Portfolio analysis with robust optimization method: An application on BIST100 stocks

The asset allocation is the main problem that investors face in the portfolio selection. The investors aim the optimal asset allocation that maximizing the expected return of portfolio while minimizing the risk of portfolio. But, completely eliminating the risk of investment is not possible. In a investment, the investor would undertakes the model based risks besides of systematic risks and unsystematic risks. Incorrect estimation of parameters, incorrect model, errors in calculation are examples of the model based risks. While the classical portfolio models such as Markowitz's mean variance include the model based risks, the portfolio models making optimization by regarding the uncertainty would eliminate these risks. Uncertainty based models like robust optimization construct robust portfolios by taking account the worst realization of asset returns within uncertainty sets. Thus, the solution of model remains optimal with high probability, while investors are protected against the model based risks. Construction of proper uncertainty sets increase the reliability of the model solution in the Robust optimization method. Since the expected returns calculated from historical data do not guarantee an accurate estimate of the assets, some robust estimators sholud be used. In this context, the bootsrap method was used to create uncertainty sets in the analysis. Bootstrap method makes inference about population parameters via sub-samples withdrawn from existing sample. The critical values of distribution of means that calculated from sub-samples form the border of uncertainty sets. So, the method enables to form uncretainty sets with predetermined confidence level. The aim of this thesis is to combine bootstrap method and robust optimization, and to get robust results related to both expected return rates and optimality of portfolio models. Thus, thanks to robust optimization the solution of portfolio model would stay feasible in high probability, while maksimum and mininmum values that expected returns being able to take would be determined via bootstrap method. Although it is technically possible to optimize a lot of objective function in the asset allocation problems, we preferred to optimize the model that has Sharpe ratio in the analysis. The bootstrap uncertainty sets, which were created with 99%, 97.5%, 95%, 90%, 80% and 70% confidence levels, were integrated into the robust model. Thus, by comparison with market retuns, the portfolios that yielded higher expected returns were composed. In the analysis the robust model proposed by Bertsimas and Sim (2004) is used, in this way the number of uncertian parametres that represented with gama has been added to the models. The results of analysis show that the constituted portfolios are robust both as parametres and as solution.