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## Section: New Results

### On the cross-sectional distribution of portfolio returns

Participants : Ioannis Emiris, Apostolos Chalkis.

The aim of the paper [24] 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 also for equal asset returns.

This is a joint work with Ludovic Calès (JRC - European Commission - Joint Research Centre, Ispra).