Review of Quantitative Finance and Accounting, 12 (1999): 135–157
© 1999 Kluwer Academic Publishers, Boston. Manufactured in The Netherlands.
The Estimation of Systematic Risk under
Differentiated Risk Aversion: A Mean-Extended Gini
RUSSELL B. GREGORY-ALLEN
College Retirement Equities Fund (CREF), New York, NY 10017 USA
Department of Economics, Monaster Center for Economic Research, Ben Gurion University of the Negev,
Beer Sheva, 84105 Israel, e-mail: email@example.com
Abstract. This paper examines a mean-Gini model of systematic risk estimation that resolves some econo-
metric problems with mean-variance beta estimation and allows for heterogeneous risk aversion across investors.
Using the mean-extended Gini (MEG) model, we estimate systematic risks for different degrees of risk aversion.
MEG betas are shown to be instrumental variable estimators that provide econometric solutions to biases
generated by the estimation of mean-variance (MV) betas. When security returns are not normally distributed,
MEG betas are proved to differ from MV betas. We design an econometric test that assesses whether these
differences are signiﬁcant. As an application using daily returns, we estimate MEG and MV betas for U.S.
Key words: Beta, mean-Gini, normality test, instrumental variable estimation
As a measure of systematic risk, beta has dominated the world of ﬁnance since its
inception in the sixties. Typically, under mean-variance (MV), beta is estimated using
ordinary least-squares (OLS). Notwithstanding its widespread application, there are nu-
merous problems related to the use of beta in the estimation of systematic risk (its
nonstationarity over time (Kim, 1993), to name only one).
In this paper, we address and quantify two speciﬁc problems associated with mean-
variance betas. The ﬁrst deals with econometric biases that may arise in estimating betas;
the second with the implications inherent in assuming normally distributed returns. Both
problems are critical in the estimation of betas because they can bias or invalidate the
evaluation of systematic risk, thereby rendering investor portfolios inoptimal.
To solve these problems, we propose the mean-extended Gini (MEG) model as an
alternative to the MV beta. We demonstrate the econometric advantages of using MEG in
beta estimation. When the market model used to estimate systematic risk is misspeciﬁed,
MV betas may be biased. MEG betas, because they are instrumental variables estimators,
provide an econometric solution to the speciﬁcation bias.
@ats-ss2/data11/kluwer/journals/requ/v12n2art3 COMPOSED: 01/13/99 1:32 pm. PG.POS. 1 SESSION: 43