Unbiased estimation,price discovery and market efficiency:Relationship between futures prices and spot prices

The paper analyzes and clarifies some long-existing misunderstandings in theoretical and empirical studies on the relationship between futures prices and their underlying spot prices.It illustrates in theory that in most cases futures prices are not unbiased estimates of future spot prices and whether futures prices are unbiased estimates of future spot prices is not appropriate test models of futures markets' efficiency.It proposes that the lead-lag relationship between futures prices and current spot prices should be the appropriate definition of price discovery of futures.It also points out there are two kinds of futures markets' efficiency-pricing efficiency and information efficiency and only a futures market with pricing efficiency could hedge risk as effectively as possible.At last It proposes three models appropriate to test the relationship between futures prices and spot prices and apply these models to testing the pricing efficiency,lead-lag relationship and information efficiency of SP 500 index spot and futures market from September 21,1990 to December 20,2007.