Portfolio Choice Models Based on Second-Order Stochastic Dominance Measures: An Overview and a Computational Study
In this chapter we present an overview of second-order stochastic dominance-based models with a focus on those using dominance measures. In terms of portfolio policy, the aim is to find a portfolio whose return distribution dominates the index distribution to the largest possible extent. We compare two approaches, the unscaled model of Roman et al. (Mathematical Programming Series B 108: 541–569, 2006) and the scaled model of Fabian et al. (Quantitative Finance 2010). We constructed optimal portfolios using representations of the future asset returns given by historical data on the one hand, and scenarios generated by geometric Brownian motion on the other hand. In the latter case, the parameters of the GBM were obtained from the historical data. Our test data consisted of stock returns from the FTSE 100 basket, together with the index returns. Part of the data were reserved for out-of-sample tests. We examined the return distributions belonging to the respective optimal portfolios of the unscaled and the scaled problems. The unscaled model focuses on the worst cases and hence enhances safety. We found that the performance of the unscaled model is improved by using scenario generators. On the other hand, the scaled model replicates the shape of the index distribution. Scenario generation had little effect on the scaled model. We also compared the shapes of the histograms belonging to corresponding pairs of in-sample and out-of-sample tests and observed a remarkable robustness in both models. We think these features make these dominance measures good alternatives for classic risk measures in certain applications, including certain multistage ones. We mention two candidate applications.