Please answer in full Please show how you obtained your answ

Please answer in full. Please show how you obtained your answer by providing a step by step way of getting there. Please bold your answer and please follow the directions for rounding purposes as well. Thanks in advance.

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 rate of 4%. The probability distribution of the risky funds is as follows: Expected Return Standard Deviation Stock fund (S) Bond fund (B) 17% 14 5% 18 The correlation between the fund returns is 0.09 What is the Sharpe ratio of the best feasible CAL? (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.) Sharpe ratio

Solution

The Weight of the optimal risky portfolio invested in the stock fund is given by:
E(rS) = 17%, E(rB) = 14%, ?S = 35%, ?B= 18%, Cov(rS,rB) = Correlation * ?S * ?B = 0.09 * 35% * 18% = 0.567%
Weight of S W(S)= `
[E(rS) - rf] × ?B² - [E(rB) - rf] × Cov(rS,rB)/([E(rS) - rf] × ?B² + [E(rB) - rf] × ?S² - [E(rS) - rf + E(rB) - rf] × Cov(rS,rB)) = [(0.17 - 0.04) × 0.18²] - [(0.17 - 0.04) × 0.00567]/
[(0.17 - 0.04) × 0.18²] + [(0.14 - 0.04) × 0.35²] - [(0.17 - 0.04 + 0.14 - 0.04) × 0.00567] = 0.2292

wB = 1 - 0.2292= 0.7708

The mean and standard deviation of the optimal risky portfolio are:
E(rP) = (0.2292 × 0.17) + (0.7708 × 0.14) = 0.146876

?p = [(0.2292 × 0.35²) + (0.7708 × 0.18²) + (2 × 0.2292 × 0.7708 × 0.00567)]1/2
= 0.234636


The Sharpe ratio of the best feasible CAL is:

(E(rp) - rf) / ?p
= (0.146876 - 0.04) / 0.234636 = 0.4555


Best of Luck. God Bless