On Measuring Nonlinear Risk with Scarce Observations

19 Pages Posted: 31 Mar 2008 Last revised: 22 Jun 2016

See all articles by Alexander S. Cherny

Alexander S. Cherny

Moscow State University

Raphael Douady

Riskdata; Stony Brook university ; CES Univ. Paris 1

Stanislav A. Molchanov

University of North Carolina (UNC) at Charlotte

Date Written: March 27, 2008

Abstract

We consider the problem of measuring the risk of a portfolio with scarce observations by linking it to several risk factors. A typical example is measuring the risk of a hedge fund. It is assumed that from the available data one can estimate the joint law of all the factors as well as all the 2-dimensional joint laws of the portfolio's return and increments of each factor. The problem is to recover the conditional mean of the portfolio's return given the values for all factors. We present an analytic computationally feasible solution of this problem for the case when the joint law of factors is a Gaussian copula. A shorter and more practical version of this paper can be found on SSRN under the name, "On Measuring Hedge Fund Risk."

Keywords: Cross-term risk, factor risk, Gaussian copula, hedge fund replication, hedge fund risk, idiosyncratic risk, monomial risk, non-linear regression, risk measurement

JEL Classification: G29

Suggested Citation

Cherny, Alexander S. and Douady, Raphael and Molchanov, Stanislav A., On Measuring Nonlinear Risk with Scarce Observations (March 27, 2008). Available at SSRN: https://ssrn.com/abstract=1113730 or http://dx.doi.org/10.2139/ssrn.1113730

Alexander S. Cherny (Contact Author)

Moscow State University ( email )

Faculty of Mechanics and Mathematics
Department of Probability Theory
Moscow, 119992
Russia
007 095 939 14 03 (Phone)
007 095 939 14 03 (Fax)

HOME PAGE: http://mech.math.msu.su/~cherny

Raphael Douady

Riskdata ( email )

6, rue de l'Amiral Coligny
Paris, 75001
France

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

Stony Brook university ( email )

Stony Brook, NY 11794
United States

CES Univ. Paris 1 ( email )

106 bv de l'Hôpital
Paris, 75013
France

Stanislav A. Molchanov

University of North Carolina (UNC) at Charlotte ( email )

9201 University City Boulevard
Charlotte, NC 28223
United States
704 687 45 73 (Phone)

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