Exam II Practice Problems
Econ 435 Fall 2001
There will be MC questions on the lecture note and readings.
Below are some practice problems.
1)
Stock X has an expected return of 12% and a variance of 30%
Stock Y has an expected return of 13% and a variance of 35%
There is a risk-free asset with a return of 4%
Yingbin and Chris are risk averse. I give Yingbin $100 and tell her to invest it in
stock X, stock Y, and a risk-free asset. Yingbin is a Ph.D. candidate so she
computes Cov(X,Y) and chooses the portfolio to maximize his utility. She invests
$20 in Stock X and $30 in Stock Y.
I give Chris $200 and tell him to invest it in stock X, stock Y, and a risk-free
asset. Chris maximizes his utility by investing $50 in stock X.
How much does
Chris invest in the risk-free asset?
2)
Stock X and Y have returns consistent with the CAPM. Stock X has a
variance of 30% and an expected return of 10%. Stock Y has a variance of
45% and an expected return of 12%. The entire market of risky securities
has an expected return of 12% and a variance of 20%.
If the risk-free
rate is 2%, what is the beta of stock X with the market?
3)
Stocks X, Y, and Z have expected returns consistent with the Arbitrage
Pricing Theorem.
E[R
n
] = a + b
1n
f
1
+ b
2n
f
2
+ b
3n
f
3
Where E[R
n
] is the expected return of n-th stock.
a
= .05 = the risk-free rate
The betas of stocks X, Y, Z and a fourth stock, Stock A, can be found in the
following table.
Stock
Expected
Return
b
1n
b
2n
b
3n
X
.1
1
0
0
Y
.15
0
1
0
Z
.1
0
0
1
A
?
-1
1
1
What is the expected return of stock A?

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