Minimax portfolio optimization: empirical numerical study

Abstract

In this paper, we carry out the empirical numerical study of the l_∞ portfolio selection model where the objective is to minimize the maximum individual risk. We compare the numerical performance of this model with that of the Markowitz's quadratic programming model by using real data from the Stock Exchange of Hong Kong. Our computational results show that the l_∞ model has a similar performance to the Markowitz's model and that the l_∞ model is not sensitive to the data. For the situation with only two assets, we establish that the expected return of the minimum variance model is less than that of the minimum l_∞ model when both variance and the return rate of one asset is less than the corresponding values of another asset.

Keywords:

• variance
• standard deviation
• portfolio selection
• risk aversion measures
• numerical study

Acknowledgements

This work was supported by the Research Grants Council of Hong Kong.