Spanning with futures contracts

Regression-based testing techniques have long been used to quantify whether the efficient frontier of a set of assets spans the frontier of a larger collection of investments. This paper derives regression-based spanning tests for the case in which the investment possibilities set contains, or is constituted by, futures contracts for which marked-to-market margins are explicitly taken into account. Two empirical applications illustrate our results.

► We derive test for spanning for futures contracts.
► Futures returns is a non-linear function of the current price of the underlying contract.
► These tests can evaluate the gains for diversification for futures with different margin costs.
► We empirically evaluate the benefits from expanding portfolios of NYMEX futures.