Measuring relative risk aversion

Abstract

This note intends to estimate the Coefficient of Relative Risk Aversion (CRRA). The underlying model is expected utility and certainty equivalence. The utility function selected is of the power form and is shown to be independent of initial wealth. This property makes the results applicable to any individual, whatever her initial wealth, or even to a market measure. The equity premium that the CRRA must explain is calculated to be 9.5%. The CRRA is calibrated by assuming six different economies from an economy with two states of nature to an economy with seven states of nature, that all describe the same distribution of returns. The calibrated CRRAs are between 4.2 and 5.4. Running 100 replications of samples of 6000 observations of the risky outcome shows that the CRRA that satisfies the constraint on the equity premium is 4.5, a figure which is reasonable and plausible.