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Unformatted text preview: Chapter 12 Risky Asset In this chapter we provide an alternative and simplified model of behavior under uncertainty. 12.1 MeanVariance Utility In the last chapter we examined the expected utility model of choice under uncertainty. Another approach to choice under uncertainty is to describe a consumers preference by considering just a few summary statistics about the probability distribution of the consumer’s wealth. Let us suppose a random variable w takes on values w s , for s = 1 ,...,S with probability π s . Then the mean of this probability distribution is μ w = S X s =1 π s w s The variance of the probability distribution is σ 2 w = S X s =1 π s ( w s μ w ) 2 The meanvariance model assumes that the utility of a probability dis tribution that gives the investor wealth w s with probability of π s can be 1 2 CHAPTER 12. RISKY ASSET expressed as a function of the mean and variance of that distribution, u ( μ w ,σ 2 w ), or if you prefer, u ( μ w ,σ w ), where we use the standard devia tion rather than the variance to measure the “spread” of the distribution. The “spread” of the distribution is a measure of riskiness of the wealth distribution. Other things equal, a higher expected return is good, while a larger variance is bad. This is just another way to state the assumption that people are typically averse to risk....
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This note was uploaded on 03/14/2010 for the course ECON microecono taught by Professor Yy during the Spring '10 term at Seoul National.
 Spring '10
 YY
 Microeconomics, Utility

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