Review of Quantitative Finance and Accounting, 13 (1999): 249±260
# 1999 Kluwer Academic Publishers, Boston. Manufactured in The Netherlands.
A Model of Return Volatility with Application to
Estimating Relative Risk Aversion
Department of Finance, George Washington University, Washington, D.C. 20052
ROBERT F. PHILLIPS
Department of Economics, George Washington University, Washington, D.C. 20052, e-mail: firstname.lastname@example.org
Abstract. We estimate a monthly return volatility model that allows for the abrupt changes in volatility often
observed in returns data. Using this model we are able to identify key months likely to correspond to draws from a
high volatility regime. Using our model in conjunction with Merton's (1980) model relating expected risk premia
to risk we obtain reasonable estimates of the coef®cient of relative risk aversion.
Key words: relative risk aversion, volatility, mixture
JEL Classi®cation: 522
Two important areas of general interest in economics and ®nance have been estimating a
coef®cient of relative risk aversion and modeling the volatility of returns to stocks. Pratt's
(1964) coef®cient of relative risk aversion is the wealth elasticity of the marginal utility of
wealth, and under certain conditions it will be the equilibrium market price of market risk.
Pindyck (1988) asserts that estimates of this parameter fall in the range of 2 to 6 in asset
demand studies, but Merton (1980) reports his own estimates which vary from about 1 to
26 depending on the sample period. Citing a large body of empirical literature, Mehra and
Prescott (1985) restrict the parameter to be less than 10 a priori. Different estimates of
relative risk aversion from different data and methodologies can provide clues for building
better theoretical models (see Thaler, 1987).
Interest in stock market volatility extends back more than 30 years when Mandelbrot
(1963) ®rst observed serial correlation in volatility. More recently, researchers have sought
to model volatility in order to investigate the implications of excess volatility on the
ef®cient market hypothesis (e.g., Shiller, 1981; and Poterba and Summers, 1986) while
others have investigated the causes of changes in volatility (e.g., Schwert, 1989). One of
the stylized facts which has emerged from the literature is that the underlying return
generating process is non-normal (e.g., Beedles, 1979; Taylor, 1986; Friedman and
Laibson, 1989). Stock returns are truncated at minus one due to limited liability, and are
skewed right with excess kurtosis.
Poterba and Summers' (1986) widely cited paper is representative in that, like many
other studies, it models current volatility as depending on past volatility linearly. Poterba