Question

Chapter 6 Homework Instructions I help Question 8 (of 10) Save & Ext Submit 8. value 10.00 points 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 4.4%. The probability distributions of the risky funds are: Expected Return Standard Deviation Stock fund (S) Bond fund (B) 28% 5% The correlation between the fund retums is .0214. What is the reward-to-volatility ratio of the best feasible CAL? (Do not round intermediate calculations. Round your answer to 4 decimal places.) Reward-to-volatility ratio References eBook & Resources Worksheet Learning Objective: 06-03 Construct efficient portfolios and use the Sharpe ratio to evaluate portfolio efficiency Check my work

Answer 1

Step 1: calculate COV matrix , By use formula $Cov(s,b)=\rho _s_b\sigma _s\sigma _b$

	stock	bond
stock	1156	20.3728
bond	20.3728	784

The weight of Stock fund in optimal portfolio :

" Ers) - ry [E(rs) – 15 093 - [E(TB) – ry Cou(B, S) + [E(TB) - r o's - [E(rs) - rs + E(TB) - ry Cou(B, S)

W_s =((14-4.4)*28^2 -(5-4.4)*20.3728)) /((14.4-4.4)*28^2+(5-4.4)*34^2-(14-4.4+5-4.4)*20.3728)

W_s = 0.90252

W_b = 1-W_s =0.09748

Expected return = 0.9025*14%+ 0.09748*5%= 13.12%

Standard deviation = (0.90252²*34² +0.09748²*28²+ 2*0.90252*0.09748*28*34)^0.5 = 33.415%

The reward to volatility ratio for CAL

E(r) - Rf / Standard Deviation =  13.12- 4.4 /33.415 = 0.260961