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Chapter 13 33
Chapter 13
Risky Assets
The first part of this chapter is just notation and review of the concepts of
mean and standard deviation. If your students have had some statistics, these
ideas should be pretty standard. If they haven’t had any statistics, then be sure
to get the basics down before proceeding.
The big idea here is in Figure 13.2. In mean-standard deviation space, the
“budget constraint” is a straight line. Again, all of the technical apparatus of
consumer theory can be brought to bear on analyzing this particular kind of
choice problem. Ask what happens to the “price of risk” when the risk-free
rate goes down. What do students think this will do to the budget line and
the portfolio choice? Don’t let them guess—make them give reasons for their
statements.
Section 13.2 is a little bit of a fudge. I do give the actual definition of beta in
a footnote, but I don’t really go through the calculations for the Capital Asset
Pricing Model.
The idea of the risk-adjusted interest rate and the story of how returns adjust
is a nice one and should be accessible to most students who understood the case
of adjustment with certainty.
It might be worth pointing out that participants in the stock market take all
this stuff very seriously. There are consulting services that sell their estimates
of beta for big bucks and use them as measures of risk all the time.
Risky Assets
A. Utility depends on mean and standard deviation of wealth.
1. utility = u(μw,σ
w)
2. this form of utility function describes tastes.
B. Invest in a risky portfolio (with expected return rm)andarisklessasset(with
return rf)
1. suppose you invest a fraction xin the risky asset
2. expected return = xrm+(1−x)rf
3. standard deviation of return = xσm
4. this relationship gives “budget line” as in Figure 13.2.
34 Chapter Highlights
C. At optimum we must have the price of risk equal to the slope of the budget
line: MRS =(rm−rf)/σm
D. Measuring the risk of a stock — depends on how it contributes to the risk of
the overall portfolio.
1. βi= covariance of asset iwith the market portfolio/standard deviation of
market portfolio
E. Equilibrium
1. the risk-adjusted rates of return should be equalized
2. in equations:
3. suppose asset jis riskless; then
4. this is called the Capital Asset Pricing Model (CAPM)
F. Examples of use of CAPM
1. how returns adjust — see Figure 13.4.
