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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 Please do not quote without the authors’ consent.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: P.R.Draper@exeter.ac.uk

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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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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