Question

This question has two sub-questions.

Assume that t-bills generates a return of 3 %. Which of the following risky portfolios is the optimal risky portfolio?

Now assume that you wish to have a total expected return on your portfolio of 5 %, how much of your funds should be invested in the optimal risky portfolio, and how much in t-bills, respectively?

	E(r)	σ
Portfolio A	10 %	26 %
Portfolio B	11 %	31 %
Portfolio C	8 %	25 %

Select one:

a. Portfolio C is the optimal risky portfolio and you should have 40 % in the risky portfolio and the rest in t-bills.

b. Portfolio A is the optimal risky portfolio and you should have 39 % in the risky portfolio and the rest in t-bills.

c. At least two of the risky portfolios are equally preferable.

d. I cannot tell which risky portfolio that is optimal with the given information.

e. Portfolio B is the optimal risky portfolio and you should have 30 % in the risky portfolio and the rest in t-bills.

f. Portfolio C is the optimal risky portfolio and you should have 48 % in the risky portfolio and the rest in t-bills.

g. Portfolio A is the optimal risky portfolio and you should have 29 % in the risky portfolio and the rest in t-bills.

h. Portfolio B is the optimal risky portfolio and you should have 25 % in the risky portfolio and the rest in t-bills.

Answer 1

g. Portfolio A is the optimal risky portfolio and you should have 29 % in the risky portfolio and the rest in t-bills.

Please refer to below spreadsheet for calculation and answer. Cell reference also provided.

C D E F | risk free rate 3% nm + E(r) Portfolio A Portfolio B Portfolio C 10% 11% 8% 26% 31% 25% Sharpe ratio 0.27 0.26 0.20 NO OF Optimal risky portfolio Portfolio-A Optimal risky portfolio is a portfolio on efficient frontier which have highest sharpe ratio (reward to risk ratio). Portfolio-A has highest sharpe ratio thus, A is optimal risky portfolio. 12 13 14 Expected return of your Portfolio 5% 15 Proportion of optimum risky portfolio-A 29% 18

Cell reference -

JUT В C risk free rate 0.03 Er) Portfolio A Portfolio B Portfolio C 0.1 0.11 0.08 0.26 0.31 Sharpe ratio =(C5-$C$2)/D5 =(C6-$C$2)/D6 =(C7-$C$2)/D7 0.25 Optimal risky portfolio Portfolio-A Optimal risky portfolio is a portfolio on efficient frontier which have highest sharpe ratio (reward to risk ratio). Portfolio-A has highest sharpe ratio thus, A is optimal risky portfolio. Expected return of your Portfolio 0.05 Proportion of optimum risky portfolio-A =(C14-C2/C5-C2)

Hope this will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.