Risk Model and the Model Risk: Probabilistic DecisionTheory Applied to One Often Overlooked Risk

Abstract

Traditional portfolio management theory suffers from several insurmountable shortcomings: unrealistic model of stock returns, the ill-posed matrix inversion problem, and difficulties with consistent incorporation of analysts’ and PM’s views. Despite some breakthroughs like the Black-Litterman approach, it is generally believed that the modern portfolio theory framework is not sufficiently rich and powerful to offer solutions to problems that modern investment practitioners face. The author suggests that the probabilistic decision theory provides the necessary toolset to develop the necessary analysis and optimization portfolio management framework. In this short article the author outlines the methodology and applies it to problems of increased complexity. The author shows that in the probabilistic decision theory the optimal composition of the portfolio is necessarily user-dependent: PM’s and analysts’ views are incorporated as the prior probability distributions, constraints and risk tolerances are intertwined with the optimization procedure and the model risk is consistently included in the consideration.