Problem 6-10 A pension fund manager is considering three mutual funds. The first
ID: 2715245 • Letter: P
Question
Problem 6-10
A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a sure rate of 3.0%. The probability distributions of the risky funds are:
Please attempt!!!
What is the reward-to-volatility ratio of the best feasible CAL? (Do not round intermediate calculations. Round your answer to 4 decimal places.)
A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a sure rate of 3.0%. The probability distributions of the risky funds are:
Explanation / Answer
Given, E(Rs) =Expected return on Stock= 12%
E(Rb) =Expected Return on Bond=5%
Ss = Std.deviation of stock Stock fund = 41%
Sb =Std.deviation of bond fund = 30%
Correlation =0.0667
Rf = Risk free rate = 3%
Now, Covariance between stock and bond = Cov(S,B) = Correlation*Ss*Sd = 0.0667*41*30 = 83.271
Weight of Stock fund = Ws
Ws= {[E(Rs) -Rf]*Sb^2 -[E(Rb) -Rf]*Cov(B,S)}/{[E(Rs)-Rf]*Sb^2 + [E(Rb)-Rf]*Ss^2 - [E(Rs) -Rf +E(Rb)-Rf]Cov(B,S)}
Ws ={[12-3]*900-[5-3]*83.271}/{[12-3]*900+[5-3]*1681-[12-3+5-3]*83.271
Ws =7933.458/10546.019
Ws =0.7523
Wd = 1- Ws =0.2477
E(Rp)= Expected return on porfolio =0.7523*12+0.2477*5 =10.27%
Sp= Std. dev of porfolio = sqrt[0.7523^2*1681+0.2477^2*900+ 2*0.7523*0.5909*83.271]
Sp= 32.21%
Reward to volatiltiy Ratio of the best fesaible CAL is =[E(Rp) - Rf]/Sp = [10.27-3]/32.21 =0.2257
Hence Reward to volatiltiy Ratio of the best fesaible CAL is 0.2257