Under-Diversification and the Size Effect
44 Pages Posted: 23 May 2019
Date Written: April 24, 2019
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: Suggested Citation