

684

[0.0

014]

[0.0

2][0

.036

][0

.04]

[0.1

17]

[0.0

87]

[1.2

8]






TAB

LE

10(a

)C

ontin

ued.

Dep

end

ent

Ad

jR-

vari

able

Co

nst

'L

EW

Pı

MR

ıO

IıT

S1

!D

ol

�D

RE

C�

Do

l_In

tsq

uar

e

TS

Xfin

EQ

-1�0

.000

3�0

.046

��

0.90

9��

�0.0

310.

085

0.14

7��0

.002

0.76

9[0

.001

][0

.014

][0

.036

][0

.03]

[0.0

8][0

.08]

[0.0

07]

EQ

-2�0

.000

6�0

.05��

�0.

914��

��0

.032

0.06

20.

135�

�3.2

4��0.

773

[0.0

01]

[0.0

15]

[0.0

35]

[0.0

3][0

.088

][0

.081

][1

.53]

TS

Xut

ilitie

sE

Q-1

0.00

040.

007

0.70

5��

�0.0

23�0

.007

0.11

�0.0

005

0.70

5[0

.001

][0

.013

][0

.03]

[0.0

31]

[0.0

9][0

.077

][0

.004

]E

Q-2

0.00

040.

007

0.70

5��

�0.0

23�0

.01

0.12

0.05

0.70

5[0

.001

][0

.014

][0

.03]

[0.0

3][0

.08]

[0.0

7][1

.22]

TS

Xhe

alth

EQ

-1�0

.000

20.

006

0.67

��

�0.0

50.

142

0.08

8�0

.001

0.37

4[0

.002

][0

.03]

[0.0

59]

[0.0

5][0

.15]

[0.1

1][0

.006

]E

Q-2

�0.0

002

0.00

70.

67��

��0

.05

0.13

20.

088

0.10

40.

374

[0.0

02]

[0.0

3][0

.06]

[0.0

5][0

.15]

[0.1

2][1

.90]

TS

Xco

nsst

EQ

-10.

0007

�0.0

3��

0.56

��

�0.0

006

0.01

4�0

.041

�0.0

0006

0.63

5[0

.001

][0

.011

][0

.03]

[0.0

22]

[0.0

9][0

.06]

[0.0

04]

EQ

-20.

0007

�0.0

3��

0.56

��

�0.0

007

0.01

3�0

.041

�0.1

680.

636

[0.0

01]

[0.0

11]

[0.0

3][0

.022

][0

.09]

[0.0

6][0

.88]





72 K. Smimou

TAB

LE

10(b

)The

Can

adia

neq

uity

-sec

tor

retu

rns

and

optim

ally

wei

ghte

den

ergy

futu

res

port

folio

s,O

WP

;sam

ple

size

D56

4.

Dep

end

ent

Ad

jR-

vari

able

Co

nst

'L

OW

Pı

MR

ıO

IıT

S1

!D

ol

�D

RE

C�

Do

l_In

tsq

uar

e

TS

Xen

ergy

EQ

-10.

003

0.18

6��

1.13

��

�0.0

0�0

.062

0.04

0.00

30.

88[0

.002

][0

.02]

[0.0

3][0

.00]

[0.0

9][0

.08]

[0.0

04]

EQ

-20.

003

0.18

5��

1.13

��

�0.0

0�0

.045

0.04

�0.7

80.

883

[0.0

03]

[0.0

2][0

.032

][0

.00]

[0.0

9][0

.07]

[1.9

3]T

SX

mat

EQ

-10.

003

�0.0

241.

22��

��0

.00

�0.0

81�0

.33��

0.00

40.

682

[0.0

04]

[0.0

4][0

.067

][0

.00]

[0.1

5][0

.16]

[0.0

11]

EQ

-20.

004

�0.0

261.

21��

��0

.00

�0.0

2�0

.28��

9.62

��

0.69

6[0

.004

][0

.04]

[0.0

6][0

.00]

[0.1

6][0

.137

][2

.95]

TS

Xin

dE

Q-1

�0.0

02�0

.087

��

0.95

��

0.00

0.03

0.00

2�0

.003

0.82

3[0

.002

][0

.02]

[0.0

2][0

.00]

[0.0

8][0

.06]

[0.0

04]

EQ

-2�0

.002

�0.0

86��

�0.

95��

�0.

000.

005

�0.0

05�1

.58�

0.82

4[0

.002

][0

.018

][0

.02]

[0.0

0][0

.08]

[0.0

6][0

.96]

TS

Xtr

ans

EQ

-1�0

.003

�0.0

98��

�0.

88��

�0.

000.

154

0.02

4�0

.004

0.69

[0.0

03]

[0.0

3][0

.039

][0

.00]

[0.1

2][0

.08]

[0.0

05]

EQ

-2�0

.000

3�0

.096

��

0.88

��

0.00

0.12

60.

02�0

.88

0.69

[0.0

003]

[0.0

3][0

.04]

[0.0

0][0

.11]

[0.0

86]

[1.7

3]






TAB

LE

10(b

)C

ontin

ued.

Dep

end

ent

Ad

jR-

vari

able

Co

nst

'L

OW

Pı

MR

ıO

IıT

S1

!D

ol

�D

RE

C�

Do

l_In

tsq

uar

e

TS

Xfin

EQ

-1�0

.001

�0.0

7��

0.92

4��

0.00

0.1

0.15

3��0

.003

0.77

1[0

.002

][0

.022

][0

.04]

[0.0

0][0

.09]

[0.0

8][0

.007

]E

Q-2

�0.0

02�0

.07��

�0.

925��

�0.

000.

061

0.12

9��5

.19��

0.77

9[0

.002

][0

.02]

[0.0

34]

[0.0

0][0

.09]

[0.0

8][2

.15]

TS

Xut

ilitie

sE

Q-1

0.00

30.

031

0.69

��

�0.0

0�0

.03

0.11

�0.0

001

0.70

6[0

.002

][0

.02]

[0.0

3][0

.00]

[0.0

9][0

.07]

[0.0

05]

EQ

-20.

003

0.03

10.

69��

��0

.00

�0.0

30.

120.

210.

706

[0.0

03]

[0.0

2][0

.03]

[0.0

0][0

.09]

[0.0

7][1

.72]

TS

Xhe

alth

EQ

-1�0

.02��

��0

.07��

0.70

5��

0.00

��

0.27

7�0.

101

�0.0

025

0.39

[0.0

05]

[0.0

31]

[0.0

3][0

.00]

[0.1

5][0

.11]

[0.0

06]

EQ

-2�0

.016

��

�0.0

68��

0.70

6��

0.00

��

0.26

�0.

09�1

.03

0.39

[0.0

05]

[0.0

3][0

.06]

[0.0

0][0

.15]

[0.1

1][1

.87]

TS

Xco

nsst

EQ

-1�0

.001

3�0

.033

��0.

56��

�0.

000.

03�0

.043

�0.0

001

0.63

5[0

.002

][0

.015

][0

.03]

[0.0

0][0

.09]

[0.0

6][0

.004

]E

Q-2

�0.0

013

�0.0

33��

0.56

��

0.00

0.03

�0.0

44�0

.18

0.63

5[0

.002

][0

.015

][0

.03]

[0.0

0][0

.09]

[0.0

6][1

.22]

In-s

ampl

epr

edic

tabi

lity

test

sof

Can

adia

neq

uity

sect

orre

turn

sw

hile

cond

ition

ing

fore

nerg

yfu

ture

spo

rtfo

lios,

and

othe

rrel

evan

tcon

trol

varia

bles

,ove

rthe

sam

ple

perio

d.(W

eekl

yda

ta;s

ampl

epe

riod:

Apr

il20

03–J

anua

ry20

14).

For

furt

her

deta

ils,s

eeTa

ble

9on

page

64(n

otes

)an

dS

ectio

n4.

2.1.





74 K. Smimou

ways, it is natural to expect some differences between Canada and the United Statesin dynamic linkage in terms of statistical and economical significances, persistenceand magnitude.

Table 10 on page 70 presents the results of our estimations using Canadian equitysectors with and without the interaction effects of energy futures and currency move-ment (US dollar). Parts (a) and (b) provide the results using the equally weighted andoptimally weighted portfolios, respectively. Again, using the Canadian equity sectors,results in part (a) using EWP show that the energy futures portfolio (proxy perfor-mance energy futures market) factor shows a statistically and economically significantimpact on the prediction of equity sectors. This is positive only in the case of energybut negative in the case of the financials, industrials, transport and consumer staplessectors. An increase in the energy futures market predicts an increase of Canadianenergy-sector equity and a concurrent decline of other sector returns, or no impact atall (as in the case of the utilities and materials sectors). In part (b) of Table 10, thesame observation is maintained qualitatively, even when we use the other proxy ofthe energy futures portfolios market (OWP).

Periods of high appreciation of the US dollar index futures contracts accompaniedcontemporaneously by high energy futures markets will further depress the perfor-mance of the financial sector. However, they will also generate a large surge in thematerials sector. Our results clearly show that during periods of high appreciation ofthe US dollar, some of the equity sectors gain (or lose) more than other sectors via(and conditional on the state of) the energy channel, or in response to a high increaseof the energy futures market. It is not surprising that the basic materials benefit fromthe positive movement of energy futures during periods of high appreciation of theUS dollar. This is because the basic materials sector consists of the mining and refin-ing of metals, chemical production and forestry products, which tend to depend onthe export and trade channel with the rest of the world. In addition, they tend to besensitive to supply-and-demand fluctuations, because the price of raw materials, suchas gold or other metals, is largely demand driven; thus, an appreciation of the USdollar is a rewarding period for this sector.

In our model with interaction term Dol_Int, @Y=@Dol D ! C �EWP .or OWP/,we can compute how the dependent variable (say, the materials (mat) or financials(fin) sector) changes as the energy futures market (EWP or OWP) varies. The EWP(OWP) variable ranges between �0.465 and 0.273 (�0.186 and 0.163; see Table 1 onpage 45), so the total contemporaneous impact of the changes in the US dollar indexon the basic materials sector in part (a) (part (b)) of Table 10 on page 70 varies from�3.18% to 1.37% (�2.06% to 1.28%), remaining positive as long as the EWP (OWP)return is greater than 5.02%, ie, 0.31/6.18 (2.91%, ie, 0.28/9.62). This is true only for30% (38%) of our sample over the full range of possibilities that EWP (OWP) cantake. Since this value corresponds to a weekly movement, we can conclude that the






US dollar index tends to increase its impact on the materials sector in response to thehigh, positive performance of energy futures.

Again, when we take into account the US dollar fluctuations by designating currencyinteraction with EWP (or OWP) in our model, our results clearly show that the totalcontemporaneous impact of changes in the US dollar index on the financial sector inpart (a) (part (b)) of Table 10 on page 70 varies from �0.74% to 1.64% (�0.72% to1.09%). It remains positive as long as the EWP (OWP) return is lower than 4.167%,ie, 0.135/3.24 (2.49%, ie, 0.129/5.19), being positive in the majority of values in oursample, 69% (60%). Therefore, the US dollar index futures return tends to exhibitfurther positive effects on the financial sector return directly and via interaction withhigher energy futures.19

In addition, the findings divulge further economic insights and implications forpractitioners (asset management). This is in line with Roll (2011), who argued thattrue diversification benefits are not related to correlation, and that diversificationdepends on the volatility that remains unexplained by the underlying factors afterreweighting. In that context, we could infer from the results in Table 9 on page 64and Table 10 on page 70, using the multifactorR-square explanation, some additionalinsight to support our previous results and elucidate the promotion of an argumentfor diversification benefits by holding energy futures per se.

From an asset-allocation perspective, cross-market correlations are clearly infor-mative; however, Carrieri et al (2007) argued that they do not provide a completeand accurate measure of diversification benefits. Pukthuanthong and Roll (2009) alsoconsidered cross-market correlations inadequate as measures of market integration.Roll (2011) proved theoretically that correlation is misleading when evaluating diver-sification benefits. That is, low or negative correlation between bundles of assets doesnot properly measure the potential benefits of diversification, whereas the R-squaresfrom Pukthuanthong and Roll (2009) do. In that context, our results in Table 9 onpage 64 and Table 10 on page 70, given that we are using a number of relevant factors,are in line with Roll (2011) and Pukthuanthong and Roll (2009), since we rely onprincipal components analysis as well (Connor and Korajczyk 1988; Roll and Ross1980). Thus, the adjusted R-square is the measure that assists us in capturing thediversification benefits that can be gleaned from energy, dollar and equity indexes. Inthis paper, adjusted R-squares are slightly lower in the case of some sectors, and alow R-square implies greater diversification benefits.

19 We note that the results in Table 9 on page 64 and Table 10 on page 70 are stable over the sampleperiod under study. Multiple diagnostic tests (eg, the Hansen, Ramsey, and Goldfeld–Quandt tests)were completed to support our assertions.





76 K. Smimou

5 PORTFOLIO HOLDINGS AND SECTOR-ROTATION STRATEGY

5.1 Sector-rotation strategy enhanced by energy futures:US evidence

Past studies based on Markowitz’s optimal portfolio allocation algorithm attemptedto determine the optimal vector (weights) Xj for various rates of return to derive theefficient frontier (the locus of efficient portfolios) and show the benefits of such diver-sification. In this section, we attempt to close the gap in the literature by enhancingsector rotation using the energy futures portfolios under a mean–variance framework.Our objective is to examine to what extent investment in energy futures enhancesportfolio performance for investors engaging in an optimal sector-rotation strategyover various time periods. We will track this performance via modified Sharpe ratios(see, for example, Jobson and Korkie 1981). In this section, we are more concernedwith the equity-sector rotation and thus allow short sales. Managers attempt to benefitfrom changes in market conditions over the business cycle by underweighting someequity sectors and overweighting other sectors; thus, both long and short positionsare possible while anticipating double alphas. By means of quadratic programming,the optimal solution is achieved for the full sample period (FP) and two subperiods(2P) (periods 1 and 2 are obtained by dividing the full period into two equal sub-sample sizes). Then, we again divide the full sample period, this time into four equalsubperiods (4P) such that each period represents an equal subsample size. Our fullsample (FP) period covers April 2003 to January 2014 (n D 564); thus, the samplesize of each subsample under the 2P rotation equals 282, while under the 4P rotationit equals 141. In fact, when we divide the full sample into two subsamples (2P), theyare coincidentally generated around the 2008 GFC as the dividing factor.

Further, for all possible time horizon subsample periods, including the full period(FP), we search for the optimal selection portfolios using four possible scenarios whilemeasuring the Sharpe ratios to tap the performance of each solution. A higher Sharperatio implies a better performance of the optimal portfolios, though our purpose isto clearly compare the performance of the equity-sector rotation against no equityrotation over any selected time period. However, our ultimate objective is to examinehow inclusion of the energy futures (either individually or in the form of an equallyweighted portfolio or optimally weighted portfolio) enhances the performance.

We complete a mean–variance (MV) equity-sector rotation using returns from allselected equity-sector indexes without energy futures in scenario (a). We then repeatsearching for the optimal solution for all sector returns with five individual energyfutures contracts in the sample that is scenario (b). We repeat searching for an opti-mal solution using all equity-sector returns and the equally weighted energy futuresportfolio (EWP) that is scenario (c). Finally, we once again carry out an all-inclusive






equity-sector rotation with the optimally weighted energy futures portfolio in thesample to establish scenario (d).

Sharpe ratios (SRs) are calculated as SRj D .Rj �Rf /=�j , whereRj is the averageweekly portfolio rate of return during a specified investment period, and Rf is theaverage weekly risk-free rate of return (or US t-bill return) during the investmentperiod.20 In this paper, for simplicity and the purposes of analytical tractability, weassume that Rf equals zero. We deem that this assumption is realistic, given thecurrent low value of the three-month t-bill rate of the United States and Canada,notably during the sample period of April 2003–January 2014.21 The Sharpe ratiois a composite measure for evaluating the performance of each optimal portfolio,including a relative measure of the portfolio’s benefit-to-risk ratio. It is calculated asits mean in excess of the risk-free rate based on the three-month US t-bill market ratedivided by the standard deviation of portfolio returns.

Figure 1 on the next page, Figure 2 on the next page, Figure 3 on page 79 andFigure 4 on page 79 represent all the possible scenarios by depicting the compositionof the overall optimal portfolios over the sample period under the MV rotation strategy(2P) among all included US equity sectors without or with energy futures (left-handscale), with the Sharpe ratio in the right-hand scale.

Figure 5 on page 80, Figure 6 on page 81, Figure 7 on page 82 and Figure 8 onpage 83 again show the results of the composition of the optimal portfolios while usingall of the possible scenarios (a) to (d) following an MV rotation strategy four times (4P)over the sample period. The results from Figures 1–4 and Figures 5–8 clearly showthat there are ample gains from a sector-rotation strategy from one period to another(either 2P or 4P), such that under scenario (a) investors gain additionally by engagingin dynamic rotation following the MV framework. Of course, our results show that the

20 Due to space limitations, we rely exclusively on the Sharpe ratio, in line with many past studies. Infact, one could extend this examination using a number of performance measures, which are widelyknown in the literature and mutual fund industry, such as the Sortino ratio, Omega ratio and thealpha of the alternative portfolios (see, for example, Elton et al 2003; Chevalier and Ellison 1999a;Chevalier and Ellison 1999b). The main result and conclusion would hold, and it would only extendthe length of our paper; thus, we decide to focus on one of the well-known performance measures,which is particularly relevant under a mean–variance framework.21 We propose using a zero risk-free rate in this section to allow us to track the changes from oneperiod to another, since we are keen to understand the effect of the inclusion of proposed energyfutures portfolios on the overall performance while we change the rebalancing frequency from oneperiod to another. In this setting, the inclusion of the actual risk-free rate in the calculation willinhibit and mask the benefit of various rebalancing frequencies. For example, based on the datafrom Thomson Datastream, the three-month t-bill rates in the United States and Canada over theperiod 2003–2008 were 2.75 and 3.042%, respectively, while for the period 2009–January 2014they were 0.088 and 0.7695% for the United States and Canada, respectively. Thus, to simplify thecomparison between various strategies, we assumed a zero risk-free rate.





78 K. Smimou

FIGURE 1 Equity-rotation strategy using US equity sectors with/without energy futures,2P: scenario (a).

0.113

0.081 0.088

0

0.02

0.04

0.06

0.08

0.10

0.12

–80–60–40–20

204060

120

W_NY_energy W_N&Y_financials W_NY_healthW_S&P_energy W_S&P_industrials W_S&P_healthW_S&P_financials W_S&P_utilities Sharpe ratio, right

–100

0

80100

Period 1

Period 2

Full period%

Evolution of the composition of the optimal allocation using mean–variance equity-sector rotation, completed for allincluded US equity sectors in the left-hand scale with the Sharpe ratio in the right-hand scale.

FIGURE 2 Equity-rotation strategy using US equity sectors with/without energy futures,2P: scenario (b).

0.138

0.073

0.098

0

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

W_NY_energy W_NY_financials W_NY_healthW_S&P_energy W_S&P_industrials W_S&P_healthW_S&P_financials W_S&P_utilities

Sharpe ratio, right

–80

–60

–40

–20

20

40

60

–100

0

80

100

Crude oilHeating oil Natural gas GasolineElectricity

Period 1

Period 2Full period

%

Evolution of the composition of the optimal allocation using mean–variance equity-sector rotation, completed withUS equity sectors and individual energy futures contracts.






FIGURE 3 Equity-rotation strategy using US equity sectors with/without energy futures,2P: scenario (c).

0.125

0.074 0.090

0

0.02

0.04

0.06

0.08

0.10

0.12

0.14

W_NY_energy W_NY_financials W_NY_healthW_S&P_energy W_S&P_industrials W_S&P_healthW_S&P_financials W_S&P_utilitiesSharpe ratio, right

–80

–60

–40

–20

20

40

60

–100

0

80

100

EWP

Period 1

Period 2Full period%

Evolution of the composition of the optimal allocation using mean–variance equity-sector rotation, completed withUS equity sectors and an equally weighted energy futures portfolio.

FIGURE 4 Equity-rotation strategy using US equity sectors with/without energy futures,2P: scenario (d).

0.214

0.128

0.159

0

0.05

0.10

0.15

0.20

0.25

–80

–60

–40

–20

20

40

60

–100

0

80

100

W_NY_energy W_NY_financials W_NY_healthW_S&P_energy W_S&P_industrials W_S&P_healthW_S&P_financials W_S&P_utilitiesSharpe ratio, right

OWP

Period 1

Period 2Full period%

Evolution of the composition of the optimal allocation using mean–variance equity-sector rotation, completed withUS equity sectors and an optimally weighted energy futures portfolio.





80 K. Smimou

FIGURE 5 Equity-rotation strategy using US equity sectors with/without energy futures,4P: scenario (a).

0.222

0.0650.046

0.128

0.088

0

0.05

0.10

0.15

0.20

0.25

–150

–100

–50

0

50

100

150

W_NY_energy W_NY_financials W_NY_health

W_S&P_energy W_S&P_industrials W_S&P_health

W_S&P_financials W_S&P_utilities Sharpe ratio, right

Period 1Period 2

Period 3Period 4

Full period%

Evolution of the composition of the optimal allocation using mean–variance equity-sector rotation completed for allincluded US equity sectors.

addition of the energy futures enhances the performance of all portfolios, especiallywhen this strategy is completed using optimally built energy futures (OWP).

In part (a) of Table 11 on page 84, we present a comparative analysis of the Sharperatios (reward-per-risk ratios) with four possible optimal portfolio holdings (scenar-ios) without/with optimally weighted and equally weighted (or individual futures con-tracts) energy futures portfolios (OWP and EWP). This analysis involved performinga dynamic sector-rotation strategy using the mean–variance framework either twice(2P) or four times (4P) over the full sample period to show the benefits of includingindividual futures contracts versus an equally weighted or optimally weighted energyfutures portfolio in order to enhance the performance of an equity-sector rotationstrategy.

If the information ratio suggested in finance literature (see, for example, Goodwin1998) is developed to serve as a measurement of the special information that anactive portfolio reveals through its return, we want to measure the excess return of anequally weighted or optimally weighted energy futures portfolio per the total risk ofthe portfolio. We are merely using it to measure historical performance against the






FIGURE 6 Equity-rotation strategy using US equity sectors with/without energy futures,4P: scenario (b).

0.255

0.085

0.027

0.128 0.098

0

0.05

0.10

0.15

0.20

0.25

0.30

–150

–100

–50

0

50

100

150



W_S&P_financials W_S&P_utilities

Sharpe ratio, right

Crude oil

Heating oil Natural gas Gasoline

Electricity

Period 1Period 2

Period 3Period 4

Full period%

Evolution of the composition of the optimal allocation using mean–variance equity-sector rotation completed usingUS equity sectors and individual energy futures contracts.

other strategies, and we are not making asset allocation decisions based on this ratio.To be able to clearly articulate differences in terms of reward to risk by engaging inmean–variance equity-sector rotation, enhanced by the use of energy futures to capturechanges in market conditions, we compute a compounding Sharpe ratio (SRc) as ageometric mean of the SRj;p , such that p is the period we intend to engage in arotation, and p D 2 or 4 implies the number of Sharpe ratios we use as a result of atwice or four-times rotation, respectively, over the full sample period. Based on theUS data in part (a) of Table 11 on page 84, we can see that the rotation frequencyfrom 2P to 4P clearly indicates that an investor adds return per risk in excess of whatis achieved without any rotation, such that, as we increase the frequency of rotation,the gain also increases, as presented in this paper.22 Based on scenario (a), we can

22 Investors and portfolio managers are well aware of other constraints (such as transactions costs,principles and policy statements that engender constructed funds and fund companies’ policiesin general), which may limit the number of rotations they can adopt notably during a challengingdomestic economic climate or a GFC.As in many examples, tactical strategies require the availabilityof funds or financing that is free from short-lived restrictions.





82 K. Smimou

FIGURE 7 Equity-rotation strategy using US equity sectors with/without energy futures,4P: scenario (c).

0.248

0.067

0.037

0.124

0.090

0

0.05

0.10

0.15

0.20

0.25

0.30



W_S&P_financials W_S&P_utilities EWP

–150

–100

–50

50

100

150

0

Sharpe ratio, right

Period 1

Period 2Period 3 Period 4

Full period%

Evolution of the composition of the optimal allocation using mean–variance equity-sector rotation, completed usingUS equity sectors and an equally weighted energy futures portfolio.

see that the difference shows an 11.5% gain in terms of return per risk by utilizingsector rotation. This can reach 21.09%, as we construct our energy futures portfoliobased on an optimally weighted portfolio, a situation that clearly exceeds scenario (c)with its equally weighted energy futures portfolio. Further, as we increase rotationfrequency from 2P to 4P, it becomes apparent that differences and gain in performanceexceed that of the no-rotation strategy (FP), which is 51.32% in terms of return perrisk. We note the superior performance of the portfolios when adding various energyfutures portfolios, as suggested by the earlier correlation analysis. Also, the standarddeviation was reduced tremendously from scenario (a) to scenario (d).

5.2 Sector-rotation strategy enhanced by energy futures: Canadianevidence

In this section, using Canadian equity sectors, we examine the performance of variousmean–variance portfolios constructed on the basis of the statistical analysis carried outfor the full period and the subsamples, while advancing the sector-rotation strategy.






FIGURE 8 Equity-rotation strategy using US equity sectors with/without energy futures,4P: scenario (d).

0.194

0.157

0.013

0.195

0.159

0

0.05

0.10

0.15

0.20

0.25



W_S&P_financials W_S&P_utilities OWPSharpe ratio, right

–150

–100

–50

50

100

150

0

Period 1Period 2

Period 3

Period 4 Full period%

Evolution of the composition of the optimal allocation using mean–variance equity-sector rotation, completed usingUS equity sectors and an optimally weighted energy futures portfolio.

Thus, our evaluation of benchmark performance is concerned with comparing thereturn earned on a benchmark with the return earned on other stock indexes. Part (b)of Table 11 on the next page shows the performance measures, both Sharpe ratiosusing the full period and the compounding Sharpe ratios (SRc;MV). The Sharpe ratio,which is a relative measure of a portfolio’s benefit-to-risk ratio, shows that includingenergy futures adds more value to the performance of the portfolios (scenario (d)).

The Canadian results echo what we have shown before. Using both rotation frequen-cies (2P or 4P), we note that energy futures portfolios (EWP or OWP) were chosenwith a positive proportion. This was done to recommend a long position to lower theoverall portfolio standard deviation and achieve higher portfolio performance.

Figure 13 on page 89, Figure 14 on page 90, Figure 15 on page 91 and Figure 16on page 92 show that, in the case of the 4P equity rotation with the energy futuresportfolios, the allocation keeps increasing: 10.51%, 19.66%, 25.16% and 31.67%,respectively, from period 1 to period 4. Thus, a mean–variance equity-rotation strategycan efficiently help lower the total risk of the portfolio while taking into accountthe market-condition changes by underweighting some sectors while overweightingothers. Further, taking a long position in energy futures also helps us end up with a





84 K. Smimou

TABLE 11 Comparison of Sharpe ratios (reward-per-risk ratios) with four possible optimalportfolio holdings (scenarios) without/with optimally weighted and equally weighted (orindividual futures contracts) energy futures portfolios (OWP and EWP) by performing adynamic sector-rotation strategy using the mean–variance (MV) framework either twice(2P) or four times (4P) over the full sample period.

(a) US evidence

Scenarios‚ …„ ƒ(a) (b) (c) (d)

Sharpe ratios (full period, FP) 0.088 0.098 0.090 0.159Sharpe ratios SRc;MV (2P) 0.203 0.221 0.208 0.37Difference (2P, FP) 0.115 0.123 0.118 0.21

Sharpe Ratios (FP) 0.088 0.098 0.090 0.159Sharpe ratios SRc;MV (4P) 0.535 0.576 0.553 0.67Difference (4P, FP) 0.447 0.478 0.462 0.51

(b) Canadian evidence

Scenarios‚ …„ ƒ(a) (b) (c) (d)

Sharpe ratios (FP) 0.080 0.088 0.080 0.137Sharpe ratios SRc;MV (2P) 0.213 0.216 0.202 0.282Difference (2P, FP) 0.133 0.128 0.122 0.144

Sharpe ratios (FP) 0.080 0.088 0.080 0.137Sharpe ratios SRc;MV (4P) 0.422 0.443 0.385 1.12Difference (4P, FP) 0.342 0.355 0.305 0.987

Here, we show the benefits of including individual futures contracts (versus an equally weighted or optimally weightedenergy futures portfolio) in order to enhance the performance of an equity-sector rotation strategy.The four scenariosrepresent the cases when we optimize using (a) only equity sectors, (b) equity sectors with individual energy futurescontracts, (c) equity sectors with equally weighted energy futures portfolios and (d) equity sectors with optimallyweighted energy futures portfolios.“Difference” implies the gain achieved by engaging an MV sector-rotation strategy(either 2P or 4P) over the sample period. The sample size of each subsample under 2P rotation D 282. The samplesize of each subsample under 4P rotation D 141.

Sharpe ratio that is higher by 98.7% (from 0.137 to 1.12) than if we decided not tooptimally rotate the composition of the portfolios (see part (b) of Table 11).

Part (b) of Table 11 clearly shows the benefits of engaging in the equity-sectorrotation alone. Results are visible under scenario (a) as we improve the performanceby 13.3% if the rotation is accomplished only twice, or by 34.2% if it is accomplishedfour times. Yet, with the inclusion of the energy futures portfolios, as in scenario (d),






FIGURE 9 Equity-rotation strategy using Canadian equity sectors with/without energyfutures, 2P: scenario (a).

0.081

0.122

0.080

0

0.02

0.04

0.06

0.08

0.10

0.12

0.14

–60

–40

–20

0

20

40

60

80

100

120

W_TSX_energy W_TSX_materials W_TSX_industrials

W_TSX_transport W_TSX_financials W_TSX_utilities

W_TSX_health W_TSX_consumer staples Sharpe ratio, right

Period 1

Period 2

Full period

%

Evolution of the composition of the optimal allocation using mean–variance equity-sector rotation, completed for allincluded Canadian equity sectors.

we can see a tremendous extra gain in terms of performance that hovers between14.44% and 98.7%, as in scenario (d). Scenario (b), which calls for the inclusion ofindividual energy contracts, offers additional benefits; however, they cannot exceedthose of the other scenarios such as (d). Under scenario (b), optimal portfolios shiftedand suggested additional weight toward individual energy futures contracts by takinga long position most of the time, with the exception of electricity. The result is inline with previous studies (see, for example, Gorton and Rouwenhorst 2006; Erband Harvey 2006; Smimou 2010). It is clearly shown that the inclusion of individualenergy futures (9.64% to 33.66%; see Figure 13 on page 89, Figure 14 on page 90,Figure 15 on page 91 and Figure 16 on page 92) could deliver a better risk-returnrelationship.

5.3 Sector-rotation strategy enhanced by energy futures:robustness analysis

In this section, we expand our optimal rotation strategy using conditional value-at-risk(CVaR). It is well documented that the nonnormality of asset returns is an empiricalregularity that is due to time-varying parameters or other extreme realizations (see, for





86 K. Smimou

FIGURE 10 Equity-rotation strategy using Canadian equity sectors with/without energyfutures, 2P: scenario (b).

0.107 0.099

0.088

0

0.02

0.04

0.06

0.08

0.10

0.12

–60

–40

–20

0

20

40

60

80



W_TSX_health W_TSX_consumer staples

Sharpe ratio, right

Crude oil


Electricity

%

Period 1Period 2

Full period

Evolution of the composition of the optimal allocation using mean–variance equity-sector rotation, completed usingCanadian equity sectors and individual energy futures contracts.

example, Zakamouline and Koekebakker 2009; Ranaldo and Favre 2005; Ait-Sahaliaand Brandt 2001). Thus, an investor should allocate their wealth among a set of assetsthat exhibits some properties of the nonnormal distribution, with the knowledge thathigher moments affect portfolio allocation (see, for example, Harvey and Siddique2000; Athayde and Flôres 2001).

In the Markowitz model presented in Section 3.1.1, model (1), we used a portfolio’svariance as a measure of risk. However, the variance is not the only possible measure ofrisk. Thus, it is crucial to expand our search for diversification benefits by using othermeasures of risk that focus returns below the target level, such as CVaR; notably,futures returns do not necessarily follow normal distributions. We note that CVaRis a measure that quantifies the losses that might be encountered in the tail (seeRockafellar and Uryasev 2002). Thus, the objective of most investors is to minimizethe expected risk while meeting the expected level of return alternatively. This is doneusing a different risk measure than variance: CVaR (see Rockafellar and Uryasev 2000;Rockafellar and Uryasev 2002).

The variance measures the dispersion of returns around the expected value whena large value indicates greater dispersion and the uncertainty of future returns also






FIGURE 11 Equity-rotation strategy using Canadian equity sectors with/without energyfutures, 2P: scenario (c).

0.086

0.107

0.080

0

0.02

0.04

0.06

0.08

0.10

0.12



W_TSX_health W_TSX_consumer staples EWP

–60

–40

–20

0

20

40

60

80

100

%

Period 1

Sharpe ratio, right

Period 2

Full period

Evolution of the composition of the optimal allocation using mean–variance equity-sector rotation, completed usingCanadian equity sectors and an equally weighted energy futures portfolio.

becomes greater. If we want to select investments with low variances in a nonnormaldistribution, we would reduce disproportionately the upside of the distribution. Someinvestors may only be concerned with the risk of return below the mean (downsiderisk), which is measured by the semivariance or semistandard deviation. Thus, themethod of mean–semivariance was proposed to model this situation (see Markowitz1959; Mao 1970).

CVaR, which is an extension of VaR, is a risk-assessment method used to reducethe probability that a portfolio will incur large losses. It assesses the likelihood that aspecific loss will exceed the VaR at a given confidence level. The discussion has beendirected here toward minimizing CVaR. We specify a probability, � , eg, 0:1, and thenwe want the model to choose

(a) a target value, CVaR,

(b) a portfolio composition,

so as to Max� � target � Œexpected shortfall below target�. Thus, at an optimum, theprobability of missing the target is about � . We would like to have both a high target,





88 K. Smimou

FIGURE 12 Equity-rotation strategy using Canadian equity sectors with/without energyfutures, 2P: scenario (d).

0.163

0.102

0.138 0.14

0.16

0.18



W_TSX_health W_TSX_consumer staples OWP

Sharpe ratio, right

–40

–20

0

20

40

60

80

%

0

0.02

0.04

0.06

0.08

0.10

0.12

Period 1

Period 2

Full period

Evolution of the composition of the optimal allocation using mean–variance equity-sector rotation, completed usingCanadian equity sectors and an optimally weighted energy futures portfolio.

which we achieve with a probability of approximately 1 � � , and a low expectedshortfall when we miss the target.

At this point, we need to re-examine our previous results in light of another method-ology. Thus, we approach our robustness analysis using a different risk metric tocapture variations, if any, in investment opportunities. To rule out the possibility ofcapturing “incorrect” diversification benefits, we expand our examination in this sub-section by using the CVaR method to support or challenge our previous results. Thisis for robustness purposes, and to more clearly elucidate the case of portfolio man-agement using energy futures and equity-sector rotation strategy. This exercise willinterest investors with both mean–variance and other risk metrics objectives who aresearching for the optimal portfolios. It will also assist in our effort to uphold thispaper’s main result, and rule out any selection bias regarding the methodology orsample used.

Table 12 on page 93 shows the Sharpe ratios for three possible scenarios (a), (c)and (d). Since we are using a different risk metric, CVaR, we intend to compute astandard Sharpe ratio similar to the one in Table 11 on page 84. We also proposea slightly modified Sharpe ratio that measures relative portfolios’ benefit to risk,






FIGURE 13 Equity-rotation strategy using Canadian equity sectors with/without energyfutures, 4P: scenario (a).

0.277

–0.084

0.137

0.069

0.080

–0.15

–0.10

–0.05

0

0.05

0.10

0.15

0.20

0.25

0.30

–40

–20

0

20

40

60

80

%

–60

–80

100

120

140

Period 1Period 2

Period 3 Period 4

Full period



W_TSX_health W_TSX_consumer staples Sharpe ratio, right

Evolution of the composition of the optimal allocation using mean–variance equity-sector rotation, completed for allincluded Canadian equity sectors.

such that the risk is CVaR (the objective function of the CVaR optimization model).Our results clearly support the main conclusion, as illustrated in Table 11, under themean–variance framework. Here, we maintain the same observation that great gainscan be made by engaging in optimal sector rotation, since all the differences shownin Table 12 on page 93 are positive. In addition, the gains are greater as we movefrom scenario (a), only equity sectors, to scenario (d), using an optimally weightedenergy futures portfolio. Of course, even under a different CVaR risk metric, therotation frequency remains a crucial factor in the effort to achieve higher performancefrom the overall portfolios. The portfolios with optimally weighted energy (OWP)outperformed those with equally weighted energy (EWP) across various time horizonsand regardless of the rotation frequency used.

Moreover, by minimizing the CVaR, the result shows that it is still optimal toallocate a proportion between 10% and 23% to optimally weighted energy futuresportfolios in the case of the United States, and between 12% and 22% for Canada.23

23 Under scenario (c), the optimal allocation to EWP is between 2.73% and 15.65% for the UnitedStates, and between 0.25% and 13.02% for Canada. Due to space limitations, the full results of ouroptimal allocations are not reported, but they are available from the author(s) upon request.





90 K. Smimou

FIGURE 14 Equity-rotation strategy using Canadian equity sectors with/without energyfutures, 4P: scenario (b).

0.297

–0.055

0.107

0.0640.088

0

0.05

0.10

0.15

0.20

0.25

0.30

0.35



W_TSX_health W_TSX_consumer staples

Sharpe ratio, right

Crude oil


Electricity

–60

–40

–20

0

20

40

60

80

%

100

–0.10

–0.05

Period 1Period 2

Period 3Period 4

Full period

Evolution of the composition of the optimal allocation using mean–variance equity-sector rotation, completed usingCanadian equity sectors and individual energy futures contracts.

Overall, we observe that the fraction of the portfolio devoted to energy futures port-folios is fairly consistent. However, the fractions of equity sectors vary significantlywhen the risk measure changes. Thus, the evidence lends support to the argumentsin favor of diversification using energy futures, regardless of the measures of risk inthe objective. In addition, the standard Sharpe ratio based on the standard deviationin the denominator could not offer a visible comparison. With the modified Sharperatio, however, our results again imply a better performance for the optimal portfoliounder scenario (d) in Table 12 on page 93 versus that in Table 11 on page 84, whichlists results of rotating among equity sectors with OWP with the maximum Sharperatio achieved when we used the CVaR metric to enhance the risk relationship of theUS investor’s portfolio.24

24 Here, we need to make a caveat that the results presented in this paper are only for energy futures.






FIGURE 15 Equity-rotation strategy using Canadian equity sectors with/without energyfutures, 4P: scenario (c).

0.282

–0.087

0.115

0.062 0.080



W_TSX_health W_TSX_consumer staples EWP

Sharpe ratio, right

–40

–20

0

20

40

60

80

%

–0.15

–0.10

–0.05

0

0.05

0.10

0.15

0.20

0.25

0.30100

–60

Period 1Period 2

Period 3 Period 4

Full period

Evolution of the composition of the optimal allocation using mean–variance equity-sector rotation, completed usingCanadian equity sectors and an equally weighted energy futures portfolio.

6 CONCLUSION

Commodity and currency movements including oil, the US dollar and equity marketperformance are widely presented in daily news. Moreover, based on the documentedresearch into microstructure, investors have been advised to take into considerationequity sectors and commodity futures behaviors in light of their fundamental long-term properties in order to provide effective diversification for stock and bond port-folios. In that context, it is worthwhile fully understanding the drivers and buildingblocks of historical sector returns while interacting with energy futures, because theyoffer possible future values to better serve investors.

The purpose of this paper was to delve into optimal equity-sector rotation in theUnited States and Canada, and to determine the impact of energy futures portfolios,together with other relevant macro and market factors known to capture the move-ment of business cycles. Given today’s challenging economic climate, such ques-tions are increasingly pertinent. Three major contributions have been presented andsupported based on the empirical results, in addition to conclusions in the existingliterature. First, we find that the energy futures market exerts a great deal of predictive





92 K. Smimou

FIGURE 16 Equity-rotation strategy using Canadian equity sectors with/without energyfutures, 4P: scenario (d).

0.554

–0.004

0.230

0.116

0.138

–0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

W_TSX_energy W_TSX_materials W_TSX_industrialsW_TSX_transport W_TSX_financials W_TSX_utilities

W_TSX_health W_TSX_consumer staples OWPSharpe ratio, right

–40

–20

0

20

40

60

80

%

100

–60

Period 1

Period 2Period 3

Period 4

Full period

Evolution of the composition of the optimal allocation using mean–variance equity-sector rotation, completed usingCanadian equity sectors and an optimally weighted energy futures portfolio.

ability on the US and Canadian equity-sector markets in terms of magnitude, sign andstatistical significance using two types of portfolio (equally weighted and optimallyweighted). With in-sample prediction, the use of energy futures grants additionalinformation regarding the dynamic interaction within two countries that differ eco-nomically; this tactic better serves investors and policymakers in a forward-lookingframework. Second, under the premise that not all sectors of the economy performwell at the same time, thus the need for a maximally effective method to preserve gain,we proposed an optimal strategy to capture and uphold the gain and assist with tim-ing the economic cycle while benefiting from commodity diversification by holdingenergy futures.

Third, distinct from some past studies, we addressed the role of energy futuresrecommended for use as a hedge against expected inflation and gas industries, whileincorporating into our analysis the fluctuation of the US dollar. Our results showedthat, in some instances, changes in exchange rate (high volatility) through interac-tion with energy futures offer additional insights regarding the performance of someselected equity sectors, such that US financials and health sectors, and Canadianindustrials, financials and materials, should be taken into consideration when portfolio






TABLE 12 Comparison of Sharpe ratios (reward-per-risk ratios) with three possible optimalportfolio holdings (scenarios) without/with optimally weighted and equally weighted energyfutures portfolios (OWP and EWP) by performing a dynamic sector-rotation strategy usingthe CVaR method either 2P or 4P over the full sample period.

(a) US evidence

Scenarios‚ …„ ƒ(a) (c) (d)

Sharpe ratios (FP) 0.001 0.001 0.001Sharpe ratios SRc;CVaR (2P) 0.002 0.002 0.002Difference (2P, FP) 0.001 0.001 0.001Modified Sharpe ratio (FP) 0.287 0.302 0.326Modified Sharpe ratio (2P) 0.877 0.874 0.972Difference 0.59 0.573 0.646

Sharpe ratios (FP) 0.001 0.001 0.001Sharpe ratios SRc;CVaR (4P) 0.004 0.004 0.004Difference (4P, FP) 0.003 0.003 0.003Modified Sharpe ratio (FP) 0.287 0.302 0.326Modified Sharpe ratio (4P) 3.456 3.909 4.871Difference 3.169 3.608 4.545

(b) Canadian evidence

Scenarios‚ …„ ƒ(a) (c) (d)

Sharpe ratios (FP) 0.001 0.001 0.001Sharpe ratios SRc;CVaR (2P) 0.003 0.003 0.003Difference (2P, FP) 0.002 0.002 0.002Modified Sharpe ratio (FP) 0.248 0.253 0.269Modified Sharpe ratio (2P) 1.191 1.18 1.275Difference 0.943 0.926 1.006Sharpe ratios (Full period) 0.001 0.001 0.001Sharpe ratios SRc;CVaR (4P) 0.006 0.005 0.006Difference (4P, FP) 0.005 0.005 0.005Modified Sharpe ratio (FP) 0.248 0.253 0.269Modified Sharpe ratio (4P) 4.84 4.85 5.27Difference 4.592 4.597 5.001

Here, we show the benefits of including individual futures contracts (versus an equally weighted or optimally weightedenergy futures portfolio) in order to enhance the performance of an equity-sector rotation strategy.The four scenariosrepresent the cases when we optimize to search for optimal allocation selection using (a) only equity sectors,(b) equity sectors with individual energy futures contracts, (c) equity sectors with equally weighted energy futuresportfolio or (d) equity sectors with optimally weighted energy futures portfolio, respectively. “Difference” implies thegain achieved by engaging a mean CVaR (MCVaR) sector-rotation strategy (either 2P or 4P) over the sample period.Due to space limitations, the results for scenario (b) are not reported; they are available from the author(s) uponrequest. Unlike the standard Sharpe ratio, the modified Sharpe ratio is a relative measure of a portfolio’s benefit-to-risk ratio. It is calculated as its mean in excess of the risk-free rate based on the three-month US t-bill market rate,assumed to equal zero, divided by the CVaR risk of the portfolio (ie, the objective of the CVaR optimization model).





94 K. Smimou

managers are building their equity-sector rotation strategies to enhance the benefitsof diversification.

In the same direction, Greer (2000) looked at the rebalancing effect and showedthe importance of commodity benefits in a period of unexpected rises of inflation. Weshowed that energy futures portfolios offer potential diversification gains to investors,and the gains from international diversification are even more impressive when othernon-US equity sectors are included. Further, our results are robust to different chosentime periods and various risk metrics of the performance of efficient portfolios con-structed from different combinations of equity sectors and energy futures portfolios.This supports the finding that US and Canadian investors can benefit from diversifyinginto optimal energy futures portfolios to enhance their dynamic sector strategies andhedge against expected inflation, while taking advantage of changes in the businesscycle. An investor who frequently rotates their portfolio holdings would be better offdecreasing the investment proportion during a period less promising to some specificsector’s diversification, revising their position to achieve protection when it is mostneeded. Indirectly, the findings also show that an investment in foreign energy futures(individual contracts or portfolios), such as we see from a Canadian investor’s per-spective, may offer the diversifying properties that investors look for to reduce overallrisk and enhance return.

This result will prove to have some practical and policy implications. Policymakersand institutional investors can learn from the predictive ability of energy futureswhen assessing the potential performance of various equity-based strategies, includingrotation and tactical strategies. At the very least, they can enhance their understandingregarding the determinants and drivers behind the movement of some crucial equitysectors that represent the backbone of the country’s macroeconomy. Building anactive, effective, equity-based strategy while taking advantage of the cyclical marketconditions should only be achievable with a better understanding of the energy futuresmarket; this suggests that an optimal energy futures portfolio not only is relevant forinstitutional investment, but also has real forward effects on the state of the economyand economic policy frameworks via its impact on the performance of the most crucialsectors of the economy.

DECLARATION OF INTERESTThe authors report no conflicts of interest. The authors alone are responsible for thecontent and writing of the paper.

ACKNOWLEDGEMENTSThe author is grateful to the editor-in-chief, Arthur Berd, and an anonymous refereefor excellent suggestions and helpful comments. Remaining errors, if such there be,are of course, my own.






REFERENCES

Acharya, V.V., Lochstoer, L. A., and Ramadorai, T. (2013). Limits to arbitrage and hedging:evidence from commodity markets. Journal of Financial Economics 109, 441–465.

Aguenaou, S., Gwilym, O. A., and Rhodes, M. (2011). Open interest, cross listing, andinformation shocks. Journal of Futures Markets 31(8), 755–778.

Ait-Sahalia, Y., and Brandt, M. (2001). Variable selection for portfolio choice. Journal ofFinance LVI(4), 1297–1351.

Andriosopoulos, K., and Nomikos, N. (2014). Performance replication of the spot energyindex with optimal equity portfolio selection: evidence from the UK, US, and Brazilianmarkets. European Journal of Operational Research 234, 571–582.

Athayde, G. M., and Flores, R. G. (2001). Finding a maximum skewness portfolio: a generalsolution to three-moments portfolio choice.Journal of Economics, Dynamics and Control28, 1335–1352.

Avramov, D., and Wermers, R. (2006). Investing in mutual funds when returns arepredictable. Journal of Financial Economics 81, 339–377.

Balli, F., Basher, S. A., and Louis, R. J. (2013). Sectoral equity returns and portfolio diversi-fication opportunities across the GCC region. Journal of International Financial Markets,Institutions and Money 25, 33–48.

Bartram, S. M., and Bodnar, G. M. (2009). No place to hide: the global crisis in equitymarkets in 2008/2009. Journal of International Money and Finance 28, 1246–1292.

Basher, S., Haug, A., and Sardorsky, P. (2012). Oil price, exchange rates, and emergingstock markets. Energy Economics 34, 227–240.

Batten, J. A., and Lucey, B. M. (2007). Volatility in the gold futures market. ResearchPaper 07-25, HKUST Business School. URL: http://ssrn.com/abstract=1008722.

Bessembinder, H. (1992). Systematic risk, hedging pressure, and risk premiums in futuresmarkets. Review of Financial Studies 5(4), 637–667.

Bessembinder, H., and Seguin, P. (1992). Futures-trading activity and stock price volatility.Journal of Finance 47, 2015–2034.

Bhargava, V., and Malhotra, D. (2007). The relationship between futures trading activityand exchange rate volatility, revisited. Journal of Multinational Financial Management17, 95–111.

Bodie, Z., and Rosansky, I. (1980).Risk and return in commodity futures.Financial AnalystsJournal 36, 27–39.

Brennan, M., and Subrahmanyam, A. (1996). Market microstructure and asset pricing:on the compensation for illiquidity in stock returns. Journal of Financial Economics 41,441–464.

Brunnermeier, M., and Pedersen, L. H. (2009). Market liquidity and funding liquidity. Reviewof Financial Studies 22, 2201–2238.

Büyüksahin, B., and Robe, M. A. (2014). Speculators, commodities, and cross-marketlinkages. Journal of International Money and Finance 42, 38–70.

Capie, F., Mills, T. C., and Wood, G. (2005). Gold as a hedge against the dollar. Journal ofInternational Financial Markets, Institutions, and Money 15, 343–352.

Carrieri, F., Errunza, V., and Hogan, K. (2007). Characterizing world market integrationthrough time. Journal of Financial and Quantitative Analysis 42(4), 915–940.





96 K. Smimou

Chang, C.-L., McAleer, M., and Tansuchat, R. (2009). Modeling conditional correlations forrisk diversification in crude oil markets. Journal of Energy Markets 2(4), 29–51.

Chang, E., Chou, R. Y., and Nelling, E. F. (2000). Market volatility and the demand forhedging in stock index futures. Journal of Futures Markets 20, 105–125.

Chen, N.-F., Roll, R., and Ross, S.A. (1986).Economic forces and the stock market.Journalof Business 59, 383–403.

Chen, S. S. (2009). Predicting the bear stock market: macroeconomic variables as leadingindicators. Journal of Banking and Finance 33, 211–223.

Cheng, I.-H., and Xiong, W. (2014). The financialization of commodity markets. AnnualReview of Financial Economics 6, 419–441.

Chevalier, J., and Ellison, G. (1999a). Are some mutual fund managers better than others?Cross-sectional patterns in behavior and performance. Journal of Finance 54(3), 875–899.

Chevalier, J., and Ellison, G. (1999b). Career concerns of mutual fund managers. QuarterlyJournal of Economics 14(2), 391–432.

Chng, M. T. (2009). Economic linkages across commodity futures: hedging and tradingimplications. Journal of Banking and Finance 33, 958–970.

Clark, T. E., and West, K. D. (2007). Approximately normal tests for equal predictiveaccuracy in nested models. Journal of Econometrics 138(1), 291–311.

Cologni, A., and Manera, M. (2008). Oil prices, inflation and interest rates in a structuralcointegrated VAR model for the G-7 countries. Energy Economics 38, 856–888.

Connor, G., and Korajczyk, A. R. (1988). Risk and return in an equilibrium APT: applicationof a new test methodology. Journal of Financial Economics 21, 255–289.

Cornell, B. (1981).The relationship between volume and price variability in futures markets.Journal of Futures Markets 20, 5–18.

Cunado, J., and Perez de Garcia, F. (2005). Oil prices, economic activity and inflation:evidence from some Asian countries.Quarterly Review of Economics and Finance 45(1),65–83.

De Ville De Goyet, C., Geert, D., and Sercu, P. (2008).Testing the martingale hypothesis forfutures prices: implications for hedgers. Journal of Futures Markets 28(11), 1040–1065.

Driesprong, G., Jacobsen, B., and Maat, B. (2008). Striking oil: another puzzle? Journal ofFinancial Economics 89(2), 307–327.

DuBois, C. H. (1992). Tactical asset allocation: a review of current techniques. In ActiveAsset Allocation, State-of-the-Art Portfolio Policies, Strategies and Tactics, Arnott, R. D.,and Fabozzi, F. (eds). Probus, Chicago, IL.

Elder, J., Miao, H., and Ramchander, S. (2012). Impact of macroeconomic news on metalfutures. Journal of Banking and Finance 36, 51–65.

Elton, E. J., Gruber, M. J., and Blake, C. R. (2003). Incentive fees and mutual funds. Journalof Finance 58(2), 779–804.

Erb, C. B., and Harvey, C. R. (2006). The strategic and tactical value of commodity futures.Financial Analysts Journal 62(2), 69–97.

Estrella, A., and Mishkin, F. S. (1998). Predicting US recessions: financial variables asleading indicators. Review of Economics and Statistics 80(1), 45–61.

Fabozzi, F., Focardi, S., and Jonas, C. (2010). Investment management after the globalfinancial crisis. Course Paper, Research Foundation of CFA Institute, Charlottesville,VA.






Filis, G., Degiannakis, S., and Floros, C. (2011). Dynamic correlation between stock marketand oil prices: the case of oil-importing and oil-exporting countries. International Reviewof Financial Analysis 20(3), 152–164.

Fishe, R.P., and Smith, A.D. (2012). Identifying informed traders in futures markets.Journalof Financial Markets 15(3), 329–359.

Frankel, J. A. (2014). Effects of speculation and interest rates in a “carry trade” model ofcommodity prices. Journal of International Money and Finance 42, 88–112.

Froot, K. A., and Stein, J. C. (1991). Exchange rates and foreign direct investment: animperfect capital markets approach. Quarterly Journal of Economics 106, 1191–1217.

Fuertes, A.-M., Miffre, J., and Rallis, G. (2010). Tactical allocation in commodity futuresmarkets. Journal of Banking and Finance 34(10), 2530–2548.

German, H., and Kharoubi, C. (2008). WTI crude oil futures in portfolio diversification: thetime-to-maturity effect. Journal of Banking and Finance 32, 2553–2559.

Glosten, L. R., and Jagannathan, R. (1994). A contingent claims approach to performanceevaluation. Journal of Empirical Finance 1, 133–166.

Goetzmann, W., and Ibbotson, R. (1990).The performance of real estate as an asset class.Journal of Applied Corporate Finance 3, 65–76.

Goodwin, T. H. (1998). The information ratio. Financial Analysts Journal 54(4), 34–43.

Gorton, G., and Rouwenhorst, G. K. (2006). Facts and fantasies about commodity futures.Financial Analysts Journal 62(2), 47–67.

Goyal, A., and Welch, I. (2008). A comprehensive look at the empirical performance ofequity premium prediction. Review of Financial Studies 21(4), 1455–1508.

Grammatikos, T., and Saunders, A. (1986). Futures price variability: a test of maturity andvolume effects. Journal of Business 59, 319–330.

Granger, C. W. (1969). Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37(3), 424–438.

Greer, R. J. (2000). The nature of commodity index returns. Journal of AlternativeInvestments 3(1), 45–52.

Hamilton, J., and Herrera, A. (2004). Oil shocks and aggregate macroeconomic behavior:the role of monetary policy. Journal of Money, Credit, and Banking 36(2), 265–286.

Harvey, C. R. (1988).The real term structure and consumption growth. Journal of FinancialEconomics 22, 305–333.

Harvey, C. R. (1989). Forecasts of economic growth from the bond and stock markets.Finanical Analysts Journal 45(5), 38–45.

Harvey, C. R., and Siddique, A. (2000). Conditional skewness in asset pricing tests. Journalof Finance 55, 1263–1295.

He, Z., and Kryzanowski, L. (2007). Cost of equity for Canadian and US sectors. NorthAmerican Journal of Economics and Finance 18, 215–229.

Hearn, B., and Piesse, J. (2009). Sector level cost of equity in African financial markets.Emerging Markets Review 10, 257–278.

Henriksson, R., and Merton, R. (1981). On market timing and investment performance II:statistical procedures for evaluating forecasting skills. Journal of Business 54, 513–534.

Heston, S. L., and Rouwenhorst, G. K. (1994). Does industrial structure explain the benefitsof international diversification? Journal of Financial Economics 36(1), 3–27.





98 K. Smimou

Hirshleifer, D. (1988). Residual risk, trading costs, and commodity futures risk premia.Review of Financial Studies 1, 173–193.

Hong, H., and Yogo, M. (2012). What does futures market interest tell us about themacroeconomy and asset prices? Journal of Financial Economics 105(3), 473–490.

Horta, P., Mendes, C., and Vieira, I. (2010). Contagion effects of the subprime crisis in theEuropean NYSE Euronext markets. Portuguese Economic Journal 9(2), 115–140.

Hu, C., and Xiong, W. (2013). Are commodity futures prices baromter of the global econ-omy? In Apres le Deluge: Finance and the Common Good After the Crisis, Weyl, G. E.,Glaeser, E. L., and Santos, T. (eds). University of Chicago Press.

Huang, R. D., Masulis, R. W., and Stoll, H. R. (1996). Energy shocks and financial markets.Journal of Futures Markets 16(1), 1–27.

Jarque, C., and Bera, A. (1980). Efficient tests for normality. Economics Letters 6, 255–259.Jensen, G. R., Mercer, J. M., and Johnson, R. R. (2002). Tactical asset allocation and

commodity futures. Journal of Portfolio Management 28(4), 100–111.Jiang, G. J., Yao, T., and Yu, T. (2007). Do mutual funds time the market? Evidence from

portfolio holdings. Journal of Financial Economics 86, 724–758.Jobson, J., and Korkie, B. (1981). Performance hypothesis testing with the Sharpe and

Treynor measures. Journal of Finance 36, 889–908.Joy, M. (2011). Gold and the US dollar: hedge or haven? Finance Research Letters 8(3),

120–131.Kaminsky, G. L., and Reinhart, C. M. (2000). On crises, contagion, and confusion. Journal

of International Economics 51, 145–168.Kaminsky, G., Reinhart, C. M., and Vegh, C. A. (2003). The unholy trinity of financial

contagion. Journal of Economic Perspectives 17(4), 51–74.Karpoff, J. (1987). The relation between price changes and trading volume: a survey.

Journal of Financial and Quantitative Analysis 22, 109–126.Kilian, L. (2009). Not all oil price shocks are alike: disentangling demand and supply shocks

in the crude oil market. American Economic Review 99, 1053–1069.Kilian, L., and Murphy, D. (2014). The role of inventories and speculative trading in the

global market for crude oil. Journal of Applied Econometrics 29(3), 454–478.Longstaff, F. A. (2010). The subprime credit crisis and contagion in financial markets.

Journal of Financial Economics 97(3), 436–450.MacKinnon, J. G., and White, W. (1985). Some heteroskedasticity-consistent covariance

matrix estimators with improved finite sample properties. Journal of Econometrics 29(3),305.

Malik, F., and Ewing, B. T. (2009). Volatility transmission between oil prices and equitysector returns. International Review of Financial Analysis 18, 95–100.

Mao, J. (1970). Essentials of portfolio diversification strategy. Journal of Finance 25, 1109–1121.

Markowitz, H. (1952). Portfolio selection. Journal of Finance 7, 77–91.Markowitz, H. (1959). Portfolio Selection: Efficient Diversification of Investments. Wiley.Marshall, B. R., Nguyen, N. H., and Visaltanachoti, N. (2013). Liquidity commonality in

commodities. Journal of Banking and Finance 37, 11–20.McCracken, M.W. (2007). Asymptotics for out of sample tests of Granger causality. Journal

of Econometrics 140, 719–752.






Mensi, W., Beljid, M., Boubaker, A., and Managi, S. (2013). Correlations and volatil-ity spillovers across commodity and stock markets: linking energies, food, and gold.Economic modelling 32, 15–22.

Miffre, J., and Rallis, G. (2007). Momentum strategies in commodity futures markets.Journal of Banking and Finance 31, 1863–1886.

Milonas, N. T. (1991). Measuring seasonalities in commodity markets and the half-montheffect. Journal of Futures Markets 11(3), 331–345.

Moerman, G. A. (2008). Diversification in euro area stock markets: country versus industry.Journal of International Money and Finance 27, 1122–1134.

Mork, K. (1994). Business cycles and the oil market. Energy Journal 15, 15–38.

Murphy, J.J. (2004). Intermarket Analysis:Profiting from Global Market Relationships.Wiley.

Naes, R., Skjeltorp, J. A., and Odegaard, B. A. (2011). Stock market liquidity and thebusiness cycle. Journal of Finance 66(1), 139–176.

Narayan, P.K., Narayan, S., and Zheng, X. (2010).Gold and oil futures markets:are marketsefficient? Applied Energy 87(10), 3299–3303.

Olson, E., Vivian, A. J., and Wohar, M. E. (2014). The relationship between energy andequity markets: evidence from volatility impulse response functions. Energy Economics3, 297–305.

Park, J., and Ratti, R. (2008).Oil price shocks and stock markets in the US and 13 Europeancountries. Energy Economics 30, 2587–2608.

Pukthuanthong, K., and Roll, R. (2009). Global market integration: a better way to measureit and its application. Journal of Financial Economics 94(2), 214–232.

Ranaldo, A., and Favre, L. (2005). Hedge fund performance and higher-moment marketmodels. Journal of Alternative Investments 8(3), 37–51.

Rockafellar, T. R., and Uryasev, S. (2000). Optimization of conditional value-at-risk. Journalof Risk 2(3), 21–41.

Rockafellar, T. R., and Uryasev, S. (2002). Conditional value-at-risk for general lossdistribution. Journal of Banking and Finance 26, 1443–1471.

Roll, R. (2011). Volatility, correlation, and spread ETFs as factors. Working Paper, UCLA.

Roll, R., and Ross, S. A. (1980). An empirical investigation of the arbitrage pricing theory.Journal of Finance 35(5), 1073–1103.

Rouwenhorst, G. K. (1998). European equity markets and EMU: are the differencesbetween countries slowly disappearing. Working Paper, Yale University.

Rzepczynski, M., Belentepe, C. Y., Feng, W., and Lipsky, P. (2004). “Black Gold”: tradingcrude oil for greater portfolio efficiency: a comparison with commodity indexes. Journalof Alternative Investments 7(2), 44–50.

Sadorsky, P. (2000). The empirical relationship between energy futures prices andexchange rates. Energy Economics 22, 253–266.

Singleton, K. (2014). Investor flows and the 2008 boom/bust in oil prices. ManagementScience 60, 300–318.

Smimou, K. (2010). Stock market and agricultural futures diversification: an internationalperspective. Journal of Alternative Investments 12(4), 36–57.

Smimou, K. (2012). Does gold learn from the greenback or the equity? Working Paper,University of Ontario Institute of Technology.





100 K. Smimou

Soucek, M. (2013). Crude oil, equity and gold futures open interest co-movements. EnergyEconomics 40, 306–315.

Switzer, L. N., and El-Khoury, M. (2007). Extreme volatility, speculative, efficiency, andthe hedging effectiveness of the oil futures markets. Journal of Futures Markets 27(1),61–84.

Wang, C., andYu, M. (2004).Trading activity and price reversals in futures markets. Journalof Banking and Finance 28, 1337–1361.

White, H. (1980). A heteroskedasticity-consistent covariance matrix estimator and a directtest for heteroskedasticity. Econometrica 48, 817–838.

Young, M., Sullivan, P., Alastair, G., and Nokhasteh, A. (1998). Sector versus country: whenis an asset class an asset class? Report, Goldman Sachs Investment Research, London.

Zakamouline, V., and Koekebakker, S. (2009). Portfolio performance evaluation with gen-eralized Sharpe ratios: beyond the mean and variance. Journal of Banking and Finance33, 1242–1254.





We also offer daily, weekly and live news updates

Visit Risk.net/alerts now and select your preferences

Asset Management

Commodities

Derivatives

Regulation

Risk Management

CHOOSE YOUR PREFERENCES

Get the information you needstraight to your inbox

RNET16-AD156x234-NEWSLETTER.indd 1 21/03/2016 09:27


Research Paper

Under the radar: structural alpha in thesmall-cap equity market

Elena Ranguelova, Jonathan Feeney and Yi Lu

Investcorp, 280 Park Avenue, 37th Floor, New York, NY 10017, USA;emails: [email protected], [email protected], [email protected]

(Received July 31, 2015; accepted August 7, 2015)

ABSTRACT

As the hedge fund industry has grown over the last decade, alpha has become moreelusive. This paper examines several properties of the US small-cap equity marketand identifies a number of structural inefficiencies that may be exploited to generatealpha. We show that small-cap equities are covered by fewer analysts and that theiranalyses are published less frequently, with “noisier” earnings forecasts than thosepublished for large-cap equities. We also demonstrate that large hedge fund investorstend to gravitate to large-cap stocks. Further, despite limited attention from either thesell side or the buy side, we confirm that most mergers and acquisitions deals occuramong small caps. Lastly, the majority of returns from small caps are driven by stock-specific factors rather than by industry or style-related variables. In conclusion, webelieve small-cap stocks offer more fertile ground than large caps for alpha-focusedinvestors.

Keywords: small caps; inefficiency; hedge funds; analyst coverage; alpha.

Corresponding author: E. Ranguelova Print ISSN 2047-1238 j Online ISSN 2047-1246Copyright © 2015 Incisive Risk Information (IP) Limited

101




102 E. Ranguelova et al

1 HEDGE FUND ALPHA HAS BECOME MORE ELUSIVE

The hedge fund industry has grown significantly over the past fifteen years, fromUS$540 billion in 2001 to US$2.9 trillion in 2015 Q1 (HFR 2015). Meanwhile, alpha– the return that investment managers deliver beyond what the market offers them –has significantly declined, as shown in Figure 1 on the facing page. In 2001, hedgefunds in the HFRI Composite Index generated a rolling three-year alpha of C25%.Alpha peaked at approximately C35% in 2002, then decreased before plateauingbetween C5% and C10% after 2008.1 Strategies with lower barriers to entry – such aslong/short equities – have experienced the steepest decay in alpha generation as moreplayers have entered the industry.2 Within the long/short equities strategy, managersfocused on small- and mid-cap stocks have generated more alpha and exhibited lessalpha decay than their large-cap-focused peers since mid-2004, as shown in Figure 2on the facing page.

What is it that has helped small-cap managers preserve their edge, and why hasit occurred? It has been widely accepted that the small-cap equity space provides amore attractive opportunity set for alpha generation through investments in “underthe radar” stocks identified by talented stock pickers. We believe managers who focuson small- and mid-cap equities can benefit from the “structural alpha” that existsin this space by exploiting inefficiencies, such as the limited volume and quality ofinformation (eg, fewer analysts, less-frequent publication of research reports, andsignificant dispersion of earnings estimates), and because the playing field is lesscrowded than for large caps. To support our hypothesis, we have developed a robustdata set that examines the structural characteristics of the equity universe acrossvarious market capitalizations.

2 TRADING VOLUMES HAVE DECLINED

First, we consider how trading volumes have evolved over the last ten years for stocksincluded in the Standard & Poor’s 500 (S&P 500) and Russell 2000 indexes, the twomain indexes that track large- and small-cap companies, respectively. We obtainedthe total monthly trading volume for each stock within both indexes and dividedthis number by the stock’s free float. We used this normalized measure of tradingvolume to compute an average monthly number across the constituents of each index.We have plotted these monthly averages from January 2006 to February 2015 inFigure 3 on page 104, which shows a significant downward trend for both indexes,indicating decreasing trading volumes. The decline for small caps, however, is much

1 The alpha estimation methodology is explained in detail in Appendix 1, which is available online.2 Alpha has been more resilient, however, for niche strategies with higher barriers to entry, such as“distressed credit and event”.





Under the radar: structural alpha in the small-cap equity market 103

FIGURE 1 Alpha generation decay: HFRI Composite Index, rolling three-year average(January 2001–January 2015).

0

5

10

15

20

25

30

35

40

%

Jan 2001 Jan 2008 Jan 2015

Sources: Investcorp, Bloomberg.

FIGURE 2 Less alpha decay in small-cap stocks: hedge fund strategies, rolling three-yearalpha (January 2001–January 2015).

Jan 2001 Jan 2008 Jan 20150

10

20

30

40

50

60

70

%

HE allHE small-cap funds

Sources: Investcorp, Bloomberg.

more pronounced (from 27% in 2006 to 10% in early 2015, ignoring spikes), whilelarge-cap volume has shrunk from 21% to 16%, half the rate for small caps.

We surmise that as overall trading volume and turnover have decreased during thelast ten years, the income that investment banks have derived from these activities has






FIGURE 3 Trading volume comparison: Russell 2000 and S&P 500 (January 2006–February 2015).

21.3% 16.0%

26.8%

10.4%

5

10

15

20

25

30

35

40

45

Russell 2000: down 65%

S&P 500: down 25%

Mon

thly

tra

ding

vol

ume

(as

perc

enta

ge o

f fr

ee f

loat

)

Jan 05 Jan 07 Jan 09 Jan 11 Jan 13 Jan 15

Liquidity in small caps has declined by 65% since 2006, while for large caps the decline has been 25%.Sources: Investcorp, FactSet.

also shrunk. The result is that banks have concentrated their analytical resources onthe more profitable segment of the market capitalization spectrum, leaving small-capequities materially under-covered by sell-side analysts.

3 SMALL-CAP EQUITIES ARE MATERIALLY UNDER-COVERED BYSELL-SIDE ANALYSTS

In this section, we examine various aspects of sell-side coverage for small- and large-cap equities. We focus on the number of analysts covering each stock, the numberof analyst publications per stock over a given period, and the dispersion of analystforecasts as indicators of consensus or quality of information. These three points leadus to the same conclusion: small-cap equities are materially under-covered comparedwith large-cap stocks.

3.1 The number of analysts covering small-cap equities issignificantly smaller than for large-cap equities

We begin by comparing the number of analysts covering stocks in the S&P 500and Russell 2000 indexes. The S&P 500 includes the 500 largest companies withcommon stock listed on the New York Stock Exchange or the NASDAQ. As of April2, 2015, the capitalization of companies in the S&P 500 ranged from US$2.8 billion






TABLE 1 Sell-side analyst coverage (March 2015).

S&P 500 Russell 2000

Average 24 8Median 23 7Minimum 1 0Maximum 58 31

Source: Bloomberg, as of March 13, 2015.

to US$730 billion, with a median of US$19 billion and an average market cap ofUS$39 billion.

The Russell 2000 index includes the smallest 2000 of the 3000 largest US compa-nies. As of April 2, 2015, the market cap of stocks in the Russell 2000 ranged fromUS$5 million to US$16 billion, with a median of US$755 million and an averagemarket cap of US$1 billion. We used Bloomberg data to count the number of sell-side analysts following each stock in the corresponding index, as shown in Table 1.The median count of analysts covering S&P 500 stocks was twenty-three, while forRussell 2000 stocks the figure was seven. Some stocks in the Russell 2000, such asLoral Space & Communications, had no sell-side coverage at all. In contrast, Apple,the most widely covered stock in the S&P 500, was followed by fifty-eight analysts.This is nearly twice as many as the number of analysts that cover the most widelycovered stock in the Russell 2000, American Eagle Outfitters, which was covered bythirty-one analysts.

Next, we broadened our study to the S&P Broad Market Index, which includesapproximately 3000 US stocks. We looked at analyst coverage data available via theFactSet database, and we divided this index into market capitalization deciles. Thesmallest decile includes companies with market caps of US$200 million or less. Thetop decile includes companies with market caps of US$17 billion or more. In Figure 4on the next page, the box plots show the distribution of analyst coverage across decilesand, consistent with our expectations, analyst coverage increases monotonically alongwith market capitalization.

3.2 Publication frequency is significantly lower for small caps

Now that we have established that fewer analysts tend to cover smaller-cap stocks,we go on to ask how often they review or publish reports on these stocks. To answerthis question, we used the data service Capital IQ to count the number of publicationsfor the ten largest and ten smallest constituents of the S&P 500 and Russell 2000indexes over the previous thirty days, three months, six months and one year. Weused a broad definition of publications, including research reports, research notes,






FIGURE 4 The number of analysts per market cap size decile (March 2015).

<$200m

$200m–$400m

$400m–$700m

$700m–$1bn

$1bn–$1.5bn

$1.5bn–$2.5bn

$2.5bn–$4bn

$4bn–$7bn

$7bn–$17bn

>$17bn

0

5

10

15

20

25

30

35

40

45

1 2 3 4 5 6 7 8 9 10

Highest non-outlier value

Lowest non-outlier value25th percentile

75th percentileMedian

Decile

Decilevalues

Small cap Large cap

Sources: Investcorp, FactSet as of March 18, 2015. For clarity, outliers with values that are 1.5 � IQR (interquartilerange: for example, the distance between the 25th and 75th percentiles) less than the 25th percentile or 1.5 � IQRgreater than the 75th percentile have been excluded.

earnings estimates, fixed-income reports, industry overview articles relating to thecompany, initiation-of-coverage memos, financial models, rating change notices andsummaries of reporting results. Our results are reported in Table 2 on the facing pageand Table 3 on the facing page.

We find that the difference in publication frequency for members of the two indexesis substantial. On average, there were thirty-six updates for a large S&P 500 stockversus ten for a large Russell 2000 stock (a ratio of 3.6:1) for the thirty-day period priorto our study.3 This ratio stayed within a 4:1 range for the prior three-, six- and twelve-month periods.When we compare the coverage of the largest ten stocks in the S&P 500with the smallest ten stocks in the Russell 2000, the ratio jumps to approximately 7:1across periods. While Russell 2000 stocks may receive initial coverage, fewer updatesare published. We believe that this relative lack of information accounts for a portionof the inefficiency that persists in the small-cap equity market. We also believe that thispersistent inefficiency creates more uncertainty around earnings estimates and pricingfor these companies and, therefore, more opportunities for talented stock pickers to

3 For example, there were eighty-three publications onApple and forty-two on Google (the top stocksin the S&P 500) compared with thirteen publication on American Eagle Outfitters (the top stockin the Russell 2000) and four on the York Water Company (the smallest stock in the Russell 2000)over the prior thirty days.






TABLE 2 Average number of analyst publications per stock (March 2015).

S&P 500 Russell 2000‚ …„ ƒ ‚ …„ ƒLargest 10 Smallest 10 Largest 10 Smallest 10

Last 30 days 36 14 10 6Last 3 months 104 50 27 14Last 6 months 204 100 51 29Last 12 months 389 188 100 51

Source: Capital IQ. Analyst publications are broadly defined to include research reports, research notes, earnings-per-share estimates, fixed-income reports, industry overview articles, initiation-of-coverage memos, financial models,rating change notices and summaries of reporting results.

TABLE 3 Ratio of average number of analyst publications per stock (March 2015).

S&P 500 vs. Russell 2000‚ …„ ƒ S&P 500 largest 10 versusLargest 10 Smallest 10 Russell 2000 smallest 10

Last 30 days 3.6 2.3 6.0Last 3 months 3.9 3.6 7.4Last 6 months 4.0 3.4 7.0Last 12 months 3.9 3.7 7.6

Source: Capital IQ. Analyst publications are broadly defined to include research reports,research notes, earnings-per-share estimates, fixed-income reports, industry overviewarticles, initiation-of-coverage memos, financial models, rating change notices and sum-maries of reporting results.

generate alpha. This leads on to the topic of our next section, which examines thereturn on opportunities.

3.3 The dispersion of analyst forecasts is higher for small caps

We have established that (1) fewer analysts cover small-cap stocks and (2) they tendto publish less frequently. But when they dispense research, how useful are theiranalyses for investors? We use dispersion of earnings estimates as a measure ofthe “noise” around analyst forecasts. Low dispersion indicates consensus amonganalysts and sends a clear message to investors. High dispersion indicates greateruncertainty around a company’s fundamentals and sends a less clear message toinvestors. Below, we compare the dispersion of analyst earnings forecasts acrossstocks with different market capitalization and find a strong correlation between sizeand consensus.






FIGURE 5 The dispersion of analyst forecasts per market cap size decile (March 2015).

0

10

20

30

40

50

60

70

<$200m

$200m–$400m

$400m–$700m

$700m–$1bn

$1bn–$1.5bn

$1.5bn–$2.5bn

$2.5bn–$4bn

$4bn–$7bn

$7bn–$17bn

>$17bn

1 2 3 4 5 6 7 8 9 10Decile

Decilevalues

Small cap Large cap

%

Highest non-outlier value

Lowest non-outlier value25th percentile

75th percentileMedian

Sources: Investcorp, FactSet as of March 18, 2015. For clarity, outliers with values that are 1.5 � IQR (interquartilerange: for example, the distance between the 25th and 75th percentiles) less than the 25th percentile or 1.5 � IQRgreater than the 75th percentile have been excluded.

First, we define dispersion of analyst earnings per share (EPS) forecasts as thestandard deviation of the EPS forecasts for each stock, normalized by the absolute ofthe median of the forecasts across analysts for that stock:

Dispersion D StdDev.EPS/

jMedian.EPS/j :

We order the universe according to that measure and show the results in a box chartof each decile (Figure 5). The top and bottom boundaries of each box show the 25thand 75th percentiles of the distribution within that decile, and the white line is themedian. The horizontal bars outside the box mark the maximum and minimum offorecasts for each decile, and the vertical dashed lines denote the range for outliersthat have been trimmed. We find that analyst estimates for companies with marketcaps of US$7 billion or more vary in a tight range (less than 10%) and that dispersionincreases monotonically as the size of the market cap drops.

To summarize, smaller companies receive less analyst attention, resulting in cov-erage by fewer analysts, less frequent publication of reports and estimates with moredispersion than those of large-cap stocks.






FIGURE 6 The dispersion of the twenty largest event-driven funds per market cap: sizedecile (percentage of total as of April 7, 2015).

0.4% 0.3% 0.5% 0.9% 1.4% 3.0%5.8%

10.1%

21.4%

56.3%

0

10

20

30

40

50

60

<$200m

$200m–$400m

$400m–$700m

$700m–$1bn

$1bn–$1.5bn

$1.5bn–$2.5bn

$2.5bn–$4bn

$4bn–$7bn

$7bn–$17bn

>$17bn

1 2 3 4 5 6 7 8 9 10Decile

Decilevalues

Small cap Large cap

%

Sources: 13F filings from Bloomberg, Investcorp.

4 THE LARGEST HEDGE FUNDS GRAVITATE TO LARGE CAPS

Since the 2008 crisis, one of the strongest trends in the hedge fund industry has beenthat the vast majority of asset flows are directed to the largest hedge fund managers.In 2010, 80% of net asset flows went into funds with more than US$5 billion in assetsunder management. In 2011, this figure was 71%, and in 2012 more than 100% offlows went into larger funds (as there were net redemptions out of funds with assetsunder management between US$1 billion and US$5 billion) (HFR 2015).

By construction, the biggest equity-oriented hedge fund managers running assetsof US$5 billion or more allocate their capital to larger market capitalization names inorder to meet liquidity requirements. In Figure 6, we analyze the holdings obtainedfrom the 13F filings of the twenty largest managers in the event-driven space to demon-strate this effect. We have disaggregated the holdings of these funds across marketcapitalization deciles. The results indicate that the top twenty event-driven managersallocate nearly 90% of their assets under management to large-cap stocks (ie, greaterthan US$4 billion). Interestingly, the next section highlights that the majority of merg-ers and acquisitions activity is actually in small- and mid-cap stocks (market caps ofless than US$5 billion).






FIGURE 7 Announced mergers and acquisitions transactions (count).

0

1500

3000

4500

2009 2010 2011 2012 2013 2014 Q1 2015

Small cap (<$2bn) Mid cap ($2bn–$5bn) Large cap (>$5bn)

Sources: Capital IQ, Investcorp.

5 THE MAJORITY OF EVENT ACTIVITY OCCURS IN SMALL ANDMID CAPS

While less information is available for small-cap stocks and fewer institutionalinvestors allocate to this subset, it appears to be the case that much more eventactivity occurs in this universe (eg, small-cap companies are more likely to merge orbecome acquired).We used Capital IQ data to analyze merger activity across small-cap(<US$1 billion), mid-cap (US$1 billion–US$5 billion) and large-cap (>US$5 bil-lion) equities in the United States since 2009, and we show our results in Figure 7.Not surprisingly, over 90% of US merger deals have occurred in stocks with marketcaps less than US$5 billion.

Elevated levels of corporate activity tend to drive misunderstanding and mispricingin public markets (eg, companies undergoing corporate change may engender com-plex situations), and when this is combined with the generally reduced informationalflow for small caps, it may lead to opportunities to extract an analytical advantage.Furthermore, the higher incidence of catalysts in this space (evidenced by the hightransaction count) can allow this potential analytical edge to be exploited to a greaterdegree.

6 IT PAYS MORE TO “GET IT RIGHT” IN SMALL CAPS

With more events happening in small caps and less quality research available for thismarket cap, the reward for “getting it right” has the potential to be greater. Strategistsat RBC Capital Markets recently published a study called “The value of perfect






FIGURE 8 Annualized excess return from properly identifying revisions of the upcomingmonth (five-year average).

64.6%

49.8%

39.8%

0

10

20

30

40

50

60

70

Earnings Revenue Margins

%

Small cap Large cap

34.7%

21.1% 19.9%

Earnings Revenue Margins

Source: RBC.

foresight”. In the report, the returns of perfect foresight on company earnings, revenueor margins for two sets of companies were measured. The authors used the S&P 600as a proxy for the small-cap universe and the S&P 500 for the large-cap universe. Bothuniverses are broken into quintiles based on earnings revisions during the month. Atthe beginning of each month, the strategy is long the top quintile and short the bottomquintile in each respective universe. The results are then compounded over five yearsand reported in a table reproduced as Figure 8.

If an investor had the luxury of applying this strategy on earnings revisions forsmall caps, he or she would have earned C64:6% of excess return compared withC34:7% by following the same methodology for large caps. Part of this differencecan be attributed to the higher volatility of small-cap equities; however, the resultsstrongly indicate how much less efficient the small-cap equity market appears to be.We view quality fundamental research as a middle ground between perfect foresightand no insight. In an environment with limited coverage of small caps, investmentmanagers who can conduct quality research may be able to generate higher returnsby investing in small-cap equities instead of their large-cap counterparts.

7 IDIOSYNCRATIC FACTORS MATTER MORE FOR SMALL CAPS

Figures 9 and 10 on the next page were recently produced by Deutsche Bank’squantitative strategy team and they further highlight the increased opportunity setthat exists within small-cap stocks relative to large caps. Equity returns are driven






FIGURE 9 Small-cap opportunity set.

0

10

20

30

40

50

60

70

80

90

100

Stock specific Style Industry

Feb 00 Feb 02 Feb 04 Feb 06 Feb 08 Feb 10 Feb 12 Feb 14

Source: Deutsche Bank (2015).

FIGURE 10 Large-cap opportunity set.

0

10

20

30

40

50

60

70

80

90

100Stock specific Style Industry

Feb 00 Feb 02 Feb 04 Feb 06 Feb 08 Feb 10 Feb 12 Feb 14

Source: Deutsche Bank (2015).

by a multitude of factors, including broad market-wide effects that can be deter-mined by macroeconomic variables, industry-wide effects, pervasive “style” biases(eg, preference for “value” over “growth” characteristics) and, finally, idiosyncraticstock-specific factors. Between 2000 and 2008, the balance between stock-specific






drivers and a more top-down approach and industry drivers was relatively even. How-ever, the advent of aggressive global central bank policy action after the financialcrisis resulted in macroeconomic influences playing a much greater role in determin-ing the opportunity set for stocks, while the influence of stock-specific drivers wasdiminished.

The two figures deconstruct the opportunity set available to investors into moretop-down factors, such as industry and style factors (growth, value, momentum, etc),and the residual stock-specific elements. Both large-cap and small-cap top-downfactors played a far more dominant role between 2009 and 2012 than in the precedingten years. However, this effect has abated somewhat over the past three years, andstock-specific factors have increased, returning to 2004–7 levels.

This effect is much more pronounced in the small-cap opportunity set than it isfor large caps. Stock-specific influences drive approximately 80% of the small-capopportunity set as opposed to approximately 60% for large caps.

8 CONCLUSION

Hedge fund alpha has become more elusive since 2002. Strategies with lower barriersto entry, such as long/short equities, have experienced the steepest decay in alpha gen-eration. Within this strategy, however, small-cap equities remain more fertile groundfor differentiated stock picking due to a number of structural inefficiencies.

Relative to large caps, smaller-cap equity is covered by few analysts. Addition-ally, fewer publications feature small-cap stocks and a higher dispersion of earningsestimates exists for these companies. The largest hedge funds, particularly in theevent-driven space, gravitate to large-cap stocks, and yet most mergers and acquisi-tions occur in small- and mid-cap companies (those with less than US$5 billion ofmarket capitalization). Finally, returns for “getting it right” are substantially greaterfor small-cap equities than for large caps.

As a result of these structural inefficiencies, we believe that alpha-focused investorscan be rewarded by allocating to US small-cap long/short equity strategies.

DECLARATION OF INTEREST

The authors developed this research while employed as research analysts at InvestcorpInvestment Advisors LLC, which provides research advisory services on investing inhedge funds.

The information and opinions contained herein, prepared by Investcorp InvestmentAdvisers LLC (“Investcorp”) using data believed to be reliable, are subject to changewithout notice. Neither Investcorp nor any officer or employee of the firm acceptany liability whatsoever for any loss arising from any use of this publication or its






contents. Any reference to past performance is not indicative of future results. Thisreport does not constitute an offer to sell or a solicitation of an offer to purchase anysecurity and is provided for informational purposes only.

Unless otherwise noted, “Investcorp” refers to Investcorp Investment AdvisersLimited, Investcorp InvestmentAdvisers LLC, N.A. Investcorp LLC, and its affiliates.

ACKNOWLEDGEMENTS

The authors thank Ankit Agrawal, Vincent Berthelemy and Greg LaFiura for theiroutstanding research assistance.

REFERENCES

Alvarez, M.-A., Luo,Y., Cahan, R., Juss, J., Chen, Z., and Wang, S. (2012). Portfolios underconstruction: correlations and consequences. Deutsche Bank Quantitative Strategy,January 24.

Golub, J., Jamner, J., Palfrey, P., and Connor, T. (2015).The value of perfect foresight. RBCCapital Markets, March 30.

HFR (2015). HFR global hedge fund industry report – first quarter 2015. Report, HedgeFund Research.

Jussa, J., Wang, S., Rohal, G., Alvarez, M., Luo, Y., Wang, A., and Elledge, D. (2015). Thequant view. Deutsche Bank Quantitative Strategy, March 4.





Strategies - Risksubscriptions.risk.net/wp-content/uploads/2016/03/JOIS.pdf · Strategies The...

Documents

Transcript of Strategies - Risksubscriptions.risk.net/wp-content/uploads/2016/03/JOIS.pdf · Strategies The...