Assessing the Risk in Sample Minimum Risk Portfolios

52 Pages Posted: 4 May 2004

See all articles by Gopal Basak

Gopal Basak

University of Bristol - Department of Mathematics

Tongshu Ma

Binghamton University

Ravi Jagannathan

Northwestern University - Kellogg School of Management; National Bureau of Economic Research (NBER); Shanghai Jiao Tong University (SJTU) - Shanghai Advanced Institute of Finance (SAIF); Indian School of Business (ISB), Hyderabad

Date Written: April 7, 2004

Abstract

We show that the in-sample estimate of the variance of a global minimum risk portfolio constructed using an estimated covariance matrix of returns will on average be strictly smaller than its true variance. Scaling the in-sample estimate upward by a standard degrees-of-freedom related factor or using the Bayes covariance matrix estimator can be inadequate; the correction is likely to be twice as large as the standard correction when returns are i.i.d. multivariate Normal. We develop a Jackknife-type estimator of the optimal portfolio's variance that is valid when returns are i.i.d.; and a variation that may be better when returns exhibit volatility persistence.

We empirically demonstrate the need to correct for in-sample optimism by considering an optimal portfolio of 200 stocks that has the lowest tracking error when the S&P500 is the benchmark and three years of daily return data are used for estimating covariances. When the optimal portfolio is constructed using the sample covariance matrix, the standard deviation of the tracking error is 1.46 percent whereas its in-sample estimate is 0.94 percent. Standard degrees of freedom correction gives an estimate of 1.10 percent; our correction, 1.24 percent; and the weighted Jackknife, 1.36 percent.

Keywords: Minimum risk portfolios, in-sample optimism

JEL Classification: G10, G11

Suggested Citation

Basak, Gopal K. and Ma, Tongshu and Jagannathan, Ravi, Assessing the Risk in Sample Minimum Risk Portfolios (April 7, 2004). Available at SSRN: https://ssrn.com/abstract=528322 or http://dx.doi.org/10.2139/ssrn.528322

Gopal K. Basak

University of Bristol - Department of Mathematics ( email )

University of Bristol,
Senate House, Tyndall Avenue
Bristol, BS8 ITH
United Kingdom

Tongshu Ma

Binghamton University ( email )

PO Box 6001
Binghamton, NY 13902-6000
United States

Ravi Jagannathan (Contact Author)

Northwestern University - Kellogg School of Management ( email )

2001 Sheridan Road
429 Andersen Hall
Evanston, IL 60208
United States
847-491-8338 (Phone)
847-491-5719 (Fax)

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Shanghai Jiao Tong University (SJTU) - Shanghai Advanced Institute of Finance (SAIF) ( email )

Shanghai Jiao Tong University
211 West Huaihai Road
Shanghai, 200030
China

Indian School of Business (ISB), Hyderabad ( email )

Hyderabad, Gachibowli 500 019
India

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