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9. a. A long position in a portfolio (P) comprised of Portfolios A and B
will offer an expected return-beta tradeoff lying on a straight
line between points A and B. Therefore, we can choose weights such
that P = C but with expected return higher than that of
Portfolio C. Hence, combining P with a short position in C will
create an arbitrage portfolio with zero investment, zero beta, and
positive rate of return.
b. The argument in part (a) leads to the proposition that the
coefficient of 2 must be zero in order to preclude arbitrage
opportunities.
10. a. E(r) = 6 + (1.2 6) + (0.5 8) + (0.3 3) = 18.1%
b.Surprises in the macroeconomic factors will result in surprises in
the return of the stock:
Unexpected return from macro factors =
[1.2(4 – 5)] + [0.5(6 – 3)] + [0.3(0 – 2)] = –0.3%
E (r) =18.1% ? 0.3% = 17.8%
11. The APT required (i.e., equilibrium) rate of return on the stock based
on r f and the factor betas is:
required E(r) = 6 + (1 6) + (0.5 2) + (0.75 4) = 16%
According to the equation for the return on the stock, the actually
expected return on the stock is 15% (because the expected surprises on all factors are zero by definition). Because the actually expected
return based on risk is less than the equilibrium return, we conclude that the stock is overpriced.
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