Backtesting of portfolio optimization with and without risk-free asset

Abstract

A classical question in modern portfolio theory asks how the best portfolio composition can be chosen. Answering this question is definitely not easy and the general approach is to maximize the chosen risk-reward ratio. In our paper, however, we utilize the mean-variance framework introduced by Markowitz and maximize the (quadratic) utility function, which depends on the expected return (future mean return) and its variance. Simplification in terms of the applied utility function instead of the performance ratio allows portfolio backtesting over a relatively long period with a short computation time. The goal of the paper is to analyse how the risk-free asset investment possi-bility influences the ex post observed wealth path in the case of the selected period and data set. We find that the possibility of risk-free investments actually deteriorates the wealth path. Our explanation is that the simple portfolio optimization strategy proposed in the paper is unable to forecast market declines in time and reacts with a delay.