A Stochastic Convergence Model for Portfolio Selection

Abstract

Portfolio selection techniques must provide decision makers with a dynamic model framework that incorporates realistic assumptions regarding financial markets, risk preferences, and required portfolio characteristics. Unfortunately, multistage stochastic programming (SP) models for portfolio selection very quickly become intractable as assumptions are relaxed and uncertainty is introduced. In this paper, I present an alternative model framework for portfolio selection, stochastic convergence (SC), that systematically incorporates uncertainty under a realistic assumption set. The optimal portfolio is derived through an iterative procedure, where portfolio plans are evaluated under many possible future scenarios then revised until the model converges to the optimal plan. This approach allows for scenario analysis over all stochastic components, requires no limitation on the structural form of the objective or constraints, and permits evaluation over any length planning horizon while maintaining model tractability by aggregating the scenario tree at each stage in the solution process. Through focused aggregation schemes, the SC approach allows for the implementation of a lower partial variance riskmetric, which is preferred in investment selection. In simulated tests, the SC model, with scenario aggregation, generated portfolios exhibiting performance similar to those generated using the SP model form with no aggregation. Empirical tests using historical fund returns show that a multiperiod SC decision strategy outperforms various benchmarkstrate gies over a long-term test horizon under both asset-liability matching and return maximization frameworks.