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ABSTRACT
The purpose of this paper is to measure with precision the market coefficient of relative risk aversion (CRRA) by building upon the theory of expected utility. Two approaches are implemented: by bootstrapping from the original sample of stock returns, and by Gaussian Monte Carlo simulation. The paper shows that the CRRA can indeed be estimated with high precision. The final interval estimate for the CRRA is bounded between 3.01 and 3.74. This range is not only precise but also extremely reasonable.
JEL Classification codes: D81; G11; C15.
Keywords: Risk Aversion; Expected Utility; Stock Returns; Bootstrapping; Gaussian Distribution.
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1.INTRODUCTION
Relative risk aversion is determined by the curvature of the utility function, and it is crucial for the analysis of behavior under risk or uncertainty. Most economists agree that relative risk aversion should be a constant and be, hence, independent of wealth. The often-used isoelastic utility function is the following with W as wealth:
... (1)
In equation (1) the parameter g is the coefficient of relative risk aversion (CRRA). Equation (1) collapses to log utility if g is equal to 1.
In the literature on risk aversion a difference exists between the CRRA estimates of applied economists and financial economists. The former usually find the CRRA to be very close to 1 (Hansen and Singleton, 1983; Hagirawa and Herce, 1997; Azar, 2000; Evans, 2004a, 2004b; Evans and Sezer, 2004; Chetty 2006; Azar, 2011b; and Dacy and Hasanov, 2011). Hansen and Singleton (1983) give a range for the CRRA between 0 and 2. However their estimates are imprecise and statistically insignificantly different from zero. Hagirawa and Herce (1997) report t-statistics that can be used to calculate standard errors from which confidence intervals can be obtained. The CRRA estimates are insignificantly different from +1, and they range from -1.34 to 5.15. Azar (2000) reports standard errors and these imply three ranges: 0.71-1.07, 0.84-0.95, and 1.83-1.97. The combined range is between 0.71 and 1.97. Evans (2004a, 2004b) and Evans and Sezer (2004) provide point estimates of the CRRA for many developed economies, and these lie between 1.2 and 1.78. Chetty (2006) also provides a point estimate which is 0.97. But it is difficult to guess for a range because Chetty (2006)...