Leonard Ting-Kam Wong
University of Toronto
Room: M3 3127
Excess growth rate in finance and beyond
The excess growth rate, also called the diversification return, is a fundamental concept in portfolio theory: it captures the profit of a portfolio due to rebalancing and quantifies the intrinsic volatility of a stock market. In this talk, we undertake an in-depth mathematical study of this object and explore its connections to familiar concepts in information theory like the relative, Rényi and cross entropies, the Helmholtz free energy, L. Campbell's measure of average code length, and large deviations.
Our main results consist of three characterization theorems for the excess growth rate in terms of (i) the relative entropy, (ii) the gap in Jensen's inequality, and (iii) the logarithmic divergence that generalizes the Bregman divergence. We also discuss the maximization of the excess growth rate and compare it with the growth optimal portfolio. Based on joint work with Steven Campbell.