On the cross-sectional distribution of portfolios' returns

The aim of this paper is to study the distribution of portfolio returns across portfolios and for given asset returns. We focus on the most common type of investment considering portfolios whose weights are non-negative and sum up to 1. We provide algorithms and formulas from computational geometry and the literature on splines to compute the exact values of the probability density function, and of the cumulative distribution function at any point. We also provide closed-form solutions for the computation of its first four moments, and an algorithm to compute the higher moments. All algorithms and formulas allow for equal asset returns.