What fraction of wealth would investor invest in risky asset

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Suppose an investor’s risk aversion coefficient is 3 and his utility function is U(r) = 1/2 E(r) − 1/2 A · V ar(r). Suppose there is a risk-free asset whose return is given by ¯r = 0.04. Suppose there is a single risky asset P that has an expected return of 0.1 and a variance of 0.02. Assuming the investor’s goal is to maximize utility, what fraction of wealth would the investor invest in the risky asset?

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