Multi-Period Asset Allocation under Different Risk Measures and Preferences

Liang Ying

Abstract

In this thesis, two multi-period asset allocation optimization models will be developed. The first model is developed to compare three risk measurement, expected shortfall, variance and semi-variance. The test shows that using expected shortfall as risk measurement produces the best outcome and can be easily solved. In contrast, under some circumstances, using other two risk measurement require a very long solving time, which is called "computationally unsolvable" in the following text. The second model aims to maximize the investor's utility and takes into account the risk preference and behavior of the investor. A particular behavioral utility function, piecewise linear utility function, is used in this thesis. The second model with maximizing piecewise linear utility function as objective is shown to be a better model than the first model with minimizing the expected shortfall as objective under different circumstances, like varying the required annual return and varying the volatility level.

In addition, both models: (1) allow rebalancing at the end of each investment periods; (2) use scenario generation method to get the returns for different assets; (3) take account of the transaction cost by rebalancing in the intermediate investment periods.