his paper examines empirically whether complex hedges reduce risk more than T naive or simple hedges?' Anderson and Danthine (1980,1981) derived two of the complex hedges we study. They extended a simple hedging model by introducing hedges in multiple assets and hedges of portfolios of assets. Baesel and Grant (1982) developed the third complex strategy by including trading at multiple dates. Ederington (1979) and others show that the simple hedge is the expected value of a regression coefficient. The dependent variable is the spot position. The independent variable is the futures price. Anderson and Danthine identified a similar result when there are multiple futures. The variance-minimizing futures positions are the expected values of ordinary least-squares (OLS) regression coefficients. The dependent variable is the spot position. The independent variables are the multiple futures prices. Anderson and Danthine also examined portfolios composed of linear combinations of spot positions. They showed that the risk-minimizing futures positions are linear combinations of the futures positions for the individual spot positions.
Baesel and Grant examined trading in a different contract at each of two dates. Their results extend to trading in multiple contracts at many dates. The variance-minimizing hedges are the expected values of a vector of regression coefficients. The dependent variable is always a "properly defined" spot position. The independent variables are the futures prices. The "properly defined" spot position at each trading date is the asset being hedged plus the stochastic returns from futures positions at later dates.* This paper examines the empirical value of these complex hedges which are based on more realistic assumptions. For example, the number of assets traded in futures markets is small relative to those traded in spot markets. Therefore, many potential hedgers will 'A naive hedge is a one-to-one futures position in the same asset. A simple hedge is a risk-minimizing fu-%e authors will provide on request a unified derivation of a11 of the complex hedges tested in this paper.