I need a step by step explanation on how they solved question #7. I\'m not sure

Question

I need a step by step explanation on how they solved question #7. I'm not sure where they are getting these numbers such as 11% and 3%, and I'm not sure if there is an easy formula to follow. Thank you.

N M AItC an investor with the following utility function:U Elr)-3/2 espected utility, she would choose the asset with an expected rate of return of and a standard deviation of A 12% 20% B. 10%:15% d210%; 1096 D8%, 10% C: Us 0.10-32(0.12 )-8.5% highest utility of choices. 6) Arn investo r invests 30% of his wealth in a risky asset with an expected rate of return of 0.13 and a variance of 0.03 and 70% in a T-bill that pays 6%. His portfolio's expected return and standard deviation are andrespectively A. 0. 114; 0.128 B. 0.087: 0063 C 0.295; 0.125 0.081; 0.052 D: E(r)-0.3(13%) + 0.7(6%)-8.1%; sd(P) . 0.3(0 03)1/2-5.19%. What percentages of your money must be invested in the risky asset and the risk-free asset, respectively, to form a portfolio with an expected return of 0.08? 7) A. 85% and 15% B. 75% and 25% C. 62.5% and 37.5% D. 57% and 43% Answer: C: 8% w1(11%) + (1-w1)(396); 8%-11%w1 + 3%-3%w1; 5%-8%w1; w1 0.625; 1- w1-0.375

Explanation / Answer

11% and 3% are the returns on risky and risk free asset respectively. These must have been given in the original question, otherwise question cannot be solved.

Let W1 is the proportion of investment in the risky asset

Hence (1 - W1) is the proportion of investment in the risk free asset.

Expected return on a portfolio = (Expected return on asset 1 x Proportion of asset 1) + (Expected return on asset 2 x Proportion of asset 2)

0.08 = (0.11 x W1) + [(0.03 X (1 - W1)]

0.08 = 0.11W1 + 0.03 - 0.03W1

0.08W1 = 0.05

W1 = 0.05/0.08

= 0.625

Hence, proportion of investment in the risky asset =0.625 or 62.5%

Proportion of investment in the risk free asset = 1 - W1

= 1 - 0.625

= 0.375

= 37.5%

Kindly give a positive rating if you are satisfied with the answer. Feel free to ask if you have any doubts. Thanks.

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