Portfolio Optimization and Monte Carlo Simulation

Abstract

This paper uses Monte Carlo simulation of a simple equity growth model with resampling of historical financial data to estimate the probability distributions of the future equity, earnings and payouts of companies. The simulated equity is then used with the historical P/Book distribution to estimate the probability distributions of the future stock prices. This is done for Coca-Cola, Wal-Mart, McDonald’s and the S&P 500 stock-market index. The return distributions are then used to construct optimal portfolios using the “Markowitz” (mean-variance) and “Kelly” (geometric mean) methods. It is shown that variance is an incorrect measure of investment risk so that mean-variance optimal portfolios do not minimize risk as commonly believed. This criticism holds for return distributions in general. Kelly portfolios are correctly optimized for investment risk and long-term gains, but the portfolios are often concentrated in few assets and are therefore sensitive to estimation errors in the return distributions.

Keywords: Portfolio Optimization, Mean-Variance, Kelly, Monte Carlo Simulation