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