Investigation of a lead‐lag relationship between spot stock indices and their futures contracts

Abstract

onsidering the newness of stock index futures, considerable analysis has been C done of the relationship between spot and futures indices, including some empirical examination of lead-lag relationships. However, most studies thus far have lacked objective measures of the timing relationship connecting the two series. This article presents results of a study conducted to provide an objective measure of this timing relationship. PREVIOUS, RELATED STUDIESZeckhauser and Niederhoffer (1983) looked at the early experience with market index futures and found indications that futures prices appear to have some ability to anticipate movements in the spot index, particularly in the near term. Their analysis consisted of computing the basis (difference between the price of the futures contract and the price of the spot index) at closing, a variable they call the premium. This variable was examined with three different movements in the spot price-to the next day open, to the next day close, and to the close three days later. Looking at the period of study as a whole, they found that the larger the premium, the greater is the tendency for the spot to rise. Kipnis and Tsang (1983) evaluated and compared risk characteristics of the various contracts and maturities and found daily futures price moves can be inconsistent with the market: NYSE and S&P 500 futures moved oppositely to the market 15% to 18% of the time, whereas Value Line futures were inconsistent 27% of the time. In addition to reflecting changes in carrying costs, they found that changes in the premium or discount of futures also appear to anticipate the forthcoming direction of the markets. AnthonyFurthermore, they note that the futures market tendency to lead the stock market is evident on an intra-day basis. One example they cite is the trade-by-trade, minute-by-minute chart of price movements for both the S&P 500 futures contract and the actual S&P 500 stock index on December 7, 1982. Simply by inspection of the two graphs, they suggest that peaks and troughs for the December futures contract lead stock market turns by about five to 20 minutes. However, they warn that futures prices are more volatile than the stock market, which implies that they are also vulnerable to many minor false moves which cannot be distinguished easily from real turns until after the fact.Modest and Sundaresan (1982) provide a comparative study of three stock index futures contracts and their price behavior. In a simplified perfect market setting, they show that for a value-weighted arithmetic index such as the S&P 500, the discounted futures price must equal the current spot price (adjusted for dividends) to prevent arbitrage. For a geometric index such as the Value Line, they show that the previous equality becomes an inequality. When transactions costs are recognized, the discounted futures prices can fluctuate within a bounded interval without giving rise to arbitrage profits.Grant (1982) argues that there is a difference in the pricing of market index futures contracts as compare...

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