Mean-variance Efficiency of the Market Portfolio and Futures Trading

An intertemporal CAPM is derived, in which mean-variance efficiency of the market portfolio is neither necessary nor a sufficient condition, when, in addition to the usual cash assets, non-redundant futures contracts trade. A (3 + K) mutual fund separation is obtained in place of the usual (2 + K) fund, where K is the number of state variables. Mean-variance efficiency of the market portfolio is a necessary condition only when cash assets solely trade.

LIOUI, A. and PONCET, P. (2001). Mean-variance Efficiency of the Market Portfolio and Futures Trading. Journal of Futures Markets, pp. 329-346.