Note that (7.36) implies risk aversion must be larger if consumption volatility is smaller or the maximum Sharpe ratio is larger. Also, using the approximation log(1+ x) ≈ x, the lower bound on ρ in (7.36) is approximately κ/σ, and, using the approximation ex ≈ 1+ x, the upper bound on κ is approximately ρσ.

(b) Explain why the weak inequalities in (7.36) must be equalities when the market is complete.

(c) In the data analyzed by Mehra and Prescott (1985), the standard deviation of the market return is 16.54%. Derive a lower bound on the representative investor’s risk aversion ρ by using this and the other Mehra-Prescott data in Section 7.3 in conjunction with (7.36). Note:

You will find this bound is much more reasonable than the estimate of 47.6 presented in Section