CAPM Question
Consider an economy in two periods, t=0 and t=1. At t=0, the market index is trading at a value
of $100. At t=1, the index either rises to $130 in case of a boom (with probability 1/2), or falls to
$90 in case of a recession (with probability 1/2). A large utility company ABC is in this economy,
and its stock price at t=0 is $20. At t=1, the stock price either rises to $22 if the economy is in a
boom time, or falls to $19 if the economy is in a recession. Neither the index nor the ABC stock
pays dividends during this time, and the riskfree rate is
R
f
= 2%.
1. What are the expected value and the variance of the return on the market index? What are
the expected value and the variance of the return on ABC stock?
2. What is the covariance between the index return and the return on ABC stock? What is the
market
β
of the ABC stock?
3. Assuming that CAPM holds, compute the expected return of ABC stock predicted by CAPM.
Is it the same as the expected return calculated in (a)? If not, which one is higher?
1
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View Full Document4. Is this fact that ABC has a diﬀerent expected return than CAPM prediction consistent with
what you’ve learned in the course?
5. Now, consider a more sophisticated asset pricing model than CAPM to correctly predict the
expected returns. Let
HML
=
R
H

R
L
denote the excess return of value stocks over growth
stocks, and
SMB
=
R
S

R
B
the excess return of small stocks over big stocks. Suppose that
ABC has a beta of zero with respect to HML. The beta of ABC and the market index is still
what you computed in (b). If the expected value of SMB is
E
[
SMB
] = 0
.
03(3%). Assuming
that this FamaFrench 3factor model correctly prices the stock ABC, what should be the
beta of ABC with respect to SMB?
Portfolio choice
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 Fall '08
 SZEIDL
 Capital Asset Pricing Model

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