Assume that you
recently graduated with a major in finance, and you just landed a job as a
financial planner with Barney Smith Inc., a large financial services
corporation. Your first assignment is to
invest $100,000 for a client. Because
the funds are to be invested in a business at the end of one year, you have
been instructed to plan for a one-year holding period. Further, your boss has restricted you to the
following investment alternatives, shown with their probabilities and
associated outcomes. (Disregard for now the items at the bottom of the data;
you will fill in the blanks later.)
Returns On
Alternative Investments
Estimated Rate Of Return
State of the
T- Alta Repo Am. Market 2-stock
economy prob. Bills Inds Men Foam portfolio portfolio
Recession 0.1 8.0% -22.0% 28.0% 10.0%* -13.0% 3.0%
Below avg 0.2 8.0 -2.0 14.7 -10.0 1.0
Average 0.4 8.0 20.0 0.0 7.0 15.0 10.0
Above avg 0.2 8.0 35.0 -10.0 45.0 29.0
Boom 0.1 8.0 50.0 -20.0 30.0 43.0 15.0
r-hat (.gif”>) 1.7% 13.8% 15.0%
Std dev (?) 0.0 13.4 18.8 15.3
Coef of var (cv) 7.9 1.4 1.0
beta (b) -0.86 0.68
*Note that the
estimated returns of American Foam do not always move in the same direction as
the overall economy. For example, when
the economy is below average, consumers purchase fewer mattresses than they
would if the economy was stronger.
However, if the economy is in a flat-out recession, a large number of
consumers who were planning to purchase a more expensive inner spring mattress
may purchase, instead, a cheaper foam mattress.
Under these circumstances, we would expect American Foam’s stock price
to be higher if there is a recession than if the economy was just below
average.
Barney
Smith’s economic forecasting staff has developed probability estimates for the
state of the economy, and its security analysts have developed a sophisticated
computer program which was used to estimate the rate of return on each
alternative under each state of the economy.
Alta Industries is an electronics firm; Repo Men collects past-due
debts; and American Foam manufactures mattresses and other foam products. Barney Smith also maintains an “index fund”
which owns a market-weighted fraction of all publicly traded stocks; you can
invest in that fund, and thus obtain average stock market results. Given the situation as described, answer the
following questions.
What are
investment returns? What is the return
on an investment that costs $1,000 and is sold after one year for $1,100?
b. 1. Why is the
t-bill’s return independent of the state of the economy? Do t-bills promise a
completely risk-free return?
b. 2. Why
are Alta Ind.’s returns expected to move with the economy whereas Repo Men’s
are expected to move counter to the economy?
Answer:
c. Calculate
the expected rate of return on each alternative and fill in the blanks on the
row for.gif”> in the table above.
Answer:
d. You should recognize that basing a decision solely on
expected returns is only appropriate for risk?neutral individuals. Since your client, like virtually everyone,
is risk averse, the riskiness of each alternative is an important aspect of the
decision. One possible measure of risk
is the standard deviation of returns.
1. Calculate this
value for each alternative, and fill in the blank on the row for ? in the table
above.
Answer:
d. 2. What type of risk
is measured by the standard deviation?
d. 3. Draw a graph which shows roughly the shape of the probability distributions for Alta Inds,
Am Foam, and T-bills.
Answer:
e. Suppose
you suddenly remembered that the coefficient of variation (CV) is generally
regarded as being a better measure of stand-alone risk than the standard
deviation when the alternatives being considered have widely differing expected
returns. Calculate the missing CVs, and
fill in the blanks on the row for CV in the table above. Does the CV produce the same risk rankings as
the standard deviation?
Answer:
1. Calculate the expected return (.gif”>p), the
standard deviation (?p), and the coefficient of variation (cvp)
for this portfolio and fill in the appropriate blanks in the table above.
f. 2. How does the
riskiness of this 2-stock portfolio compare with the riskiness of the
individual stocks if they were held in isolation?
Answer:
Answer:
h. 1. Should portfolio
effects impact the way investors think about the riskiness of individual
stocks?
h. 2. If you decided to
hold a 1-stock portfolio, and consequently were exposed to more risk than
diversified investors, could you expect to be compensated for all of your risk;
that is, could you earn a risk premium on that part of your risk that you could
have eliminated by diversifying?
Answer:
i smith’s
computer program are as :
Security Return (.gif”>) Risk (Beta)
Market 15.0 1.00
T-Bills 8.0 0.00
Repo Men 1.7 (0.86)
l. 1. Write out the security market line (SML)
equation, use it to calculate the required rate of return on each alternative,
and then graph the relationship between the expected and required rates of
return.
l
Answer:
m. 1. Suppose investors raised their inflation
expectations by 3 percentage points over current estimates as reflected in the
8 percent t-bill rate. What effect would
higher inflation have on the SML and on the returns required on high- and
low-risk securities?
m
Answer:
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