Alpha and Alpha Decay in Continuous Time

Abstract:     
This paper analyzes a modified Sharpe ratio (SR) and alpha decay (the speed of alpha losing its value) in a continuous-time model. We show that even under the mean-variance framework, SR is not a sufficient statistic. Holding SR constant, an increase in alpha decay may be associated with a big drop in performance due to a smaller intertemporal hedging benefit. A higher SR may represent worse performance without controlling for alpha decay. These results are robust in the presence of trading costs. The empirical implication is that when comparing investors' performance, we should control for their investment styles determined by the speed of their information decay. For example, fundamental investors usually use information with slow alpha decay, but statistical arbitragers usually use information with fast alpha decay. The arbitragers may achieve a higher SR but not necessarily a better performance.

Number of Pages in PDF File: 27

Keywords: Performance, the Sharpe ratio, alpha decay, intertemporal hedging benefit

JEL Classification: D11, D91, G11, C61

working papers series