CHAPTER 13: Risky Assets
TRUE/FALSE
1. If two assets have the same expected rate of return but different variances, a risk-averse investor
should always choose the one with the smaller variance, no matter what other assets she holds.
2. If the returns on two assets are negatively correlated, then a portfolio that contains some of each will
have less variance in its return per dollar invested than either asset has by itself.
3. If the mean is plotted on the horizontal axis, and the variance on the vertical, then indifference curves
for a risk averter must slope upward and to the right.
4. If you invest half your money in a risk-free asset and half your money in a risky asset such that the
standard deviation of the return on the risky asset is s, then the standard deviation of the return on your
investment portfolio is s/2.
MULTIPLE CHOICE
1. Firm A sells lemonade and firm B sells hot chocolate. If you invest $100 if firm A, in one year you will
get back $(30 + T) where T is the average temperature (Fahrenheit) during the summer. If you invest
$100 in firm B, in one year you will get back $(150 − T), where T is the average temperature during
the summer. The expected value of T is 70 and the standard deviation of T is 10. If you invest $50 in
firm A and $50 in firm B, what is the standard deviation of your return on your investment?
a.
10
b.
20
c.
5
d.
0
e.
None of the above.
2. A risk-free asset is available at 5% interest. Another asset is available with a mean rate of return of
15% but with a standard deviation of 5%. An investor is considering an investment portfolio consisting
of some of each stock. On a graph with standard deviation on the horizontal axis and mean on the
vertical axis, the budget line that expresses the alternative combinations of mean return and standard
deviation possible with portfolios of these assets is a straight line with
a.
slope 2.
b.
slope −3.
c.
increasing slope as you move left.
d.
slope −1.
e.
slope −1/3.
3. Marvin is an expected utility maximizer. He chooses his portfolio so as to maximize the expected
value of 2,000,000x − x2. If m is the mean of Marvin’s income and s is the standard deviation,
Marvin’s income as a function of the mean and standard deviation is
a.
U = 2,000,000m − s2.
b.
U = 2,000,000m − s.
c.
U = m − s/2,000,000.
d.
U = 2,000,000 + s.
e.
None of the above.
4. You have been hired as a portfolio manager for a stock brokerage. Your first job is to invest $100,000
in a portfolio of two assets. The first asset is a safe asset with a sure return of 4% interest. The second
asset is a risky asset with a 26% expected rate of return, but the standard deviation of this return is
10%. Your client wants a portfolio with as high a rate of return as possible consistent with a standard
deviation no larger than 4%. How much of her money do you invest in the safe asset?
a.
$22,000
b.
$40,000
c.
$64,000
d.
$36,000
e.
$60,000
5. Bill owns an export business. The expected profit from his business is $100,000 a year. For every 1%
increase in the value of the Japanese yen relative to the dollar, its profits increase by $20,000. Bill
plans to buy one of two firms. One is an import business which returns an expected profit of $70,000.
For every 1% increase in the value of the Japanese yen relative to the dollar, the profits of this firm
shrink by $5,000. The second is a safe domestic firm which is certain to yield him $70,000 a year. The
two firms cost the same. If Bill is risk averse,
a.
he should buy the domestic firm.
b.
he should buy the import firm.
c.
he should buy half of each of these two firms.
d.
it doesn’t matter which he buys.
e.
he should buy 80% of the domestic firm and 20% of the import firm.
6. Suppose that Ms. Lynch in Workouts Problem 13.1 can make up her portfolio using a risk-free asset
that offers a surefire rate of return of 10% and a risky asset with an expected rate of return of 25%,
with standard deviation 5. If she chooses a portfolio with an expected rate of return of 25%, then the
standard deviation of her return on this portfolio will be
a.
2.50%.
b.
8%.
c.
5%.
d.
10%.
e.
None of the above.
7. Suppose that Ms. Lynch in Workouts Problem 13.1 can make up her portfolio using a risk-free asset
that offers a surefire rate of return of 5% and a risky asset with an expected rate of return of 10%, with
standard deviation 5. If she chooses a portfolio with an expected rate of return of 6.25%, then the
standard deviation of her return on this portfolio will be
a.
0.63%.
b.
2.50%.
c.
1.25%.
d.
4.25%.
e.
None of the above.
8. Suppose that Ms. Lynch in Workouts Problem 13.1 can make up her portfolio using a risk-free asset
that offers a surefire rate of return of 10% and a risky asset with an expected rate of return of 15%,
with standard deviation 5. If she chooses a portfolio with an expected rate of return of 12.50%, then
the standard deviation of her return on this portfolio will be
a.
5%.
b.
5.50%.
c.
2.50%.
d.
1.25%.
e.
None of the above.
9. Suppose that Fenner Smith of Workouts Problem 13.2 must divide his portfolio between two assets,
one of which gives him an expected rate of return of 15% with zero standard deviation and one of
which gives him an expected rate of return of 30% and has a standard deviation of 5%. He can alter the
expected rate of return and the variance of his portfolio by changing the proportions in which he holds
the two assets. If we draw a “budget line” with expected return on the vertical axis and standard
deviation on the horizontal axis, depicting the combinations that Smith can obtain, the slope of this
budget line is
a.
3.
b.
−3.
c.
1.50.
d.
−1.50.
e.
4.50.
10. Suppose that Fenner Smith of Workouts Problem 13.2 must divide his portfolio between two assets,
one of which gives him an expected rate of return of 10% with zero standard deviation and one of
which gives him an expected rate of return of 25% and has a standard deviation of 5%. He can alter the
expected rate of return and the variance of his portfolio by changing the proportions in which he holds
the two assets. If we draw a “budget line” with expected return on the vertical axis and standard
deviation on the horizontal axis, depicting the combinations that Smith can obtain, the slope of this
budget line is
a.
1.50.
b.
−1.50.
c.
−3.
d.
3.
e.
4.50.
11. Suppose that Fenner Smith of Workouts Problem 13.2 must divide his portfolio between two assets,
one of which gives him an expected rate of return of 15% with zero standard deviation and one of
which gives him an expected rate of return of 55% and has a standard deviation of 10%. He can alter
the expected rate of return and the variance of his portfolio by changing the proportions in which he
holds the two assets. If we draw a “budget line” with expected return on the vertical axis and standard
deviation on the horizontal axis, depicting the combinations that Smith can obtain, the slope of this
budget line is
a.
2.
b.
−4.
c.
4.
d.
−2.
e.
6.
PROBLEM
1. If you invest $100 now in firm A, in one year you will get back $(30 + T), where T is the average
temperature during the next summer. If you invest $100 now in firm B, in one year you will get back
$(180 − T). The expected value of T is 70 and the standard deviation of T is 10.
a. Draw a graph showing the combinations of expected return and standard deviation that you can
have by dividing $100 between stock in A and stock in B. (Hint: Expected value has the property
that E(ax + b) = aE(x) + b and standard deviation has the property that SD(ax + b) = [(absolute
value of a) times SD(x)] + b.)
b. What is the expected value and standard deviation of the safest investment strategy you can make
by this means?
c. What is the highest expected value you can achieve?