Inferring risk aversion from the portfolio decision

This dissertation examines how to infer risk aversion based on observed portfolio decisions. It consists of five chapters. Chapters 1 and 2 are introduction and literature review respectively.;Chapter 3 focuses on the role of uncapitalized future income and investigates the slope of relative risk aversion for consumption, an essential property of utility functions for consumption. The motivation is from the fact that uncapitalized future income is often modeled as a component of current wealth in theory, while it is not in most empirical studies. By examining risky asset allocations in multiperiod consumption-investment optimization problems, I analytically show that utility functions for consumption can exhibit either decreasing relative risk aversion (DRRA) or constant relative risk aversion (CRRA), depending on whether uncapitalized future income is introduced to provide another source of consumption. These findings can be used to reinterpret recent empirical evidence at micro level that there is essentially no wealth effect on households’ financial asset allocations.;Chapter 4 examines how to infer the magnitude of the Pratt-Arrow measures of risk aversion for wealth, based on a single portfolio choice. Three different procedures are evaluated. First, the existing approach that leads to a point estimate at the initial wealth and estimates risk aversion in the small is discussed. The second approach uses quadratic utility as an approximation to the true utility, and generates an estimate of risk aversion in the large, based only on the mean and variance of the risky asset return. The third approach directly employs functional forms for utility function or risk aversion to estimate risk aversion in the large. Computed solutions indicate that assuming functional forms for utility or risk aversion performs much better in estimating relative risk aversion over a wide range of the risky return distributions.;Chapter 5 uses theoretical findings in Chapters 3 and 4 to reinterpret empirical evidence on relative risk aversion presented in three important published papers. The first conclusion is that relative risk aversion for liquid financial wealth is probably constant. Second, relative risk aversion for consumption that comes from liquid financial wealth can be decreasing if uncapitalized future income is incorporated into dynamic consumption-investment optimization problems. Third, the opinions on the magnitude of relative risk aversion for Arrow-Pratt wealth are still divergent but at the mean return it usually does not exceed 10 unless for extremely impoverished investors.