Portfolio Optimization and the Distribution of Firm Size

30 Pages Posted: 16 Jun 2008

See all articles by Ran Duchin

Ran Duchin

University of Washington - Michael G. Foster School of Business

Moshe Levy

Hebrew University of Jerusalem - Jerusalem School of Business Administration

Date Written: June 2008

Abstract

The empirical distribution of firms' market capitalizations is shown to be in excellent agreement with a very skewed lognormal distribution: the largest firms are about 1000 times larger than the median firm. Can this skewed size distribution be consistent with mean-variance portfolio optimization and realistic return parameters? We show that the expected returns implied by the empirical size distribution and portfolio optimization agree with the empirical average returns. Moreover, the portfolio optimization framework can provide a constructive explanation for the observed lognormal distribution. Thus, portfolio optimization is not only consistent with the empirical size distribution, it can actually explain it.

Keywords: firm size, portfolio optimization, mean-variance analysis, lognormal distribution, Gibrat process, CAPM

JEL Classification: G11, L11, G3

Suggested Citation

Duchin, Ran and Levy, Moshe, Portfolio Optimization and the Distribution of Firm Size (June 2008). Available at SSRN: https://ssrn.com/abstract=1146308 or http://dx.doi.org/10.2139/ssrn.1146308

Ran Duchin (Contact Author)

University of Washington - Michael G. Foster School of Business ( email )

Box 353200
Seattle, WA 98195-3200
United States

Moshe Levy

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

Mount Scopus
Jerusalem, 91905
Israel

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