Managing Underperformance Risk in Project Portfolio Selection

We consider a project selection problem where each project has an uncertain return with partially characterized probability distribution. The decision maker selects a feasible subset of projects so that the risk of the portfolio return not meeting a specified target is minimized. To model and evaluate this risk, we propose and justify a general performance measure, the Underperformance Riskiness Index (URI). We define a special case of the URI, the Entropic Underperformance Riskiness Index (EURI), for the project selection problem. We minimize the EURI of the project portfolio, which is the reciprocal of the absolute risk aversion (ARA) of an ambiguity averse individual with constant ARA who is indi↵erent between the target return with certainty and the uncertain portfolio return. The EURI extends the riskiness index of Aumann and Serrano (2008) by incorporating the target and distributional ambiguity, and controls the underperformance probability for any target level. Our model includes correlation and interaction e↵ects such as synergies. Since the model is a discrete nonlinear optimization problem, we derive the optimal solution using Benders decomposition techniques. We show that computationally e cient solution of the model is possible. Furthermore, the project portfolios generated by minimizing the underperformance risk are more than competitive in achieving the target with those found by benchmark approaches, including maximization of expected return, minimization of underperformance probability, mean-variance analysis, and maximization of Roy’s safety-first ratio (1952). When there is only a single constraint for the budget, we describe a heuristic which routinely provides project portfolios with near optimal underperformance risk.