Theoretical and Empirical Estimates of Mean-Variance Portfolio Sensitivity

24 Pages Posted: 16 Feb 2010 Last revised: 10 Dec 2013

See all articles by Andrzej Palczewski

Andrzej Palczewski

University of Warsaw - Faculty of Mathematics, Informatics, and Mechanics

Jan Palczewski

University of Leeds - School of Mathematics

Date Written: December 10, 2013

Abstract

This paper studies properties of an estimator of mean-variance portfolio weights in a market model with multiple risky assets and a riskless asset. Theoretical formulas for the mean square error are derived in the case when asset excess returns are multivariate normally distributed and serially independent. The sensitivity of the portfolio estimator to errors arising from the estimation of the covariance matrix and the mean vector is quantified. It turns out that the relative contribution of the covariance matrix error depends mainly on the Sharpe ratio of the market portfolio and the sampling frequency of historical data.

Theoretical studies are complemented by an investigation of the distribution of portfolio estimator for empirical datasets. An appropriately crafted bootstrapping method is employed to compute the empirical mean square error. Empirical and theoretical estimates are in good agreement, with the empirical values being, in general, higher.

Keywords: Investment analysis, asset allocation, mean-variance portfolio, estimation error, bootstrap

JEL Classification: C13, C52, G11

Suggested Citation

Palczewski, Andrzej and Palczewski, Jan, Theoretical and Empirical Estimates of Mean-Variance Portfolio Sensitivity (December 10, 2013). Available at SSRN: https://ssrn.com/abstract=1553073 or http://dx.doi.org/10.2139/ssrn.1553073

Andrzej Palczewski

University of Warsaw - Faculty of Mathematics, Informatics, and Mechanics ( email )

Banacha 2
Warsaw, 02-097
Poland

Jan Palczewski (Contact Author)

University of Leeds - School of Mathematics ( email )

Leeds, LS2 9JT
United Kingdom

HOME PAGE: http://www.maths.leeds.ac.uk/~jp

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