Assume there is a risk-free asset. Consider an investor with quadratic utility (w )2/2 and no

Assume there is a risk-free asset. Consider an investor with quadratic utility

−(w˜ −ζ )2/2 and no labor income.

(a) Explain why the result of Exercise 2.5 implies that the investor will choose a portfolio on the mean-variance frontier.

(b) Under what circumstances will the investor choose a mean-variance efficient portfolio? Explain the economics of the condition you derive.

(c) Re-derive the answer to Part

(b) using the orthogonal projection characterization of the quadratic utility investor’s optimal portfolio presented in Section 3.5.