Integrated Framework for Portfolio Risk Management

Abstract

Various risk measures are managed in a unique integrated framework for portfolio selection problems. They include normal risk (volatility), asymmetric risk (skewness), “fat-tail” risk (kurtosis) and downside risks, i.e. semi-variance, modified Value-at-Risk, and modified expected shortfall. The framework allows investors to change their preferences regarding these risks flexibly. The efficiency of the proposed approach is highlighted in its ability to handle investors’ risk preferences well. Verification is deployed by performing portfolio selection experiments in developed markets (e.g. the U.S. stock market), emerging markets (e.g. the South Korean stock market) and global investments. A preselection process dealing with datasets that include a large number of stocks is also introduced to eliminate stocks that have low diversification potential. Portfolios are evaluated by four performance indices, i.e. the Sortino ratio, the Sharpe ratio, the Stutzer performance index, and the Omega measure, both in-sample and out-of-sample tests. High performance and also well-diversified portfolios can be obtained if modified Value-at-Risk, variance, or semi-variance is concerned whereas emphasising only skewness, kurtosis or higher moments in general produces low performance and poorly diversified portfolios. The results also demonstrate that the proposed approach is superior in terms of overall performance and diversification level compared to a conventional higher moment portfolio optimization model. In addition, while ranking portfolios based on the four performance measures we find that these measures result in almost similar ranking outcomes in the U.S. and Korean stock investments, and slightly less similar in the global investments.