Your client would like to invest $10,000 in two risky assets A and B where
Stock A has an expected return of 4% and standard deviation of 10%
Stock B has an expected return of 6% and standard deviation of 20%
correlation (A,B)=0.5
Her utility function is U(μ, σ) = μ − ασ2, where her risk aversion is 3. How much should you invest in stock A and B so that she can receive the greatest utility?
Portfolio return is M = w*4%+(1-w)*6%
Portfolio SD, S= ((w*10%)^2+((1-w)*20%)^2+2*w*(1-w)*10%*20%*0.5)^.5
Utility = M - 3*S^2
Then we use Excel solver to maximize utility
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