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216 Part Two Risk- Portfolio risk and return Percival Hygiene has $10 million invested in long-term corpo-
rate bonds. This bond portfolio’s expected annual rate of return is 9%, and the annual stan-
dard deviation is 10%.
Amanda Reckonwith, Percival’s financial adviser, recommends that Percival consider
investing in an index fund that closely tracks the Standard & Poor’s 500 Index. The index has
an expected return of 14%, and its standard deviation is 16%.
a. Suppose Percival puts all his money in a combination of the index fund and Treasury bills.
Can he thereby improve his expected rate of return without changing the risk of his port-
folio? The Treasury bill yield is 6%.
b. Could Percival do even better by investing equal amounts in the corporate bond portfolio
and the index fund? The correlation between the bond portfolio and the index fund is +.1. - Cost of capital Epsilon Corp. is evaluating an expansion of its business. The cash-flow
forecasts for the project are as follows:
Factor Expected Risk Premium (%)Market 6.4
Interest rate –0.6
Yield spread 5.1Years Cash Flow ($ millions)0 – 100
1–10 + 15The firm’s existing assets have a beta of 1.4. The risk-free interest rate is 4% and the expected
return on the market portfolio is 12%. What is the project’s NPV?- APT Some true or false questions about the APT:
a. The APT factors cannot reflect diversifiable risks.
b. The market rate of return cannot be an APT factor.
c. There is no theory that specifically identifies the APT factors.
d. The APT model could be true but not very useful, for example, if the relevant factors
ch a nge u np r e d ict ably. - APT Consider the following simplified APT model:
Factor Risk Exposures
Market Interest Rate Yield Spread
Stock (b 1 ) (b 2 ) (b 3 )P 1.0 –2.0 –0.2
P^2 1.2 0 0.3
P^3 0.3 0.5 1.0Calculate the expected return for the following stocks. Assume rf = 5%.- APT Look again at Problem 19. Consider a portfolio with equal investments in stocks P, P^2 ,
and P^3.
a. What are the factor risk exposures for the portfolio?
b. What is the portfolio’s expected return?