Minimum-variance futures hedging under alternative return specifications

Abstract

It is widely believed that the conventional futures hedge ratio, is variance-minimizing when it is computed using percentage returns or log returns. It is shown that the conventional hedge ratio is variance-minimizing when computed from returns measured in dollar terms but not from returns measured in percentage or log terms. Formulas for the minimumvariance hedge ratio under percentage and log returns are derived. The difference between the conventional hedge ratio computed from percentage and log returns and the minimum-variance hedge ratio is found to be relatively small when directly hedging, especially when using near-maturity futures. However, the minimum-variance hedge ratio can vary significantly from the conventional hedge ratio computed from percentage or log returns when used in cross-hedging situations. Simulation analysis shows that the incorrect application of the conventional hedge ratio in crosshedging situations can substantially reduce hedging performance.

Optimal hedge ratio and hedging effectiveness of stock index futures: evidence from India

“…Terry (2005) established that an alternative specification of returns might have a significant impact on the hedge ratio particularly in cross-hedging strategies. Finally, as a robustness check we examined the results with two alternative returns specifications, namely, absolute rate of change and actual change itself.…”

Hedging emerging market bonds and the rise of the credit default swap

“…OLS is preferred to an error correction model because Lien (2005a, b) shows that OLS can provide a superior hedge ratio in an out of sample context even when the statistical properties of the data favor the error correction model. Price changes are preferred as Terry (2005) shows that OLS hedge ratios computed from price changes are variance minimizing but the same hedge ratio computed from log returns or percentage returns are not variance minimizing. In summary the hedge ratio β is from the OLS regression as previously shown in (1).…”

Statistical properties of post-sample hedging effectiveness

“…Terry (2005) compared hedging effectiveness when price differences, percentage returns and logarithmic returns are adopted to derive minimum variance hedge ratios. Akaike Information Criterion (AIC) is applied to determine the lag order, N (Frino, deB Harris, McInish, & Thomas, 2004;Ghosh & Gilmore, 1997).…”