Consider a CARA investor with n risky assets having normally distributed returns, as studied in Section 2.4,
Question:
Consider a CARA investor with n risky assets having normally distributed returns, as studied in Section 2.4, but suppose there is no risk-free asset, so the budget constraint is ι
φ = w0. Show that the optimal portfolio is
φ = 1
α
−1
μ +
αw0 − ι
−1μ
αι
−1ι
−1
ι.
Note: As will be seen in Section 5.2, the two vectors −1
μ and −1ι play an important role in mean-variance analysis even without the CARA-normal assumption.
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