Portfolio Selection by Robust Optimization

Abstract

This paper discusses the portfolio selection based on robust optimization. Since the parameters values of the portfolio optimization problem such as price of the stock, dividends, returns, etc. of per share are unknown, variable and their distributions are uncertain because of the market and price volatility, therefore, there is a need for the development and application of methodologies for decision making under uncertainty. Robust optimization is a tractable alternative to the other programming in these problems. This paper has investigated a specific robust optimization approach as the Bertsimas and Sim's model to the portfolio selection problem in which the unknown and variable return of an asset is modeled by budgeted polyhedral uncertainty sets and the effect of different definitions of the bounds on the uncertainty sets and show that robust models yield well diversified portfolios, in terms of the number of assets and asset weights. The data set used in this paper, include the monthly returns of the 30 stocks that randomly selected from the 78 stocks of the Tehran Stock Exchange, from 1385 to 1390.

Keywords

• portfolio selection
• robust optimization
• uncertainty modeling