Financial/Actuarial Mathematics Seminar

We provide simple, easy-to-test criteria for the existence of relative arbitrage in equity markets. These criteria postulate essentially that the excess growth rate of the market portfolio, a positive quantity that can be estimated or even computed from a given market structure, be "sufficiently large". We show that conditions which satisfy these criteria are manifestly present in the U.S. equity market.  We then construct examples of abstract markets in which the criteria hold. These abstract markets allow us to isolate conditions similar to those prevalent in actual markets, and to construct explicit portfolios under these conditions. We study in some detail a specific example of an abstract market which is volatility-stabilized, in that the return from the market portfolio has constant drift and variance rates, while the smallest stocks are assigned the largest volatilities. A rather
interesting probabilistic structure emerges, in which time changes and the asymptotic theory for Bessel processes (the radial parts of multidimensional Brownian motions) play crucial roles. 

This is joint work with Dr. Robert Fernholz.