Risk Analysis in Theory and Practice
Presenting a mix of conceptual analyses and applied problems, this book provides useful insights into the economic rationality of decision-making under uncertainty.
TABLE OF CONTENTS Risk Analysis in Theory and Practice
Chapter 6: Mean-Variance Analysis
Under the expected utility model, consider a utility function U( x) where x ? ( w + a) is terminal wealth. Analyzing behavior under risk in a mean-variance context implies that expected utility can be expressed as EU( x) = W( M, V), where M ? E( x) is the mean of x and V ? Var( x) is the variance of x. This mean-variance approach is quite attractive in applied risk analysis given that the estimation of the first two moments of the distribution of x is often relatively easy to obtain empirically. But, besides its convenience, can we justify this mean-variance approach under fairly general conditions? This chapter evaluates the arguments underlying the mean-variance approach.
THE CASE OF CARA PREFERENCES UNDER NORMALITY
We showed in Chapter 4 that, under constant absolute risk aversion (CARA) and the normality of the distribution of x, maximizing EU( x) is equivalent to maximizing [ M ? r/2 V], where r = ? U ?/ U ? is the constant Arrow Pratt absolute risk aversion coefficient. In this case, decision analysis under risk can be conducted in the context of an additive mean-variance objective function. While convenient, both the normality assumption and CARA preferences appear rather restrictive. For example, this does not allow risky prospects that have skewed probability distribution. Also, CARA implies the absence of wealth effects.
THE CASE...
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