I. INTRODUCTION
edging in futures markets provides a means of shifting the risk of spot price H changes within an economy. Participation in these markets exposes hedgers to the risk of variation in the time pattern of spot and futures prices. Thus hedging programs are described as substituting basis risk for price risk.' This article develops a measure of the basis risk which results from a nonstationary covariance matrix summarizing the rates of change of spot and futures prices. This is termed basis-estimation risk. Basis risk from this source is shown to be related to the degree of participation in the futures market and variation in the second-moment estimators used to determine the optimal risk-minimizing hedge ratio. A method for calculating this basis risk is introduced and empirical evidence is produced to demonstrate the significance of basis-estimation risk in hedging operations.
This perspective on hedging operations is distinct from previous research in this area. Previous research utilizing estimators for risk-minimizing hedge ratios essentially regards the covariance matrix of spot and futures price changes as stationary.2 Hedge effectiveness measures such as the R2 measure of Ederington (1979) and the Risk-Return Measure of Howard and DRntonio (1984) are developed under this ~ondition.~ The model proposed here emphasizes the role of a nonstationary covariance matrix in the determination of basis risk. Bawa, Brown, and Klein (1979) study the effect of estimation risk on security valuation models and conclude that estimation risk tends to decrease investment in 'Cootner (1967) refers to this substitution as specializing the risk faced by hedgers. This approach emphasizes managerial incentives to replace exogenously determined sources of risk with sources of risk which fall within the scope of managerial control.
2Research examining the covariance matrix for currency futures includes Grammatikos and Saunders (1983) who explore alternative procedures to estimate hedge ratios. Their evidence suggests these covariance matrices are not stationary. In addition, Eldridge (1984) demonstrates that volatility of futures price changes apparently responds to parallel contracts simultaneously traded on other exchanges.
'For a review of hedge effectiveness measures utilizing the RZ measure in currency futures, see Dale (1981) and Hill and Schneeweis (1982).