Chapter 8 Risk and Rates of Return 261
a. What is the holding company’s beta?
b. If the risk-free rate is 6% and the market risk premium is 5%, what is the holding
company’s required rate of return?
c. ECRI is considering a change in its strategic focus; it will reduce its reliance on
the electric utility subsidiary, so the percentage of its capital in this subsidiary
will be reduced to 50%. At the same time, it will increase its reliance on the
international/special projects division, so the percentage of its capital in that
subsidiary will rise to 15%. What will the company’s required rate of return be
after these changes?
Suppose you owned a portfolio consisting of $250,000 of long-term U.S. government
bonds.
a. Would your portfolio be riskless? Explain.
b. Now suppose the portfolio consists of $250,000 of 30-day Treasury bills. Every
30 days your bills mature, and you will reinvest the principal ($250,000) in a new
batch of bills. You plan to live on the investment income from your portfolio, and
you want to maintain a constant standard of living. Is the T-bill portfolio truly
riskless? Explain.
c. What is the least risky security you can think of? Explain.
The probability distribution of a less risky expected return is more peaked than that of a
riskier return. What shape would the probability distribution be for (a) completely certain
returns and (b) completely uncertain returns?
A life insurance policy is a financial asset, with the premiums paid representing the
investment’s cost.
a. How would you calculate the expected return on a 1-year life insurance policy?
b. Suppose the owner of a life insurance policy has no other financial assets—the
person’s only other asset is “human capital,” or earnings capacity. What is the
correlation coefficient between the return on the insurance policy and the return
on the human capital?
c. Life insurance companies must pay administrative costs and sales representatives’
commissions; hence, the expected rate of return on insurance premiums is generally
low or even negative. Use portfolio concepts to explain why people buy life insurance
in spite of low expected returns.
Is it possible to construct a portfolio of real-world stocks that has an expected return equal
to the risk-free rate?
Stock A has an expected return of 7%, a standard deviation of expected returns of 35%, a
correlation coefficient with the market of !0.3, and a beta coefficient of !0.5. Stock B has an
expected return of 12%, a standard deviation of returns of 10%, a 0.7 correlation with the
market, and a beta coefficient of 1.0. Which security is riskier? Why?
A stock had a 12% return last year, a year when the overall stock market declined. Does
this mean that the stock has a negative beta and thus very little risk if held in a portfolio?
Explain.
If investors’ aversion to risk increased, would the risk premium on a high-beta stock
increase by more or less than that on a low-beta stock? Explain.
If a company’s beta were to double, would its required return also double?
In Chapter 7, we saw that if the market interest rate, rd, for a given bond increased,
the price of the bond would decline. Applying this same logic to stocks, explain
(a) how a decrease in risk aversion would affect stocks’ prices and earned rates of
return, (b) how this would affect risk premiums as measured by the historical
difference between returns on stocks and returns on bonds, and (c) what the
implications of this would be for the use of historical risk premiums when applying
the SML equation.
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