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

Quantitative Finance, 2013, Forthcoming

Johnson School Research Paper Series No. 39-2011

34 Pages Posted: 22 Sep 2011 Last revised: 27 Oct 2013

Marcos Lopez de Prado

AQR Capital Management, LLC; Cornell University - Operations Research & Industrial Engineering; RCC - Harvard University

Matthew Foreman

University of California, Irvine

Date Written: June 15, 2013

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

Suggested Citation

López de Prado, Marcos and Foreman, Matthew, A Mixture of Gaussians Approach to Mathematical Portfolio Oversight: The EF3M Algorithm (June 15, 2013). Quantitative Finance, 2013, Forthcoming. Available at SSRN: https://ssrn.com/abstract=1931734 or http://dx.doi.org/10.2139/ssrn.1931734

Marcos López de Prado (Contact Author)

AQR Capital Management, LLC ( email )

One Greenwich Plaza
Greenwich, CT 06830
United States

HOME PAGE: http://www.aqr.com

Cornell University - Operations Research & Industrial Engineering ( email )

237 Rhodes Hall
Ithaca, NY 14853
United States

HOME PAGE: http://www.orie.cornell.edu

RCC - Harvard University ( email )

1875 Cambridge Street
Cambridge, MA 02138
United States

HOME PAGE: http://www.rcc.harvard.edu

Matthew Foreman

University of California, Irvine ( email )

Mathematics Department
Irvine, CA 62697-3125
United States

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