2

Expiration-Day Effects of the All Ordinaries Share Price Index Futures: Empirical Evidence and Alternative Settlement Procedures
by

Hans R. Stoll Robert E. Whaley

Abstract: Stock index futures were the most successful financial innovation of the 1980s. In spite of their widespread use internationally, they continue to be criticised for causing aberrations in the stock market, particularly on expiration days when futures contracts are cash-settled. This paper examines expiration-day effects of the Sydney Futures Exchanges All Ordinaries Share Price Index (SPI) futures and discusses alternative futures settlement procedures. Our investigations indicate that, while index stock trading volume is abnormally high near the close on expiration days, price movements are not different from those observed on other days. In other words, the SPI futures cash settlement at the close appears to have worked well through our sample period. This study also describes and analyses the two basic alternative cash settlement proceduresa single price settlement and an average price settlement. Keywords:
STOCK INDEX FUTURES; INDEX ARBITRAGE; PROGRAM TRADING; EXPIRATION-DAY EFFECTS; SETTLEMENT PROCEDURES. Owen Graduate School of Management, Vanderbilt University, Nashville TN 37203, US. Fuqua School of Business, Duke University, Durham NC 27706, USA; E-mail: whaley@mail.duke.edu
The authors acknowledge the support of the Sydney Futures Exchange and the Catalyst Institute, Chicago, IL. We thank Stephen Gray for helpful comments and Anthony Collins of the Sydney Futures Exchange for assistance in obtaining the data used in the empirical analyses.
Australian Journal of Management, Vol. 22, No. 2, December 1997, The University of New South Wales

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1.

Introduction

tock index futures contracts were, perhaps, the most successful financial innovation of the 1980s. The first contract was the Chicago Mercantile Exchanges S&P 500 futures, which began trading in the US in April 1982. 1 The contract design quickly spread to almost every major financial futures market worldwidethe Sydney Futures Exchanges Australian All Ordinaries Share Price Index futures first traded in 1983; the London International Financial Futures Exchanges FTSE 100 futures in 1984; the Hong Kong Futures Exchanges Hang Seng Index futures in 1986; the MATIFs CAC-40 index futures in 1988; the Osaka Stock Exchanges Nikkei 225 futures in 1988; and DTBs DAX index futures in 1990. The primary reason for the success of stock index futures markets is that index futures provide a fast and inexpensive means of changing stock market risk exposures internationally. Suppose, for example, that a stock portfolio manager fears a downturn in the US stock market over the next few weeks and wants to eliminate his market risk exposure. Selling S&P 500 index futures is a quicker and cheaper means of eliminating US stock market risk than selling the portfolios stocks. Moreover, selling futures allows the manager to maintain his exposure to the idiosyncratic risk of the stocks that he has identified as being winners. Alternatively, suppose that an international fund expects the Japanese stock market to race ahead of other stock markets worldwide. The quickest and easiest way to gain exposure to the Japanese stock market is to buy Nikkei index futures. Over time this long futures position can be replaced with direct investment in Japanese stocks, but the stock market purchases can be made in a slower, less costly, and more orderly fashion. All stock index futures contracts call for cash settlement on the expiration day. Cash settlement eliminates the cost and difficulty of delivering the many individual stocks in the index. Conversely, final settlement of most other futures contracts is by delivery. Sellers of wheat futures are, for example, obliged to deliver wheat if they have not traded out of their contracts before maturity. By contrast, sellers of stock index futures have no obligation to deliver the underlying stocks. The futures position is closed out at the settlement price determined by the rules of the exchange. Until recently, the Share Price Index (SPI) futures settled at the closing price of the All Ordinaries Share Price Index (AOI) on the expiration day of the futures contract. Beginning with the March 1997 contract, the futures has settled at the prices determined in a special call auction market that occurs fifteen minutes after the stock market close. Index expirations attract considerable attention, primarily because of the large volume of trading, but also at times because of sharp price changes. In the US, the triple witching hour (ie, the last hour of trading on the third Friday of the quarterly month when index futures, index options, and equity options expire simultaneously) attracted considerable attention from exchanges, regulators, and the general public in the mid 1980s. In Australia, the 29 March 1996 expiration
1. Technically speaking, the S& P 500 futures was the first successful index futures contract. The Kansas City Board of Trade introduced a futures contract on the Value Line index in February 1982, two months earlier than the CMEs S& P 500 contract. The contract had limited success, however, because the Value Line index was geometrically-weighted, undermining the futures contracts effectiveness as a hedging vehicle.

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was quite controversial. According to press reports, large sales of stocks, apparently as part of an index arbitrage unwinding, occurred late in the day, causing the AOI to fall by 21 points. In this study, we analyse this expiration along with other recent expirations. Stock index expirations have been studied in a number of academic papers. Widely known are a series of studies by Stoll and Whaley (1986, 1987, 1990a, 1991) and Stoll (1988) that examine expiration-day effects of US index derivatives. Across all contract expirations since the inception of index futures, they find that the effects are remarkably consistent: index stock trading volume is abnormally high and observed price movements are small and within the bounds of transaction costs. Karolyi (1996) examines Nikkei 225 futures contract expirations, and, like Stoll and Whaley, concludes that the expiration of the Nikkei 225 futures induces abnormal trading volume but economically insignificant price effects. Another branch of stock index futures research examines the degree to which the stock index futures price and the stock index level are properly aligned through index arbitrage. Papers in this branch of the academic literature include MacKinlay and Ramaswamy (1988), Stoll and Whaley (1990b), Miller, Muthuswamy and Whaley (1994), and Abhyankar (1995). One reason for a divergence of the stock index futures price and the reported stock index level is that stock indexes are usually computed from the last trade prices of the component stocks.2 Because stocks do not trade continuously, the reported stock index is always a stale indicator of stock index portfolio value. Stock index futures prices, on the other hand, are always current. A second reason for divergence is that transaction costs limit index arbitrage of small price misalignments. This paper examines expiration-day effects of the All Ordinaries Share Price Index futures and discusses alternative settlement procedures. First, we provide the background on the Australian Stock Exchanges (ASX) All Ordinaries Share Price Index and its derivatives. In section 3, we describe the potential sources of expiration-day price effects. We summarise prior research on expiration effects in section 4. Our methods for measuring empirically the presence of expiration effects are discussed in section 5. The data are briefly described in section 6. Expiration volume effects are analysed in section 7. Our findings as to price effects of the fourteen expirations of the SPI futures between March 1993 and June 1996 are presented in section 8. Alternative settlement procedures are discussed in section 9. The conclusions and recommendations are presented in section 10.

2.

Australian Stock Index Futures

The ASXs All Ordinaries Index underlies the Sydney Futures Exchanges index futures contract. The AOI is a value-weighted index of approximately 320 of the ASXs largest stocks that make up over 95% of the market value of all Australian stocks. The index value began at 500 on 31 December 1979 and stood at about

2.

A notable exception to this rule is the FTSE-100 index, which is computed on the basis of bid/ask price midpoints.

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2330 in October 1996. The value of the index on day t is the prior days closing index value times the change in the market value of the index, that is It = Vt C It 1 , Vt B

where It is the index value on day t, IC1 is the closing index value on day t1, Vt is t the aggregate market value of the stocks in the index on day t, and Vt B is the base aggregate market value of the stocks for the beginning of day t. The base value reflects any overnight changes (between t1 and t) in the index composition due to delistings, additions, capital changes, and the like. Futures and options on the AOI have traded on the Sydney Futures Exchange since February 1983 and June 1985, respectively. Current contract specifications are provided in table 1. Table 1 Specifications of the Share Price Index (SPI) Futures and Futures Option Contracts Traded on the Sydney Futures Exchange
Futures on the All Ordinaries Share Price Index Contract Unit Minimum Tick Size Contract Months Last Trading Day Trading Hours A$25 times ASX All Ordinaries Share Price Index. One index point, except on the last trading day when the minimum is 0.1 index points. March, June, September, December. Last business day of the contract month. 9.50 a.m. 12.30 p.m. and 2.00 p.m. 4.00 p.m. 1 SYCOM : 4.40 p.m. 6.00 a.m.

Put and Call Options on the All Ordinaries Share Price Index Futures Contract Unit Minimum Tick Size Contract Months Last Trading Day Striking Price Exercise Trading Hours One All Ordinaries Share Price Index futures contract. Option prices are quoted at minimum intervals of 0.1 index points. March, June, September, December plus serial months. Last business day of the contract month. Set at intervals of 25 index points. May be exercised on any business day up to and including the expiration day. 9.50 a.m. 12.30 p.m. and 2.00 p.m. 4.00 p.m. 1 SYCOM : 4.40 p.m. 6.00 a.m.

Note:

1. Sydney Computerised Overnight Market.

The SPI futures has a quarterly expiration cycle (ie, March, June, September, December) and expires on the last business day of the contract month. The current

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minimum tick size is 1.0 index point except for the expiration month when it is 0.1 index point.3

3.

Sources of Expiration-Day Effects

Expiration-day price effects may arise from a combination of factors including the existence of index arbitrage opportunities, the cash settlement feature of index options and futures, the stock market procedures for accommodating the unwinding of arbitrage positions in the underlying index stocks, and attempts to purposely manipulate prices. This section discusses each of these possibilities. 3.1 Stock Index Arbitrage Index arbitrage links the price of the futures or option contract to the level of the underlying index. In the absence of transaction costs, the equilibrium relation between the index futures price, F, and the index level, S, is: F = S(1 + r d), (1)

where r is the riskless rate of interest and d is the dividend yield of the stock index portfolio over the remaining life of the futures.4 If actual prices deviate from this equilibrium (and the magnitude of the deviation exceeds transaction costs), arbitrageurs buy or sell the component index stocks and take an offsetting position in the index futures. If the futures price exceeds the right side of equation (1), for example, arbitrageurs sell index futures and buy index stocks. The simultaneous purchase of the basket of stocks in the index portfolio is called program trading. 3.2 Cash Settlement Index arbitrage positions are frequently unwound at the expiration of the futures contract. If an index futures expires at the close, the futures self-liquidates through cash settlement at the closing index level. The stock position, on the other hand, must be liquidated through trades in the marketplace. An arbitrageur who is long the underlying stocks and short the index futures contract must sell the underlying stocks at their closing prices. As long as the stocks are sold at the same prices used in calculating the index value for cash settling the futures contract, the arbitrageur exits his position risklessly, independent of the level of the prices at which the stocks are sold. If many arbitrageurs liquidate positions at the same time and in the same direction, price effects are possible. 3.3 Stock Market Procedures The severity of price effects on expiration day depends in part on the stock market procedures for accommodating order imbalances that may arise when arbitrage positions are unwound. If the underlying market for the index stocks is deep and
3. 4. The minimum tick size of the SPI futures was increased and the contract denomination reduced in 1993. For an analysis of these changes, see Martini and Dymke (1995). Equation 1 assumes that interest and dividends are paid at the maturity of the futures contracts.

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if suppliers of liquidity are quick to respond to selling or buying pressure, the price effects of large arbitrage unwindings will be small. If unjustified price effects were known to occur, knowledgeable investors would stand ready to buy underpriced stocks and sell overpriced stocksactions that would normally limit price effects to fall within the bounds of transaction costs. If market mechanisms are not well designed to offset sudden imbalances, however, the price effects may be substantial. In the case of index futures contracts that settle at the close, arbitrage positions must be unwound at closing prices. In the US, arbitrageurs place marketon-close (MOC) orders, indicating their desire to trade at the closing price, whatever it may be. If large MOC orders are received late in the day and investors to take the other side are difficult to locate, price effects are possible. Modifications in trading mechanisms such as requiring early placement of MOC orders, can reduce the risk of unexpected imbalances at the close. 3.4 Manipulation Expiration-day stock price effects may also arise from attempts to manipulate stock prices. Such attempts may occur directly in the way an arbitrage position is unwound or indirectly through arbitrage unwindings that benefit other positions. An index arbitrageur who is long stocks and short futures, for example, may try to profit directly by quietly selling a portion of his stocks prior to expiration and then forcefully selling the remaining position at the prices used to determine the futures settlement price. If the futures settlement price (at which the arbitrageur settles the short position) is successfully driven down to a level lower than the average price at which the long position in stocks is sold, the arbitrageur makes a profit in liquidating the arbitrage position. Many index arbitrageurs attempt to do this, not only at expiration but also on days prior to expiration. The risk in this strategy is self-evident: once stocks have been sold without also liquidating the corresponding amount of futures, arbitrageurs are no longer perfectly hedged, and they face basis risk. If stock prices were to rise and the futures contract to close higher, arbitrageurs would lose. This strategy also reduces the number of shares available for sale at the expiration point, consequently reducing the ability to influence the futures settlement price. An index arbitrageur might engage in indirect manipulation, not to benefit the arbitrage account but to benefit another account. Suppose, for example, a broker is instructed to buy stocks for one account (an order unrelated to index arbitrage) while, at the same time, is unwinding a long-stock/short-futures arbitrage position for another account. By selling the stocks forcefully at the prices used to determine the futures settlement price, the broker may lower stock prices for the benefit of the buyer. No harm is done to the index arbitrage account because the loss due to the decline in stock prices is offset by gain on the long stock index futures position. A broker confident that prices can be forced lower can also benefit by selling index futures or stocks prior to the expected price decline. The manipulation effort will fail and the effect on stock prices will be limited, however, if other knowledgeable investors are standing ready to buy at bargain prices and thereby keep prices from falling.

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4.

Prior Evidence on Expiration-Day Effects

In the period before June 1987, all US stock index futures and options cash settled at the closing price. Studies of expiration-day effects during this period found large volume effects and small price effects during the last hour of trading on quarterly expiration days (Stoll & Whaley 1986, 1987). Price effects were smaller when options alone expired. Starting with the June 1987 expiration, the CMEs S&P 500 futures contract settled at an index value calculated from the opening prices of the component stocks, while the CBOEs S&P 100 index options continued to settle at the close. Stoll and Whaley (1991) analyse the effect of this change in settlement procedures. They find substantial volume effects and small price effects around the time of expiration. Table 2 summarises the Stoll and Whaley findings. Table 2 Volume and Price Effects around Quarterly Expirations of the S&P 500 Futures Contract, January 1985 through June 1989
Number of Observations Volume1 Effects Pre June 1987 Expiration Days Non-Expiration Days Post June 1987 Expiration Days Non-Expiration Days Price Effects2 Pre June 1987 Expiration Days Non-Expiration Days Post June 1987 Expiration Days Non-Expiration Days Notes: 9 17 0.211% 0.056% 0.281% 0.012% 9 18 0.366% 0.124% 0.061% 0.002% 9 17 9.4% 5.5% 26.3% 8.5% 9 18 20.8% 8.5% 6.6% 8.7% Friday Close Friday Open

1. Volume is the percentage of two-day volume in index stocks trading in the last half hour before Friday close or in the first half hour of trading on Friday morning. 2. Price effects are the percent portfolio reversal in the half hour after expiration. Source: Stoll and Whaley (1991), tables II, III, V.

In the period before June 1987, when the S&P 500 futures contract expired at the close, volume in the last half-hour before the close averaged 20.8% of two-day volume on expiration days and 8.5% of two-day volume on non-expiration days. After the change, when the S&P 500 futures contract expired at the open, volume
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at the open averaged 26.3% of two-day volume on expiration days but only 8.5% on non-expiration days. In summary, the volume effects are extraordinary. Stoll and Whaley measure price effects by the extent to which the S&P 500 index price reverses after the expiration. In the period before June 1987, when the S&P 500 futures contract expired at the close, the average price of the S&P 500 stocks reversed on Monday after the Friday expiration by 0.366%. A reversal is a price decline (increase) followed by a price increase (decline). The reversal on expiration days compares with a reversal of 0.124 on non-expiration days, a net effect of 0.242%. Stoll and Whaley conclude that this effect is within the bounds of trading costs. For example, the minimum bid-ask spread, which is $0.125, amounts to 0.417% of the typical stock price of $35.00. Switching the expiration to the opening after June 1987 resulted in an observable, albeit small, price effect at the opening: 0.281% on expiration days versus 0.012% on non-expiration days. A price effect was also observed at Friday close, presumably because certain futures and options contracts continued to expire at the Friday close. Day and Lewis (1988) calculated implied volatilities from index option prices around index options and futures expirations in the period March 1983 to December 1986. They found a noticeable increase in implied volatility around both quarterly and monthly (non-quarterly) expirations. In an analysis of the behaviour of individual stocks on quarterly expirations in the period before 1986, Stoll and Whaley (1990a) found that stocks in the index behaved like non-index stocks: all stocks exhibited price reversals, but stocks in the index displayed a greater tendency to reverse in the same direction. The interpretation of expiration-day price effects depends on the standard against which the effects are measured. As Roll (1984) and Stoll (1989) have noted, price reversals are to be expected after transactions as prices move between bid and ask levels. Stoll (1988) compared expiration-day effects with various measures of market impact costs and found that . . . the average expiration-day price effect is roughly of the same magnitude as the price impact observed in a normal transaction. Nevertheless, policy makers remain concerned about price effects that are substantially in excess of the average. Expiration-day effects of index futures contracts in other countries have not been studied to the same degree as those in the US. The only exception is a comprehensive investigation of the Nikkei 225 index futures contract by Karolyi (1996). Applying methodology similar to that used by Stoll and Whaley (1991), Karolyi examines abnormal price and volume effects for Japanese stocks during the period May 1988 through November 1991. Consistent with the Stoll-Whaley findings, Karolyi documents abnormally large trading volume at the point of expiration and small but economically insignificant price effects (about 0.20%).5

5.

Procedure for Measuring Expiration-Day Effects

We measure two aspects of expiration-day effects: abnormal trading volume and abnormal price movements. Abnormal trading volume is measured by the ratio of
5. It is interesting to note that, in spite of Karolyis evidence, the settlement of the index futures was moved from the close to the open.

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the dollar trading volume in the last half-hour on expiration day to total dollar trading volume on that day. Evidence of abnormal trading activity in the stock market during the last half-hour of the futures contract life would be consistent with index arbitrage unwinding. To measure abnormal price movements, we compute (a) the variance of stock returns on expiration days compared to nonexpiration days, and (b) the degree to which index arbitrage unwinding drives stock prices away from their equilibrium levels. A larger variance on expiration days than on other days would reflect the presence of larger price changes. If large price changes are attributable only to unwinding activity, prices should rebound in the opposite direction after the futures contract has expired. We compare price reversals after expirations to price reversals after non-expiration days. In this section, we describe our measurement procedures. 5.1 Abnormal Trading Volume In this study, trading volume of an individual stock is defined as the sum of the dollar values of all trades in a particular interval, that is,
no. of trades

Trading volume =

i=1

price per sharei no. of sharesi.

(2)

Daily trading volume is the sum of the dollar values of all trades during the day, from market opening at 10.00 a.m. until market close at 4.00 p.m.6 Trading volume at the close is defined as the dollar value of all trades that occur in the last thirty minutes of trading of that stock. If the stock trades right up until the close at 4.00 p.m., this interval is defined as 3.30 p.m. 4.00 p.m. Where the stocks last trade is before the close, say, 3.45 p.m., the interval is defined as 3.15 p.m. 3.45 p.m. Relative trading volume at the close is then defined as the ratio of trading volume at the close to total daily trading volume. A relative trading volume figure of 10%, for example, means that 10% of the stocks trading volume took place in the last half-hour of the day. If trading took place at a uniform rate throughout the day, the relative trading volume figure should be 8.33% (ie, thirty minutes divided by six hours). To measure abnormal trading volume, a benchmark for what is normal is needed. In this study, normal trading volume is defined as relative trading volume at the close on the days exactly one and two weeks prior to the expiration day. For the March 1993 contract expiration on 31 March 1993, for example, the control group measures are computed for 24 March 1993 and 17 March 1993. To measure abnormal trading activity, we test for a meaningful difference between the average relative trading volume on expiration days and the average relative trading volume on non-expiration days for the same set of stocks. 5.2 Variance of Stock Returns To determine whether stock index expirations bring increased volatility to the stock market, we calculate the variance of the five-minute return in individual
6. During our sample period, the Australian Stock Exchange (ASX) and the Sydney Futures Exchange (SFE) closed early on four (pre-holiday) expiration days: 12/93, 3/94, 12/94 and 12/95.

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stocks on expiration days in comparison to non-expiration days. We also measure the variance of the five-minute return in the SPI futures contract price for expiration and non-expiration days. Five-minute returns are calculated on the basis of the last transaction price in each five-minute interval.7 5.3 Individual Stock Reversals Volatility of stock returns could reflect either new information or unwarranted volatility associated with expirations. New information would cause permanent price changes in stocks, whereas unwarranted volatility would cause temporary price changes. Temporary price effects are measured by the degree to which stock prices reverse after the futures contract expiration. One measure of reversal is the individual stock reversal, which is based on individual stock returns around the close. Stock is return before the close, R b,i, is defined as the return over the last thirty minutes of the day, that is, Rb,i = Pclosei Pclose30i , Pclose30i (3)

where P close30,i is stock is price thirty minutes before the market close on expiration day, and Pclose,i is stock is price at the close. Stock is return after the close, R a,i, is defined as the return from the close until the following mornings open, that is, Ra,i = Popeni Pclosei , Pclosei (4)

where P open,i is stock is price at the open on the following morning. Based on these two stock returns, an individual stock reversal is defined as: REVi =
Rai Rai

if Rbi < 0 if Rbi 0 .

(5)

The stock reversal REV i is positive when the sign of the stock return after expiration is the opposite of the sign of the return before expiration, and the stock reversal is negative when stock price movement after expiration continues in the same direction as before. The abnormal stock reversal is measured by using the sample of control group dates described earlier. A normal stock reversal is defined as the stock reversal observed on the days exactly one and two weeks prior to the expiration day. Stock reversals can be expected even on normal days as stock prices bounce between the bid and the ask.8 To measure the abnormal stock reversal, we test for a meaningful difference between the average reversal on expiration days and the
7. 8. If no trade takes place in an interval, the last transaction price from the preceding interval is used. The tick size is smaller in Australia than in the US (one Australian cent versus US 12.5). Although average stock prices are also lower (A$7 versus US$35), the percentage tick size is smaller in Australia and consequently the bid-ask bounce can also be expected to be lower.

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average reversal on non-expiration days for the same set of stocks. Average stock reversal is computed as:
1 n REV = n REVi . i=1

(6)

5.4 Portfolio Reversal The average stock reversal may overstate the size of any systematic disruption in the stock market since individual stocks may reverse in opposite directions. The average stock reversal can be positive (because of the bid-ask bounce) without there being a common reversal for all stocks. Unwinding of an arbitrage position requires purchases or sales of portfolios of stocks, which could generate a common reversal. To account for this possibility, we calculate a portfolio reversal, defined as:
Rap if Rbp < 0 REVp = R if Rbp 0 . ap

(7)

where 1 n 1 n Rb,p = n Rb,i and Ra,p = n Ra,i, i=1 i=1 and n is the number of stocks considered. The portfolio reversal would normally be less than the average stock reversal but would equal the average stock reversal when all stocks reverse in the same direction.

6.

Data

This study analyses the expiration-day effects of the fourteen SPI futures expirations during the period January 1993 through June 1996. The data used in this study were provided by the Sydney Futures Exchange (SFE) and the Australian Stock Exchange (ASX). Specifically, the SFE provided intraday trade prices for the SPI futures as well as the AOI, and the ASX provided trade-by-trade data for the twenty or so largest market capitalisation stocks in the AOI. A list of the stocks used in our analyses is provided in appendix A.

7.

Expiration-Day Volume Effects

The analysis of volume effects is based on data for a sample of the AOIs twenty or so largest stocks. Table 3 summarises the abnormal trading volume results for the fourteen expirations. For the 31 March 1993 expiration, for example, the sample consists of nineteen stocks, which is approximately 50% of the total market value of the AOI. On that day, the average proportion of total dollar trading volume occurring during the last thirty minutes of the day was 35.03%. In

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Table 3 Average Proportion of Total Daily Trading Volume Accounted for in the Last Half Hour of Trading on Expiration Days and Non-Expiration Days for Each SPI Futures Contract Expiration in the Period January 1993 through June 1996
Contract Month Expiration Days Relative Number of Trading Observations Volume 19 19 20 20 20 20 20 21 21 21 21 21 20 20 283 35.03% 30.77% 21.07% 28.52% 28.69% 20.13% 29.58% 40.47% 20.43% 28.74% 34.11% 43.54% 46.51% 23.31% 30.81% Non-Expiration Days Relative Number of Trading Observations Volume 38 38 40 40 40 40 40 42 42 42 42 42 40 40 566 17.89% 18.22% 18.71% 27.36% 23.33% 23.14% 18.25% 24.11% 19.67% 17.66% 22.50% 23.77% 17.94% 22.01% 21.07%

t-ratio

9303 9306 9309 9312 9403 9406 9409 9412 9503 9506 9509 9512 9603 9606 All

5.24 3.58 0.69 0.18 1.34 0.72 2.84 2.53 0.22 3.44 2.94 3.07 7.02 0.35 8.57

contrast, the average proportion for the non-expiration days, 17 and 24 March 1993, was 17.89%. The t-ratio reported in the last column, 5.24, indicates that the difference is significant in a statistical sense. In other words, the trading volume of index stocks at the close on the March 1993 expiration was significantly higher than on non-expiration days. The t-ratios of the other contract expirations indicate that the result is general. On eight of fourteen expirations, trading volume is significantly higher than normal. Of the remaining six, five show higher trading volume at the close, although the difference is not significant in a statistical sense. On one expiration, June 1994, trading volume at the close appears slightly lower than normal. The largest relative volume occurred on the March 1996 expiration which has been the subject of a regulatory inquiry. When all of the relative trading volume data are pooled, the average closing volume on expiration days is 30.81% as compared to 21.07% on non-expiration days. Index unwinding appears to induce abnormally high stock market trading. Whether this trading disrupts the stock market is addressed next.

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8.

Expiration-Day Price Effects

8.1 Expiration-Day Price Behaviour of the Reported Index and the Futures To provide a general understanding of the price movements during the most recent fourteen SPI futures contracts expirations, five-minute price levels for the AOI and the SPI futures are plotted for each expiration for the period from the open of trading on the day of expiration until noon on the day following expiration. The results are contained in appendix B. In addition, summary index price levels are provided in table 4. Table 4 Level and Returns of the All Ordinaries Share Price Index at the Expiration of the Nearby SPI Futures Contract
Contract Month 9303 9306 9309 9312 9403 9406 9409 9412 9503 9506 9509 9512 9603 9606 Expiration Expiration Day Open Day Close 1,678.3 1,718.3 1,952.3 2,154.6 2,091.3 1,975.2 2,030.6 1,932.7 1,884.8 2,034.1 2,118.8 2,199.7 2,236.8 2,241.9 1,667.4 1,739.0 1,963.9 2,172.8 2,051.3 1,988.8 2,028.1 1,912.8 1,906.5 2,016.0 2,135.7 2,200.6 2,231.4 2,242.1 Noon on Day Following Expiration 1,660.9 1,749.3 1,958.5 2,167.9 2,012.7 1,966.2 2,028.9 1,911.8 1,901.9 2,008.8 2,136.3 2,222.6 2,225.6 2,241.7 Open-toClose-to- Portfolio Close Return Noon Return Reversal 0.65% 1.20% 0.59% 0.84% 1.91% 0.69% 0.12% 1.03% 1.15% 0.89% 0.80% 0.04% 0.24% 0.01% Average 0.39% 0.59% 0.27% 0.23% 1.88% 1.14% 0.04% 0.05% 0.24% 0.36% 0.03% 1.00% 0.26% 0.02% 0.39% 0.59% 0.27% 0.23% 1.88% 1.14% 0.04% 0.05% 0.24% 0.36% 0.03% 1.00% 0.26% 0.02% 0.19%

To interpret the figures, consider the March 1993 expiration. On this expiration day, the AOI opened at 10.00 a.m. at a level of 1678.3. It increased slightly and then proceeded to fall steadily throughout the day. Shortly after 2.00 p.m. the index began to rise, and then fell modestly by the close of trading at 4.00 p.m. The SPI futures price series begins before the index because the futures market opens ten minutes earlier (at 9.50 a.m.). The futures price movements are similar to the index during the day, except that no futures prices appear between 12.30 p.m. and 2.00 p.m. because the futures market is closed.9 The futures market closed at
9. In a normal day of trading, the SPI futures contract does not trade between 12.30 p.m. and 2.00 p.m. On days in which the stock market closes at 1.00 p.m. due to an upcoming holiday, the futures market trades past 12.30 p.m. until 1.10 p.m. and then closes for the day. Four early closures are included in our sample: 12/93, 3/94, 12/94 and 12/95.

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4.10 p.m., ten minutes after the stock market. Note that the last reported futures price of the day and the last reported index level are the same, reflecting the current cash settlement procedure for the SPI futures. Note also that no futures prices appear on the day following expiration since the futures contract has expired. We first calculate the variance of five-minute returns of the SPI futures contract on expiration days and on non-expiration days. To our surprise, as indicated in table 5, the average variance over the fourteen expiration days is less than the average variance over fourteen non-expiration periods. Table 5 Variance of Five-Minute Returns of the SPI Futures Contract on Expiration Days and Non-Expiration Days in the Period January 1993 through June 1996
Average Return Variance ( 10 ) Contract Month 9303 9306 9309 9312 9403 9406 9409 9412 9503 9506 9509 9512 9603 9606 Mean Expiration Days 0.000477 0.000333 0.000239 0.000833 0.001749 0.000608 0.000481 0.000440 0.000691 0.001111 0.000810 0.000326 0.000451 0.000740 0.000664 NonExpiration Days 0.000770 0.000718 0.000592 0.000606 0.001307 0.001103 0.000519 0.001033 0.000485 0.001192 0.000909 0.000515 0.000924 0.000353 0.000788
3

In ten of the fourteen cases, the within-day variance of five-minute returns is less on expiration days than on non-expiration days. This failure to find expiration-day volatility may reflect the fact that volatility occurs near the close rather than throughout the entire day. Price of individual stocks near the closing is examined later in this study. To gauge whether the stock market reversed as a result of the expiration of the futures, we compare the open-to-close return for the AOI on expiration day with the close-to-noon return on the day following expiration. These data are in table 4. For the March 1993 expiration day, the AOI fell from 1678.3 to 1667.4 for an open-to-close return of 0.65%. From the close on expiration day to noon the
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following day, the return was 0.039%. Since both returns are negative, the portfolio reversal is negative. For this expiration, the index level did not reverse after expiration, indicating that there were no abnormal effects associated with the expiring futures. Scanning the portfolio reversals of the AOI reported in table 4, we find that virtually no reversal appears to be of consequence. More reversals are negative than positive (ie, eight of fourteen), and the average reversal across all expirations is negative (ie, 0.19%). Only reversal for June 1994 appears large and positive. The market rose by 0.69% on expiration day, and then fell by 1.14% by noon on the day following the announcement. Examination of the figure for the June 1994 expiration (in appendix B) clarifies the event. The figure shows that the stock market opened higher on the expiration day. Recall that the reported index level is computed on the basis of last trade prices, and the first computation made at the beginning of the day is based primarily on the previous days closing levels. Within minutes the index began trading at a level of about 1988, and it stayed there most of the day. Attributing this pattern of index movement to the unwinding of stock index arbitrage positions is difficult. The March 1996 expiration, which has been the subject of a regulatory investigation, shows a continuation rather than a reversal. The sharp price decline at the markets close was not reversed the following Monday. Holding constant other factors, this price pattern implies that the closing price was not an abnormal price. If it had been, market forces would have caused the price to reverse on the Monday after the expiration day. On the other hand, if other factors were not constantif, for example, bad news arrived that kept prices from reboundinga reversal may have been obscured. It is difficult to draw conclusions about a single expiration, but taken together the data on all the expirations in our sample show no indication of an expiration effect. 8.2 Expiration-Day Price Reversals in Individual Stocks The figures in appendix B provide an overall view of the behaviour of the index and the index futures price on the expiration day and the day thereafter. A more accurate picture, however, can be obtained by looking at individual stocks. If the unwinding of index arbitrage positions disrupts the stock market, increased volatility and significant price reversals should be observed in individual stocks. The volatility of five-minute stock returns on expiration days and nonexpiration days is first measured for each of the twenty or so stocks in the sample for each of the fourteen expiration days. Table 6 presents the average variance across the stock for each expiration day. The overall average variance on expiration days (0.00062) is nearly twice the overall variance on non-expiration days (0.00034), and the difference is statistically significant on eight of the fourteen days. On two of the remaining days (March and June 1996 expirations), the average variance is less on the expiration day than on the corresponding nonexpiration day. Because expiration-day volatility tends to occur near the close, the return volatility of the largest stocks is also examined over the last two hours of expiration days. The results in table 7 are similar to those in table 6. The average variance of five-minute returns in the last two hours of trading is about twice as large on expiration days as on non-expiration days. The difference is statistically significant in nine of fourteen days.
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Table 6 Average Five-Minute Stock Return Variance for Largest Stocks in the AOI on Expiration Days and Non-Expiration Days for Each SPI Futures Contract Expiration in the Period January 1993 through June 1996
Expiration Days Contract Month Number of Observations 19 19 20 20 20 20 20 21 21 21 21 21 20 20 Average Return Variance 3 ( 10 ) 0.007234 0.004254 0.007586 0.006494 0.006909 0.006950 0.003226 0.003921 0.010887 0.009184 0.007978 0.006099 0.002996 0.002842 0.006183 Non-Expiration Days Number of Observations 38 38 40 40 40 40 40 42 42 42 42 42 40 40 Average Return Variance 3 ( 10 ) 0.003342 0.002632 0.003247 0.001589 0.002807 0.004550 0.002833 0.001789 0.002479 0.008902 0.002412 0.002930 0.003159 0.005269 0.003424 * * * * * * * *

9303 9306 9309 9312 9403 9406 9409 9412 9503 9506 9509 9512 9603 9606 Mean Note:

* = statistically significant.

These results indicate some increased volatility in individual stock returns that is not reflected in the volatility of index futures returns in table 5, presumably because the stock fluctuations are idiosyncratic. The increased volatility in individual stocks could come directly as a result of index expiration or indirectly as a result of the higher level of volume on expiration days. To assess whether there is a direct effect of the index expiration on stock prices, we next examine if closing prices on expiration days are temporary deviations from equilibrium. Temporary deviations are inferred if the price change at the close is reversed the following morning. If the higher volatility of individual stocks on expiration days is directly attributable to index futures expirations that temporarily drive prices away from equilibrium, we should observe systematic reversals. On the other hand, if the higher volatility is simply the result of greater volume or other factors, systematic reversals would not be observed. Abnormal price effects are measured by comparing stock price changes in the last thirty minutes of the expiration day to stock price changes from the

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Table 7 Average Five-Minute Stock Return Variance for Largest Stocks in the AOI During the Last Two Hours on Expiration Days and Non-Expiration Days for Each SPI Futures Contract Expiration in the Period January 1993 through June 1996
Expiration Days Contract Month 9303 9306 9309 9312 9403 9406 9409 9412 9503 9506 9509 9512 9603 9606 Mean Note: Number of Observations 19 19 20 20 20 20 20 21 21 21 21 21 20 20 Average Return Variance 3 ( 10 ) 0.007719 0.007825 0.015922 0.004824 0.006450 0.007407 0.003106 0.005127 0.017195 0.004625 0.005851 0.003574 0.005359 0.003879 0.007062 Non-Expiration Days Number of Observations 38 38 40 40 40 40 40 42 42 42 42 42 40 40 Average Return Variance 3 ( 10 ) 0.003235 0.003379 0.002855 0.000978 0.002653 0.005956 0.002894 0.001433 0.002383 0.008619 0.002923 0.001370 0.004938 0.002245 0.003276 * * * * * * * * *

* = statistically significant.

expiration-day close until the following mornings opening transaction price. A price change between the close and the opening that reverses the price change in the last thirty minutes of the prior day would be evidence of an expiration effect. Summary results, classified by expiration day, are reported in table 8. To understand how to interpret these results, again consider the March 1993 expiration. On this expiration day, the average reversal for the stocks in the index is 0.24%. This means that the index stocks did reverse, on average, but not by very much. Indeed, this expiration reversal is less than the comparable average stock reversal on the non-expiration days, 0.53%. The t-ratio reported in the last column, 1.42, indicates that there is no significant difference between the reversals observed on expiration days and those observed on non-expiration days, at least for the index stocks examined at the March 1993 contract expiration. The interpretation of the results for the other contract expirations is similar. Most of the expiration days and non-expiration days have positive reversals, and the difference between their levels is not meaningful statistically. Across all contracts, the average stock reversal is 0.11% on expiration days, but this value is not significantly different from the average reversal of 0.05% on non-expiration days.
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Table 8 Average Stock Reversal for Largest Stocks in the AOI on Expiration Days and Non-Expiration Days for Each SPI Futures Contract Expiration in the Period January 1993 through June 1996
Expiration Days Contract Month 9303 9306 9309 9312 9403 9406 9409 9412 9503 9506 9509 9512 9603 9606 All Number of Observations 19 19 20 20 20 20 20 21 21 21 21 21 20 20 283 Average Stock Reversal 0.24% 0.10% 0.33% 0.28% 0.07% 0.70% 0.05% 0.07% 0.06% 0.06% 0.08% 0.10% 0.33% 0.13% 0.11% Non-Expiration Days Number of Observations 38 38 40 40 40 40 40 42 42 42 42 42 40 40 566 Average Stock Reversal 0.53% 0.19% 0.44% 0.20% 0.04% 0.17% 0.04% 0.08% 0.06% 0.09% 0.03% 0.19% 0.00% 0.09% 0.05% tratio

1.42 0.18 1.01 0.54 0.03 0.52 0.09 0.01 0.00 0.15 0.05 0.10 0.33 0.04 0.68

Aside from the fact that the average stock reversals are no different on expiration days than non-expiration days, the size of the reversals are small in economic terms. Consider, for example, the March 1993 expiration when index stocks had an average reversal of 0.24%. The average share price of the nineteen stocks included in the sample on this day was about $7.00. This means that the size of the reversal is a mere 1.7. The average stock reversal across expirations was 0.11%. Using a $7 share price, the typical reversal amounts to less than a penny (0.77). The results in table 8 imply that unwinding of stock index arbitrage positions does not disrupt the stock market, at least insofar as the market is reflected in the price movements of high capitalisation stocks. 8.3 Expiration-Day Portfolio Price Reversals Return reversals in individual stocks are to be expected as stock prices bounce between the bid and ask sides of the market. Consequently the small reversals found for individual stocks are a surprise. Expiration day price effects can be problematical insofar as all stock reverse in the same direction. If stocks reverse in the same direction, the reversal in the return of a portfolio of stocks would be significant. Since individual stock reversals were not found, a portfolio reversal is unlikely. Nevertheless, for completeness, portfolio return reversals were calculated
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for the sample of the twenty largest stocks. The data in table 9 confirm that no evidence exists of any systematic portfolio reversals. The average reversal over the fourteen expirations is 0.05%, essentially a zero effect. Table 9 Average Portfolio Reversal for Largest Stocks in the AOI on Expiration Days and Non-Expiration Days for each SPI Futures Contract Expiration in the Period January 1993 through June 1996
Expiration Days Contract Month Number of Observations 19 19 20 20 20 20 20 21 21 21 21 21 20 20 Average Portfolio Reversal 0.32% 0.11% 0.35% 0.34% 1.02% 0.65% 0.02% 0.32% 0.26% 0.29% 0.00% 0.25% 0.33% 0.24% 0.05% Non-Expiration Days Number of Observations 38 38 40 40 40 40 40 42 42 42 42 42 40 40 Average Portfolio Reversal 0.50% 0.04% 0.96% 0.54% 0.31% 0.01% 0.34% 0.55% 0.37% 0.10% 0.34% 0.17% 0.02% 0.01% 0.08%

9303 9306 9309 9312 9403 9406 9409 9412 9503 9506 9509 9512 9603 9606 Average

8.4 Summary of SPI Expiration-Day Effects The empirical results provided in this section are consistent with the studies of the US and Japanese markets: trading volume in the stock market at the time of expiration is abnormally high, but the associated price effects are economically insignificant. Indeed, the average price reversal for Australian Stock Exchange index stocks on expiration days is insignificantly different from zero. Based on this evidence, a change in the procedures used to settle the SPI futures contract does not appear to be warranted. Nonetheless, given the SFEs recent change in settlement to a call auction market fifteen minutes after the stock market close, it is worthwhile to consider the merits of alternative settlement procedures.

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9.

Alternative Settlement Procedures

As noted earlier, index futures expiration-day effects occur primarily because index arbitrage positions are not self-liquidating. While the futures contract settles automatically, the arbitrageur is forced to liquidate his stock position on his own. The process by which stock positions are liquidated can influence stock prices. In turn, the process by which stock positions are liquidated is influenced by the rules for determining the index futures settlement price. The purpose of this section is to describe the merits of alternative settlement procedures in light of the potential for trading abuses. 9.1 Delivery One method for contract settlement is delivery. In general, delivery contracts are more common than cash settlement contracts. If the underlying stocks were to be delivered by the short to the long, the root cause of potential price effects would be eliminated. An arbitrageur who bought (sold short) stock and sold (bought) futures would simply deliver (take delivery of) the underlying stocks against the futures. Without concentrated demand to buy or sell index stocks from index arbitrage positions, no price effect would be induced.10 As a practical matter, delivery is not possible because of the cost and difficulty of transferring a large portfolio of stocks. The AOI contains about 320 stocks. Settlement by delivery would require the delivery of 320 stocks in the same proportions as they exist in the index. While technically feasible, the cost of making such delivery is likely to outweigh the benefit. Consequently, all active stock index futures contracts call for cash settlement.11 9.2 Cash Settlement Procedures Ruling out delivery as a viable means for settling an index futures contract leaves cash settlement. Under cash settlement, the choices are few: whether to use a single price or an average price, whether to settle at the open or at the close, and whether to make other changes in stock market procedures. To begin, the current cash settlement procedures of the worlds major index futures contracts are summarised in table 10. 9.2.1 Single Price The US, German, and Japanese index futures contracts settle at an index level based on a single price for each of the index stocks. For some contracts, the single price is the opening price for the day; for others, it is the closing price. Ideally, the settlement price should reflect the true condition of the market and should be based on reasonable depth of trading. Typically, the stock market exhibits greater trading volume and depth at the open and the close than at other times of the day, so basing a settlement index level on prices at these times makes sense.

10. Other delivery problems might arise, however. For example, in a short squeeze (where the shorts have difficulty in acquiring the stock for delivery), stock prices might temporarily be forced up. 11. Karolyi (1996) notes that the Osaka Exchanges Kabusaki fifty index futures contract called for delivery of 1,000 shares of each of the fifty largest stocks in the Nikkei index. The contract was later changed to permit cash settlement.

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Table 10 Cash Settlement Procedures for Selected Index Futures and Index Options Contracts
Settlement Price Futures Contract S & P 500 (Chicago Mercantile Exchange) All Ordinaries Share Price Index (Sydney Futures Exchange) FTSE 100 (London International Financial Futures Exchange) CAC-40 (MATIF) DAX (Deutsche Terminboerse) Nikkei 225 (Osaka Securities Exchange) Option Contract S & P 100 (Chicago Board Options Exchange) American-style option exercisable any day at a settlement price calculated from the closing prices of the index stocks. Special S& P 500 index value calculated from the opening prices of each of the stocks in the index. If stock fails to trade on the expiration day, the prior days close is used. Closing value of the ASX All Ordinaries Share Price Index on the last day of trading calculated to one decimal place from the closing prices of the component stocks. Settled at 10.30 a.m. on the basis of the FTSE cash index values averaged over the period 10.10 a.m. 10.30 a.m. Settled at 4.00 p.m. on the basis of the CAC40 cash index values averaged over the period 3.40 p.m. 4.00 p.m. DAX cash index value calculated from the opening prices of the index stocks on the Frankfurt Stock Exchange. Settled at special opening price calculated from the opening prices of the Nikkei index stocks.

From a users standpoint, a single price provides the greatest benefit. The effectiveness of arbitrage and hedging activities depends on convergence between cash and futures prices. With a single settlement price, convergence is ensured. This means that the arbitrageur has no basis risk whatsoever since underlying stock positions are unwound at the stock prices that match the price at which the futures contract settles. A hedger, who may have basis risk arising from imperfect correlation with an underlying position, need not be concerned about additional basis risk arising out of a lack of convergence at settlement. The decision whether to use the opening or closing price in contract settlement rests on the desire that the buying and selling interest be representative of the markets true condition and not be unduly influenced by the expiration itself. At the close, the sale of stocks as part of large index arbitrage unwindings can put price pressure on stocks because there is insufficient time to locate the other side of the trade. At the opening, however, the sale of stocks can more easily be postponed until the other side can be found. The opening of a stock under selling pressure, for example, can be postponed until sufficient numbers of buyers are located. Many markets open with an auction procedure that tabulates buy and sell orders and disseminates information on order imbalances to the market in order to attract additional traders. Stoll and Whaley (1991) evaluate the effectiveness of the CMEs decision to move from closing prices to opening prices in the settlement of the S&P 500 futures and futures options. They conclude that
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empirically the change had little effect on the size of the stock reversals. This may be attributable to the role of the specialist and the fact that the opening procedure on the NYSE is not a fully disclosed auction market. Aside from the market depth consideration, the decision about whether to use opening or closing prices has another elementperceived market integrity. The reported index level disseminated throughout the day is based on the last trade prices of the index stocks. If settlement occurs at the close, the settlement price is computed on the basis of the closing prices of each of the stocks and equals the last reported price for the index on that day. Settlement at the open, however, is different. While the index continues to be reported as normal, there is a special index level computed on the basis of the opening price of each stock. Since all stocks do not open at the same time, this settlement price is not available until the last index stock has opened and may be different from any index level reported for the trading day. For the March 1993 S&P 500 futures contract expiration, for example, the settlement price based on the opening prices of each of the stocks was 454.19. The highest reported level of the S&P 500 on that day, however, was about 453. Although hedgers and arbitrageurs are not harmed by this phenomenon, the fact that the settlement price is well away from any reported index level for the day may be regarded with suspicion by some market participants. Stock market procedures affect the possibility of manipulating a single settlement price. So long as mechanisms are available to respond to sudden buying or selling pressure, a single price settlement is no easier to manipulate than are other settlement procedures. Settlement at the opening has the advantage that the opening can be delayed if buying or selling pressure threatens to push a stocks price away from equilibrium; the disadvantage is that the index settlement value will differ from the regularly reported index level. Settlement at the closing price is less confusing for investors because the index settlement value is the same as the closing index level; however, late unannounced buying or selling pressure may be more difficult to deal with. Adjustments in stock market procedures such as early warning of large index unwindings can help overcome some of these drawbacks. 9.2.2 Average Price The UK and French index futures settle at an average price of the underlying index calculated over a period of time. The UK price is the average price of the FTSE index calculated over the period 10.10 p.m. 10.30 a.m. The CAC-40 price is an average of index prices over the period 3.40 p.m. 4.00 p.m. The average price is used on the grounds that an average is more difficult to influence than a single price. Also an average may be more appropriate where the stock market is a dealer market, as in the UK, because a dealer market is not well suited to arriving at a single auction price that reflects the interests of all market participants. From the perspective of hedgers and arbitrageurs, an average price is less desirable than a single price because it introduces basis risk. To unwind their positions, index arbitrageurs must buy or sell the proper amount of their stock positions at each of the index prices that are averaged in arriving at the settlement price. This is a difficult and impractical task. Since there is no way of guaranteeing that the stock position will be unwound at the futures contract settlement price, basis risk occurs.
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Some argue that an average price is more difficult to manipulate than a single price, but this is not necessarily the case. If the total potential volume available to determine the single price is the same as the potential volume of the twenty trades determining the average price, influencing each of twenty prices that are used to calculate an average over a twenty-minute interval should be as easy as influencing a single price at the end of twenty minutes. The average settlement price has the advantage that the evolution of the settlement price can be observed. If index arbitrage unwindings put selling pressure on stock prices, the first of twenty index prices will be lower. Observing this price, value investors who judge the price to be too low can enter buy orders at favourable prices. The same response from value investors is possible, however, in a single price settlement in which opportunity exists to search for more buyers or sellers before the final price is determined. A single price settlement has the advantage of focusing all trading interest at one point such as the open or close. Although a manipulator knows that point, so do all the value traders who wish to take advantage of mispricing. The presence of value traders keeps prices from deviating very much from their equilibrium values. The average settlement price, like the opening settlement price, may be dramatically different from reported index levels. Suppose the settlement value were based on five index values observed over the last five minutes. Assume those values were 100, 99, 98, 97 and 96. The reported index level at the end of the interval is 96 while the settlement price is 98. This type of discrepancy may cause investor confusion, thereby inducing a perception that markets are not operating fairly. The average settlement price seems most appropriate when the underlying stock market is a dealer market in which buying and selling interests are not directly exposed. The quotes of a dealer at a moment of time may not reflect the market clearing price that would result if all buyers and sellers decided to trade with that dealer. Quotes are indicated prices, and it may be desirable to collect a sample across dealers and through time of such indications. The need for an average settlement price is less clear in a continuous auction market where all buying and selling interest can be reflected in a single market clearing price. 9.3 Stock Market Procedures Index settlement procedures are influenced by stock market procedures, and stock market procedures, in turn, affect the viability of alternative index futures settlement procedures. A single price settlement requires a mechanism that allows index arbitrageurs to unwind at that price and, at the same time, provides liquidity for the potentially large volume of trading at the point of index expiration. US markets allow traders to place market-on-close (MOC) orders or market-on-open (MOO) orders. As their names imply, such orders are market orders that are to be traded at the closing price or opening price of the stock. They facilitate the unwinding of an arbitrage position. An issue is whether liquidity to offset arbitrage unwindings is supplied by the stock market. Can a large MOC order to sell placed in the last five minutes of trading, for example, be traded at reasonable prices, or will market prices be depressed? Stock market mechanisms can be modified to facilitate the provision of liquidity in response to large arbitrage unwindings. For example, it may be
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desirable to require early disclosure of MOC (or MOO) orders by arbitrageurs. If the rest of the market does not know large sell orders will be placed it may not have sufficient time to respond. A remedy for such a problem might be that MOC or MOO orders will be honoured only if placed thirty minutes in advance. A continuous auction market (such as the NYSE or the ASX) is one in which market orders are executed at resting limit orders.12 The risk is that a market order placed to unwind an index arbitrage position will overwhelm resting limit orders and cause a temporary price effect. Traders should be given an opportunity to respond to this opportunity to buy at favourable prices. An alternative to a continuous auction market is a call auction market. A call auction market accumulates orders over some period of time and executes at a single price that maximises the volume of trade. The outcomes of a call auction are sensitive to the design of the auction market. The key to a reasonable outcome is prior disclosure of the likely market clearing price and the opportunity for traders to change their orders. Transparency of the auction is also desirable because it eliminates the possibility that certain participants have private information about the orders submitted to the auction. The opportunity to re-contract gives the market a chance to supply liquidity if the indicated clearing price deviates from equilibrium. Traders may attempt to game call markets, however, by placing false orders and withdrawing them at the last minute, and many traders will wait until the last minute to place their orders. It may therefore be necessary to provide incentives for traders to place orders in a timely fashion and not to withdraw them. The introduction of a call auction at the close would require suspension of the continuous market. Consequently, a call auction mechanism is most natural at the open, and is an argument for using the open rather than the close as a settlement price. In addition at the open, liquidity is provided as traders have the opportunity to accumulate orders overnight. Finally, the design of the auction is complicated by the fact that auctions occur simultaneously in many correlated stocks. These auctions must be designed so that information about the market clearing price in one stock can be used to provide information about the optimal market clearing price in another stock. Empirical evidence in Amihud and Mendelson (1987) and Stoll and Whaley (1990c) shows that return volatility on the NYSE is greatest around the auctiontype opening than at other times. This reflects the difficulty of correctly reflecting in the opening auction price the overnight news in a stock as well as the information conveyed by the opening price of other stocks. Volatility also results from the fact that the auction is usually a one-shot auction with limited transparency and limited pre-opening disclosure. The recently introduced ASX closing auction, which takes place fifteen minutes after the market close, has the advantage that not much new information must be incorporated in the auction price, but it has the disadvantage that volume may be less than it would be in an opening auction. 9.4 Other Issues Other suggestions have been made to deal with expiration price effects. These include disclosure by index arbitrageurs, telescoping of positions, and changes in
12. For a recent paper on the Australian stock market, see Aitken and Frino (1996).

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expiration days. Arbitrageurs might be required to disclose positions so that the market could anticipate the direction of unwindings. Such a requirement, aside from being an administrative nightmare, would be difficult to enforce. How would the reports be made and to whom? Telescoping positions is the reduction of arbitrage positions as expiration is approached. Such a requirement, also an administrative nightmare, would impose basis risk on arbitrageurs who would be forced to unwind positions early. Some have argued that a Friday expiration is particularly troublesome because of the additional uncertainty of the upcoming weekend. The SPI futures do not necessarily expire on Friday (although ten of the fourteen expirations in our sample are on Friday). If settlement is at the opening, traders have the rest of the day to trade out of a position before the weekend.

1 0 . Conclusions and Recommendations

The empirical investigations of the SPI futures contract expirations conducted in this study indicate that, while some expiration-day volume effects are evident in the Australian stock market, there is no evidence of a systematic price effect. The absence of any abnormal price movement is inconsistent with the evidence reported for the United States and Japan, where small, economically insignificant, price movements were observed. Abnormal price effects due to an expiration are measured by the extent to which prices reversereturn to normalafter the expiration. The average reversal in a portfolio of the top twenty or so Australian stocks is negligible, reflecting perhaps a lesser degree of index arbitrage activity in Australia or the fact that index arbitrage unwindings occur before the expiration day. In summary, settling the SPI futures at the close appears to have worked satisfactorily. Beginning with the March 1997 expiration, the SPI futures have cash-settled at the prices of the stocks established in a special call auction market fifteen minutes after the stock market close. Whether this new procedure is the best among the available alternatives is open to debate. This study analyses the two basic alternative cash settlement proceduresa single price settlement and an average price settlement. The single price settlement focuses all buying and selling interest at one known point in time. This leads to depth of trading and reduces the chance that the price will deviate from equilibrium. Settlement at a single price also eliminates basis risk because hedgers can guarantee that the unwinding of the stock position and futures contract position takes place at the same price. The average price settlement tends to be used where the underlying market is a dealer market. In view of the fact that the Australian stock market is a computerised continuous auction market, the single price settlement appears more appropriate than the average price settlement. The average price procedure also has the disadvantage that it introduces basis risk. Single price settlement can take place either at the opening or at the close. Each approach has its benefits and costs. The benefit of a special index opening price as the settlement price is that the opening can be postponed until supply and demand are in balance. The disadvantage is possible confusion among investors because the regular index value differs from the special index value used to settle futures contracts. The closing price has the disadvantage that buying or selling pressures may be difficult to handle when little time is left at the end of the trading
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day. It has the advantage that the index settlement value and the regularly disseminated index are the same. Both procedures seem to work reasonably well according to experience in the United States. A single price settlement can be facilitated by using a call auction mechanism for trading the stocks underlying the index. A call auction aggregates orders over time and executes orders at a single price that maximises volume of trade. A call auction is most natural at the open, at which time overnight orders have also accumulated. The outcome of the call auction is, however, sensitive to its design. Care should be taken to give market participants an opportunity to observe the likely clearing price and to re-contract. Traders also need incentives to place orders in a timely fashion and not to withdraw them. Markets are remarkably adaptive. If expiration-day price effects were to occur, value traders looking for favourable prices would be ready to provide liquidity. Critical to successful settlement is that stock market mechanisms be designed to make it easy for traders to respond quickly if large volume pushes prices away from equilibrium. (Date of receipt of final typescript: July 1997 Accepted by Tom Smith, Area Editor.)

References
Abhyankar, A.H. 1995, Return and volatility dynamics in the FTSE 100 stock index and stock index futures markets, Journal of Futures Markets, vol. 15, Jun., pp. 45788. Aitken, M. & Frino, A. 1996, The accuracy of the tick test: Evidence from the Australian stock exchange, Journal of Banking and Finance, vol. 20, Dec., pp. 171529. Amihud, Y. & Mendelson, H. 1987, Trading mechanisms and stock returns: An empirical investigation, Journal of Finance, vol. 42, Jul., pp. 53353. Day, T. & Lewis, C. 1988, The behavior of the volatility implicit in the prices of stock index options, Journal of Financial Economics, vol. 22, Oct., pp. 10322. Froot, K. & Perold, A. 1995, New trading practices and short run market efficiency, Journal of Futures Markets, vol. 15, Oct., pp. 73165. Karolyi, A.G. 1996, Stock market volatility around expiration days in Japan, Journal of Derivatives, vol. 4, Winter, pp. 2343 MacKinlay, A.C. & Ramaswamy, K. 1988, Index futures arbitrage and the behavior of stock index futures prices, Review of Financial Studies, vol. 1, Summer, pp. 13758. Martini, C.A. & Dymke, R.J. 1996, Liquidity in the Australian SPI futures market following a redenomination of the contract, in Seventh Annual Asia-Pacific Futures Research Symposium Proceedings, Part II, Fall, Chicago Board of Trade, Chicago, pp. 5582. Miller, M., Muthuswamy, J. & Whaley, R. 1994, Mean reversion of S& Ps 500 index basis changes: Arbitrage-induced or statistical illusion? Journal of Finance, vol. 49, Jun., pp. 479513. Roll, R. 1984, A simple implicit measure of the bid-ask spread in an efficient market, Journal of Finance, vol. 39, Sep., pp. 1,12739. Stoll, H.R. 1988, Index futures, program trading and stock market procedures, Journal of Futures Markets, vol. 8, Aug., pp. 391412.

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Stoll, H.R. 1989, Inferring the components of the bid-ask spread: Theory and empirical tests, Journal of Finance, vol. 44, Mar., pp. 11534. Stoll, H.R. & Whaley, R.E. 1986, Expiration day effects of index options and futures, Monograph Series in Finance and Economics, Monograph 19863. Stoll, H.R. & Whaley, R.E. 1987, Program trading and expiration day effects, Financial Analysts Journal, vol. 43, Mar.Apr., pp. 1628. Stoll, H.R. & Whaley, R.E. 1990a, Program trading and individual stock returns: Ingredients of the triple witching brew, Journal of Business, vol. 63, Jan., pp. S165S192. Stoll, H.R. & Whaley, R.E. 1990b, The dynamics of stock index and stock index futures returns, Journal of Financial and Quantitative Analysis, vol. 25, Dec., pp. 44167. Stoll, H.R. & Whaley, R.E. 1990c, Stock market structure and volatility, The Review of Financial Studies, vol. 3, Spring, pp. 3771. Stoll, H.R. & Whaley, R.E. 1991, Expiration-day effects: What has changed? Financial Analysts Journal, vol. 47, Jan.Feb., pp. 5872.

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December 1997

Appendix A
All Ordinaries Share Price Index Stocks Used the Analyses of Abnormal Trading Volume and Price Behaviour
Contract Months Ticker Stock Weight (%) AMC ANZ BHP BIL BOR CBA CCL CML CRA CSR FBG FLC LLC NAB NCP NCPDP PDP WBC WMC WOW WPL AMCOR Ltd Australia and New Zealand Bank Broken Hill Properties Brambles Industries Boral Ltd Commonwealth Bank Australia Coca-Cola Amatil Coles Myer Ltd CRA Ltd CSR Ltd Fosters Brewing Fletcher CHA Lend Lease Corp National Australia Bank News Corp Ltd News CorpPref PAC Dunlop Ltd Westpac Banking WMC Ltd Woolworths Ltd Woodside Petroleum Total 1.506 2.981 10.570 1.273 1.041 1.660 2.554 1.472 3.836 1.342 1.398 0.982 1.519 5.508 3.969 1.650 0.853 3.453 3.038 0.962 1.561 53.128 1993 M J 1994 1995 1996 S D M J S D M J S D M J

19 19 20 20 20 20 20 21 21 21 21 21 20 20

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Stoll & Whaley: EXPIRATION-DAY EFFECTS OF SPI FUTURES

Appendix B
Plots of SPI Futures Prices and AOI Levels on Expiration Days During the Period, March 1993 through June 1996 Prices are at five-minute intervals from the open on the expiration day to noon on the day following expiration. The AOI levels are plotted as a solid bold line, and the SPI futures prices are plotted as a light line. Figure B1 March 1993
1,700

1,690

1,680

1,670

1,660

1,650 open 12:30 2:00 close open noon

AOI

SPI Futures P

167

AUSTRALIAN JOURNAL OF MANAGEMENT Figure B2 June 1993

1,760

December 1997

1,750

1,740

1,730

1,720

1,710 open 12:30 2:00 close open noon

Figure B3 September 1993

1,990

1,980

1,970

1,960

1,950

1,940 open 12:30 2:00 close open noon

AOI

SPI Futures P

168

Vol. 22, No. 2

Stoll & Whaley: EXPIRATION-DAY EFFECTS OF SPI FUTURES Figure B4 December 1993

2,190

2,180

2,170

2,160

2,150

2,140 open close open noon

Figure B5 March 1994

2,100

2,080

2,060

2,040

2,020

2,000 open close open noon

AOI

SPI Futures P

169

AUSTRALIAN JOURNAL OF MANAGEMENT Figure B6 June 1994

2,000

December 1997

1,990

1,980

1,970

1,960

1,950 open 12:30 2:00 close open noon

Figure B7 September 1994

2,050

2,040

2,030

2,020

2,010

2,000 open 12:30 2:00 close open noon

AOI

SPI Futures P

170

Vol. 22, No. 2

Stoll & Whaley: EXPIRATION-DAY EFFECTS OF SPI FUTURES Figure B8 December 1994

1,950

1,940

1,930

1,920

1,910

1,900 open close open noon

Figure B9 March 1995

1,930

1,920

1,910

1,900

1,890

1,880 open 12:30 2:00 close open noon

AOI

SPI Futures P

171

AUSTRALIAN JOURNAL OF MANAGEMENT Figure B10 June 1995

2,050

December 1997

2,040

2,030

2,020

2,010

2,000 open 12:30 2:00 close open noon

Figure B11 September 1995

2,150

2,140

2,130

2,120

2,110

2,100 open 12:30 2:00 close open noon

AOI

SPI Futures P

172

Vol. 22, No. 2

Stoll & Whaley: EXPIRATION-DAY EFFECTS OF SPI FUTURES Figure B12 December 1995

2,230

2,220

2,210

2,200

2,190

2,180 open close open noon

Figure B13 March 1996

2,260

2,250

2,240

2,230

2,220

2,210 open 12:30 2:00 close open noon

AOI

SPI Futures P

173

AUSTRALIAN JOURNAL OF MANAGEMENT Figure B14 June 1996

2,270

December 1997

2,260

2,250

2,240

2,230

2,220 open 12:30 2:00 close open noon

AOI

SPI Futures P

174