A Robust Portfolio Construction Using the Bootstrap Method to Extract Multidimensional Uncertainty Sets: An Application on BIST100 Stocks

Asset allocation is the main problem of portfolio management. The goal is to maximize the portfolio's expected return while minimizing investment risk by allocating assets optimally. However, it is not possible to exclude all investment risks due to prediction errors, optimization of incorrect models, uncertainties in parameters, etc. The classical models used in portfolio theory disperse model-based risks but ignore the uncertainties of the predicted parameters. Besides, uncertainty-based models, such as robust optimization help to eliminate uncertainty risks in addition to model-based risks. Robust optimization constructs portfolios by considering worst-case realizations of asset returns within uncertainty sets. In this way, the model's solution remains optimal with high probability, while investors are protected from model-based risks. In this paper, we develop a robust optimization formulation based on Bertsimas and Sim (2004) and combine the model with the bootstrap method to create optimal portfolios. The results show that the expected return of the portfolios decreases as the uncertainty of the robust model increases. The expected return of the robust portfolio is as good as that of the classical portfolio for a moderate level of uncertainty. Out of the sample, the robust portfolios outperform the equally weighted portfolio and the target index