Question

Suppose that a well-diversified portfolio has an expected return of 11% and that the following two factors have an impact changes to GDP (Fi), and changes to unexpected inflation (F2), The risk free rate is 8%. The APT equation is: on this portfolio's returns: -0.05 + β| (0.035) + β2 (0.0825) (i) Suppose that the sensitivity of the well-diversified portfolio to GDP is (-1.25). What is its sensitivity to unexpected inflation? 5 Marks) (ii If one rebalances this well-diversified portfolio, such that the expected return remains the same but the exposure to inflation is reduced to zero, what will its sensitivity to GDP be? (5 Marks)

Answer 1

(i)

Sensitivity to GDP or is equal to -1.25. Substituting this value in the given equation we get

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$0.11=0.05+(-1.25)(0.035)+\beta_2(0.0825)$

or $\beta_2=1.26$

(ii)

If exposure to inflation is reduced to zero, $\beta_2$ is zero. Substituting this value in the given equation we get

$0.11=0.05+\beta_1(0.035)$

or $\beta_1=1.71$