Homework: Chapter 7 Part One
VIII. Questions and Problems
Questions and Problems
Basic
7.1 Returns: Describe the difference between a total holding period return and an expected
return.
Solution:
The holding period return is the total return over some investment or "holding" period. It
consists of a capital appreciation component and an income component. The holding
period return reflects past performance. The expected return is a return that is based on
the probability-weighed average of the possible returns from an investment. It describes
a possible return (or even a return that may not be possible) for a yet to occur investment
period.
7.2 Expected Returns: You are watching an old game show on rerun television called “Let’s
Make a Deal” in which you have to choose a prize behind one of two curtains. One of the
curtains will yield a gag prize worth $150, and the other will give you a car worth $7,200.
The game show has placed a subliminal message on the curtain containing the gag prize,
which makes the probability of choosing the gag prize equal to 75 percent. What is the
expected value of your selection, and what is the standard deviation of that selection?
Solution:
E(prize) =0 .75($150) + (0.25) ($7,200) = $1,912.50
σ2prize = 0.75($150 - $1,912.50)2 + (0.25) ($7,200 - $1,912.50)2
= $9,319,218.75 =>
σprize = ($9,319,218.75)1/2 = $3,052.74
7.3 Expected Returns: You have chosen biology as your college major because you would
like to be a medical doctor. However, you find that the probability of being accepted to
medical school is about 10 percent. If you are accepted to medical school, then your
starting salary when you graduate will be $300,000 per year. However, if you are not
accepted, then you would choose to work in a zoo, where you will earn $40,000 per year.
Without considering the additional educational years or the time value of money, what is
your expected starting salary as well as the standard deviation of that starting salary?
Solution:
E(salary) = 0.9($40,000) + (0.1) ($300,000) = $66,000
σ2salary = 0.9($40,000 - $66,000)2 + (0.1) ($300,000 - $66,000)2 =
$6,084,000,000 =>
σsalary = ($6,084,000,000)1/2 = $78,000
7.4 Historical Market Performance: Describe the general relation between risk and return
that we observe in the historical bond and stock market data.
Solution:
The general axiom that the greater the risk, the greater the return describes the historical
returns of the bond and stock market. If we look at Exhibit 4 in the text, we see that
small stocks have averaged the greatest returns but they also have the greatest standard
deviation for the returns. When compared to large stocks, the average return and
standard deviation of the small stocks are greater. Large stock average returns and
standard deviation numbers are larger than those of long-term government bonds, which
are larger than those of intermediate term government bonds, which in turn are larger
than those of U.S. Treasury Bills. The comparison shows that the riskier the investment
category, the greater the average return as well as standard deviation of returns.
7.5 Single Asset Portfolios: Stocks A, B, and C have expected returns of 15 percent, 15
percent, and 12 percent, respectively, while their standard deviations are 45 percent, 30
percent, and 30 percent respectively. If you were considering the purchase of each of
these stocks as the only holding in your portfolio, then which stock should you choose?
Solution:
Since the holding will be made in a completely undiversified portfolio, then we can
calculate the risk per unit of return for each stock, the coefficient of variation, and choose
the stock with the lowest value.
CV(RA) = 0.45/0.15 = 3.0
CV(RB) = 0.30/0.15 = 2.0
CV(RC) = 0.30/0.12 = 2.5 ===> Choose B
Alternatively, we could have noted that the expected return for A and B was the same
with A having a greater degree of risk. B and C have the same degree of risk but B
has a greater expected return. This would lead you to the conclusion, just as our
coefficient of variation calculations did, that Stock B is superior.
7.6 Diversification: Describe how investing in more than one asset can reduce risk through
diversification.
Solution:
An investor can reduce the risk of his or her investments by investing in two or more
assets whose values do not always move in the same direction at the same time. This is
because the movements in the values of the different investments will partially cancel
each other out.
7.7 Systematic Risk: Define systematic risk.
Solution:
Risk that cannot be diversified away is called systematic risk. It is the only type of risk
that exists in a diversified portfolio and it is the only type of risk that is rewarded in asset
markets.
7.8 Measuring Systematic Risk: You are expecting the returns on the market portfolio to be
negative in the near term. Since you are managing a stock mutual fund, you must remain
invested in a portfolio of stocks. You are allowed to adjust the beta of your portfolio.
What kind of beta would you recommend for your portfolio?
Solution:
If we confine our analysis to portfolios with positive beta values, and since beta describes
how much and what direction our portfolio is expected to vary with the market portfolio,
then we should construct a very low beta portfolio. In that case, our portfolio is not
expected to have losses quite as large as that of the market portfolio. A large beta
portfolio would have larger losses than that of the market portfolio. If we could construct
a negative beta portfolio then we would like to construct as negative of a portfolio beta as
possible.
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