Index futures, program trading, and stock market procedures

Index Futures, Program Trading, and Stock Market Procedures

Hans R. Stoll

ince their introduction in 1982 and 1983, stock index futures and options S contracts have attracted record setting interest. The S&P 500 index futures contracts, which represents a claim on a $150,000 portfolio of stocks, regularly registers dollar volumes substantially in excess of the dollar volumes of all individual stocks on the New York Stock Exchange. Similarly the S&P 100 put and call index options contracts, which represent claims on a $30,000 portfolio of stocks, regularly trade in excess of the New York Stock Exchange dollar volume. In effect, the volume of stock trading is now greater on futures and options markets then on the stock market itself. While LaSalle Street has thus become a formidable competitor in the equity markets, volume and li- quidity on Wall Street does not appear to have declined. Indeed the reverse appears to be true.

The sudden success of index futures and options combined with long stand- ing suspicion of futures and options have led to concerns that futures and options markets may have a destabilizing effect on traditional stock markets. Particular concern has been expressed with respect to expiration days of index futures and options and other days on which large price declines have occurred. The purpose of this paper is to examine trading links between futures and the stock market and to evaluate modifications in trading procedures that might alleviate market congestion and price effects observed particularly on expiration days.

The evidence on volume and price effects on expiration days is first reviewed. The price effects appear to be temporary technical effects due to order imbalances in the stock market late on the expiration day of index futures contracts. In section XI the expiration day price effect is interpreted in terms of the bid-ask effect that is observed in the normal course of trading. Based on comparisons to the normal cost of trading, the average expiration day effect is not large. However price effects on certain expiration days substantially exceed the average effect. In section 111 various proposals for modifications in index expiration procedures are reviewed.

In view of the decision of the Chicago Mercantile Exchange to use the opening as the settlement price for the S&P 500 index futures contract, section IV

Working Papcr 87-13. Financial support from the Columbia Futures Center is gratefully acknowledged. This article is based upon a paper presented at the Conference On The Impact of Stock Index Futures

Trading at The Center For The Study of Futures Markets, Columbia University, June 8, 1987.

Hans R. Stoll is the Anne Marie and Thomas B. Walker, Jr. Professor of Finance at Vanderbilt University

The Journal of Futures Markets, Vol. 8, No. 4, 391-412 (1988) 0 1988 by John Wiley & Sons, Inc. CCC 0270-73 14/88/040391-22sO4.00

examines trading procedures at the opening on the New York Stock Ex- change. Unlike other prices during the trading day, the opening price is deter- mined by an auction market procedure administered by the specialist. Empiri- cal evidence indicates that the volatility of opening prices is greater than the volatility of closing prices or other prices during the trading day. This evidence and an analysis of current opening procedures imply that opening procedures ought to be modified to provide for more complete disclosure of opening imbalances and likely opening prices, particularly on expiration days.

In section V the arguments for and against the use of the opening price as the settlement price for index futures and options contracts are presented. On balance, the opening appears to have certain advantages over the closing price. In particular the specialist’s ability to delay the opening makes it possible to take the necessary time to find the other side of large and sudden imbalances and makes “game playing’’ less likely.

In section VI portfolio trading is briefly considered. Modifications of expiration day procedures cannot eliminate the price effect resulting from the real cost of market-making when imbalances in a large number of stocks arise, as on expiration days. Only more efficient procedures for trading portfolios of stocks can eliminate such costs.

I. TRIPLE WITCHING HOUR

Stoll and Whaley (1986, 1987) have examined expiration day effects in detail. They find large volume effects and certain price effects on quarterly expirations during the last hour of trading, the triple-witching hour. At that time, index futures, index options, and individual stock options expire. Price effects are not significant when options alone expire, and no effects are observed for stocks not in the S&P 500 index.

A. Sources of Expiration Day Effects

The sources of expiration day effects are the cash settlement feature of index futures contracts and the resultant need to unwind index arbitrage positions by program selling of index stocks via market-on-close orders late on the expiration day.

Index arbitrage links index futures and cash prices. In a world without transaction costs, equilibrium requires

where: F = index futures price S = index cash price r = riskless rate of interest for the period remaining until maturity of the

futures contract

392/ STOLL

d = dividend yield on the stocks in the index for the period remaining to

If the equality, ( l) , is violated by more than transaction costs, arbitragers buy or sell the component index stocks and take offsetting positions in futures. For example, if F - S/S c r - d , buy the index stocks, earn a dividend yield of d , borrow money (or incur an opportunity cost of r ) and sell futures at F. The process of buying the index stocks is called “program trading,’’ although the term “portfolio trading” would be more descriptive. If held to maturity, the arbitrage profit is guaranteed. The arbitrage position would be unwound prior to maturity if a profit greater than the guaranteed profit could be earned.

At maturity, the futures contract self-liquidates because index futures call for cash settlement. The settlement price is the closing value of the cash index on the expiration day (the third Friday of the expiration month). In other words, the arbitrager earns a profit or loss that is the difference between the initial futures price and the settlement price at expiration. (This is not exactly true since the futures contract calls for daily settlement.) In order to remain hedged following the expiration day, the arbitrager must either roll into the next futures contract or sell the underlying index stocks. If the stocks are sold, they should be sold at the closing price on the New York Stock Exchange so that losses (gains) on the futures contract are offset by gains (losses) in the stocks. When many arbitragers liquidate arbitrage positions at the same time, large volume and noticeable price effects have been observed.

maturity of the futures contract

B. Evidence on Expiration Day Effects

Volume effects. Table I contains data on open interest in the S&P 500 index futures on the expiration day along with stock market data. Data on quarterly Friday expirations through December 20, 1985 are averaged separately from data since that time. This is done to provide greater comparability with the Stoll/Whaley (1986) study that examined data through December 20, 1985.

Several points are worth making with respect to the open interest and volume data: ( 1 ) open interest on the expiration day is large and is increasing through time. On December 20, 1984 the value of open interest was less than $2 billion. On June 19, 1987, the value of open interest was $4.7 billion; (2) last hour stock market volume is extremely large on expiration days, averaging 73 million shares in 1986 to 1987. Average hourly volume in 1986 was 22 million shares; and (3) while stock market volume remains substanital, the ratio of stock market volume to open interest appears to have declined somewhat over time.

Price Effects. Table I1 contains data for price effects on quarterly expirations as measured by S&P 500 index values. Stoll and Whaley (1986) found evidence of price effects on expiration days. Prices were more volatile on such days than on other days and prices tended to reverse on the day after the expiration day. A reversal is an indication that the preceding price was tempo- rarily out of line. In non S&P 500 stocks, volatility on expiration days was no greater than on other days, and reversals were not observed. Table I1 reports S&P 500 index values at 60 minutes prior to the expiration day close, at the close, and at 30 minutes after the exchange opening on the following day. In

TRADING PROCEDURES /393

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5 9/

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5 12

/20/

85

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292

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Table 11 PRICE EFFECTS OF S&P 500 INDEX FUTURES FRIDAY EXPIRATIONS

% S&P 500 Index Values YO Returns

Date -60 Mins. Settlement* +30 Mlns. 1 t + l Reversal

6/15/84 9/21/84

12/21/84 3/ 15/85 6/21/85 9/20/85

12/20/85

Average 3/21/86 6/20/86 9/19/86

12/19/86 3120187 6/19/87

Average Grand Avg.

149.78 167.79 165.04 178.27 187.74 183.11 211.10

177.55

235.96 244.89 231.00 245.95 296.62 304.80

259.87

215.54

149.03 148.81 165.67 165.99 165.51 165.98 176.53 177.03 189.61 187.93 182.05 184.60 210.94 209.96

177.05 177.19

233.34 234.82 247.58 245.64 232.21 233.01 249.73 248.72 298.17 297.81 306.16 305.70

261.20 260.95

215.89 215.85

-0.501 - 1.263

0.285 -0.976

0.996 -0.579 -0.076

-0.302

-1.110 1.098 0.524 1.537 0.523 0.446

0.503

0.069

-0.148 0.193 0.284 0.283

-0.886 1.401

-0.465

0.095

0.634 -0.784

0.345 -0.404 -0.121 -0.150

-0.080

0.014

-0.148 0.193

-0.284 0.283 0.886 1.401

-0.465

0.267

0.634 0.784

-0.345 0.404 0.121 0.150

0.291

0.278 -

Notes: *Index close until 3/20/87. Index opening value thereafter. (A special opening value is calculated).

Table I1 the reversal is measured by giving the Monday return a positive value if the return on Monday has a sign opposite to the sign of the Friday return; otherwise the Monday return is given a negative value. A reversal therefore has a positive sign in the last column of Table 11. A continuation of the price in the same direction has a negative sign.

The average reversal calculated over positive and negative values in the last column of Table I1 is .267 percent for the quarterly Friday expirations prior to 1986, and is .29 percent for the expirations in 1986 and 1987. The number, .267 percent is somewhat less than the number reported in the StoWWhaley study because the earlier expirations are excluded in Table I1 and because the December 20, 1985 expiration would have exhibited a reversal if the last 30 minutes on Friday had been used to calculate the return rather than the last hour. On that day, prices rose at the close although they declined over the last hour.

A key feature of expiration days is the apparent difficulty in predicting the direction of unwindings and the direction of price effects.

II. INTERPRETATION OF EXPIRATION DAY PRICE EFFECTS

A. Standards

Whether one concludes that expiration day price effects are justified or not depends on the standards against which these effects are measured:

TRADING PROCEDURES 1395

Standard 1: Price effects should be zero since no new information is being conveyed by the unwinding of arbitrage positions.

Standard 2: Price effects should be the normal effect that one observes when stocks are sold at the bid price or purchased at the ask price. Prices normally recover after a purchase by a dealer at the bid price and they normally decline after a sale by a dealer at the ask price. The expiration day price reversal should be evaluated in terms of these normal reversals.

Standard 3: The expiration day price effects should be evaluated in terms of the price effects that are associated with large imbalances.

Standard 1 is excessively severe. Even in a market in which trading is not associated with new information, trading imbalances will arise and will cause prices to be on the bid side of the market or on the ask side of the market depending on whether there is selling pressure or buying pressure. This will be the case in auction markets as well as in dealer markets.

Standard 2 sets as the standard the bid-ask effect that one would observe under normal trading conditions.

Standard 3 is too lenient. Large imbalances could be used to justify almost any price reversal. A large imbalance may, for example, impose additional costs of finding the other side or make it possible for potential suppliers of immediacy to extract monopoly returns. But these are costs one should be able to avoid.

B. The Cost of Immediacy: Components of the Quoted Bid-Ask Spread

If expiration day price effects are to be evaluated in terms of the normal costs of providing immediacy, it is appropriate to review the key cost components in providing immediacy. Dealers, such as the specialist on the New York Stock Exchange, and other investors provide immediacy to anxious sellers by buying shares at the bid price or to anxious buyers by selling shares at the ask price. At any moment of time the quoted bid-ask spread, A , - B,, reflects four components to varying degrees: order processing cost, inventory holding cost, adverse information cost, and a monopoly profit.’ The order processing cost compensates the provider of immediacy for the out-of-pocket cost of handling an order. The inventory holding cost compensates the dealer for the risk of holding a portfolio he would rather not hold. The adverse information cost reflects the fact that dealers make losses to traders who have information superior to the dealer’s information: prices will tend to fall after a purchase by the dealer and will tend to rise after a sale by the dealer. To compensate for losses to informed traders, the dealer must widen the bid-ask spread vis-a-vis all traders in order to increase his revenue from traders not trading on the basis of superior information. Finally a monopoly premium may arise in certain markets if there are entry restrictions on dealers and other suppliers of immediacy.

Expiration Fridays are distinguished from normal trading periods by the fact that imbalances are observed in nearly all 500 stocks in the S&P 500 index. What is the “normal” cost of providing immediacy when an imbalance in

‘These components are discussed in greater detail in Stoll (1978). The adverse information cost components is modeled in Copeland and Galai (1983) and Glosten and Milgrom (1985). See also Stoll(1985a) for a survey of market-making.

396/ STOLL

all 500 stocks occurs as compared with the cost of providing immediacy in one stock at a time? First, since arbitrage unwindings are not information based, suppliers of immediacy need not be concerned with adverse information. This ought to narrow the spread on the expiration day, all other things constant. In other words, suppliers of immediacy, knowing that program trades on the expiration day are not information based, should be prepared to pay a somewhat higher bid price or to ask a somewhat lower ask price than is normally the case.

A second factor that is expected to narrow the spread in a stock index as compared with a spread for any individual stock is the fact that a stock index is a diversified portfolio. As a result, the inventory holding cost associated with holding an index is less than the cost associated with holding an individual stock. Stoll (1978) and Ho and Stoll (1981) show that the holding cost of a dealer is ka, where k is a parameter that measures the dealer’s willingness to take on risk and a measures the return variability of the inventory. Since the return variability of a portfolio representing the market, such as the S&P 500 portfolio, is approximately one-half the return variability of the typical stock in the market, the holding cost associated with supplying immediacy in a diversified portfolio is approximately one-half the holding costs associated with that in the typical stock. In other words, at the Friday close, a supplier of immediacy would prefer to take a million dollar position in a diversified portfolio over taking a position of the same size in a single security. Unfortunately current institutional arrangements require individual stocks in a portfolio to be traded at different locations on the floor through different specialists. This fact may cause the specialist and other suppliers of immediacy to establish a bid-ask spread that reflects the holding cost associated with individual stocks rather than the holding cost associated with trading a portfolio of stocks.

A factor that raises the cost of supplying immediacy on expiration days is that, on expiration days, transactions in different securities tend to be highly correlated. On normal trading days a supplier of immediacy who makes a market in several stocks can expect that purchases of some stocks will be offset by sales of others, with the result that the total funds committed may be much less than the total immediacy supplied. In other words, proceeds of short sales from some securities can be used to fund the purchase of other securities. On an expiration day, on the other hand, all stocks tend either to be bought or to be sold. Thus the total commitment of funds will tend to be greater.

A related factor that raises the cost of immediacy is the limited availability of capital on short notice. If expirations are a surprise, suppliers of immediacy are in a temporary monopoly position that may make it possible to buy stocks at a bid price that is lower than normal or to sell stocks at an ask price that is above normal.

C. Measuring Market Impact; Quoted Spread, Realized Spread, and Price Reversals

The quoted spread, A , - B,, reflects the four cost components just enumerated. The realized spread reflects what dealers and other suppliers of immediacy actually earn. Because prices tend to be lower after a dealer purchase and tend to be higher after a dealer sale, the average difference between the price

TRADING PROCEDURES 1397

at which a dealer sells and the price at which a dealer buys is less than the quoted spread. Suppose for the purposes of illustrating this point that transactions are reversed immediately. Then the realized spread is

A,+1 - B, after a dealer purchase at B,

and

A, - B , + , after a dealer sale at A,.

That the realized spread is less than the quoted spread means that

The relationship between the quoted and realized spread is illustrated in Figure 1 for the case of dealer purchase at B,. In the presence of adverse information, the dealer assumes that a sale to him contains some adverse information; and as a result lowers both the asking price and the bid price. This is illustrated by the decline in the “true” price in the figure. In addition the bid and ask prices would also be lowered relative to the “true” price under an inventory adjustment view of the spread, A lower bid price discourages further sales to the dealer and a lower ask price encourages purchases from the dealer. In long run equilibrium, the realized spread covers the dealer’s out-of-pocket order processing costs, provides compensation for the risk he assumes, and yields any monopoly premium he is able to extract from the market. The real-

‘Time t t+ I

A -

A

“‘l’rue” price

€3

- Figure 1

Quoted Spread and Realized Spread.

ized spread would not reflect the adverse information cost component that is reflected in the quoted spread.

The average price reversal observed following an expiration day bears a close relation to the realized spread. If one assumes that suppliers of immediacy are always able to reverse their positions on Monday morning at the ask price, the reversal represents what the suppliers of immediacy earned. In that case, the reversal is directly comparable to the realized spread. On the other hand, if Monday prices are at the market bid-side one-half the time and at the market ask-side one-half the time, the expiration day price reversal ought to be compared with one-half the realized spread.

D. Magnitude of Price Effects in Different Types of Transactions

Table 111 contains data on market impact costs associated with different types of transactions. Average quoted spreads in the period 1975 to 1979 are 1.5 percent and .65 percent respectively for equal weighted and value weighted indices of all New York Stock Exchange stocks. The realized spread as estimated by Roll (1984) in the period 1975-1980 is .51 percent. This figure is an equally-weighted average over all New York Stock Exchange stocks. Roll’s estimate is perhaps on the low side, and he reports a higher number based on weekly rather than daily prices. The realized spread calculated from specialist incomes by Stoll (1985b) is however even lower at .39 percent. In part this is due to the fact that this estimate weighs stocks by volume. Roughly speaking, an estimate of the realized spread which is one half the quoted spread appears to be quite reasonable.

In addition to the expiration day price reversal of about .28 percent, Table I11 contains the estimate by Holthausen, Leftwich, and Mayers (1987) of the average price reversal in the largest dollar blocks sold in 1982. This figure of

Table IIl ESTIMATES OF MARKET IMPACT COSTS

Quoted spread on an equally-weighted portfolio of NY SE stocks, 1975- 1979 1 .SO% (Stoll/Whaley, 1983) Quoted spread on a value-weighted portfolio of NYSE stocks, 1975-1979 0.65% (StoWWhaley, 1983) Realized spread implied by the serial covariance of transaction prices, equal weighting of NYSE 0.51% (Roll, 1984) Realized spread implied by NYSE specialist’s income, trading volume weights, 1975-1980 0.39% (Stoll, 1985b) Price reversal in large block sales of NYSE stocks, 1982 (Holthausen/Leftwich/Mayers, 1987) Expiration day price reversals (From Table 11)

0.65%

0.28%


.65 percent is the average difference between the closing price on the day and the price of the block. The price reversal is larger than -6.5 percent if blocks are defined as the percentage of the equity represented by the block trade or as a fraction of normal trading volume. On the other hand, block purchases exhibit no price reversals.

The expiration day price reversal is directly comparable to the block trade price reversal and is significantly less. The price reversal associated with block transactions is usually interpreted as the necessary cost of providing immediacy in transactions of that size. Block price effects are not as noticeable as expiration day effects since different blocks trade at different times during the trading day while expiration day effects occur in all index stocks at the expiration day close.

Based on the data in Table I11 a reasonable estimate of the realized spread on a value weighted index of all stocks is .4 percent. On the basis of this standard, the average expiration day price reversal is less than the average change between the bid and the ask in normal trading situations. A more conservative comparison is to compare the expiration day price effect to one-half the realized spread. In that case, the average expiration day price effect is somewhat larger than the price impact observed in normal transactions.

On balance, the average expiration day price effect is roughly of the same magnitude as the price impacts observed in normal transactions that reflects the cost of supplying immediacy. It is substantially less than the average price effect around large block transactions.

Given this evidence, what is all the fuss about? In part, the fuss is not warranted. But in part the fuss is about particular expiration days in which price reversals substantially in excess of the average effect occurred. For example, in 1986, price reversals of .784 percent (June) and .634 percent (March) occurred. In 1985 reversals of 1.40 percent (September) and .886 percent (June) were observed. These large price reversals seem to be caused by unexpectedly large trading imbalances. On other days, price reversals were small or price continuations were observed. The result is an average price effect which is not large. From a policy perspective, the issue is whether appropriate trading procedures exist to handle unexpected imbalances and thereby to avoid instances of large price reversals.

III. PROPOSED SOLUTIONS FOR EXPIRATION DAY PRICE EFFECTS

A number of proposals for alleviating expiration day price effects have been made. All are aimed at reducing trading imbalances late in the trading day. Early recommendations for change were contained in a letter from the SEC requesting industry comments on expiration day price effects (October, 1985). The recommendations were aimed primarily at changing settlement procedures in futures contracts. Included were recommendations to telescope position limits, to use an average of prices rather than the closing price as the settlement price, to shift expiration days for different derivative instruments, and to disclose arbitrage positions.

In June of 1986 the Securities and Exchange Commission suggested modifications in expiration day procedures that are aimed at providing for early disclosure in trading imbalances. The SEC proposals reflect a change in empha-

sis from modifications of futures contracts, such as telescoping or averaging, to modifications of stock market trading procedures that would alleviate trading imbalances. Three suggestions were made by the SEC.

Disclosure of Market-on-Close (MOC) Orders Before the Close

Under this proposal, anyone wishing to place a MOC order would do so one- half hour before the close. If the MOC order is not placed by that time, the trader is not guaranteed a trade at the closing price. Beginning with the Sep- tember 1986 expiration, the New York Stock Exchange has implemented this proposal on an experimental basis for a subset of the major stocks in the S&P 500 index. The reactions have been mixed.

The proposal has the desirable objective of providing for early disclosure of trading imbalances. But there are some problems. First, under the proposal MOC orders may be canceled. The ability to cancel such orders can lead to game playing. For example investors could signal an imbalance in one direction thereby pushing market prices, then cancel MOC orders and take a position in the opposite direction at favorable prices. In the experiments con- ducted thus far, there is little evidence that orders have been canceled; but that possibility would always exist. To avoid it, careful monitoring would be required. A simpler procedure would seem to be to forbid canceling of such orders.

A second problem arises from the fact that investors who fail to place MOC orders early may still be able to execute at the close with ordinary market orders. Arbitrage positions are held by major brokerage firms who have an established relationship with the specialist on the floor. The specialist will typi- cally try to accommodate market orders at the close even if such brokerage firms fail to place MOC orders at the required time.

Third, the proposal provides only a partial picture of imbalances since many orders need not be disclosed, and those MOC orders responding to the initial imbalances need not be disclosed before the close.

These problems have been in evidence to some extent under the experiment. In the December 1986 expiration, disclosure of MOC orders indicated a significant sell imbalance, which conditioned the market to a price decline. How- ever, at the close, a brokerage firm came in with large volume of MOC buy orders that forced the market up. Modifications of the experiment have been requested by the SEC to the effect that MOC orders related to index arbitrage unwindings must be placed within one-half hour of the close even if such orders serve to offset existing imbalances. Subsequent MOC orders may not be related to index arbitrage unwindings and may only be placed in response to initially reported imbalance. It is clearly evident, however, that as the rules become more complicated the problem of enforcement becomes equally complicated.

Trading Halt

A second suggestion for procedures near the close is to halt trading before the close (for one-half hour or 15 minutes, say) in order to give the market time to respond to imbalances. This procedure, in effect, switches the New York


Stock Exchange from a continuous market to a call-auction market at that time. While there is nothing wrong with this procedure in principle, a variety of institutional arrangements would have to be established. Given this suggestion, it is a small step to the third suggestion which is to use the opening price.

Opening Price

Establishment of the opening price occurs after an overnight trading halt and follows, roughly speaking, auction market procedures. Thus, if an auction market procedure is to be used, it may be quite appropriate to focus on the opening rather than to establish a new trading halt somewhere near the close. The Chicago Mercantile Exchange has adopted the opening price on the expiration Friday as the settlement price for its S&P 500 index futures contract. The NYSE Composite Index options and futures are also being settled at the opening price. The Chicago Board Options Exchange has followed suit with respect to its S&P 500 option. However, the other index products continue to settle at the closing price on Friday. Given the partial adoption of the opening price idea, it seems appropriate to analyze the opening trading procedure in some detail. In the next section procedures for opening a stock on the New York Stock Exchange are discussed. Then the pros and cons of the opening price as the index futures settlement price are presented.

IV. TRADING AT THE OPENING

Unlike trading during the day, the New York Stock Exchange opening follows a call auction market procedure, roughly speaking. Market and limit orders are accumulated overnight, and all orders executed at the opening are traded at the same price. The specialist, using OARS (opening automated reporting system), determines imbalances of market orders. (OARS does not include limit orders in its imbalance calculation.) The specialist may choose to make up the imbalance out of his own account and open the stock so long as the price at which he opens is within a tolerance of the preceding day’s closing price. For certain price changes, the specialist is required to make a “pre- opening notification” over the inter-market-trading system (ITS) to specialists on other exchanges. If the price change threatens to be substantial-$2 or more on a stock over $20 or $1 or more for stocks selling at less than $20-the specialist may not open the stock without permission and oversight from a floor governor. Under those circumstances, procedures for disseminating imbalances and quote indications not only over ITS but through other means are presumably followed. The purpose of the dissemination of such information is to bring in orders on the other side so that the stock price will open at the true underyling equilibrium price.

At the opening, the specialist has more discretion and power than at other times during the day. The specialist has a picture of the supply demand situation available to no one else in the market, and he can participate in the opening for his own account on the basis of that information. Consider a simple example: Suppose the specialist has received some market orders to sell and no market orders to buy and has no limit orders. In that case, the specialist

4021 STOLL

could open stock down some amount even though fundamental values warrant an opening price equal to the preceding day’s closing price.

A. Analysis of the Specialist Role in the Opening2

Figure 2 provides a framework for analyzing the role of the specialist in open- ings. The demand and supply curves (DD and SS) represent the number of shares to be purchased at each price. The vertical component represent market orders and the sloped component represents limit orders. Suppose that no new information has arrive so that the prior day’s closing price, P*, is the equilibrium price. Because of chance, demand exceeds supply at P* as shown in Figure 2-a. In the absence of any disclosure requirements, the specialist is a monopolist in this case. The optimal behavior of the specialist is to look at the marginal curve to the excess demand curve as shown in Figure 2-b. He will open the stock at Po, above the equilibrium price, and sell I shares for his own account. He will cover his position on average at the true equilibrium price P* and make the difference, Po - P*. To limit the power of the specialist in this type of situation, investors can place limit orders. For example, buyers would

Price

A B Quantity

Figure 2-a Demand and supply at the opening. At the prior day’s closing price, the imbalance

is (B-A).

I Price

Marginal Excess demand

0 I (3-4 Quantity

Figure 2-b Specialist’s response to an imbalance in the absence of disclosure. Specialist sells

the quantity, I, at the price, Po.

21n writing this section, I have benefited from discussions with Tim Devinney.

TRADING PROCEDURES 140.3

place limit orders somewhat above the preceding day’s close to assure a trade and to avoid an excessive price increase. Similarly sellers might place limit orders somewhat below the preceding day’s close to assure a trade and avoid an excessive price decline. The risk is that a major move in the market equilibrium price will cause such orders to miss the market. Ho, Schwartz, and Whit- comb (1985) analyze in greater detail the order of placement strategy of traders in a one-shot auction market of this type. They show that there is a ten- dency for order placement strategies in such an environment to cause prices to be more volatile than otherwise.

One way to avoid such problems, while at the same time reducing the power of the specialist, is to require disclosure of the demand and supply situation. Under current regulations, if the specialist intends to open stock more than $.25 from the preceding day’s close, he is supposed to send a “pre-opening notification” over ITS to specialists in other exchanges. This message conveys information about the amount and direction of an imbalance. The specialist is then supposed to wait 10 to 15 minutes for additional orders that might lessen the imbalance. If the opening is likely to be more than $2 away from the preceding close (on a stock selling for more than $20) the specialist must seek a floor governor’s permission to open a stock. In such situations, it is typical for the specialist to disclose the imbalance to the crowd and to upstairs brokerage offices as well as to specialists on other exchanges.

Complete disclosure of the demand and supply situation along with sufficient reaction time can result in an opening price that reflects the true underlying price. However two factors make this result difficult to achieve: One, prac- tical problems of providing for speedy and complete information as to the nature and extent of an imbalance and of receiving new trading indications and revisions of existing trading intentions and Two, the interest of the specialist in maintaining control. The specialist benefits from certain small imbalances that he can meet at prices over which he has some discretion.

These two factors make it difficult for the opening price to settle down to the try underlying equilibrium price. It is not the purpose of this paper to specify the procedures that ought to be followed at the opening. However it may be helpful to list briefly some of the major issues that seem to arise: One, under what circumstances should the pre-opening notification procedure be followed? Currently a potential price change from the preceding close triggers the notification procedure. What if the equilibrium price falls and the stock opens at the preceding day’s close while the specialist takes a short position? Would it not be simpler to disseminate a pre-opening notification every day and make it generally available on quote screens?; Two, what information should be contained in the pre-opening notification? Currently an indicated opening price range is disseminated. For example in Figure 2 the specialist might quote the price range PI to P*, or Po to P*. In addition to price information, it is desirable to disclose data on imbalances as well. However if limit orders are included (as they should be), imbalances will be different at different prices, and it is impractical to disclose all possible imbalance. As a practi- cal matter, it may be sufficient to disclose the imbalance at the preceding day’s closing price along with the price indication. Following this procedure, both price and quantity information is conveyed; and this should allow market participants to make reasonably informed judgments as to their own trading in-

404/ STOLL

tentions; Three, who should receive pre-opening notification information? Under current procedures the recipients of information on the supply and demand situation are not clear. For example it appears that in many circumstances only specialists on other exchanges linked to the New York Stock Ex- change via ITS are notified. In other cases broader dissemination is made. Presently it appears that the nature and breadth of such dissemination is under the discretion of the specialist to a considerable degree and Four, how many iterations ought there to be? The purpose of the pre-opening notification procedure is to generate orders from the other side and perhaps to allow existing orders to be cancelled or modified. Such actions will result in a new potential clearing price that need not be equal to the preceding day’s closing price or to the equilibrium price. As a result, additional notifications and trade modifications will be necessary. Practically speaking there is likely to be an imbalance of orders at the equilibrium price even after several iterations of the notification procedure. In such circumstances the specialist stands to gain because “He who discloses last wins.”3

While procedures for handling the opening deserve additional analysis and discussion, several steps seem appropriate at this time. (a) Broader and more frequent dissemination of information about the supply and demand situation prior to the opening. (b) More complete information that includes not only the indicated opening price range but also the current imbalance at the preceding day’s closing price. (c) Provide for sufficient iterations to limit the size of potential imbalances and price fluctuations.

B. Empirical Evidence

Empirical evidence suggest that something is different about opening prices as compared with other prices during the day. In a paper analyzing transactions data, Wood, McInish, and Ord (1985) find that price volatility at the opening exceeds price volatility during other times of the day. In a recent paper Amihud and Mendelson (1987) examined daily returns calculated from closing prices as

and daily returns calculated from opening prices as

where 0, is the opening price on day t and C, is the closing price on day t . Figure 3 illustrates the calculations of two returns, R,,, Rot, from four prices.

3From “Excorcising Triple Witching Hour,” a statement of the Alliance of Floor Brokers.


Time Ct-1 01- 1 ct ot

Figure 3 Calculation of opening and closing returns. Closing price is denoted

by C and opening price is denoted by 0. Each return covers the same period of time.

Amihud and Mendelson examined the Dow Jones Industrial Stocks in the period February 1982 to February 1983. They find that “Var(R,) exceeds Var(R,) for 29 out of 30 stocks . . . and on average, the variance of open returns is 21 percent greater than that of the close-to-close returns.’’ This result implies that prices reverse around the opening, for if close-to-close returns are less variable than open-to-open returns, the opening price must be more likely to hit extreme values than the closing price. Price reversals are means by which suppliers of immediacy, such as the specialist, make profits. Amihud and Mendelson find that skewness and kurtosis are also greater for returns calculated from opening prices than for returns calculated from closing prices. Amihud and Mendelson show that “most of the auto-correlation coefficients of the open to open returns are negative (23 out of 30). . . . On the other hand, the auto-correlations for returns based on closing prices are positive. Negative auto-correlation is a reflection of price reversals, which is consistent with the hypothesis that prices tend to reach extremes at the opening.

This evidence suggests that the opening trading procedures produce greater volatility and implies the existence of profit opportunities for the specialist along the lines of the theoretical framework just described. It suggests further that improvements in opening procedures are warranted, particularly in view of the fact that the opening is to be used on expiration days.

We now turn to the arguments for and against the use of the opening price as the settlement price for index futures contracts.

V. THE OPENING AS SETTLEMENT PRICE FOR STOCK INDEX FUTURES

The Chicago Mercantile has received CFTC approval to use the value of the S&P 500 index at the opening on the expiration day as the settlement price for S&P 500 index futures contracts. Trading in the S&P 500 index futures will cease on Thursday, and contracts remaining outstanding will be settled at the opening price on Friday morning. This procedure was implemented for the first time in the June 1987 expiration of the S&P 500 futures contract. The futures options on the S&P 500 index (traded on the CME) and the S&P 500 index options traded on the CBOE will follow the same procedure to cash settle at the opening. Settlement procedures for futures and options on the New York Stock Exchange index have also been changed, but the remaining index products will continue to settle at the close.

In this section of the paper the arguments for and against the use of the opening price are enumerated.

CONTRACTS: PROS ANI) CONS

4061 STOLL

A. Arguments for the Opening

One, at the opening, procedures for dealing with large imbalances exist. On the expiration day a large number of orders request transactions at the same single price. Such requests are more suited to a call auction market than to a continuous dealer market. While it might be possible to provide for a trading halt near the close to arrange an auction market in those securities contained in the index, use of the opening price rather than the close price has the advantage that a natural trading halt precedes the determination of the opening price. Furthermore that trading halt affects all securities, not only those contained in indices. At the opening, procedures exist for accumulating and cal- culating imbalances and for disseminating information about the opening imbalances. However, as indicted in the preceding section, current procedures for opening stocks appear to have flaws and deserve to be reviewed and modified.

Two, at the opening, the specialist has time to find the other side. Because New York Stock Exchange trading in all stocks must cease at 4 o’clock, last- minute orders generating substantial imbalances can cause substantial price changes as the other side can only be found at “distress” prices. At the opening, the specialist can delay opening a stock in order to take the time to provide for a broader dissemination of an order imbalance.

Three, at the opening there is no weekend risk. To the extent that expiration day price effects reflect the cost of providing immediacy, use of the opening price should lower those costs because inventory positions would not have to be carried over the weekend. As a result, suppliers of immediacy, such as the specialist, would be willing to take the other side of an imbalance at a smaller price concession.

Four, at the opening, “game playing” is more difficult. In principle, index arbitragers should not be reluctant to disclose well before the close their intentions to place market-on-close orders to unwind positions in index stocks. Any adverse effects of such disclosure will be offset by beneficial effects in the futures market position. Such timely disclosure has not always occurred under current expiration day procedures. Expiration day price effects have been as- cribed to market-on-close orders arriving very late in the trading day. Index arbitragers may find it desirable to delay notification of arbitrage unwindings in the knowledge that price effects of such unwindings may benefit other positions held by the arbitrager or its customer. For example an index arbitrager may wish to use index arbitrage unwindings to create good prices for cus- tomers who wish to buy index stocks. Alternatively an index arbitrager may use arbitrage unwindings to move index prices and thereby create profit opportunities in the index futures markets. A firm that will be required to buy stocks to unwind arbitrage positions may choose, on the expiration day, to purchase the expiring futures contract in anticipation of a price increase resulting from its arbitrage unwindings. In a competitive market this type of “game playing” is limited by the presence of other traders that prevent prices from reaching unwarranted levels. However if the reaction time is very short, as it is near the close, these competitive forces may not come into play.

At the opening, “game players” must aim at a moving target rather than the fixed target that is available to them if futures contract settle at the closing


price. Attempts to influence the opening price can be offset by a delay in the opening which allows competitive forces to come into play. In addition by halt- ing trading in the futures contract on the preceding day, front running in the futures market is limited because anyone taking a position in the futures market on Thursday is required to bear the overnight risk until the settlement on Friday.

B. Arguments Against the Opening

One, use of the opening price as the settlement price will not mitigate expiration day price-effects. If the expiration day price-effect is a fundamental cost of providing immediacy, a change from the closing price to the opening price will not alter that cost and therefore will not alter the price effect. The argument in favor of the opening price is that it will eliminate price-effects that exceed the cost of providing immediacy.

Two, use of the opening price is undesirable because individual investors participate more heavily at the opening than at the close. Any volatility due to the expiration day effect will therefore have a greater impact on individual investors than under current procedures.

Three, the specialist has too much power over the opening price. As indicated earlier, the specialist has considerable discretion and power at the opening because he is the last to observe the supply and demand situation and can take actions that benefit himself. Settling at the closing price has the advantage that the specialist is reluctant to participate for his own account because of weekend risk. As a result he has a greater interest in closing at the underlying equilibrium price. Empirical evidence indicates that opening prices hit extreme values more frequently than closing prices. Concern about the quality of opening prices therefore seems to be legitimate, and modifications in opening procedures seem to be appropriate.

Four, use of the opening price causes investor confusion. First, confusion may arise because index futures will settle at the closing price on all days except the expiration day. Only on the expiration day will the opening price be used. Furthermore, as it currently stands, only the S&P 500 futures contracts will settle at the opening while other contracts will continue to settle at the close on the expiration day. Second, confusion will arise because on the expiration day two index values will be required, one averaging the opening prices of all the stocks in the S&P 500 index and one reflecting the current prices of all the stocks in the S&P 500 index. If the opening is delayed in certain stocks, these two index values will be different.

Five, use of the opening will transfer expiration day price effects to the Thursday close. Because index futures trading will end on Thursday, un- hedged futures market positions will tend to be liquidated on Thursday to avoid overnight uncertainty and uncertainties with respect to the Friday expiration price. As a result, expiration day price effects will be transferred to the Thursday closing price. One argument against this view is that index arbitragers have no reason to unwind early. If the expiration day price effect is due to the unwinding of index arbitrage positions, the effect will not be transferred to Thursday. In addition any early unwindings will be carried out so as to min-

408/ STOLL

imize price effects since there is no guarantee that futures contracts and stock prices will converge on Thursday.

Six, switching to the opening for some contracts b r t not for others poses new problems. An example of such a problem involves spreaders between the S&P 500 futures contract that will expire at the opening and other derivative instruments such as the MMI index futures that will expire at close. For example, consider a spreader who has a short position in MMI index futures and a long position in S&P 500 index futures. If the spreader wishes to carry his hedged position to the close on Friday, he will buy S&P 500 index stocks at the Friday opening to offset the fact that his long futures position will be closed out. By using a market-on-opening order, any increase in the price of these stocks will be offset by an increase of the price at which his long futures position is closed out. At the end of the day, the spreader places market-on-close orders for the same stocks, and his short position in the MMI futures is closed out at the closing price on Friday. Similar scenarios will be possible for spreaders using futures on other indices or index options. The concern is that there will be a whipsaw effect with increased volatility at the open and the close. Whether this is a serious problem is, however, questionable. Spreading activ- ity of this type may have the beneficial effect of transferring some of the expiration effect from Friday opening to Friday close. In view of the fact that the S&P 500 futures contract is by far the way most actively traded, this may be desirable.

Seven, use of the opening price poses special problems for index options. Because index options (except for the S&P 500 index option) are American options that can be exercised early, option traders like to be able to trade in the options market immediately prior to expirations in order to offset the adverse effects of major price moves. If options were to settle at the opening rather than the closing price on Fridays, writers of options would face a considerable period of time during which they would be unable to make offsetting positions in the options market. For example, a writer of a straddle might find the put exercised against him after the Thursday close and, if prices increased at the opening, the call exercised against him at the open. The solution for this type of problem seems however to be quite simple: liquidate such a position before the expiration day.

C. Evaluating the Success of the Opening

On balance it seems to make considerable sense to use the opening price as the opposed to the closing price as the settlement price for index futures contracts. At the opening the specialist has the time, if necessary, to find the other side, and “game playing” is more difficult. Switching to the opening has the side benefit that increased attention to opening procedures may improve those procedures in a way that will eliminate the excessive price volatility presently ob- servable. Indeed, improvement in opening procedures ought to be an essential ingredient of the switch to the opening.

Whether the opening proves successful can be evaluated by examining price reversals around the opening. If in future expirations using the opening, price reversals exceed the price reversals justified by the normal cost of providing


immediacy, one will be able to conclude that opening procedures have not solved the problem.

VI. PORTFOLIO TRADING

While the use of the opening price as the settlement price for futures contracts rather than the closing price may eliminate some of the price effects resulting from unexpected imbalances late in the trading day, it is unlikely that the use of the opening price will eliminate all price effects. Under current procedures for trading on the New York Stock Exchange, providers of immediacy such as the specialist must be compensated for the cost they incur. The cost of trading all the stocks in a stock index can be substantial under current market procedures.

A more fundamental solution to expiration day price effects and to market congestion on other days is to modify the procedure by which portfolios of stocks are traded. Currently individual stocks are traded at different posts on the stock exchange floor, and specialists view each stock as a separate entity rather than as part of a portfolio. An alternative approach is to trade standard portfolios directly at a single location on the trading floor.

The major innovation of index futures is that index futures contracts provide a low cost indirect means of trading portfolios of stocks. Direct trading of individual stocks pursuant to a single order has been termed program trading. It has been estimated that the cost of trading index futures is approximately 1/15 of the cost of trading the corresponding program of underlying stocks. While index futures trading is a satisfactory substitute for trading programs of underlying stocks for investors interested in short term trading, it is not an appropriate substitute for long term investors or others that for one reason or another need to take possession of the underlying stocks.

Procedures for directly trading portfolios are developing rapidly. Major upstairs brokers are prepared to quote bids and offer portfolios. Such quotes are made easier by the ability to hedge in index futures and options. Floor execu- tion is reasonably rapid, particularly when DOT, a computerized system for transmitting orders to the appropriate specialist post, is used. However portfolio trading is in its infancy and substantial improvements in the speed and reduction in the cost of portfolio trading are po~sible .~

VII. SUMMARY AND CONCLUSIONS

Arbitrage links futures and cash stock index prices. Because of the cash settlement feature of index futures contracts, closing out arbitrage positions requires that underlying stocks comprising the index be traded in the stock market (program trading). Such trading has sometimes caused market congestion and price effects. In 1986-87, last hour volume on quarterly expirations averaged 77 million shares as compared with normal hourly volume in 1986 of 22 million shares. The average temporary price effect in 1986-87 on the quarterly expirations was .29 percent. This effect is comparable in magnitude to the

4See H. Stoll (1987) for a detailed discussion of portfolio trading and for a proposal to trade standard portfolios directly.

410/ STOLL

normal movement between bid and ask prices during normal trading periods. However on certain expiration days much larger effects have been observed.

Various solutions for expiration day price effects have been proposed. Early recommendations emphasized modifications in the futures contract, such as telescoping or averaging. More recent suggestions from the Securities and Ex- change Commission emphasized modifications of trading procedures in the stock market. One of these suggestions, to settle index futures at the Friday opening price rather than the Friday closing price, has been adopted by the Chicago Mercantile Exchange.

In view of this change to use the opening price rather than the closing price, the paper examines trading procedures at the opening in some detail. At the opening, the specialist has considerable power, particularly if no disclosure is required of the demand and supply situation. Empirical evidence indicates that opening prices are more volatile than closing prices and exhibit price reversals. These empirical results and the analysis of current opening procedures suggest that modifications in opening procedures might be warranted, particularly on expiration days. More frequent and more complete dissemination of information on the size of imbalances and likely opening prices along with the greater opportunity for market participants to revise trading intentions prior to the opening appear to be desirable.

The arguments for and against the use of the opening price are presented. The principal advantage of the opening price is that the opening can be delayed more easily than the close in circumstances in which a large imbalance of orders suddenly appears. “Game playing” therefore becomes more difficult. Arguments against the opening include concerns that the opening won’t solve the problem, that the specialist has too much discretion and power at the opening, that individual investors may be adversely affected or may be con- fused, and certain other concerns. On balance, however, given appropriate modifications in opening procedures, the opening appears to offer the possibility of dealing more efficiently with large trading imbalances of the type that have occurred on certain expiration days.

Use of the opening is unlikely to eliminate the price effects associated with the normal cost of providing market-making services. Under current trading procedures the cost of trading large portfolios of stock, commissions and bid- ask spread, are still substantial. Under current procedures a portfolio of stocks is traded by trading each of the individual stocks at the appropriate specialist’s post on the New York Stock Exchange floor. Those costs will not be eliminated until more efficient procedures for trading portfolios are de- vised. One approach would be to trade directly standard portfolios such as the S&P 500 index, the S&P 100 index, and other stock indices on the stock exchange floor at a single post.

Bibliography Amihud, Y . , and Mendelson, H. (1987, July): “Trading Mechanisms and Stock Re-

Copeland, T. C., and Galai, D. (1983, December): “Information Effects on the Bid- turns,” Journal of Finance, 42533-553.

Ask Spread,” Journal of Finance, 38: 1457-1469.


Glosten, Lawrence, and Milgrom, Paul (1985, March): “Bid, Ask and Transaction Prices in a Specialist Market with Heterogeneously Informed Traders,” Journal of Financial Economics, 14:71-100.

Ho, Thomas, and Stoll, Hans R. (1981, March): “Optimal Dealer Pricing Under Transactions and Return Uncertainty, ” Journal of Financial Economics, 9:47-73.

Ho, T., Schwartz R., and Whitcomb, D. (1985, March): “The Trading Decision and Market Clearing Under Transactions Price Uncertainty,” Journal of Finance,

Holthausen, R., Leftwich, R., and Mayers, D. (1987, December): “The Effect of Large Block Transactions on Security Prices: A Cross-Sectional Analysis,” Journal of Financial Economics, 19~237-267.

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Stoll, H. (1978, September): “The Supply of Dealer Services in Securities Markets,” Journal of Finance, 33:1133-1151.

Stoll, H. (1985a): “Alternative Views of Market-Making,’’ in Market Making and the Changing Structure of the Securities industry, Amihud, Ho, and Schwartz, Eds. Lexington Books, Lexington, MA.

Stoll, Hans R. (1985b): “The Stock Exchange Specialist System: An Economic Analy- sis,” Monograph Series in Finance and Economics, Monograph 1985-2, New York University, Salomon Brothers Center, 49 pp.

Stoll, H., and Whaley, R. (1983, June): “Transaction Costs and the Small Firm Ef- fect,” Journal of Financial Economics, 1257-79.

Stoll, H., and Whaley, R. (1987, March/April): “Program Trading and Expiration Day Effects,” Financial Analysts Journal, 16-28.

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Stoll, H. (1987): “Portfolio Trading,” Working paper, Owen Graduate School of Management, Vanderbilt University.

Wood, R., McInish, T., and Ord, J . (1985, July): “An Investigation of Transaction Data for NYSE Stocks,” Journal of Finance, 40:723-739.

40:21-42.

Documents

Index futures, program trading, and stock market procedures