Dynamic Alpha: A Spectral Decomposition of Investment Performance Across Time Horizons

Abstract

Copyright: © 2018 INFORMS The value added by an active investor is traditionally measured using alpha, tracking error, and the information ratio. However, these measures do not characterize the dynamic component of investor activity, nor do they consider the time horizons over which weights are changed. In this paper, we propose a technique to measure the value of active investment that captures both the static and dynamic contributions of an investment process. This dynamic alpha is based on the decomposition of a portfolio’s expected return into its frequency components using spectral analysis. The result is a static component that measures the portion of a portfolio’s expected return resulting from passive investments and security selection and a dynamic component that captures the manager’s timing ability across a range of time horizons. Our framework can be universally applied to any portfolio and is a useful method for comparing the forecast power of different investment processes. Several analytical and empirical examples are provided to illustrate the practical relevance of this decomposition.