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Suppose that there is one risk free asset with return rf and one risky asset with normally distributed returns, r

∼ N(μ,σ^2). Show that the mean-variance utility function is equivalent to the CARA utility u(r) = −e^−Ar (they are representations of the same preferences). Use the fact that if a random variable x is distributed normally with mean μx and variance σ^2 x, then

E[e^ax] = e^aμx+ 1/2^a2 sig,a^2 x

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