Robust porteføljeoptimering: Riskikobaserede porteføljer som et robust alternativ til mean-variance porteføljer

Abstract

Mean-variance analysis is the theoretical foundation of modern portfolio theory. In the mean variance-framework, portfolio construction is limited to an optimal weighting between the expected return (mean) and the risk (variance) of an investment. As such, the method provides a very simple and intuitive way to make investment desicions, but in practice this method has its limitations. Mean-variance optimized portfolios are known to be very sensitive to changes in the inputparameters. Following a mean-variance investment strategy can imply very high transaction costs, and theese portfolios have also been proven to produce large unintuitive bets, that perform poorly out-of-sample. By performing a simple simulation study, I show that the mean-variance portfolio is indeed very sensitive to estimation error in the inputparameters. The estimated mean-variance portfolio has an average expected Sharpe ratio of 0.132, whereas the true optimal mean-variance portfolio has an expected Sharpe ratio of 0.256. By applying a long-only constraint and varying the number of historical observations used in estimating the inputparameters, it is shown, that constraining the portfolios weights implies great improvemnet to the expected Sharpe ratio of the estimated mean-variance portfolio. Increasing the number of historical observations, also improves the estimated portfolio, but this effect is rather limited. By applying Principal Component Analysis to the true and the estimated correlation matrices, my results imply that the suboptimality of the mean-variance portfolio’s performance is caused, to a great extend, by estimation error in the expected return. This fact incourages the use of riskbased portfolio strategies, that totally ignore the expected return, as they only take the covariancematrix of returns as inputparameter. A theoretical examination of these risk-based methods and their properties, gives some intuition on why, these methods may perform better out-of-sample, even though, they don’t account for expected returns by any means. By performing a backtest, I evaluate out-of-sample performance of the mean-variance portfolio, and some of the most well known risk-based methods. I find strong empirical evidence that riskbased optimization strategies can indeed, serve as a robust alternative to the classical mean-variance optimized portfolio.