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Stability of the S&P 500 futures market efficiency conditions

Brenner and Kroner (1995) laid out the necessary conditions for futures market efficiency when the asset price data are characterized by stochastic trends. Specifically, a no arbitrage profit condition implies that spot, futures and cost-of-carry will be cointegrated, unless the cost-of-carry is stationary, in which case spot and futures will be cointegrated. This is examined for the S&P 500 futures market. The results are intriguing since evidence is initially found that spot and futures are themselves cointegrated. But a deeper analysis demonstrates that this cointegrating relationship is not stable. However, including the three-month Treasury bill rate as a proxy for the cost-of-carry yields one stable cointegrating (or equilibrium) relationship. This suggests that the evidence of cointegration between spot and futures alone is spurious and that researchers need to be careful about conclusions drawn from cointegration analysis of market efficiency conditions.