IMA Complex Systems Seminar

1:30, Thursday, May 20, 2004             



A New Measure of Managers Performance Based on the “Stochastic Discount Factor”


Luis Roman

Worcester Polytechnic Institute
100 Institute Road
Worcester, MA 01609



Measuring a manager’s performance has been the subject of extensive research in recent years, in particular for hedge funds since these are described as skill-based investment strategies. Skill-based strategies obtain returns from the unique skill or strategy of the trader. More recently, hedge fund returns have been shown to be driven largely by market factors such as changes in credit spreads or market volatility, so one can think of their returns as a combination of manager skill and an underlying return to the strategy itself. But, the question of whether fund managers can deliver expected returns in excess of naive benchmarks has long been controversial. Previous studies of hedge funds performance have used single- or multifactor models, and these are also referred to as unconditional approaches. On the other hand, another approach is based on the "Stochastic Discount Factor" (SDF), whose existence is granted in the absence of arbitrage opportunities. However, in general, controversy about results using the SDF, and how it should be implemented have occupied the minds of many researchers interested in performance evaluation. In this talk, we present a new measure of manager’s performance assuming that the dynamics of the underlying assets are described by a system of stochastic differential equations. Under this new measure, some of the ambiguities surrounding the SDF can be clarified, and also, when applied to simple cases, it derives some equilibrium equations, which are variants of the Capita Asset Price Model (CAPM).