Discretionary Government Intervention, and the...
Transcript of Discretionary Government Intervention, and the...
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Discretionary Government Intervention, and theMispricing of Index Futures
Paper Number 02/07
Paul DraperUniversity of Exeter, U.K.
Joseph K.W. FungHong Kong Baptist University, Hong Kong
November 2002
Abstract
This paper examines how and to what extent direct market intervention by the Hong Konggovernment in both the stock and futures markets affected the pricing relationship betweenthe Hang Seng Index futures and the cash index during the period of the Asian financialcrisis. The study avoids infrequent trading and non-execution problems by using tradeablebid and offer quotes for the constituent stocks of the index. The results show that arbitrageefficiency was impeded during, and in the immediate aftermath of, the intervention. Thefindings suggest that discretionary government action introduces an additional risk factor forarbitrageurs that continue to disrupt normal market processes even after the governmentceases to intervene. The continued disruption following the government’s actions in themarket also stems from a poorly developed stock loan market that impedes short selling, aswell as a lack of liquidity in the market.
Preliminary Draft. Please do not quote without the authors’ consent.
We would like to acknowledge with thanks help received from the Hong Kong Futures Exchange, the StockExchange of Hong Kong, Exchange Fund Investment Ltd, the Hong Kong Securities Clearing Co. Ltd., andHang Seng Index Services Ltd. in providing the data. We have also benefited from the comments on an earlierdraft of the paper entitled “Onscreen Trading of Stocks and the Mispricing of Index-Futures during FinancialCrisis and Government Intervention”, of seminar participants at the Securities and Futures Commission, theInstitute for Monetary Research of the Hong Kong Monetary Authority and the Financial ManagementAssociation, Seattle, the Federal Reserve Bank of Atlanta, and of the following individuals: Prof. S.K. Tsangand Kenneth Chan of Exchange Fund Investment Ltd., Prof. Paul McGuinness of the Chinese University ofHong Kong, Guy Meredith and Matthew Yiu of the Institute for Monetary Research (HKMA), Kevin Cheng andElton Cheng of the Hong Kong Futures Exchange, and Lilian Lam of the Hang Seng Index Services Ltd.Excellent research assistance has been provided by C.K. Chan, Thomas Kong, K. M. Lam and Castor Pang. Weare grateful to Hong Kong Baptist University for a faculty research grant.
Paul Draper is Professor of Finance at the University of Exeter. Joseph K.W. Fung is an Associate Professor ofFinance in the Department of Finance and Decision Sciences,Hong Kong Baptist University.
Contact Author: Professor Paul Draper, School of Business & Economics, University of Exeter, StreathamCourt, Rennes Drive, Exeter EX4 4PU, Devon, UK Tel: +44 1392 263218 email: [email protected]
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ISSN 1473 2904
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Discretionary Government Intervention and the
Mispricing of Index Futures
1. Introduction
Government intervention in the foreign exchange and interest rates markets is widely
observed. For example, the Federal Reserve and the Bundesbank frequently intervened to
affect the Deutschmark exchange rate vis-à-vis the U.S. dollar1, whilst the Federal Reserve
through its Open Market Operations (OMO) and the operation of its discount window
actively affects interest rates in the U.S. Intervention in the stock market is uncommon2.
This study examines a unique event in which the government of Hong Kong, a long-term
supporter of laissez faire, suspecting market manipulation by a number of hedge funds,
intervened directly and extensively in the stock market during the Asian financial crisis. The
study provides empirical evidence on the extent to which both awareness of government
intervention in the market, and the government’s purchase of securities affected equilibrium
asset prices. In contrast to previous studies that have examined the effect of intervention on
interest rates and currencies, this paper investigates the distortion of index futures prices due
to stock market intervention.
Fung and Draper (2002) examine the performance of the HK index futures market and show
that the market, despite the Asian financial crisis provided few arbitrage opportunities. They
attribute this to the electronic screen-based trading system and the open limit order book that
provided market transparency during chaotic trading conditions. Prior to intervention,
despite, for example, a one day market fall of 10% on 23 October 1997, the futures price
remained within the no-arbitrage bounds (Diagram 13). In contrast, all-out government
intervention in the stock market on August 28 saw the futures persistently priced at a large
discount relative to the cash index (Diagram 2). This study examines the extent to which
direct intervention by the government disrupted the normal relationship that exists between
the index and index futures prices. Government officials acted on the basis of a different set
of information and with different objectives from normal market traders. Limited
1 Naranjo and Nimalendran (2000) find that the Federal Reserve and the Bundesbank intervened in the dollar-mark market on 704 and 1166days, respectively, out of 4723 trading days between January 1976 and December 1994.2 The Taiwan government occasionally intervenes in the market through the operation of a stock market support fund. The interventions areof relatively small magnitude.3 The day was excluded from the sample analyzed in Fung and Draper (2002).
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information on the scale and scope of intervention, and the possibility of further discretionary
intervention created a potentially large adverse selection cost for market participants.
Consequently, discretionary government intervention had a pronounced effect on the market
beyond the immediate market impact effects. Intervention by the government introduced an
extra element of risk and uncertainty into the market place, the impact of which is related to
the relative magnitude of actual and potential intervention.
The Hong Kong government, intervened directly in the stock and futures market between
August 14 and 28. During that period, the government bought in excess of 7.3% of the total
market capitalization of all the stocks comprising the main market index. The government
also indicated that its remaining free reserves would allow it to build-up its total holding to
more than 30% of the total market capitalization of the index stocks4, creating a substantial
potential threat to the market and the arbitrage process. This paper assesses the market
disruption during the intervention period and examines the factors that affected it. In
particular, the paper focuses on the role of short selling and difficulties in the stock lending
market.
The intervention occurred against the backdrop of the Asian financial crisis. For comparative
purposes, the paper examines arbitrage efficiency between the futures and cash markets for
the most volatile days both during and prior to government intervention. Unusual interday
and intra-day volatility mark the sample period. Harris (1989) and Miller, Muthswamy, and
Whaley (1994) show that the bias induced by the effect of infrequent trading and non-
execution in the reported index is more pronounced with higher frequency data and greater
market volatility. To alleviate these problems in measuring the cash index, following Fung
and Draper (2002), the study uses indices that are reconstructed from active bid and offer
quotes of all the constituent stocks. The use of these indices also reduces the effect of bid-ask
bounce. The stocks in this study are traded electronically via a screen-based trading system
and open limit order book, providing a high level of pre- and post-trade market transparency.
The data obtained from the system is not affected by the reporting time lags inherent in a
floor-trading environment. To capture the highly clustered dividend payments for the index
stock, the study accounts for actual (ex-post) dividend payment streams in estimating the
accrued dividends in the index portfolio.
4 The market capitalization of the index is over 70% of the capitalization of the entire market.
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The results reveal that prior to intervention, despite the high frequency and magnitude of
mispricings, price adjustment in the stock and futures markets remained dynamically efficient
even for days with very high volatility. Intervention, however, disrupted efficient price
adjustment and a large negative basis remained for a month subsequent to the intervention, a
reflection in part of the difficulty of short selling, a result of low liquidity in the market
arising from the large government holding and of government pressure. This suggests that
intervention affected market efficiency. The intervention added a new risk element to
arbitrage activities, a result of the difficulty of conducting open term repos in the stock loan
market. The effect is aggravated by the lack of overall liquidity in a small market.
The remainder of the paper is organized as follows. Section 2 reviews the literature,
discusses government intervention in Hong Kong in the context of the institutional
arrangements of the market and sets out a hypothesis for test. Section 3 describes the data
and the methodology adopted in the empirical investigation of the event whilst section 4
summarizes and interprets the empirical findings.
2.1 Literature review
In a frictionless market, the index futures and the underlying cash index basket are perfect
substitutes. The actual futures price should be equal to the theoretical (or “fair”) futures price
determined by the cost-of-carry condition, to avoid arbitrage. The fair futures price is equal
to the ex-dividend value of the stock index basket on the expiration day of the contract5; i.e.,
Ft* = FVT(St) – FVT(D),
where St is the value of the underlying cash index at a particular point in time on day t; Ft*
represents the time-synchronous theoretical futures price corresponding to the cash index FVT
(St) and FVT (D), represent the future value on the expiry day T of the index basket and of the
total cash dividend accrued to the stock basket between the two dates. If the futures is trading
above its fair value, arbitrageurs will short futures and buy the relatively underpriced index
basket; they will sell short the index basket and go long the futures when the opposite is true.
Such trading activities will restore the parity between the actual and theoretical futures prices
whenever a violation occurs.6.
5 See Cornell and French (1983) and Modest and Sundaresan (1983)6 According to contract specification, FT = ST. Arbitrageurs will short futures and buy the index basket when the futures is overpriced (i.e.,when the actual futures price (Ft) is above the fair value (Ft
*)). When the futures is underpriced (i.e., when the actual futures price is belowthe fair value (Ft<Ft
*)), arbitrageurs will buy futures and short the index. Consequently, in the absence of market frictions, the actual futures
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Shleifer and Vishny (1997) model the limits to arbitrage when conducted by relatively few
professional, highly specialized investors who combine their knowledge with the resources of
outside investors to take large positions. A three period, three participant (noise traders,
arbitrageurs and investors who do not trade on their own) model is sufficient to reveal that
“performance-based arbitrage is particularly ineffective in extreme circumstances, where
prices are significantly out of line and arbitrageurs are fully invested….Arbitrageurs might
bail out of the market when their participation is most needed”. Additional institutional
constraints on short selling reinforce the conclusion that arbitrage may not be effective in
extreme circumstances. In addition, in any market there are a number of risks to arbitrage
that prevent the futures from aligning perfectly with the fair value. These risks include
trading costs in establishing and unloading the arbitrage portfolio7; and the risks arising from
trade execution that depend on the persistence of the mispricing, market volatility, and
market microstructure. .
Limits to Arbitrage and US experience in 1987
The level of execution risk is affected by the microstructure of the trading system and the
efficiency of the market. The risk of execution varies substantially between different trading
systems. During the 1987 U.S. stock market crash, execution of limit orders was delayed by
as much as 45 minutes so that the reported index failed to reflect actual market conditions.
Advances in electronic trading and the operation of an open limit order book now allow for a
high level of pre- and post-trade market transparency; execution, confirmation, and revision
of trade take only seconds so that the risk of execution is reduced substantially. However, the
risk of execution still depends on market volatility and the speed at which arbitrageurs exploit
the observed mispricing.
To calculate the mispricing, the value of the index basket, which reflects the current prices of
the component stocks as well as the prospective execution price for index arbitrage purpose,
has to be identified. However, reported stock indices are mainly based on the last traded
prices of the component stocks. Infrequent trading of some stocks in the index delays the
adjustment of the index upon arrival of market information and is indicated by significant
price must always equal the fair value at any point in time since arbitrage is instantaneous whenever a mispricing emerges. The relationshipis widely known and there are arbitrageurs specializing in exploiting any potential opportunity.
7 The trading costs are largely deterministic in nature and can be accounted for in calculating the pricing errors and the potential arbitrageprofit to arbitrageurs.
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autocorrelation in the reported index. Harris (1989) shows that the problem of infrequent
trading is aggravated in volatile market conditions. Miller, Muthuswamy, and Whaley,
(1994) show that the effect of infrequent trading increases as the measurement interval is
reduced, and note that infrequent trading can significantly distort the value of the index at the
morning open particularly if a number of index stocks do not trade when the market opens
following a large over-night information shock. According to Miller et al. although the S&P
500 futures opened 7% down on October 19 1987 major stocks including IBM did not
actually trade at the opening. Kleidon (1992) argues that this helps explain the large negative
basis exhibited by the futures during the first 90 minutes of trading on October 19 and 208.
A large negative basis should have attracted arbitrageurs to provide liquidity to hedgers and
speculators in the futures market (Grossman, 1988a). However, delayed routing and
execution of stale limit orders dragged the index far behind the futures under the extremely
volatile market conditions during the crash. It was difficult for arbitrageurs to act upon the
observed large negative basis since the extent of the stale price effect on the reported index
was largely unknown. In addition, there was little information on the feasible execution price
of the basket portfolio given the market situation.
Hong Kong experience in 1997
Fung and Draper (2002) examine the relative pricing efficiency between the index futures
and the underlying cash index in the Hong Kong market for an extended period between May
1996 and April 1998. They find, following the outbreak of the Asian financial crisis in May
1997, the frequency and magnitude of index-futures mispricings increased but the absolute
size of the potential arbitrage profits remained limited. The findings support the notion that
the transparency and execution efficiency of the screen-based stock trading system together
with the open limit order book, even under extremely volatile market situations, generate a
high degree of arbitrage efficiency helping to maintain the pricing integrity between the index
futures and the cash stock markets.
8 Kleidon (1992) suggests that the antiquated order process system may have caused the large negative basis. A number of U.S. studies haveexamined the relationship between index futures and its underlying cash index surrounding the stock market crash on October 19, 1987. OnOctober 19, the S&P 500 futures was below the cash index by 28 points at the close when the index was around 230. The negative basisreached a high of 40 index points on the following day. Using the S&P 100 index options and the cash index, Kleidon and Whaley (1992)provide additional evidence of the disparity between the index and the index options markets although the relationship between differentderivative securities (S&P 100 index options and S&P 500 futures) remained largely intact.
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Cheng, Fung, and Chan (2000) examine the impact of the Asian financial crisis on the pricing
relationship between the index futures and index options written against the Hang Seng
Index. In line with the findings of Kleidon and Whaley for the U.S. derivatives markets
during the 1987 crash, the study found that the Hang Seng Index futures and options prices
remain highly integrated both during the crisis and the intervention period9.
The effects of short selling restrictions in Hong Kong have also been examined. Following
Diamond and Verrecchia (1987) who show that restricting short sales slows down the
downward adjustment in security prices in reflecting bearish information, Fung and Jiang
(1999) examine the error-correction dynamics between the index and the futures. Fung and
Jiang found that the lead in price changes from futures to the spot index increases with
greater constraints on short selling10. Moreover, Jiang, Fung, and Cheng (2001) also found
that impediments against short selling weakens the contemporaneous relationship between
the futures and the cash market especially in a falling market situation and when the futures is
underpriced. Fung and Draper (1999) show that the lifting of restrictions against short selling
reduces the frequency and magnitude of under-pricing in the index futures, and increases the
adjustment speed in eliminating the under-pricing. The effect of constraints against short
selling on the index-futures price relationship is also supported by various studies of US and
European markets11.
A number of factors unique to different markets may affect the extent in which constraints
on, and costs of, short selling affect the index-futures price relation. In particular, the
severity of regulatory constraints against short selling, the level of institutional participation
in the market and the possibilities for quasi arbitrage12, the difficulty of locating willing stock
lenders and their cost, and the risk in taking short stock positions, may all be important.
9 For related studies on the arbitrage relationship between the index options and index futures for the Hong Kong market, see Fung, Cheng,and Chan (1997), Fung and Fung (1997), Cheng, Fung, and Pang (1998), and Fung and Mok (2001, 2002).10 Various costs of transacting create a natural preference for using futures for speculators to reveal their market opinions (Stoll and Whaley1988). In the US futures are traded in the pit and stocks are traded on the floor. The futures generally lead the spot by around 5 minutes(Stoll and Whaley 1990). Grunbichler, Longstaff and Schwartz (1994) found that the lead from the DAX futures to spot lengthened to 15 to20 minutes, a reflection of the fact that the futures are traded onscreen whilst the underlying stocks of the DAX index are traded on the floor.Since the futures in this study are traded in the pit and stocks are traded onscreen, the informational efficiency of the stock market should beimproved relative to the futures.11 See, for example, Figlewski and Webb (1993).12 See, for example, Chan (1992) and Neal (1996)
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2.2 Effects of Government Intervention
Naranjo and Nimalendran (2000) study intervention by the Federal Reserve and the
Bundesbank on the dollar-mark market between January 1976 and December 1994, and find,
after controlling for order processing and inventory costs, the bid-ask spread widens with
unexpected intervention. This finding is consistent with their model which shows that
unexpected government intervention increases the adverse selection cost against foreign
exchange dealers. Chaboud and LeBaron (2001) report an increase in trading volume in the
dollar-yen and dollar-market futures markets on the intervention days by the Federal Reserve
and show that both the intervention trading by the government and the announcement of
government action affect the market. This study provides empirical evidence that
government intervention in the stock market distorts the index futures price.
Intervention in the HK market
Against the backdrop of the Asian financial crisis and in the context of attacks on several
currencies including the Hong Kong dollar, fuelled by speculation on the future of the
currency peg between the Hong Kong and US dollars, the Hong Kong government, between
August 14 and 28, intervened in the stock and futures markets buying stocks and futures on
its own account. From August 14 1998 the government began to buy component stocks of
the index. Government buying intensified during the period and on August 28 the
government effectively put a floor under the prices of index stocks at an index level of 7850.
After August 28 no further intervention took place. Over the intervention period, the
government spent US$15.14bn (HK$118.1bn at the official rate of HK$7.8 per dollar) and
bought 7.3% of the outstanding shares of Hong Kong companies included in the market. The
total purchases on August 28 alone amounted to 4.5% of the total market capitalization of all
index stocks.
The government intervened in the market using foreign exchange reserves. Two funds,
Exchange and Land, were at the disposal of the government, with total overseas assets of
US$96.5bn (end of July 1998) although not all of this was available13. By the close on August
28 the government had used a little over 23% of available reserves. Turnover in the index
13 Under the currency board system the HK Monetary Authority backs the monetary base (the sum of the outstanding certificates of deposit,coins in circulation, and bills and notes issued by the Exchange fund) with foreign exchange reserves which vary from 105-112.5% of themonetary base. Given a monetary base of US$27.2bn this suggests that US$30.6bn of reserves was required for the backing portfolioleaving a free reserve of nearly US$66bn. At an index level of 7850 points, the total market value of index stocks was around $209.3bnindicating that the government could purchase more than 31% (including the 7.3% already purchased) of the outstanding shares in themarkets.
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stocks in 1997 was US$176bn against a market capitalization (end of year) of $273bn, an
annual rate of 65%14. The figures suggest that the magnitude of intervention was substantial
and could significantly reduce the liquidity of index stocks and affect the index level.
Restrictions and costs against short selling in Hong Kong
From March 25 1996 until the reintroduction of up-tick rule against short selling on
September 7, 1998, the constituent stocks of the index and a subset of large capitalization
stocks in the market could be sold short without restrictions. September 1998 saw various
‘counter manipulation’ measures established. The minimum margin required (against blue
chips and for credit-worthy stock borrowers) was 105% of the value of the stocks sold short.
In effect, the entire proceeds from short selling had to be deposited in the margin account
plus extra collateral that amounted to another 5% of the value of the transaction. However,
the effect of the up-tick rule against short selling should be largely deterministic and limited
as the rule can be bypassed easily by professional arbitrageurs and the process may only add
the cost of an extra stamp duty to the total transaction cost.15
Stock lenders are predominantly major overseas institutions that lend through their custodian
banks. The lenders include subsidiaries of large international securities dealers and custodian
banks. The firms charge the borrowers a stock-lending fee that is a stipulated percentage of
the value of the borrowed shares evaluated at the current market price. The fee ranges from
one percentage point in normal periods to as much as 40% when the market is tight16. A term
repos market does not exist for stock borrowers. The absence of a fixed term stock loan
arrangement in the market means that short sellers are exposed to call risk. Call risk is the
major consideration for short-sellers although from the stock lender’s point of view, counter-
party risk is the major concern. Call risk arises because short positions have to be covered
within 3 days or any agreed shorter period of time following a call notice17. Upon receipt of
a call notice, the borrower may negotiate another borrowing arrangement with the original
14 The annual turnover rate for 1998 was 53.37%. ‘Exchange Fact Book’, 1997 and 1998.15 To bypass the up-tick rule, an arbitrager may use a related company to lift the arbitrager’s offer at the ask price and immediately resell theshares at the bid. Hence, the arbitrager who borrows the share does not sell the shares at the bid price which is restricted by the up-tick rule.However, this procedure incurs an extra exchange trading charge (where the stamp duty is the most significant cost). If the arbitrager is thebrokerage itself, it can avoid the extra commission cost. Even in the case where the arbitrager is a client of the brokerage, the brokeragemay choose to provide a commission rebate to the client arbitrager. Hence, the net (or minimum) cost for using a related company of thearbitrager or the brokerage to buy shares is the exchange trading charges inclusive of the stamp duty against the member firm. The up-tickrule raises the effective cost and makes arbitrage less convenient.16 As this fee is highly variable and no official figures are available this study does not explicitly factor into its calculations of the lower no-arbitrage bound, the cost of borrowing. (‘The Development of the Securities Borrowing and Lending Market in Hong Kong’ July-September 1999, SFC Bulletin 37 20-33).17 Until September 24, 1998 settlement requirements specified T+2 for delivery but allowed overdue settlement during T+3 to T+5.
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lender or try to locate an alternative lender. This subjects the borrower to considerable
pressure if the market for the particular stock is tight. As a result, the borrowing cost for
rolling over a short position is highly unpredictable and introduces a major risk element in
short-stock index arbitrage18. This does not, of course, prevent institutions that already own
the shares from conducting quasi-arbitrage by selling their existing security portfolio and
substituting a futures position. However, this may explain the frequency and magnitude of
the discount in the futures contract.
Brokerage houses are selective in their offer of facilities for borrowing shares. Hence, the
risk of being called and the uncertainty as to both the cost and prospect of locating an
alternative lender for rolling-over the short position is a major hurdle to short selling. The
lack of willing stock-lenders in the market also restricts the supply although member firms
benefit from the interest spread in handling the margin deposits for short sellers.
Increased institutional participation in the market is a recent phenomenon and split between
locals and overseas institutions. This, together with the unavailability of term repos in the
market for borrowed stock, has imposed strains on the development of the stock loan market
and made short-stock arbitrage highly risky and difficult. In addition to the short selling
difficulty problems arise from the prohibition on program trading and the limited number of
terminals available per member seat. This limit raises the opportunity cost of undertaking
arbitrage and reduces profit opportunities.
2.3 Hypothesis
The difficulties associated with short selling suggest that whilst under normal circumstances
in a dynamically efficient market, the ex-ante profitability of a long-stock, short futures
arbitrage following an over-pricing signal should diminish at the same rate as a short-stock,
long futures arbitrage following an under-pricing signal, in a market traumatised by
unexpected government intervention, the mispricing following over-pricing and involving
long-stock arbitrage, should diminish much more rapidly than mispricing following an under-
pricing signal and involving short-stock arbitrage. This is due to the higher explicit cost and
inherent risk associated with stock borrowing. In extreme circumstances, short-stock, long
18 Conversations with index-arbitrageurs reveal that local arbitrage firms largely refrain from conducting arbitrage operations that requirestock borrowing.
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futures arbitrage may not take place at all resulting in persistent and large underpricing. This
suggests the hypothesis;
The frequency and magnitude of over-pricing is less than that of under-pricing due to the
extra cost, risk, and difficulty associated with short selling.
Actual and potential future interventions by the government increase the risk for speculators
and arbitrageurs in selling short stocks. In extreme situations the increased risk from short
selling may prevent speculators and arbitrageurs from correcting a large discount in the
futures price relative to the cash index. Government intervention raises the risk and
uncertainty against short-sellers and effectively chokes off short selling activities by both
classes of traders despite a large and persistent negative basis. The result is a large discount
in the futures price.
In normal market conditions, the extent of short sales will increase as the opportunities from
under-pricing increase. As the magnitude and frequency of under-pricing increases, short
sellers take advantage of the relatively higher stock price level so that short selling becomes
an alternative to shorting the futures. The greater arbitrage opportunities (short-stock, long-
futures) stimulates arbitrage and encourages arbitrageurs to increase their short stock
positions. Hence, the level of short selling is positively correlated with the frequency and
magnitude of (short-stock, long futures) arbitrage opportunities. Most importantly, the
increase in short selling by speculators and arbitrageurs helps limit the discount of the futures
price relative to the cash index and maintain the price integrity of the two markets.
In a ‘normal’ market setting, the level of short selling should be positively related to the
magnitude and frequency of short-stock, long futures arbitrage opportunities.
Sustained government intervention will disrupt this market mechanism. Consequently a
direct test of the effect of government intervention on normal arbitrage behavior is to
examine the change in the response of short sales to short stock arbitrage opportunities.
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3. Data and Methodology
All listed stocks in Hong Kong stock market are traded electronically through a computerized
screen-based trading system – the Automatic Matching System (AMS). The system provides
a continuous update of quote and trade information to the public through an electronic public
limit open book system. The electronic public limit order book significantly improves “pre
and post” trade transparency (Pagano and Roell, 1996) increasing the accuracy of the
arbitrage signal and reducing the execution risk to arbitrageurs19. Kumar and Seppi (1994)
note that price and quantity risks are important obstacles to index arbitrage. The open limit
order book system aids market transparency and provides valuable market information that
reduces the risk involved in arbitrage operations. It also reduces the potential delays in order
routing and execution that are especially pronounced during extreme market conditions.
Besides providing accurate time and price information for index arbitrageurs and traders in
general, the system allows precise measurement of the prospective executable prices of the
index basket20.
Data
To reduce, both the impact of infrequent trading in measuring the current value of the index
basket, and the inherent non-execution problem with indices based on last traded prices, the
study uses reconstructed indices based on concurrent bid and offer quotes retrieved from the
trading system (Fung and Draper, 2002). The index value is calculated only when all
concurrent bid or ask quotes of the component stocks are available at the same point in
time21. This largely eliminates the infrequent trading problem. The procedure also
eliminates the potential distortion to an index that can occur at the morning open, as a result
of an influx of significant information prior to the trading session. Non-execution is also
largely reduced since the calculated indices are based on concurrent, firm bid and ask quotes
and are potentially executable22. The data also eliminates uncertainty with respect to the
timing error associated with human handling of the reporting and transmitting of market
(trade and quote) information. The stock trading system of Hong Kong and the data available
19 “In electronic auction markets, brokers can scan the limit order book and see exactly at what price an order would execute (except for thepresence of “hidden orders”)” p.580, Pagano and Roell (1996).20 The quotes display on the trading screen of the system are firm quotes that are potentially executable immediately by punching limitorders through the computer terminals located both on and off the exchange. The quote information allows a direct calculation of thepotentially executable prices of the index baskets. The advantage of the data retrieved from the system is fully elaborated in the data andmethodology section.21 A maximum of 30 seconds in time difference in the retrieved quotes may occur since the quotes are retrieved with snap shots of the limitorder book screen every 30 seconds.
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for this study hence eliminate much of the (time and price) measurement error of the index
that affected US markets at the time of the 1987 crash.
The main data set used is the bid and ask record of all stocks listed and traded on the Hong
Kong Exchange and Clearing Limited (HKEx) for the period January 1997 to February 1999.
The data contains time-stamped bid and ask price and quantity queue records of each
individual stock taken every 30 seconds throughout the trading sessions. The Hang Seng
Index is a value weighted index of 33 blue-chip stocks. The market value of the selected 33
stocks exceeds 70% of the total capitalization of the entire market. The ask or buying (bid or
selling) price of the cash index at the end of a particular time interval is estimated by the sum
of the products between the concurrent best ask (bid) prices and their corresponding market
value weights.
Tick-by-tick transaction data for the Hang Seng Index futures is also obtained from HKEx.
The contract has been among the most heavily traded index futures contracts in the world.
The study focuses on the spot month contract. Unlike other markets, the spot month
contracts remain the most liquid except on their expiration day. The study substitutes the
next month contract for the spot month contract on the last trading day of the spot. This
substitution maintains a maximum time-to-maturity of 1-month for all the contracts used in
the analysis.
1-day, 1-week, and 1-month Hong Kong Interbank Offer rates are retrieved from Datastream
and the applicable rate estimated by interpolation. Exchange trading fees and brokerage
commissions remain largely constant throughout the study period. Members incur various
trading fees levied by the exchanges as well as stamp duty levied by the government. In
addition to compensating the members for the various fees and stamp duty, non-members
have to pay trading commissions. The pricing errors are filtered by transaction costs23. A
zero trading cost category is used as a benchmark. The zero trading cost category shows the
effect on the no-arbitrage bounds of the market impact cost due to the bid and ask spreads in
establishing and unloading the index and futures portfolio. HKEx provides daily short sales
turnover records. The (daily) total short sales turnover for index stocks is obtained by
22 According to Fung and Draper (2002) the total execution time is conservatively estimated to be between 3 to 10 minutes for index basketswith a single trading terminal. Practitioners suggest that usually more than one trading terminal is adopted to execute index arbitrage tradesand the total execution time could be reduced to around 2 minutes. Program trading is not yet permitted in the market.23 Results assuming transaction costs for a normal institutional investor are reported here.
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summing the short sales turnovers of all 33 stocks for the day. Dividend information, which
includes the ex-dividend date, and payment date for individual stocks in the extended study
period, is also obtained from the exchange.
The sample is divided into a number of sub-periods. The crisis period24 is defined as
occurring from May 14, 1997 to August 13, 1998 as the speculative attack on the Thai Baht
started on May 14. The period prior to May 14, 1997 is the pre-crisis 'normal' period. During
this period the intraday annualised standard deviation of the minute-by-minute futures
returns25 did not exceed 25%. August 14 to August 27 is the 'preliminary' intervention period
since during this time intervention on a small scale was taking place. August 28 was the day
of all-out stock market intervention.
The seven most volatile days during the crisis period prior to intervention by the government
serve as a comparison sample. These include October 23 and October 28 1997 (the standard
deviation on October 23 was 148% and that on October 28 was 141%). The other 5 days had
volatilities of between 60% and 86%. These five days26 are also analyzed separately.
August 31 to September 6, 1998 was the immediate aftermath of the intervention. The period
permits an examination of the impact of government intervention before the re-introduction
of restrictions on short selling27 of stocks on September 7. September 7 to 30 provides
information on the net effect of the interplay between the fading of the effect of direct
intervention and the impact of the reinstitution of the up-tick rule against short selling. We
also examine days with volatility between 5% and 10%; between 10% and 20%; and then by
intervals up to 60%28.
24 This in c lu de s the p e riod du ring wh ic h f ix ed ex ch a ng e ra tes w e re a ba n do ne d b y a n um be r o f co u ntrie s su ch as Th aila nd (J uly 2 , 19 9 7) . Du ring this pe r io d the Mala ys ia n r in gg itt, Phillip ine p e so , Th a i b ah t, I n do ne s ia n r in gg itt a nd Ko re an wo n d ec line d b y a t le as t 4 0%. Ho ng Ko ng r em aine d tie d to th e U S d olla r b ut c u rr en cy fe ar s a nd d o ub ts ov er th e re g io na l e co no m ie s le d to s er io us de cline s in th e s to ck m a rk et with s ig nific an t f alls a t the en d of Au gu s t 19 97 (1 5%) , at th e en d o f Oc tob er 19 97 ( 4 0%), an d ag a in a t the b e ginn ing o f J an ua r y 19 98 .25 Market volatility of the futures price for each particular day during the study period is measured by the annualized intraday standarddeviation of the minute-by-minute futures returns with continuous compounding. The standard deviation of the futures return is usedbecause it indicates the state of the market, and shows the execution risk associated with the arbitrage. Analytical results are robust with thestandard deviation of the index returns adopted as the proxy of market volatility.26 These five days are September 2, October 24, 30, and 31, 1997, and January 12, 1998. The volatility of the minute-by-minute futuresreturns on these days are 79.3%, 86.3%, 71.4%, 67.4%, and 67.9%, respectively. Results for these five days are not given here since theyare qualitatively similar to those for October 23 and 28.27 During the period a variety of institutional measures were proposed with the intention of making short selling more difficult andexpensive.For example, on 29th August the HKFE introduced a special margin rate of 150% on large open positions. It also reduced the reporting levelfrom 500 to 250 contracts. In September, HK Clearing tightened delivery requirements and made it more difficult for delivery to be delayedbeyond T+2.28 Results are available on request.
16
Methodology
i). Calculation of ex-post pricing errors
The calculation of the ex-post pricing errors of the index futures relative to the cash index
directly follows that developed in Fung and Draper (2002). To identify a potential
overpricing of the futures, the futures price29 is compared with the ask price of the index. If
the futures is overpriced, the arbitrageur shorts futures and buys the index basket at the ask
index price. To identify underpricing, the futures price is compared with the bid price of the
index. If the futures is underpriced, the strategy is to buy the futures and short sell the index
basket at the bid price. Market impact costs arising from covering the short stock positions
are also factored into the calculation. To avoid the impact of the uneven dividend payment
stream in Hong Kong, the model also accounts for the actual ex-post dividend payment of the
stocks included in the basket during the holding period of the portfolio.
The futures is overpriced at a particular time α on day t if the futures price (αt
F ) is above the
corresponding upper no-arbitrage bound (U
tFα
); i.e., αt
F > U
tFα
. Similarly, an underpricing
occurs if the futures price is below its corresponding lower no-arbitrage bound (L
tFα
); i.e.,
αtF <
LtFα
. No pricing error or arbitrage opportunity occurs if αt
F <U
tFα
or αt
F >L
tFα
.30
To allow for comparisons of the magnitude of the mispricings over different periods with
different levels of index and futures prices, the mispricings relative to the corresponding
boundary values are used in the empirical tests31. The size of an over-pricing is equal to
UttU
t
Utt FF
F
FFe
αα
α
αα >−
=+ ; (7)
Similarly, the size of an underpricing is equal to
29 The index futures market remained highly liquid throughout the event period despite heightened market volatility. The spread for the spotmonth contract remained stable at between 5 to 10 index points even for days of extremely high volatility. A constant 5 index points isadded to or subtracted from the transaction price to account for the potential bid-ask bounce in the futures price. As noted in Fung and Mok(2001), the procedure may under or over-estimate the feasible execution price of the contract; but, the size of the potential error is likely tobe very small.30 Note that the width of the no-arbitrage band as well as the value of the no-arbitrage upper or lower bounds depends on the level oftransaction costs incurred by different potential arbitrageurs. Potential arbitrageurs with higher trading cost will have a wider no-arbitrageregion, and vice versa.31 Analysis of the absolute errors provided qualitatively similar results.
17
LttL
t
tL
tFF
F
FFe
αα
α
αα <−
=− ; (8)
ii). Calculation of the ex-ante pricing errors
To test for the dynamic efficiency of the market, the study examines the direction, size and
persistence of the ex-ante pricing errors following an observed arbitrage signal (or initial
mispricing). An ex-ante pricing error is a measure of the potential profitability of executing
the arbitrage trade as indicated by the direction of the prior observed pricing error (i.e., the
signal). +lπ is the ex-ante profitability of a short futures, buy stock arbitrage trade executed
with a time lag l after observing an overpricing of the futures at time α .
UttU
t
Utt
l FFlF
FFl
αα
α
ααπ >>−
= +++ ,0;1 (9)
−lπ is the ex-ante profitability of a buy futures short stock trade with a time lag l following an
observed overpricing of the futures at time α.
LttL
t
tL
tl FFl
F
FFα
α
αα
απ <>
−= ++− ,0;11 (10)
iii). Underpricing and the relative short sales turnover of index stocks
Negative mispricings are of particular interest for this study. We expect the magnitude of
underpricing to be positively related to the execution risk and market volatility (caused by the
arrival of significant information). Increased market volatility produces greater opportunities
for mispricing, whilst the risk of execution impedes arbitrage. The standard deviation of the
intraday futures return is used as a proxy for the joint effect of these two factors. We expect
underpricing to be limited by the ability of investors to sell stocks short. A higher level of
short sales turnover in index stock (by both arbitrageurs and speculator) relative to the
amount of negative mispricing should help reduce the level of underpricing. However, due to
the forced convergence of the basis, the magnitude of the mispricing should be positively
related to the time-to-maturity of the contract. To test these hypotheses, we use the following
regression model:
et- = β1σt + β2Xt + β3τ + εt (11)
18
where et- is the average of the magnitude of the negative pricing error on day t, σ t is the
standard deviation of the intraday minute-by-minute futures returns on day t, Xt is the ratio of
the short sales turnover of index stocks to the total underpricing32 measured on day t. τ =T-t is
the time to maturity (as a fraction of a year) of the futures contract and εt is the error term of
the regression model.
iv). The effect of government intervention on the short sales behavior
To test whether government intervention affects normal short selling behavior, we use the
following model:
SITt = ϒ0+ϒ1σt + ϒ2Ut + ϒ3DtUt + ηt (12)
SITt is the short sales turnover of index stocks on day t; σt is the standard deviation of the
intraday minute-by-minute futures returns on day t; Ut is the total underpricing (again based
on zero transaction cost) measured on day t; Dt is a dummy variable that distinguishes the
effect of the total underpricing on the short sales turnover of index stocks (where Dt = 0
before August 28,1998, and Dt = 1 after August 28,1998); η t is the error term of the
regression model; and the ϒ s are the regression coefficients. After controlling for the effect
of market volatility, it is expected that ϒ3 will be negative if government action had a
negative impact on the level of short selling for given levels of underpricing.
4. Empirical results and interpretation
The study focuses on examining the impact of the Asian financial crisis and market
intervention by the government on the relative pricing relationship between the futures and its
underlying index. Table 1 provides details of the ex-post mispricings for different phases of
the crisis and intervention. Four different error (mispricing) distributions are examined in the
table. The positive error (e+) indicates the magnitude of positive mispricing and occurs when
the futures price is above the upper no-arbitrage bound. A profitable arbitrage strategy is to
short the futures (at the bid price of the futures contract) and hedge the short futures exposure
by buying the stock index. The negative error (e-) indicates the magnitude of negative
32 The presence of total underpricing
19
mispricing and occurs when the futures price is below the lower bound of the futures price.
The strategy in this case to exploit the mispricing is to sell short the constituents of the index
portfolio and hedge it with a long position in futures. The absolute value of the error |e|
ignores the direction of the bound violations and reveals the absolute magnitude of the
mispricings. The pricing errors are measured relative to the corresponding bounds and are
expressed in basis points (bps). Mispricings can be interpreted as the deviation in percentage
terms of the futures price from the respective bounds. To examine the behavior of the futures
price around the no-arbitrage bands, we assign a negative sign to e- to determine whether, on
average, the futures are under or overpriced. Consequently, the distribution of e shows how
the errors are distributed around the no-arbitrage band. If the mean of e is negative, on
average, the futures are under-priced. Given the cost and risk associated with short-selling of
stocks we expect the futures to be mostly under-priced.
The Asian Financial Crisis
Fung and Draper (2002) show that for the period prior to the financial crisis assuming zero
transaction costs the futures appear under-priced but the under-pricing is small. At a realistic
level of transactions costs the number of profit opportunities is small and it is unlikely that
any significant opportunities for profit exist. The number of instances of overpricing (e+) is
almost zero and very small when it does occur.
Despite the surge in volatility during the crisis the potential profitability from mispricing
opportunities change relatively little. In the absence of transaction costs 24% of the 30
second periods for which data was available indicated mispricings. The size of the
mispricing opportunities increased during the crisis (compared to the earlier control period)
by some 50% as did the standard deviation but the overall pattern of mispricing remained
broadly unchanged. The rise in the mean mispricing increases the opportunities for profitable
arbitrage once transaction costs are allowed for but the profits are relatively small and the
number of mispricing opportunities as a percentage of the total number of comparisons, is
very small (Table 1).
in the denominator does not automatically drive the negative relationship between et
- and Xt. et- is significantly and positively related to the
short sales turnover of index stocks; and total underpricing and Xt are not significantly correlated. The correlation between total underpricingand Xt is equal to -.07 with a p-value of .16.
20
The results for the two most volatile days are in drastic contrast with the situation observed in
US markets during the October 1987 crisis. On October 23, 1997, the government noted a
substantial accumulation of Hong Kong dollar forward positions in the overseas foreign
exchange markets whilst the Hong Kong dollar dropped to 7.75 to one U.S. dollar from the
official rate of 7.8. The government squeezed liquidity out of the banking system in an effort
to punish those who had sold Hong Kong dollar short and had to borrow Hong Kong dollars
to settle their forward positions. The over-night inter-bank rate rose to a record high of
280%, the index dropped in the morning by 1437 points to 9766 an hour before the market
close. The standard deviation of the minute-by-minute futures returns reached 114.9%.
Despite this, the relationship between the futures and the stock remained largely intact and
the fluctuation in the futures prices were largely within the no-arbitrage bounds. After
allowing for transactions costs, there were 26 violations of the no-arbitrage bounds.
Overpricing dominates during the day although the average magnitude of mispricing was
only 15.5 basis points (Table 1). The results show that the two markets were closely aligned
with each other despite the extremely difficult market condition.
Mispricing observed ex-post for different periods may persist only momentarily or for an
extended period of time. To analyse ex-ante mispricing a short or long hedge is formed at
prices prevailing 3, 5, 10, 15 and 30 minutes after the hedge initially signals mispricing.
Table 2 provides ex-ante tests of the profit opportunities (after transaction costs) assuming
that the mispricing is perceived and acted upon within these intervals. Panel A reveals the
profitability if all mispricing signals are acted upon. Panel B shows the profitability of short-
futures strategy following an overpricing signal (e+). The strategy is to short futures and
hedge with stocks. Panel C shows the profitability of a long futures strategy following an
under-pricing signal (e-).
Prior to the financial crisis, with no transaction costs, the average profit of a hedge is
generally positive following a mispricing signal although the profitability of a short hedge
(long-stock, short futures) is much less than the profitability associated with long hedges
(short stock, long futures), a reflection of short-sales difficulties. The difficulty of borrowing
stock for short sales make long-futures arbitrage signals difficult to exploit so the profitability
of trades is more persistent following such signals. However, after transaction costs (results
not shown) the profitability of arbitrage opportunities is small and quickly extinguished, even
21
given the difficulty of short selling. Most investors find it impossible to make profits. As
expected, futures pricing is well behaved and within the arbitrage bounds before the crisis
period. The futures rarely stray outside the zero cost bound.
The ex-ante results of Table 2 confirm the results of Table 1. The decline in ex-ante
profitability over longer time lags supports the notion of dynamic efficiency in the price
adjustment process in both markets. The results for October 23 and other high volatility days
add extra support to the notion of market efficiency. Mean mispricing is small and
profitability negative once transaction costs are allowed for. The fluctuations of the futures is
generally within the no-arbitrage bands.
The Period of Government Intervention
We divide the intervention period into three stages. Our preliminary intervention period
includes August 14-August 27 during which government intervention in the market was
limited. By the end of the period the government had bought around 2.8% of the stocks in
the HSI index. All-out intervention occurred on August 28 when the government intensified
its intervention and effectively put a floor under the index at a level of 7850 and bought
around 4.5% of the stocks in the index on that day. The futures33 was consistently
underpriced by over 500 basis points. No further government intervention was affected after
that day (although market participants did not know this).
The immediate post intervention period included August 28 until September 6. During the
intervention period the government enacted various measures to curb speculation. The most
important of these controls, on short selling became effective on September 7. The number
of mispricing opportunities during the first sub-period (14/8/98 – 27/8/98) was 39% of the
total. The second sub-period (28/8/98), the day of all-out intervention saw mispricings rise to
100% of total comparisons. In the following week (sub-period 3, 30/8/98 – 6/9/98), the
number of mispricing opportunities fell back to 46%.
Analysis of the intervention period indicates a dramatic rise in the error. Preliminary
intervention saw the absolute value of the error rise from an average value in the crisis period
of 33.6 to 48.9. There was also a change in sign in the mean value, a reflection of the
22
preponderance of e+ mispricings over e-. Full intervention on August 28, saw the (mean and)
absolute value rise to (-)628 basis points. In the subsequent immediate post intervention
period until short selling restrictions were re-imposed the (mean and) absolute value
remained high at (-)429.9 basis points. Large negative mispricings persisted through
September but the position gradually changed thereafter with smaller ex-post pricing errors
and ex-ante pricing errors falling so that the 'normal' relationship was restored in the post
crisis period (November 1998 onwards). In short, once intervention put a floor under prices
and whilst the threat was perceived to continue investors were reluctant to remove profitable
opportunities that involved short selling.
This general picture is confirmed by analysis of ex ante profitability during the sub periods.
August 28, the day of all-out intervention provided profitable opportunities at all levels of
transaction costs. The mean value after 3 minutes of 539.9 changed little in the following 30
minutes. Despite the high potential profit opportunities, institutions and individuals were not
tempted into the market to close the gap. Shortage of arbitrage capital is one possible
explanation but unlikely given that the profits persist despite the transaction costs. Investors
were wary of the effects of government intervention and particularly of arbitrage transactions
that involved shorting the stocks in the index. Similar conclusions hold for the period 31
August 1998-6 September 1998. Despite transaction costs profits persist and do not decline
significantly even after 30 minutes. Rather surprisingly, the preliminary intervention period
is somewhat different. It is difficult to make profits but more interestingly, the mispricing is
positive, a reflection that the government was not perceived as seeking to put a floor under
the level of the index, but rather to provide temporary price support.
The impact of government intervention is highlighted by contrasting August 28 1998, the day
of all-out intervention, with a day nearly a year earlier, October 23, 1997, when the
government resorted to penal interest rates on bank borrowing and overnight HIBOR touched
280%. On this occasion the number of mispricings reached 58% of the comparisons and the
mean mispricing was only 46.1 basis points, very much smaller than the 100% and –628
basis points on August 28 1998. Profitability on 23 October 1997 was negative despite the
observed mispricing, and contrasts sharply with the apparent very high levels of profitability
during the period of government intervention. During the intervention after allowing for
33 Note that the September contract is used on this day because the spot month contract is expiring and its movement is limited by the Asian-
23
transaction costs profitability was apparently 538bp and changed little over longer time
intervals. Government intervention affected market prices in a much more profound way
than the speculative attacks on their own. The very worst day during the Asian crisis
(October 28 1997) still had a much smaller impact that when government intervention was
pursued in earnest.
One explanation for the high level of mispricing during the intervention period that has been
suggested by market participants relates to the difficulty of borrowing stock to go short
during the intervention period. A stock borrower faces high levels of risk because of the
possibility of a call. The borrower has only two days to borrow to meet the call, posing a
substantial risk of being squeezed if the market rises, or if it proves difficult to borrow the
stock from elsewhere. This difficulty in borrowing stock meant that despite the level of
market transparency, the uncertainty surrounding potential and further government
intervention prevents short-stock long futures arbitrage. The possibility existed for the
government to continue buying up the index component stocks and maintain the index at the
level of 7800. Such purchases of index shares would necessarily dry up the stock loan
market and exert a serious squeeze on stock borrowers.
Underpricing and Short Sales Turnover of Index Stocks
The regression results (Table 3.1) reveal that futures volatility (β1) significantly and
positively affects the magnitude of underpricing. The coefficient (β2) of the short sales
turnover/total underpricing ratio is negative and significant (p-value=0.0570) supporting our
conjecture that higher short sales turnover in index stocks relative to the amount of
underpricing reduces the average magnitude of underpricing34. β3 is positive and highly
significant indicating that forced convergence of the basis causes the magnitude of the
mispricing to be positively related to the time-to-maturity of the contract.
Increased long-futures, short stock arbitrage opportunities (or underpricing) should induce
larger short sales turnover in the index. An increase in the volume of underpricing without a
commensurate increase in short sales turnover in index stocks may lead to greater
style settlement procedure for the contract.34 A regression without an intercept is used since the intercept term was not significant in the prior run. The results with and without theintercept term are largely similar. The measured underpricing is based on the assumption of zero transaction costs although results fordifferent levels of transaction costs are largely in line with the above findings.
24
underpricing. To examine this, we consider the correlation between the various measures of
short stock arbitrage opportunity and the short sales turnover ratio for index stocks (Table
3.2). We expect a higher correlation between the futures and the cash index to be observed
when increased underpricing corresponds to a higher level of short sales in index stocks (by
index and risk arbitrageurs), or when short stock arbitrage opportunities correlate with a high
level of short sales turnover ratio. Correlations between the short sales turnover ratio and the
futures volume and volatility are also provided in Table 4.
For the pre-intervention periods (and sub-periods) the correlation between the ratio of short
sales turnover, and measures of long-futures, short stock arbitrage opportunity are
predominantly positive and significant. The signs for the other two measures are correct
(although not significant). The statistical insignificance may be due to the exhaustion of
arbitrage capital in a situation of abundant arbitrage opportunities. The positive relationship
is associated with high levels of both static (based on the ex-post error distributions) and
dynamic efficiency in the markets during the crisis period.
During the preliminary intervention period (August 14-27, 1998) the relationships change.
The correlation coefficients are no longer significant. In the intermediate aftermath of
intervention, before the re-imposition of the tick rule, the short sales turnover ratio correlation
is negative (and significant) and related to the average and total magnitude of underpricing.
Larger short stock arbitrage opportunities are accompanied by (relatively) small amount of
short sales of index stocks. The inability and/or fear of arbitrageurs towards taking short
positions in index stocks to capture the large negative basis is apparent. As a result, the large
negative basis persisted during this period. For the intervention period plus its immediate
aftermath (August 14 to September 30, 1998), the coefficients, on the whole, lack
significance and are of varied sign. This explains the large and persistent mispricing for the
period as a whole. As time increases away from the intervention period, the positive
relationship between short sales and underpricing is restored and the static and dynamic
relative pricing efficiency between the futures and the cash index portfolio re-established.
The positive correlation between futures volume, futures volatility, and the short sales
turnover ratio becomes significant during and in the immediate aftermath of government
intervention, as well as during the last sub-period.
25
Government Intervention, Underpricing and Shortselling
The regression results (Table 5) show that futures volatility significantly and positively
affects the level of short selling. The coefficient for the dummy variable attached to the
magnitude of underpricing is negative and highly significant and even slightly larger than that
for the underpricing variable alone. That suggests that the total impact factor of underpricing
on the level of short selling after the intervention was close to zero (actually slightly
negative). This provides strong evidence that government intervention on August 28
drastically discouraged short selling in its aftermath.
Conclusions
The study examines mispricing opportunities over the period May 1997 – September 1998
arising out of the relative pricing of (index) stocks and index futures. Using a data set that
allows for much greater accuracy in determining executable prices for the index basket, and
after allowing for transaction costs, the study confirms the negative mispricing found in many
other studies. More importantly, the study allows an analysis of mispricing both during the
Asian financial crisis starting in May 1997, and during the period of intervention by the Hong
Kong government in August 1998. The findings show that the trading process during the
intervention distorts market prices. Moreover, the discretionary market action undertaken by
the government introduces an additional risk element in the market which affects market
efficiency even when no further intervention take place. Greater mispricing occurs with
increased market volatility. The mispricing, in turn, provides profitable opportunities.
Whilst volatility is important, the extent of the mispricing is even greater during the period of
government intervention, a reflection of the intense difficulties that arose in short selling
stocks in the index basket. The perceived difficulties in short selling persisted for some time
after intervention but as the period of intervention receded mispricing opportunities declined.
26
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Stoll, H.R. and R.E. Whaley (1990): “The Dynamics of Stock Index and Stock Index FuturesReturns,” Journal of Financial and Quantitative Analysis, Vol. 25, No. 4, 441-468.
Sutcliffe, C.M.S. (1997): “Stock Index Futures (2nd edition),” International ThomsonBusiness Press.
28
Table 1Summary Statistics of the Distribution of Ex-Post Pricing Errors for Different Phases of the Crisis and Government Intervention
Crisis Period: May 14, 1997-August 13, 1998
N=132410
October 23, 1997N=456
Preliminary InterventionPeriod: August 14–27, 1998
N=3926
August 28, 1998N=465
Post-Intervention Period(before the up-tick rule):August 31-September 6,
1998 N=2235
Post-Intervention Periodafter the Imposition of the
Up-Tick Rule: September 7-30, 1998 N=7583
No Transaction costsN Mean Med N Mean Med N Mean Med N Mean Med N Mean Med N Mean Med
e 64609 -27.9 -24.5 260 46.1 42.4 2809 42.2 43.3 465 -628.0 -568.9 2232 -429.9 -427.2 6067 -179.7 -188.3|e| 64609 33.6 27.5 260 49.8 44.1 2809 48.9 44.7 465 628.0 568.9 2232 429.9 427.2 6067 181.3 188.3E+ 8297 22.2 16.6 238 52.4 47.0 2457 52.1 47.4 N.A N.A N.A N.A N.A N.A 411 11.5 9.6e- 56312 35.3 29.4 22 21.5 14.9 352 26.7 25.0 465 628.0 568.9 2232 429.9 427.2 5656 193.6 193.8
Transaction costse 2063 -18.6 -12.2 26 15.5 12.1 114 13.2 13.6 465 -538.3 -478.7 2232 -334.2 -332.1 5028 -114.5 -110.0|e| 2063 19.1 12.5 26 15.5 12.1 114 14.2 13.8 465 538.3 478.7 2232 334.2 332.1 5028 114.5 110.0E+ 32 17.4 13.9 26 15.5 12.1 112 13.9 13.7 N.A N.A N.A N.A N.A N.A N.A N.A N.Ae- 2031 19.1 12.5 N.A N.A N.A 2 28.6 28.6 465 538.3 478.7 2232 334.2 332.1 5028 114.5 110.0
Note: UttU
t
Utt
FFF
FFe
αα
α
αα >−
=+ ; and LttL
t
tLt
FFF
FFe
αα
α
αα <−
=− ;
e+ and e- represent over-pricing and under-pricing of the futures contract relative to the upper and lower no-arbitrage bounds, respectively. They are expressed in basis points(bps). Observations falling outside the above two categories are discarded from the analysis. The absolute value of the error |e| ignores the sign of the error and reveals theabsolute magnitude of the mispricings. To check the average of the mispricings we preserve the (negative) sign of e- to determine whether, on average, the futures are underor overpriced. Consequently, the distribution of e shows how the errors are distributed around the no-arbitrage band. If the mean of e is negative, on average, the futures areunderpriced.
29
Table 2
Summary Statistics of the Distribution of Ex-Ante Pricing Errors for different Phases of the Crisis and Government Intervention.
Crisis Period: May 14, 1997-August 13, 1998
October 23, 1997 Preliminary InterventionPeriod: August 14–27, 1998
August 28, 1998 Post-Intervention Period(before the up-tick rule):August 31-September 6,
1998
Post-Intervention Periodafter the Imposition of the
Up-Tick Rule: September 7-30, 1998
Panel A: All arbitrage signalsN Mean Med N Mean Med N Mean Med N Mean Med N Mean Med N Mean Med
3Min 1918 6.1 3.9 25 -32.0 -30.1 113 6.5 12.8 463 539.9 478.7 2222 335.0 332.5 4609 116.4 111.05Min 1838 4.5 2.7 25 -16.2 -11.6 112 -1.8 10.6 451 537.8 478.7 2162 335.3 334.1 4477 116.7 111.110Min 1805 1.3 0.4 25 -45.1 -35.3 112 -11.6 2.5 443 537.2 478.7 2123 336.2 335.3 4401 116.1 110.915Min 1705 -0.5 0.3 25 -71.7 -54.7 108 -17.3 -7.4 423 534.0 478.7 2027 336.9 336.7 4200 116.6 111.230Min 1604 -2.3 -1.0 25 -92.8 -96.8 98 -28.6 -17.2 403 548.8 489.1 1931 338.1 331.7 4024 114.8 109.9Panel B: Short-hedge arbitrage signals (e+)3Min 31 -30.1 -27.1 25 -32.0 -30.1 112 6.3 12.7 N.A N.A N.A N.A N.A N.A N.A N.A N.A5Min 28 -19.1 -15.3 25 -16.2 -11.6 112 -1.8 10.6 N.A N.A N.A N.A N.A N.A N.A N.A N.A10Min 28 -45.6 -37.9 25 -45.1 -35.3 112 -11.6 2.5 N.A N.A N.A N.A N.A N.A N.A N.A N.A15Min 28 -68.6 -51.4 25 -71.7 -54.7 108 -17.3 -7.4 N.A N.A N.A N.A N.A N.A N.A N.A N.A30Min 28 -87.5 -83.4 25 -92.8 -96.8 98 -28.6 -17.2 N.A N.A N.A N.A N.A N.A N.A N.A N.APanel C: Long-hedge arbitrage signals (e-)3Min 1887 6.7 4.3 N.A N.A N.A 1 29.0 29.0 463 539.9 478.7 2222 335.0 332.5 4609 116.4 111.05Min 1810 4.9 2.8 N.A N.A N.A N.A N.A N.A 451 537.8 478.7 2162 335.3 334.1 4477 116.7 111.110Min 1777 2.1 0.9 N.A N.A N.A N.A N.A N.A 443 537.2 478.7 2123 336.2 335.3 4401 116.1 110.915Min 1677 0.6 0.8 N.A N.A N.A N.A N.A N.A 423 534.0 478.7 2027 336.9 336.7 4200 116.6 111.230Min 1576 -0.8 -0.3 N.A N.A N.A N.A N.A N.A 403 548.8 489.1 1931 338.1 331.7 4024 114.8 109.9
Notes: Panel B reports the ex-ante profitability, i.e., +lπ of a short futures long stock arbitrage executed with a time lag l after observing an overpricing signal (e+) at time α.
Panel C reports the ex-ante profitability, i.e., −lπ of a long futures short stock arbitrage executed with a time lag l after observing an underpricing signal (e-) at time α. Where
Ut
btU
t
Ut
bt
l FFlF
FFl
αα
α
ααπ >>−
= +++ ,0;1, and
Lt
atL
t
at
Lt
l FFlF
FFα
α
αα
απ <>
−= ++− ,0;11
. Panel A shows the profitability of the strategies following either signal. Five different
time lags that range from 3 to 30 minutes are adopted to examine the dynamic behavior of the error series.
33
9700
9900
10100
10300
10500
10700
10900
11100
11300
11500
10:00
10:10
10:20
10:30
10:40
10:50
11:00
11:10
11:20
11:30
11:40
11:50
12:00
12:10
12:20
12:30
14:30
14:40
14:50
15:00
15:10
15:20
15:30
15:40
15:50
16:00
future
FU(N)
FL(N)
Diagram 1 October 23, 1997 Member & Non-member (σ = 114.9%)Short index turnover = 133.38583 millionTotal under-pricing = 473.86262 basis pointsRatio = 0.2814862 million/basis point
34
7000
7200
7400
7600
7800
8000
8200
10:00
10:10
10:20
10:30
10:40
10:50
11:00
11:10
11:20
11:30
11:40
11:50
12:00
12:10
12:20
12:30
14:30
14:40
14:50
15:00
15:10
15:20
15:30
15:40
15:50
16:00
future
FU(N)
FL(N)
Diagram 2 August 28, 1998 Member & Non-member (σ = 62.5%)short index turnover = 9059.1998 million
total under-pricing = 292010.18 basic pointsratio = 0.0310235 million/basic point