Can Under-Diversification Explain the Size Effect?

Vol. 23, No. 1, 2025
by Moshe Levy

None of the explanations suggested so far for the size anomaly seems to be consistent with the empirical evidence. This paper examines under-diversification as a possible explanation for the size effect. When the portfolio weight of a stock is non-negligible, its variance is priced. As small stocks are much more volatile than large stocks, this induces a size effect. We analytically derive the relation between under-diversification and the size premium, which allows us to estimate the magnitude of the under-diversification-induced size effect. We find it to be in close agreement with the empirically measured size effect.