INTRADAY STOCK INDEX FUTURES ARBITRAGE WITH TIME LAG EFFECTS Robert T. Daigler Associate Professor Florida International University The following individuals provided helpful information concerning the institutional aspects of arbitrage trading: Ira Kawaller (CMEX), Ted Doukas (CBT), Gary Katz (NYSE), Bill Toy (Goldman Sacks), and Bill Mullen (Loomis-Sayles). July 1990 2 INTRADAY STOCK INDEX FUTURES ARBITRAGE WITH TIME LAG EFFECTS Robert T. Daigler Visiting Scholar, Stanford University 1990-91 Associate Professor Florida International University The following individuals provided helpful information concerning the institutional aspects of arbitrage trading: Ira Kawaller (CMEX), Ted Doukas (CBT), Gary Katz (NYSE), Bill Toy (Goldman Sacks), and Bill Mullen (Loomis-Sayles). July 1990 3 4 INTRADAY STOCK INDEX FUTURES ARBITRAGE WITH TIME LAG EFFECTS ABSTRACT Previous research concludes that stock index arbitrage provides risk-free profits on a consistent basis. However, these studies employed end of the day data and/or do not consider the effect of lags in the cash price on the results. This study examines potential stock index arbitrage opportunities by using five minute intervals for the S&P 500, MMI, and NYFE contracts. Realistic cost, interest rate, and dividend yield data are employed to provide reliable results. When only end of the day or early morning data are used then large arbitrage profits are recorded. Smaller profits are available for intraday data. The effect of time lags related to making cash market trades or inactivity for smaller stocks eliminates the apparent intraday arbitrage profits, except for the October-December 1987 time period. 5 INTRADAY STOCK INDEX FUTURES ARBITRAGE WITH TIME LAG EFFECTS The literature on the price behavior of stock index futures in relation to the underlying cash index has concentrated on two related issues: (1) the lead-lag relationship between the futures and cash prices, which also relates to the ability of futures to "predict" subsequent cash index prices, and (2) the pricing and arbitrage of stock index futures markets. Section I of this paper includes a summary of the research concerning these two issues. The studies on the lead-lag/price discovery relationship which uses intraday data provides consistent conclusions that futures do lead cash prices during most time periods. This lead effect of futures implies that the use of matched futures-cash prices may provide biased results for arbitrage studies. The pricing and arbitrage studies of stock index futures typically employ daily data. Using the cost of carry model, these studies usually conclude that arbitrage profits are frequent and relatively large for the time periods studied. Recently, MacKinlay and Ramaswamy (1988) use 15 minute intraday periods to examine the mispricings of stock index futures from their fair prices, as well as to examine if stock index futures prices violate an arbitrary arbitrage transactions boundary. They determine that once the mispricing value crosses one transaction boundary, e.g. the upper bound, then it is less likely to cross the opposite boundary. Moreover, these violations tend to persist for long periods of time. 6 The existence of arbitrage profits raises the question of the source of these profits. Are arbitrage profits available in these markets due to a limited supply of arbitrage capital? Or are these reported profits illusionary because of the lag effect of the cash index prices and the end of day timing difference between the futures and cash indices? Are there other factors affecting these reported profits, such as the risk involved when a subset of the index is used to undertake the arbitrage transaction? Now that the stock index futures market has matured, are such profits still available? To what extent did the market volatility in the third quarter of 1987 affect stock index arbitrage opportunities? The purpose of this paper is to investigate stock index arbitrage opportunities with intraday data and to examine the reasons for any apparent risk-free profits from this arbitrage. This paper differs from most previous research in that it employs intraday data to examine stock index arbitrage, uses a realistic cost structure, determines the effect of lags, and compares arbitrage results across the three major futures contracts (S&P 500, MMI, and NYFE). In addition, intraday results are compared to the apparent arbitrage profits existing at the end of the day and the beginning of the day. The differing contract characteristics and liquidity of the three futures contracts provide a useful comparison to investigate the aforementioned questions concerning stock index arbitrage. Section I provides an overview of the stock index futures lead-lag and pricing issues found in the literature. Section II 7 examines the factors affecting arbitrage transactions, such as the cost and risk aspects of executing an arbitrage trade. Section III relates the methodology of this paper, and Section IV provides the results of using intraday data for stock index futures arbitrage. Section V provides conclusions and implications. I. ISSUES IN THE LITERATURE The lead-lag and arbitrage/pricing issues are interrelated. If futures price changes lead cash index changes then this lead may affect reported arbitrage results. Likewise, the matching of prices for arbitrage purposes by using end of day data implicitly assumes that there is no lead effect for futures and that futures do not provide any price discovery mechanism, since futures close 15 minutes later than the cash markets. A. The Lead-Lag Relationship The lead-lag/price discovery issue has been investigated in several different ways. Kawaller, Koch, and Koch (1987) use a three stage least squares model on minute by minute S&P 500 futures and cash data for six days during 1984 and 1985; they determine that the futures contract leads the cash index for as long as 20 to 45 minutes. Laatsch and Schwarz (1988) find simultaneous pricing for minute by minute data with the Major Market Index (MMI). However, Finnerty and Park (1987) conclude that a significant lead-lag relationship exists for minute by 8 minute MMI data from August 1984 to August 1986. Herbst, McCormack, and West (1987) use spectral analysis cross correlations to determine that futures lead the cash index for the S&P 500 and Value Line futures contacts, with the lead varying from 0 to 16 minutes. Stoll and Whaley (1988a) employ correlation coefficients to examine various multiples of a five minute interval lag for the S&P 500 and MMI contracts. They determine that futures provide a price discovery function with a lead time of 5 minutes on average and up to 15 minutes or more occasionally, although the futures and cash prices are often contemporaneous. Stoll and Whaley attribute the lag effect to infrequent trading for the cash stocks. Swinnerton, Curcio, and Bennett (1988) use five minute intervals for four MMI expirations in 1986 to determine that a mispriced futures value based on the cost of carry model is only a modest predictor of the future underlying cash index, and that a lead time of five minutes is the best predictor of the cash index, although the futures provided some predictive ability up to 30 minutes later. The reasons that futures lead the cash index are threefold: (1) opinions concerning the market are registered first in the futures market due to the significantly lower transactions cost of futures over cash, (2) the greater liquidity in the futures market, and (3) futures price appear to lead the cash index because the smaller stocks in the index do not trade frequently. 9 B. Arbitrage and Pricing Cornell and French (1983) and Modest and Sundaresan (1983) completed early studies of stock index futures pricing and arbitrage with daily data by employing the cost of carry model. Cornell and French found that mispricing did exist, attributing the mispricing to a tax timing option for the stock. However, Cornell (1985) shows empirically that the tax timing hypothesis does not affect the results and the mispricings began to disappear as the contract matured. Modest and Sundaresan calculated no-arbitrage bands based on assumed transactions costs, finding that the daily futures versus cash relationships fell within the bands for the December 1982 contract. However, the transactions costs used by Modest and Sundaresan are much higher than institutions pay, and their assumption that long futures arbitrage (short cash stocks) is costly because of the uptick short sale rule does not conform to the industry practice of pension funds that initiate long arbitrage. Saunders and Mahajan (1988) adjust for several restrictive assumptions made in other arbitrage studies and then employ regression analysis on daily data from late 1982 to 1984 to examine the pricing relationships between futures and cash for the S&P 500 and NYSE contracts. They conclude that stock index futures have matured over time, although arbitrage profits are not calculated. Finnerty and Park (1989) employ intraday data on the MMI contract from August 1984 to August 1986 to examine dynamic program trading strategies. The standard deviation of the percentage difference from the theoretical cost of carry value is 10 calculated to develop a filter model that identifies profitable trades. However, no transactions costs are employed and potential lag effects are ignored. Merrick (1989) examines early unwindings and rollovers of arbitrage positions to determine if such dynamic strategies affect the profits of such transactions. Although only daily S&P 500 data are employed, Merrick finds that the effective total transactions cost is only 73% of the original transactions cost when unwindings and rollovers are employed as part of a complete arbitrage strategy. MacKinlay and Ramaswamy (1988) perform the only cost of carry pricing study involving intraday data. Using the S&P 500 contract from June 1983 to June 1987, they examine the mispricing of futures contracts from their fair value by using 15 minute intervals. MacKinlay and Ramaswamy determine that a positive or negative persistence in mispricing exists when autocorrelations are measured for eight lags of 15 minutes each. They also find that mispricings are a function of time by using a regression analysis on the average absolute daily mispricing versus the time to expiration of the futures. MacKinlay and Ramaswamy also provide some arbitrage results, although their choice of the size of the transactions bands seems to be arbitrary at .6% of the value of the cash index. They find that the average time above the upper transaction band is two hours and the average time below the lower bound is 36 minutes (using 15 minute interval data). Further analysis of the arbitrage violations leads MacKinlay and Ramaswamy to conclude