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Kata Bognar
kbognar@ucla.edu
Economics 142
Probabilistic Microeconomics
UCLA
Fall 2009
7
Capital Asset Pricing Model
Readings.
Chapter 5.3, 8.4.
Concepts.
Meanvariance utility,
β
representation.
7.1
MeanVariance 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 meanvariance 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 meanvariance 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 meanvariance utility and has strong implications about capital
markets.
•
Second, the meanvariance 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 meanvariance 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 socalled 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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View Full Document7.2
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.
•
The
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 Fall '09
 Bognar
 Utility

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