Seeking Alpha? It's a Bad Guideline for Portfolio Optimization

Posted: 20 May 2019

See all articles by Moshe Levy

Moshe Levy

Hebrew University of Jerusalem - Jerusalem School of Business Administration

Richard Roll

California Institute of Technology

Date Written: April 28, 2015

Abstract

Alpha is the most popular measure for evaluating the performance of both individual assets and funds. The alpha of an asset with respect to a given benchmark portfolio measures the change in the portfolio’s Sharpe ratio driven by a marginal increase in the asset’s portfolio weight. Thus, alpha indicates which assets should be marginally over/underweighted relative to the benchmark weights, and by how much. This study shows that alpha is actually a bad guideline for portfolio optimization. The reason is that alpha only measures the effects of infinitesimal changes in the portfolio weights. For small but finite changes, which are those relevant to investors, the optimal weight adjustments are almost unrelated to the alphas. In fact, in many cases the optimal adjustment is in the opposite direction of alpha – it may be optimal to reduce the weight of an asset with a positive alpha, and vice versa. Rather than employing alphas as a guideline, one can do much better by direct optimization with the desired constraint on the distance from the benchmark.

Keywords: Alpha, portfolio performance, portfolio optimization, mean-variance analysis

JEL Classification: G11

Suggested Citation

Levy, Moshe and Roll, Richard W., Seeking Alpha? It's a Bad Guideline for Portfolio Optimization (April 28, 2015). https://doi.org/10.3905/jpm.2016.42.5.107 . Available at SSRN: https://ssrn.com/abstract=2600084 or http://dx.doi.org/10.2139/ssrn.2600084

Moshe Levy (Contact Author)

Hebrew University of Jerusalem - Jerusalem School of Business Administration ( email )

Mount Scopus
Jerusalem, 91905
Israel

Richard W. Roll

California Institute of Technology ( email )

1200 East California Blvd
Mail Code: 228-77
Pasadena, CA 91125
United States
626-395-3890 (Phone)
310-836-3532 (Fax)

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