Unbiased Estimation, Price Discovery, and Market Efficiency: Futures Prices and Spot Prices

In most cases, futures prices are not unbiased estimates of future spot prices. The price discovery function of futures markets should be defined as the lead-lag relationship between current futures prices and current spot prices, not the unbiased estimation of future spot prices. The pricing efficiency and information efficiency of futures markets are different. Three empirical models appropriate to investigate the relationship between futures prices and spot prices were discussed. As an application, these models were used to test the pricing efficiency, the lead-lag relationship, and the information efficiency of the S&P 500 index spot and futures markets from 21 September 1990 to 20 December 2007.