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218 Part Two Risk- APT The following question illustrates the APT. Imagine that there are only two pervasive mac-
roeconomic factors. Investments X, Y, and Z have the following sensitivities to these two factors:
You can download data for the following questions from finance.yahoo.com.
Use the Beyond the Page feature to access an Excel program for calculating the efficient frontier.
(We are grateful to Darien Huang for providing us with a copy of this program.) Excel func-
tions SLOPE, STDEV, COVAR, and CORREL are especially useful for answering the following
questions.- a. Download up to 10 years of monthly returns for 10 different stocks and enter them into
the Excel program. Enter some plausible figures for the expected return on each stock and
find the set of efficient portfolios. Assume that you cannot borrow or lend.
b. How does the possibility of short sales improve the choices open to the investor? - Find a low-risk stock—Walmart or Kellogg would be a good candidate. Use monthly returns
for the most recent three years to confirm that the beta is less than 1.0. Now estimate the
annual standard deviation for the stock and the S&P index, and the correlation between
the returns on the stock and the index. Forecast the expected return for the stock, assuming
the CAPM holds, with a market return of 12% and a risk-free rate of 5%.
a. Plot a graph like Figure 8.5 showing the combinations of risk and return from a portfolio
invested in your low-risk stock and the market. Vary the fraction invested in the stock
from 0 to 100%.
b. Suppose that you can borrow or lend at 5%. Would you invest in some combination of
your low-risk stock and the market, or would you simply invest in the market? Explain.
● ● ● ● ●FINANCE
ON THE WEBInvestment b 1 b 2X 1.75 0.25
Y –1.00 2.00
Z 2.00 1.00We assume that the expected risk premium is 4% on factor 1 and 8% on factor 2. Treasury
bills obviously offer zero risk premium.
a. According to the APT, what is the risk premium on each of the three stocks?
b. Suppose you buy $200 of X and $50 of Y and sell $150 of Z. What is the sensitivity of
your portfolio to each of the two factors? What is the expected risk premium?
c. Suppose you buy $80 of X and $60 of Y and sell $40 of Z. What is the sensitivity of your
portfolio to each of the two factors? What is the expected risk premium?
d. Finally, suppose you buy $160 of X and $20 of Y and sell $80 of Z. What is your portfo-
lio’s sensitivity now to each of the two factors? And what is the expected risk premium?
e. Suggest two possible ways that you could construct a fund that has a sensitivity of .5 to
factor 1 only. (Hint: One portfolio contains an investment in Treasury bills.) Now compare
the risk premiums on each of these two investments.
f. Suppose that the APT did not hold and that X offered a risk premium of 8%, Y offered
a premium of 14%, and Z offered a premium of 16%. Devise an investment that has zero
sensitivity to each factor and that has a positive risk premium.BEYOND THE PAGEmhhe.com/brealey12eTry it! Markowitz
portfolio program