Suppose there is a risk-free asset and n risky assets. Consider an investor with quadratic utility E[

Suppose there is a risk-free asset and n risky assets. Consider an investor with quadratic utility

ζE[ ˜w] −

1 2

E[ ˜w]

2 − 1 2

var(w˜)

and no labor income. Show that the optimal portfolio for the investor is

φ = 1 1+ κ 2 (ζ −w0Rf)−1

(μ− Rfι), where

κ 2 = (μ− Rfι)

−1

(μ− Rfι).

Hint: In the first-order conditions, define γ = (μ − Rfι)

φ, solve for φ in terms of γ , and then compute γ . Note: We will see in Chapter 5 that κ is the maximum Sharpe ratio of any portfolio.