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CHAPTER 10: ARBITRAGE PRICING THEORY
AND MULTIFACTOR MODELS OF RISK AND RETURN
PROBLEM SETS
1. The revised estimate of the expected rate of return on the stock would
be the old estimate plus the sum of the products of the unexpected
change in each factor times the respective sensitivity coefficient: revised estimate = 12% + [(1 2%) + (0.5 3%)] = 15.5%
2. The APT factors must correlate with major sources of uncertainty, i.e.,
sources of uncertainty that are of concern to many investors.
Researchers should investigate factors that correlate with uncertainty
in consumption and investment opportunities. GDP, the inflation rate,
and interest rates are among the factors that can be expected to
determine risk premiums. In particular, industrial production (IP) is a good indicator of changes in the business cycle. Thus, IP is a
candidate for a factor that is highly correlated with uncertainties
that have to do with investment and consumption opportunities in the
economy.
3. Any pattern of returns can be “explained” if we are free to choose an
indefinitely large number of explanatory factors. If a theory of asset
pricing is to have value, it must explain returns using a reasonably
limited number of explanatory variables (i.e., systematic factors).
4. Equation 10.9 applies here:
E(r p) = r f + P1 [E(r1 ) r f ] + P2 [E(r2) – r f ]
We need to find the risk premium (RP) for each of the two factors: RP1 = [E(r1) r f ] and RP2 = [E(r2) r f ]
In order to do so, we solve the following system of two equations with two unknowns:
31 = 6 + (1.5 RP1) + (2.0 RP2)
27 = 6 + (2.2 RP1) + [(–0.2) RP2]
The solution to this set of equations is:
RP1 = 10% and RP2 = 5%
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