Question

24 Help Save& Exit Submit New Side You received no credit for this in the s a long-term government and corporate bond fund HW-2 and the third is a T-bill money market fund thot yields a rate of 4% The A pension fund manager is considering three mutual funds. The first is a stock fund, the band fund, and the third is a T-bill money market fund that yields a rate of 6%. The nt and corporate funds is 23 Stock Furd 1s) The correlation between the fund returns is 0.13 What is the Sharpe ratio of the best feasible CAL? What is the Sharpe ratio of the best feasible CAL? (Do not round 23 Sharpe Ratio (Rop-tf)/aop (16.72-6)/21.68-0.4945

Answer 1

1) The picture is not very clear so the returns and standard deviations are used as they can be read best. The values can be recalculated by substituting any other number.

Excel solver has been used with below formulas

Portfolio standard deviation=SQRT((sigmaR1*w1)^2+((1-w1)*sigmaR2)^2+2*SigmaR1*SigmaR2*w1*(1-w1)*rhoR1R2)

Portfolio expected return = W1*ER1+(1-W1)*ER2

Market risk premium = Portfolio expected return -Risk Free Return

Sharpe ratio= =Market risk premium/Portfolio standard deviation . use solver in this formula by maximising sharpe ratio by changing w1.

E(R1)- E(R2) sigma(R1) sigma(R2)- 37% 23% Risk free - 4% 22.00% 14.00% ho(R1,R2) 0.10 Portfolio standard Portfolio expected Market risk premium 13.33% 10.80% 11 .60% 12.40% 13.20% 14.00% 14.80% 15.60% 16.40% 17.20% 18.00% Sharpe ratio 0.6223the optimal portfolio found using solv 0.5049 In solver, set the objective as "to max" 0.5657 the Sharpe ratioby changing variables 0.6064 0.6220 0.6157 0.5952 0.5681 0.5394 0.5118 0.4865 deviation 0.416290592 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 21.42% 21.39% 20.51% 20.45% 21.22% 22.2 4% 24.87% 27.46% 30.41 % 33.61% 3700 return 17.33% 14.80% 15.60% 16.40% 17.20% 18.00% 18.80% 19.60% 20.40% 21.20% 22.00% asset weight w1

2.

E(R1)= E(R2) 3696 sigma(R1)- sigma(R2)- Risk free- 21.00% 00% 6 22% ho(R1,R2)- 0.13 Portfolio standard Portfolio expected Market risk premium 10.77% 6.00% 70% 8.00% 9.00% 1 0.00% 1 1.00% 12.00% 13.00% 14.00% 15.00% Sharpe deviation 23.85% 20.58% 19.86% 19.93% 20.75% 22.28% 24.36% 26,87% 29.69% 32.75% 36.00% return 16.77% 12.00% 13.00% 14.00% 15.00% 16.00% 17 .00% 18.00% 19.00% 20.00% 21.00% ratio 0.4518the optimal portfolio found using solver 0.2915 In solver, set the objective as "to max" 0.3524 theSharpe ratioby changing variables 0.4015 0.4335 0.4488 0.4516 0.4466 0.4378 0.4274 0.4167 0.577460448 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 asset weight w1

Let me know if you have further questions. Also, please upload a clear picture if the returns or standard deviations have been misread. Do write if you want to understand the formula better.