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ec142f09notes7 - Kata Bognar [email protected] Economics 142...

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Kata Bognar [email protected] Economics 142 Probabilistic Microeconomics UCLA Fall 2009 7 Capital Asset Pricing Model Readings. Chapter 5.3, 8.4. Concepts. Mean-variance utility, β -representation. 7.1 Mean-Variance Analysis (Section 5.3) In empirical research it is often assume that the decision maker’s preferences over risky acts can be represented by a utility function that depends only on the mean and the variance of the act such that it is increasing in the mean and decreasing in the variance. Formally: U ( μ, σ 2 ) . This is not fully consistent with our expected utility representation. Intuitively, the expected utility representation uses much more information about the risky act than just the mean and the variance. You can come up two risky acts such that the means and the variances are the same, however the two acts are different. 1 Suppose that there is such pair of risky acts and the decision maker is not indifferent between those two. Then, a mean-variance utility function cannot represent the preferences of this decision maker while it may still be possible to come up with a vNM utility that allows for an expected utility representation. However, the mean-variance form has several advantages. First, it may actually simplify theoretical modeling. Soon, we discuss the Capital Asset Pricing Model. This model is based on the assumption that the decision makers’ preferences are represented by mean-variance utility and has strong implications about capital markets. Second, the mean-variance form is more convenient for empirical purposes. Al- though we did not talk about applied work based on the theoretical results we derive you may have discussed some empirical techniques in other classes. The bottom line is that using data it is much easier to recover the two parameters necessary for the mean-variance utility than to estimate the vNM utility function. We saw that there are advantages of the mean variance from. Also, it is actually a good approximation of the expected utility in two situation. If the acts are normally distributed. This make intuitive sense since a normal distribution is fully characterized by the mean and the variance. Second, if the vNM utility is quadratic in money. 1 Distributions can be characterized by the so-called moments the first two of which are the mean and the variance. However, there are higher moments that can be different even if the means and the variances are the same for two distinct distributions. 1
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7.2 Capital Asset Pricing Model In the last section we discussed (i) how the equilibrium state prices arise endoge- nously and (ii) how to derive the equilibrium asset prices from the equilibrium state prices. The model provides a nice theoretical framework to think about equilibria in asset markets however, it is no easy to test empirically. The state prices are abstract terms and it is hard to find any real life quantity that may measure them.
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