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The risk-free asset has a return of 2.84%. The risky asset has a return of 10.06%...

The risk-free asset has a return of 2.84%. The risky asset has a return of 10.06% and has a variance of 4.12%. Karen has the following utility function: LaTeX: U=a\times\ln\left(r_c\right)-b\times\sigma_cU = a × ln ⁡ ( r c ) − b × σ c, with a=5.1 and b=5.2. LaTeX: r_cr c and LaTeX: \sigma_cσ c denote the return and the risk of the combined portfolio. Compute the optimal to be invested in the risky asset.

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Answer #1

U=5.1*ln(w*10.06%+(1-w)*2.84%)-5.2*w*sqrt(4.12%)

dU/dw=

dU/dw=0

at w=4.4386

Optimal proportion to be invested in the risky asset=4.4386

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