Consider a one-period setting. Let g denote the growth rate of consumption over the period.

(a) For any portfolio π, show that Corr[Rπ , g]

2 =

π Cov[R, g]

2

π Var[R]π Var[g]

.

(b) Show that the first-order condition for the maximization of Corr[Rπ , g]

2 implies that Cov[R, g]π Var[R]π = π Cov[R, g] Var[R]π.

(c) Explain why the consumption-mimicking portfolio of Lemma 8.2 is also the portfolio maximizing the absolute value of the correlation with consumption growth, that is | Corr[Rπ , g]|.