IMA Complex Systems Seminar
1:30, Thursday, May 20, 2004
A New Measure of
Managers Performance Based on the “Stochastic Discount Factor”
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).