Under-Diversification and the Size Effect

44 Pages Posted: 23 May 2019

See all articles by Moshe Levy

Moshe Levy

Hebrew University of Jerusalem - Jerusalem School of Business Administration

Haim Levy

Hebrew University of Jerusalem - Jerusalem School of Business Administration; Fordham University

Date Written: April 24, 2019

Abstract

Asness et. al. (2018) recently resurrect the size effect, concluding that it “…should be restored as one of the central cross-sectional empirical anomalies for asset pricing theory to explain”. We suggest a theoretical explanation for the size effect, based on the observation that many investors hold only a small number of stocks in their portfolios. Mean-variance investors require compensation for a stock’s marginal contribution to their portfolio’s variance, i.e. for the stock’s “beta” relative to the portfolio. The role of a stock’s own variance in “beta” is approximately proportional to the stock’s weight in the portfolio. It is therefore negligible in the CAPM, where all weights are very small, but can be substantial if only a small number of stocks are held in the portfolio. As small stocks tend to have higher variances, they command higher expected returns than predicted by their CAPM betas. Thus, the size effect is theoretically justified as a risk-premium and is therefore here to stay. We empirically estimate the magnitude of the under-diversification induced size effect, and show that it can fully explain the size anomaly.

Keywords: Size anomaly, small firm effect, segmented-market model, Generalized CAPM, generalized beta

JEL Classification: G11, G12

Suggested Citation

Levy, Moshe and Levy, Haim, Under-Diversification and the Size Effect (April 24, 2019). Available at SSRN: https://ssrn.com/abstract=3377242 or http://dx.doi.org/10.2139/ssrn.3377242

Moshe Levy (Contact Author)

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

Mount Scopus
Jerusalem, 91905
Israel

Haim Levy

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

Mount Scopus
Jerusalem, 91905
Israel

HOME PAGE: http://pluto.huji.ac.il/~mshlevy/

Fordham University ( email )

140 West 62nd Street
New York, NY 10023
United States

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
65
Abstract Views
318
rank
359,099
PlumX Metrics