An optimal combination of risk-return and naive hedging

Abstract

Taking an approach contrary to the mean–variance portfolio, recent studies have appealed to an older wisdom, “the naive rule provides the best solution,” to improve out-of-sample performance in portfolio selection. Naive diversification, which invests equally across risky assets, is such an example of this simple rule. Previous studies also show that a portfolio combining naive diversification with the mean–variance strategy based on minimizing expected quadratic utility losses may show strong out-of-sample performance. Using the mean squared error, this paper derives an optimal combination of nonstochastic allocation and the mean–variance portfolio. We find that this design is equivalent to the combination of the naive rule and mean–variance strategy based on minimizing the expected utility losses. As an application of this finding, we propose a regression-based combination of maximal risk-return hedging and naive hedging. Our illustration also shows out-of-sample performance of a combined hedging that is superior to that of other methods.