A Mathematical and Empirical Analysis of Rebalancing Alpha

Abstract

Rebalancing alpha is the excess return of a fixed-weight portfolio, which is regularly rebalanced, over its buy-and-hold counterpart. Two kinds of effects, both results of portfolio rebalancing, contribute to rebalancing alpha. The first is a volatility effect that arises from randomness of asset returns. The second is a return effect due to differences in asset returns. Built on previous studies, we define and analyze mathematically these two effects and by extension the rebalancing alpha. Our results clarify previous results and show the rebalancing alpha depends on “t-statistics” of pairwise excess returns. The results reveal conditions under which the rebalancing alpha is positive. Our analysis also quantifies explicitly how cross sectional serial correlations influence the return effect and the rebalancing alpha. We derive additional results for long-short portfolios, which require special treatments of return effect. Empirical examples with actual returns of asset allocation portfolios and equity sector portfolios provide verification, additional insights, and practical understanding of the results.

Keywords: Portfolio rebalancing, Rebalancing alpha, Volatility effect, Return effect

JEL Classification: G10, G11, C60