Portfolio optimization with target-shortfall-probability vector

Traditional portfolio optimization uses the standard deviation of the returns as a measure of risk. In recent years, the Target-Shortfall-Probability (TSP) was discussed as an alternative measure. From the utility-theoretical point of view, the TSP is not perfect. Furthermore it is criticized due to the insufficient description of the risk. The advantages of the TSP are the usage independent of the distribution and the intuitive understanding by the investor. The use of a TSP-vector reduces a utility-theoretical disadvantage of a single TSP and offers a sufficient description of risk. The developed Mean-TSP-vector model is a mixed-integer linear program. The CPU-Time of the program to get a solution demonstrates that the model is suitable for practical applications. A test of the performance shows, that the average return of the model when used in bear markets is equal to the results of the traditional portfolio optimization but – due to skewness – in bullish markets can achieve better returns.