Copula: A Primer for Fund Managers

Traditional equity risk models focus on estimating stock return variance-covariance matrix. Ignoring high-order moments, they implicitly assumes normal return distributions. The recent credit crisis has reminded us again that the normality assumption is insufficient in risk management. Moving away from normality requires a tractable technique to allow investigation of alternative distributions. Copula is a good choice since it helps modulise our job and enriches our distribution selection menu.This paper aims to demystify copulas for equity portfolio managers by addressing the following questions:1) What is copula and what does it represent 2) With correlation as a commonly used dependence measure, why is copula worth the extra complexity 3) What is 'tail dependence' 4) What are Gaussian, t-, Clayton, Gumbel and Frank copulas; how do they look and behave; and how to simulate 5) How to model equity markets with copulas where the dimensions are high 6) How can copula-based market model be applied to equity PM process.