AbstractThe paper presents a new methodology to estimate time dependent minimum variance hedge ratios. The so‐called conditional OLS hedge ratio modifies the static OLS approach to incorporate conditioning information. The ability of the conditional OLS hedge ratio to minimize the risk of a hedged portfolio is compared to conventional static and dynamic approaches, such as the naïve hedge, the roll‐over OLS hedge, and the bivariate GARCH(1,1) model. The paper concludes that, both in‐sample and out‐of‐sample, the conditional OLS hedge ratio reduces the basis risk of an equity portfolio better than the alternatives conventionally used in risk management. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:945–964, 2004