Managerial Finance – Problem Review Set

One
key conclusion of the Capital Asset Pricing Model is that the value an asset
should be measured by considering both the risk and the expected return of
the asset assuming that the asset is held in a well-diversified
portfolio. The risk of the asset held
in isolation is not relevant under the CAPM.

a.

True

b.

False

According
to the Capital Asset Pricing Model, investors are primarily concerned with
portfolio risk, not the risks of individual stocks held in isolation. Thus, the relevant risk of a stock is the
stock’s contribution to the riskiness of a well-diversified portfolio.

a.

True

b.

False

A
stock’s beta is more relevant as a measure of risk to an investor who holds
only one stock than to an investor who holds a well-diversified portfolio.

a.

True

b.

False

If
the expected rate of return for a particular stock, as seen by the marginal
investor, exceeds its required rate of return, we should soon observe an
increase in demand for the stock, and the price will likely increase until a
price is established that equates the expected return with the required
return. The sooner this equilibrium is
reached, the more efficient the market is judged to be.

a.

True

b.

False

5.)

Portfolio
A has but one stock, while Portfolio B consists of all stocks that trade in
the market, each held in proportion to its market value. Because of its diversification, Portfolio B
will by definition be riskless.

a.

True

b.

False

The
distributions of rates of return for Companies AA and BB are given below:

State of

Probability of

Economy

State Occurring

AA

BB

Boom

0.2

30%

-10%

Normal

0.6

10%

5%

Recession

0.2

-5%

50%

We
can conclude from the above information that any rational risk-averse
investor will add Security AA to a well-diversified portfolio over Security
BB.

a.

True

b.

False

Assume
that two investors each hold a portfolio, and that portfolio is their only
asset. Investor A’s portfolio has a
beta of minus 2.0, while Investor B’s portfolio has a beta of plus
2.0. Assuming that the unsystematic
risks of the stocks in the two portfolios are the same, then the two
investors face the same amount of risk.
However, the holders of either portfolio could lower their risks, and
by exactly the same amount, by adding some “normal” stocks with
beta = 1.0.

a.

True

b.

False

If
the price of money (e.g., interest rates and equity capital costs) increases
due to an increase in anticipated inflation, the risk-free rate will also
increase. If there is no change in
investors’ risk aversion, then the market risk premium (r_M – r_RF)
will remain constant. Also, if there
is no change in stocks’ betas, then the required rate of return on each stock
as measured by the CAPM will increase by the same amount as the increase in
expected inflation.

a.

True

b.

False

A
highly risk-averse investor is considering adding one additional stock to a
3-stock portfolio, to form a 4-stock portfolio. The three stocks currently held all have b
= 1.0 and a perfect positive correlation with the market. Potential new Stocks A and B both have
expected returns of 15%, and both are equally correlated with the market,
with r = 0.75. However, Stock A’s
standard deviation of returns is 12% versus 8% for Stock B. Which stock should this investor add to his
or her portfolio, or does the choice matter?

a.

Either
A or B, i.e., the investor should be indifferent between the two.

b.

Stock
A.

c.

Stock
B.

d.

Neither
A nor B, as neither has a return sufficient to compensate for risk.

e.

Add
A, since its beta must be lower.

Which
of the following statements is CORRECT?

a.

An
investor can eliminate virtually all market risk if he or she holds a very
large and well diversified portfolio of stocks.

b.

The
higher the correlation between the stocks in a portfolio, the lower the risk
inherent in the portfolio.

c.

It
is impossible to have a situation where the market risk of a single stock is
less than that of a portfolio that includes the stock.

d.

Once
a portfolio has about 40 stocks, adding additional stocks will not reduce its
risk by even a small amount.

e.

An
investor can eliminate virtually all diversifiable risk if he or she holds a
very large, well diversified portfolio of stocks.

Which
of the following statements is CORRECT?

a.

Collections
Inc. is in the business of collecting past-due accounts for other companies,
i.e., it is a collection agency.
Collections’ revenues, profits, and stock price tend to rise during
recessions. This suggests that
Collections Inc.’s beta should be quite high, say 2.0, because it does so
much better than most other companies when the economy is weak.

b.

Suppose
the returns on two stocks are negatively correlated. One has a beta of 1.2 as determined in a
regression analysis using data for the last 5 years, while the other has a
beta of -0.6. The returns on the stock
with the negative beta will be negatively correlated with returns on most
other stocks in the market during that 5-year period.

c.

Suppose
you are managing a stock portfolio, and you have information that leads you
to believe the stock market is likely to be very strong in the immediate
future. That is, you are convinced
that the market is about to rise sharply.
You should sell your high-beta stocks and buy low-beta stocks in order
to take advantage of the expected market move.

d.

You
think that investor sentiment is about to change, and investors are about to
become more risk averse. This suggests
that you should re-balance your portfolio to include more high-beta stocks.

e.

If
the market risk premium remains constant, but the risk-free rate declines,
then the required returns on low beta stocks will rise while those on high
beta stocks will decline.

Stock
X has a beta of 0.5 and Stock Y has a beta of 1.5. Which of the following statements must
be true, according to the CAPM?

a.

If
you invest $50,000 in Stock X and $50,000 in Stock Y, your 2-stock portfolio
will have a beta significantly lower than 1.0, provided the returns on the
two stocks are not perfectly correlated.

b.

Stock
Y’s return during the coming year will be higher than Stock X’s return.

c.

If
expected inflation increases but the market risk premium is unchanged, the
required returns on the two stocks will increase by the same amount.

d.

Stock
Y’s return has a higher standard deviation than Stock X.

e.

If
the market risk premium declines, but the risk-free rate is unchanged, Stock
X will have a larger decline in its required return than will Stock Y.

13.)

Consider
the following information for three stocks, A, B, and C, and portfolios of
these stocks. The stocks’ returns are
positively but not perfectly positively correlated with one another, i.e.,
the correlation coefficients are all between 0 and 1.

Expected

Standard

Stock

Return

Deviation

Beta

Stock
A

10%

20%

1.0

Stock
B

10

10

1.0

Stock
C

12

12

1.4

Portfolio AB has half of its funds
invested in Stock A and half in Stock B.
Portfolio ABC has one third of its funds invested in each of the three
stocks. The risk-free rate is 5%, and
the market is in equilibrium, so required returns equal expected
returns. Which of the following
statements is CORRECT?

a.

Portfolio AB has a standard
deviation of 20%.

b.

Portfolio AB’s coefficient of
variation is greater than 2.0.

c.

Portfolio AB’s required return is
greater than the required return on Stock A.

d.

Portfolio
ABC’s expected return is 10.67%.

e.

Portfolio
ABC has a standard deviation of 20%.

Stock
A has an expected return of 12%, a beta of 1.2, and a standard deviation of
20%. Stock B also has a beta of 1.2,
an expected return of 10%, and a standard deviation of 15%. Portfolio
AB has $900,000 invested in Stock
A and $300,000 invested in Stock B.
The correlation between the two stocks’ returns is zero (that is, r_A,B
= 0). Which of the following
statements is CORRECT?

a.

Portfolio AB’s standard deviation
is 17.5%.

b.

The
stocks are not in equilibrium based on the CAPM; if A is valued correctly,
then B is overvalued.

c.

The
stocks are not in equilibrium based on the CAPM; if A is valued correctly,
then B is undervalued.

d.

Portfolio AB’s expected return is
11.0%.

e.

Portfolio AB’s beta is less than
1.2.

Jane
has a portfolio of 20 average stocks, and Dick has a portfolio of 2 average
stocks. Assuming the market is in
equilibrium, which of the following statements is CORRECT?

a.

Jane’s
portfolio will have less diversifiable risk and also less market risk than
Dick’s portfolio.

b.

The
required return on Jane’s portfolio will be lower than that on Dick’s
portfolio because Jane’s portfolio will have less total risk.

c.

Dick’s
portfolio will have more diversifiable risk, the same market risk, and thus
more total risk than Jane’s portfolio, but the required (and expected)
returns will be the same on both portfolios.

d.

If
the two portfolios have the same beta, their required returns will be the
same, but Jane’s portfolio will have less market risk than Dick’s.

e.

The
expected return on Jane’s portfolio must be lower than the expected return on
Dick’s portfolio because Jane is more diversified.

Stocks
A and B each have an expected return of 15%, a standard deviation of 20%, and
a beta of 1.2. The returns on the two
stocks have a correlation coefficient of +0.6. You have a portfolio that consists of 50% A
and 50% B. Which of the following
statements is CORRECT?

a.

The
portfolio’s beta is less than 1.2.

b.

The
portfolio’s expected return is 15%.

c.

The
portfolio’s standard deviation is greater than 20%.

d.

The
portfolio’s beta is greater than 1.2.

e.

The
portfolio’s standard deviation is 20%.

During
the next year, the market risk premium, (r_M – r_RF), is
expected to fall, while the risk-free rate, r_RF, is expected to
remain the same. Given this forecast,
which of the following statements is CORRECT?

a.

The
required return will increase for stocks with a beta less than 1.0 and will
decrease for stocks with a beta greater than 1.0.

b.

The
required return on all stocks will remain unchanged.

c.

The
required return will fall for all stocks, but it will fall more for
stocks with higher betas.

d.

The
required return for all stocks will fall by the same amount.

e.

The
required return will fall for all stocks, but it will fall less for
stocks with higher betas.

Stock
A has a beta of 0.8 and Stock B has a beta of 1.2. 50% of Portfolio P is invested in Stock A
and 50% is invested in Stock B. If the
market risk premium (r_M – r_RF) were to increase but the
risk-free rate (r_RF) remained constant, which of the following
would occur?

a.

The
required return will increase for both stocks but the increase will be
greater for Stock B than for Stock A.

b.

The
required return will decrease by the same amount for both Stock A and Stock
B.

c.

The
required return will increase for Stock A but will decrease for Stock B.

d.

The
required return on Portfolio P will remain unchanged.

e.

The
required return will increase for Stock B but will decrease for Stock A.

Assume
that the risk-free rate remains constant, but the market risk premium
declines. Which of the following is
most likely to occur?

a.

The
required return on a stock with beta = 1.0 will not change.

b.

The
required return on a stock with beta > 1.0 will increase.

c.

The
return on “the market” will remain constant.

d.

The
return on “the market” will increase.

e.

The
required return on a stock with beta < 1.0 will decline.

Stock A has an expected return of 10% and a standard
deviation of 20%. Stock B has an
expected return of 13% and a standard deviation of 30%. The risk-free rate is 5% and the market
risk premium, r_M – r_RF, is 6%. Assume that the market is in
equilibrium. Portfolio AB
has 50% invested in Stock A and 50% invested in Stock B. The returns of Stock A and Stock B are
independent of one another, i.e., the correlation coefficient between them is
zero. Which of the following
statements is CORRECT?

a.

Stock
A’s beta is 0.8333.

b.

Since
the two stocks have zero correlation, Portfolio
AB is riskless.

c.

Stock
B’s beta is 1.0000.

d.

Portfolio AB’s required return is
11%.

e.

Portfolio AB’s standard deviation
is 25%.

Yonan
Corporation’s stock had a required return of 11.50% last year, when the
risk-free rate was 5.50% and the market risk premium was 4.75%. Now suppose there is a shift in investor
risk aversion, and the market risk premium increases by 2%. The risk-free rate and Yonan’s beta remain
unchanged. What is Yonan’s new
required return? (Hint: First
calculate the beta, then find the required return.)

a.

14.03%

b.

14.38%

c.

14.74%

d.

15.10%

e.

15.48%

Millar
Motors has a beta of 1.30 and an expected dividend growth rate of 5.00% per
year. The T-bill rate is 3.00%, and
the T-bond rate is6.00%. The
annual return on the stock market during the past 3 years was 15.00%. Investors expect the annual future stock
market return to be 12.00%. Using the
SML, what is Millar’s required return?

a.

12.5%

b.

12.8%

c.

13.1%

d.

13.5%

e.

13.8%

Suppose
you hold a diversified portfolio consisting of a $10,000 investment in each
of 12 different common stocks. The
portfolio’s beta is 1.25. Now suppose
you decided to sell one of your stocks that has a beta of 1.00 and to use the
proceeds to buy a replacement stock with a beta of 1.34. What would the portfolio’s new beta be?

a.

1.15

b.

1.21

c.

1.28

d.

1.34

e.

1.41

Your
firm’s analyst believes that economic conditions during the next year will be
either strong, normal, or weak, and she thinks that Crary Inc.’s returns will
have the probability distribution shown below. What’s the standard deviation of Crary’s
returns as estimated by your analyst?
(Hint: Use the formula for the
standard deviation of a population, not a sample.)

Economic

Conditions

Prob.

Return

Strong

30%

32.50%

Normal

40%

10.25%

Weak

30%

-15.75%

a.

17.77%

b.

18.71%

c.

19.65%

d.

20.63%

e.

21.66%