Portfolio Optimization and the Distribution of Firm Size

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