Portfolio management under epistemic uncertainty using stochastic dominance and information-gap theory

Portfolio management in finance is more than a mathematical problem of optimizing performance under risk constraints. A critical factor in practical portfolio problems is severe uncertainty – ignorance – due to model uncertainty. In this paper, we show how to find the best portfolios by adapting the standard risk-return criterion for portfolio selection to the case of severe uncertainty, such as might result from limited available data. This original approach is based on the combination of two commonly conflicting portfolio investment goals: 1) obtaining high expected portfolio return, and 2) controlling risk. The two goals conflict if a portfolio has both higher expected return and higher risk than competing portfolio(s). They can also conflict if a reference curve characterizing a minimally tolerable portfolio is difficult to beat. To find the best portfolio in this situation, we first generate a set of optimal portfolios. This set is populated according to a standard mean-risk approach. Then we search the set using stochastic dominance (SSD) and Information-Gap Theory to identify the preferred one. This approach permits analysis of the problem even under severe uncertainty, a situation that we address because it occurs often, yet needs new advances to solve. SSD is attracting attention in the portfolio analysis community because any rational, risk-averse investor will prefer portfolio y1 to portfolio y2 if y1 has SSD over y2. The player’s utility function is not relevant to this preference as long as it is risk averse, which most investors are (e.g. De Giorgi 2005 [7], Berleant et al. 2005 [3]).