A Mixture of Gaussians Approach to Mathematical Portfolio Oversight: The EF3M Algorithm

Abstract

An analogue can be made between: (a) the slow pace at which species adapt to an environment, which often results in the emergence of a new distinct species out of a once homogeneous genetic pool, and (b) the slow changes that take place over time within a fund, mutating its investment style. A fund’s track record provides a sort of genetic marker, which we can use to identify mutations. This has motivated our use of a biometric procedure to detect the emergence of a new investment style within a fund’s track record. In doing so, we answer the question: “What is the probability that a particular PM’s performance is departing from the reference distribution used to allocate her capital?”

The EF3M approach, inspired by evolutionary biology, may help detect early stages of an evolutionary divergence in an investment style, and trigger a decision to review a fund’s capital allocation.

Keywords: Skewness, Kurtosis, Mixture of Gaussians, Moment Matching, Maximum Likelihood, EM algorithm

JEL Classification: C01, C02, C15, C16, C38, C44