Suppose that there is one risk free asset with return r f and one risky asset with normally distributed return N (, 2

Suppose that there is one risk free asset with return r _f and one risky asset with normally distributed return ∼ N (μ, σ ² ). Show that the CARA utility u(r) = -e-Ar gives the same optimal allocation of wealth to the risky asset as the mean-variance utility function we used in class. That is, show that

α* _CARA = E[r] - r _f / Aσ ²