The Missing Risk Premium: Why Low Volatility Investing Works Eric Falkenstein 2013 Copyright 2013...

The Missing Risk Premium:Why Low Volatility Investing Works

Eric Falkenstein2013

Who am I• I’m an economics PhD who has worked as a quant,

risk manager, and portfolio manager. See more at the following websites– www.betaarbitrage.com– Falkenblog– www.efalken.com

• Old Book Finding Alpha (2009)• New Book The Missing Risk Premium, out this

spring

• My 1994 dissertation, first 3 sentences:– “This paper documents two new facts. First, over the

past 30 years variance has been negatively correlated with expected return for NYSE&AMEX stocks and this relationship is not accounted for by several well-known prespecified factors (e.g., the price-to-book ratio or size). More volatile stocks have lower returns, other things equal.”

• So, risk premiums and low-vol have been a bit of a hobby-horse

My Interest

The Stakes

“It is impossible to appreciate how the financial system works without understanding risk.” Stephen Cecchetti

"Risk is not an add-on … it permeates the whole body of thought.“

Robert C. Merton

Price1FutValueEr g

“most returns and price variation come from variation in risk premia” John Campbell

Risk free rate

Risk premium

Big Idea: this is the Risk-Return Trade-off

• In general, in practice:risk is not positively related to return

Risk and Return

• Risk aversion like aversion to smelliness• The logic applied to this idea, via a utility

function that has decreasing marginal returns, generates many mathematically consistent results that seem highly plausible

Standard Theory is Intuitive

Leveraged FirmsB vs. BBB rated BondsOut-of-the-money options vs. at-the-money optionsS and C corps vs. equity indexesHighest volatility vs. modest vol stocksR rated movies vs. G rated moviesLotto vs. ‘quick pick’ lotteries50-1 horses vs. 3-1 horses Mutual funds, currencies, futures, countries, yield curve

…And Wrong

Finance Misleading

• Most practical finance is about generating expected values

• Finding covariances to generate different discount rates is a massive waste of time, pure rationalization in practice

Conspiracy?

• Economists find standard utility functions much more productive (in theory)

• Asset managers can justify anything via ‘risk’, which is omnipresent and as yet unmeasurable

• Amenable to rigorous sequence of lectures

Standard Theory

St. Petersburg Paradox (1738): what is value of $1 paid if you get a head in a coin flip, where the payoff is (number of times coin flipped)^2?

Should be infinity

Marginal Utility

1 1 1 11 2 4 8 ...

2 4 4 161 1 1 1

...2 2 2 2

• Fundamental to economic reasoning• Marginal Revolution transformed economics

in 1860s– Walras, Jevons, Menger– Pre 1860s ‘classical’ economists: Marx, Smith,

Ricardo, Mill• Transformed Theory of Value

Basic Idea of Utility

• Global concavity of utility is the necessary and sufficient condition for the existence of a risk premium

Where does Risk Premium Come From?

• Utility not applied between goods, but to everything

• Von-Neumann-Morgenstern (1944)

Utility Theory and Risk Aversion

2U E r a

Iso-Utility Curves for Return and Volatility

Standard Deviation

Expected Return

100% investment in security with highest E(R)

100% investment in minimum variance portfolio

No points plot above the red line

All portfolios on the red line are efficient

Why we like efficient portfolios

ExpReturn

Volatility

Tobin: Two-Fund Separation Theorem

Port-1

Port-2

Port-3U4

Always hold some cash: liquidity preference

Standard Deviation

Expected Return

C 1z f B

R z r zr

Regardless of risk preference, everyone uses same risky portfolio

How to Derive The Capital Asset Pricing Model

1. every asset has same marg. valuei imaE r k

2. ,risk free rate is kf f fmE a rr k k

3. m f

mm mE r a k a

4. i im

E r rrE r

25. im

f m fm

iE r r E r r

6. aka the CAPM the SMLi f m fiE r r E r r

CAPM is the Security Market Line (SML)

Expected Return

Market Portfolio

( ) ( )

where ( ) expected return on security

risk-free rate of interest

beta of Security

( ) expected return on the market

i f i m f

E R R E R R

General Equilibrium aka Stochastic Discount Factor CAPM

' ' 10 1 '

U1. U U 1 1 1

UE r E r

3. [ ] [ ] [ ] cov( , ) 1E MR E M E R M R

ov( , ]

15. [ ]

[ ]ff RE RE M

'1' '0 0

1 cov( , )

' cov( , )

U M RR

cov( ,7.

)[ ] i m

2. 1 givU

Uen M=E MR

cov( , )8. [ ] i m

R RE R R

cov( , )11. [ ] [ ]

var( )i m

i f m fm

R RE R R E R R

12. [ ] [ ]i f m fE R R E R R

var( )9. letting R =R

i mm f

cov( , )10. [ ]

var( )

R RE R R

Asset Pricing Theory Was Always Treated Well

• 1971 Institutional Investor :“The Beta Cult: The New Way to Measure Risk.”

• Contrast with almost constantly ridiculed Efficient Markets Hypothesis, which is much more successful (eg, it’s hard to outperform the indices)

• linear in risk factors, covariances with something

• include something very like the stock market as one of the prominent factors

Hope for Final Theory

Empirical Evidence

Return VolatilitySmall Stocks 17.30% 33.4%Stocks 13% 20.2%Corporate Bonds 6.0% 8.7%Government Bonds 5.70% 9.4%T-bills 3.90% 3.2%

Volatility Often Used as a Risk Shorthand

Brealey and Myers Investments Book

From Cam Harvey (editor of Journal of Finance) website

If only this worked in more places…

The Risk Premium ProblemAfter 45 years, there are no measure of risk that are generally

positively correlated with returns

Fama and French 1992

From Campbell 2000

Fama-French (1992)

• Show beta is just a size effect• Founding father (Fama) admits CAPM is

‘incomplete’, and beta itself useless

Theory: Longer hair people are short Omitted variable: gender

Theory: high beta firms have high returns Omitted variable: size

Example of how small firm effect showed up in beta tests

CAPM Recognized as Empirical Failure

• “More empirical effort may have been put into testing the CAPM equation than any other result in finance. The results are quite mixed and in many ways discouraging.”– Mark Rubinstein

• “empirically vacuous,” – Fama and French

• “having a low, middle or high beta does not matter; the expected return is the same.– Stephen Ross

A Survey of Empirical Anomalies to the Standard Model

• The standard theory involves a specific metric of covariance, and so it could be, we simply haven’t found the right one

• As a ‘framework’, not a theory, it is non-falsifiable

• However, it’s hard to conceive of one not correlated with total volatility

• My Dissertation (1994) page 53

Total Volatility and Returns

Cross-Sectional Annual Returns Sorted by Idiosyncratic and Total Volatility

Ang,, Hodrick, Xing and Zhang (JoF 2006)

Beta and Returns: 1962-2011

Beta-Low Beta0.5 Beta1.0 Beta1.5 Beta-High

AnnRet 10.8% 11.4% 11.4% 8.2% 4.5%

AnnStdev 13.1% 11.6% 17.4% 26.2% 33.9%

Beta 0.57 0.57 1.04 1.44 1.78

• Low Rated Equities also have lower returns

Equities and bond ratings (Distress)

StockReturnsAAA 12.4%AA 13.9%A 14.3%BBB 14.2%BB 15.0%B 8.6%C -12.7%

Leverage and Equity ReturnsPenman, Richardson, and Tuna. 2007

Equity Returns Practice Theory

Volume($)> 2,000 50,000 500,000

Price> 0.01 0.1 0.01 0.1 0.01 0.1Count 7372 6685 6423 5757 4603 3939

AnnReturn -29.1% -35.4% -9.1% -13.5% -34.2% -41.0%

Penny Stocks: Eraker and Ready (2009)

Call OptionsSophie Ni (2007)Should amplify the equity risk premium the greater the out-of-the-money

• IPO has a lot of Uncertainty• Jay Ritter (see his website). 1970-2011.• 8k observations

Initial Public Offerings (IPOs)

• Deither, Malloy, and Scherbina (2002). Table 2. Data from 1983-2000.

Analyst Disagreement

• Steve Sharpe and Gene Amromin (2005). People have higher expected returns when they have lower expected volatilities

Total Volatility over Time

m mf mfE r r a b

• Contemporaneous Correlation Clearly Negative

Total Volatility over Time

m mf mfE r r a b

SPY Total Return to Overnight vs. Daily Return Periods

• Moskowitz, and Vissing-Jorgensen (2002)

Small Business Returns

Currencies: Uncovered Interest Rate Parity

% change in yen+riskprem?yenAUDr r

Sharpe 0.99 from 1976-2008 in Burnside et al (2009)Here’s Long AUD, Short JPY

• Merrill High Yield Master II (HOAO) Merrill BBB-AA Index (COCO)

• Indices here overstate realized returns

Corporate Bonds

• Dimson, Marsh, Staunton (2005)• 17 Countries, 1900-2005, Annual Data

World Country Returns

Emerging market Returns

• 1% premium from 0.25 to 3 years• No premium from 5 to 30 years• Volatility, Covariance, increasing linearly

Treasury Yield Curve

• 1% premium from 0.25 to 3 years• No premium from 5 to 30 years• Volatility, Covariance, increasing linearly

Treasury Yield Curve

• Futures return from roll• Harvey and Erb (2007) copper, heating oil, and

live cattle were on average in backwardization, • corn, wheat, silver, gold, and coffee were in

contango• It isn’t clear what covariance, volatility has to

do with this

Futures

• Devany and Walls (1999), 2015 movies from 1984-96

Movie Returns by Rating

• Snowberg and Wolfers (2009)

Sports Books: Longshot Bias

• IPO has a lot of Uncertainty• Jay Ritter (see his website). 1980-2008.• IPO Returns -3.7% annually below size-

matched firms for first 5 years

Initial Public Offerings (IPOs)

Trading Volume

• Turnover of stock a proxy for disagreement• Highly correlated with beta

Equity Risk Premium

• Top line return is not the same as average or marginal return

What is the Equity Risk Premium?

The most important constant in finance

i f i m fEr r E r r

m fE r r

• Lorie and Fisher (1964): 9.0% raw return (no bond return)• Ibbotson and Sinquefield (1976): 10.9%• Mehra and Prescott (1986): 6.2%• 1999 Barclays and CSFB estimated 8.8%• Ibbotson (1926-97): 8.9%• Finance Texts (1998): 8.5%• Ivo Welch Survey (1998): 8.5%Crash!• AIMR estimate (2002): 3.0%• WSJ survey (2005): 2.0%• CFO Magazine (2005): 5%• Ivo Welch (2009): 2%-4% at most 1%-8%

Equity Premium Evolution

• 1 to 2 to 1 has a total return of 0%• 100%, -50% return has average of 25%• Arithmetic returns useful if you rebalance, as

opposed to invest all your money at inception• Stock returns have volatility around 20%, for

the indices, which implied a 2% adjustment

Geometric vs. Arithmetic Averages

2G Ar r

• Dichev (2005)• 1, 2, 1

– return 0% if cf is {-1,0,+1}– return -17.7% if cf is {-1,-1,+1.5}

• Total return different than Internal Rate of Return based on timing of investments

• Distributions Dividends-New Money• Corr(Distributionst,Returnt+1)= +33%

• Corr(Distributionst+1,Returnt)= -27%• bad timing

Bad Market Timing

• Commissions, – 8.5% load through 1970’s to buy a mutual fund

• bid-ask cross– Stocks quoted at 8 ¾ - 9 in the 1990s– buy at 9, sell at 8 ¾, lose 2.78%– Phantom cost: most investors don’t know real time

prices• Stoll and Whaley (1983) 1.78% comm+bid-ask• Bhardwaj and Brooks (1992): 4.4% total• Currently very low if you are smart (0.2%)

Transaction Costs

• USA primary data point in World Value Weighted Index• Coincidentally, – 2-0 in World Wars– Never went communist

• Brown, Goetzmann, and Ross (1995)– Czechoslovakia, Hungary, Poland, Russia, and China all

zeroed out• Jorion and Goetzmann (1999)– US real return 350 basis points above median for 39

countries in 20th century

Survivorship Bias

• Peso-Dollar FX rate fixed from 1954-76• Higher interest rate in Peso• Peso ‘floated’ in 1976: lost 45%• Peso devalued by 82% in 1982• Small probability, big loss, explains interest rate

premium• Robert Barro (2006) argues a correct probability of a

significant catastrophe explains much of the equity premium, about 300 basis points– 2% change of a 15% to 45% GDP decline

Peso Problem

• 10% stock return: 6% post tax with a 40% tax rate• Gannon and Blume (2006) apply this to S&P500 assuming

20% turnover from 1961-2005, using actual capital gains, dividend top-tier tax rates

• Cap gain avg: 26%• Top tax rate avg; 49% (includes 6% state tax)• Lorie and Fisher (1964) found 2.2% adjustment

• Total after tax equity return 6.72%, vs. 10.62% pre tax• Long Term Municipal Bond Buyer Index return: 6.14%

• Beardstown Ladies investment club• 1983-94 return 23.4%• Best selling authors• Audited financials: 9.1%, below 14.9% for

market• Failed to include contributions

People ignore costs all the time

Investors Don’t Match Indices

• Dalbar study from the Investment Company Institute:

• 1990-2010 Annual Returns• S&P500 return: 9.1%• Average equity mutual fund investor: 3.3%

Returns not Like in Representative Agent Model

Equity Return Uncorrelated with GDP growth over a Century

Hedge Fund Money Goes to Insiders

• From Simon Lack

• Geometric vs. Arithmetic Averaging 1.0%• Survivorship Bias 1.0%• Peso Problems 1.0%• Taxes 1.0%• Adverse Market Timing 1.0%• Transaction Costs 1.0%• Sum 6.0%

• Most estimates around 3.5% for equity premium. With these additions, the Marginal Investor clearly could be seeing a 0% equity premium.

Equity Premium Subtractions

Scope of the Risk Premium Failure

Positive Risk Premium (3) Zero Risk Premium (14) Negative Risk Premium (12)1. Short End of Yield Curve2. BBB-AAA Corporate

Spread3. Efficient Equity Investor

1. Long-End of Yield Curve2. B to BBB Bond3. Futures4. Private Investments5. Movies6. Mutual Funds7. VIX and Equity8. World Equity9. Emerging Markets10. Hedge Funds11. Real Estate12. CTAs13. Private Equity14. Intraday Stock Return

1. Average Equity Investor2. Betas3. Volatility4. Financial Distress5. Trading Volume6. Analyst Disagreement7. Equity Options8. Lotteries9. Sports Betting10. Currencies11. IPO equity Returns12. MVPs

New Theory

• In general, risk and return are uncorrelated because risk is a deviation from the consensus

• This makes risk symmetric, too much or too little exposure generates similar risk

• Thus, volatile assets don’t need extra return to be held…

Basic Idea of Relative Risk and no Premium

Total Return Avg. Relative Return

X Y X Y

State 1 0 -10 –5 5 –5

State 2 20 30 25 –5 5

• Taking the first order condition, we have

• Since each agent is identical, in equilibrium each agent holds the same amount

• So• Which means, the expected return on risky

assets is te risk free rate

Utility Proof

( )2 i if E ER am s a a-= + -

i iE Ea a-=

• Taking the first order condition in the standard model we have

• This is the standard result, that higher volatility generates a higher return, linear in the variance, adjusted by the coefficient of risk aversion

• Because the exponential utility is CARA, not CRRA, higher amount in the risky asset generates a higher risk premium

Utility Proof Benchmark

2 iEfR a am s= +

• See how relative utility model explains– Why when investors take risks, they expect above

average returns– Returns are relative to the risk free rate– Don’t short assets with expected return<Rf

Relative Utility and Different Beliefs

( )2 i if E ER am s a a-= + -

2 iEfR a am s= +

• Abel (1990):

• Gali (1995):

• DeMarzo,, Kandiel, Kremer (2003):

• Roussanov (2010):

Relative Risk in academia

, 1 tt t

cU c C C

1 1, 1 a aU c C a c C

1 1 1, 1 a ag s g sU c c a c c

Outside the Box Evidence

• Like any truth, it has lots of footprints

• Within a society, rich people tend to be much happier than poor people.• But, rich societies tend not to be happier than poor societies (or not by much).• As countries get richer, they do not get happier.

Easterlin’s Paradox (1974)

• Progress and Happiness a Puzzle– Gregg Easterbrook’s The Progress Paradox, – David Myers’s The American Paradox, and – Barry Schwartz’s The Paradox of Choice

• Japan: between 1958-1987 per capita income rose 500%– No change in subjective well-being

• Knight and Song (2006): Chinese villagers more affected by relative than absolute wealth, compared to their villages

• Choose between – World A: $100,000 a year in perpetuity while others earned $90,000– World B: earn $110,000 while others earned $200,000– Most prefer World A

Easterlin’s Paradox

• Half of all stocks have expected returns below the market• Zero recommendations for firms with expected returns below

the market return

Buy Recommendations exclude low risk firms

Expected ReturnBuy!

Who cares?

• Should invest in world portfolio• Chan, Covrig, and Ng (2005): Everyone is

investing mainly in domestic portfolio • Avoiding easy way to diversify risk• Low covariance with risks from home

economy

Home Bias

• “I want a product to be defined relative to a benchmark”

Bill Sharpe• ‘Risk, see Benchmarking’Kenneth Fisher’s Only Three Questions that Count

• “small stocks were in a depression” in the 1980’sEugene Fama, Merton Miller

Everyone Benchmarks

• “…rank among our equals, is, perhaps, the strongest of all our desires.” – Adam Smith

• “Men do not desire merely to be rich, but to be richer than other men.” – John Stuart Mill

• “any individual or group of individuals, who consent to a reduction of money-wages relatively to others, will suffer a relative reduction in real wages, which is sufficient justification for them to resist it” – JM Keynes

• “The motive is emulation–the stimulus of an invidious comparison... especially in any community in which class distinctions are quite vague”– Thorsten Veblen

• Our wants and pleasures have their origin in society; we therefore measure them in relation to society; we do not measure them in relation to the objects which serve for their gratification.” – Karl Marx , Wage Labour and Capital, chapter 6

The Most Prominent Economists Can Be Read as Relative Utility Proponents

Hard Wired For Envy

• Relative Status makes more evolutionary sense than absolute wealth as a utility function

• Evidence for this instinct

Evolutionary Biology

• genetic success is always relative, why spite works

Evolutionarily Robust

• Special Utility needed for interest rate to be stable over generations

• But then, refinement really has to vary• Eye cones and color• Rayo and Becker (2007)

Reverse Dominance Hierarchies

• Chris Boehm• primates usually have dominant males• With tools, easy to kill dominant males, so

hierarchies are not ‘natural’ for humans

Imitating Others Dominant Strategy

• We copy all the time: parents, then peers, then anyone doing well

• Mark Pagel: zero, soap, the wheel, language, iPads.– Division of labor, accumulation of science, implies

innovating only after a lot of copying, and generally relying on others

Social Context Hard Wired

• Specialized neural mechanisms process social information, empathy

• Can’t ‘not see’ context• Mirror neurons tie others to us

Relative Utility Matters more than Absolute

• Econometrics• fMRI• Psychologists• rank in one’s peer group is more important

than the level of income

Endocrinology of Envy

• Robert Sapolsky found baboon status related to glucocorticoid levels

• Whitehall Studies found correlation between British civil servant grade level and mortality.

Moderation in All Things

• Greek proverb• too much, too little, both bad:– Vitamin A– Radiation– Oxygen– Politeness– Loyalty– Honesty

Exposure0 -

Risk Relative Standard

Courage Premium

• Aristocracy asserted their privileged position came from battlefield courage

• The upper classes truly were courageous in battle, as WW1 showed, but no one will pay for that, and taxes on the rich went up

Why Take Uncompensated Risk?

• Necessary, not sufficient condition for success• Every irrevocable act entails some kind of risk– We all take risks (marriage, jobs)

• Taking the right risks, at the right time, given our particular strengths, is good

Why a Negative Premium?

• With relative risk, an abnormal demand for highly volatile assets is not totally countered in equilibrium, leaving a price impact

• Higher demand, higher price, lower future return

• Without relative utility, one needs ad hoc constraints

High Vol Demand: Winner’s Curse• If no short selling….assets with higher valuation

uncertainty will have higher prices, lower returns

High Vol Demand: Overconfidence

• People are generally overconfident about their relative competency on socially desirable trates

• Overconfidence makes one happier, lowers mortality

High Vol Demand: Risk-Loving

• Preference for positive skew• Consistent with global risk aversion only if

skew risk premium <15% of standard risk premium

• Risk loving looks like overconfidence

High Vol Demand: Gambling Preferences

• Robert Sapolsky and dopamine generation based on rewards:– Higher for probabilistic payoffs

High Vol Demand: Information Costs

• High volatility stocks generate more news– Easier to form opinion– Easier to sell a story

• Falkenstein (1996) looked at mutual fund ownership and news stories, stock age

High Vol Demand: Representativeness Bias

• Great stocks of past had great risk….• “To get rich, you have to take risk.”• Prob( higher return|higher risk)=Prob(big return|big risk ) >0– So risk is correlated with higher returns (?)

prob risky

prob high return

P A B P BB A

High Vol Demand: Alpha Discovery

• Many people jump in and want to know if they have ‘it’

• Trade bio-techs, not utilities

High Vol Demand: Convex Payoffs to Stock Pickers

• Top stock analysts often have 100% winners• Mutual fund inflows highly convex– Greater value to greater volatility via call option

High Vol Demand: Asset Buyers Bullish

• Most equity buyers tend to think the market is going to rise more than the ‘equity risk premium’

• Given those beliefs, it

Academic Confabulations

‘it would be irresponsible to assume that [the CAPM] is not true’ William Sharpe

‘theoretical tour de force’ though ‘empirically vacuous’ Eugene Fama

‘stochastic discount factor(s) … so general, they place almost no restrictions on financial data’

John CampbellFinance is “the only part of economics that works”

Andy Lo

Praise for a Vacuous Theory

• Oil prices• Consumption growth• Per-capita labor income• Consumption/wealth ratio• Statistical (latent) Factors

• Etc.

Snipe hunt for factor that works

Implications

• Find weights with added constraints– No shorts– Cap on weight of 2% for S&P500, 4% for other

indices– Stocks found generally at max limit for longs– Redo each 6 months based on daily data from

prior year

MVP Construction

. . ' 1

0 0.02

Min w w

FTSEFTSE-MVP

MSCI-Eur

MSCI-MVP Nikkei

Nikkei-MVP S&P500

S&P500-MVP

AnnRet 2.7% 7.4% -0.6% 2.6% -1.6% 0.0% 4.2% 9.2%

AnnStdev 15.0% 12.0% 19.5% 13.1% 19.8% 13.5% 16.5% 12.3%

Beta 0.65 0.59 0.50 0.47

Indexes are not near 'Efficient'

Beta Strategies

Data from Jul-1962 to Jun-2012 monthly returns, annualized used top 80% of NYSE market cap (about 1500 stocks today)Portfolios with 100 stocks

Beta-Low Beta-05 Beta-10 Beta-15 Beta-High S&P500

GeoMean 11.3% 11.9% 12.2% 9.6% 6.4% 10.1%

AnnStDev 13.0% 11.6% 17.4% 26.2% 34.4% 15.1%

Sharpe 0.45 0.56 0.39 0.16 0.03 0.31

Inf. Ratio 0.10 0.22 0.21 0.15 -0.02

SMB Beta 0.53 0.34 0.69 1.45 1.78 0.26

HML Beta -0.06 0.10 -0.29 -0.96 -1.35 -0.39

Mkt Beta 0.60 0.57 1.04 1.44 1.82

Total Vol vs. Beta vs. IdioVol

Volatility Beta Idiolow high low high low high

Arith 10.3% 7.9% 12.1% 11.1% 10.5% 9.0%Geo 10.2% 2.2% 12.0% 5.3% 10.5% 3.7%Stdev 10.2% 33.5% 11.9% 34.1% 10.2% 32.5%Sharpe* 1.00 0.07 1.01 0.16 1.03 0.11

• Top 2000 stocks, extrapolated backward, 1952-2008, Sorted differently

• Assume people want to do what everyone else is doing– Appealing asset allocation based on consensus,

not volatility• Sell idea of trading envy for greed

• MVPs• Beta Arbitrage• Will deviate from the benchmark

Investment Advisor

• Focus on payoffs and probabilities– not expected returns– Not discount rates

• Don’t derive an expected return from a covariance or factor loading

Implication

piE ret a

2E ret a

Implications

• Don’t expect to be rewarded for risk taking per se

• Accept some envy; moderation in all things• People like being appreciated: it shows they

are relatively competent, a status maximizing metric

The Missing Risk Premium: Why Low Volatility Investing Works Eric Falkenstein 2013 Copyright 2013...

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