A pension fund manager is considering three mutual funds. The first is a stock f
ID: 2788333 • Letter: A
Question
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 5.5%. The probability distributions of the risky funds are:
The correlation between the fund returns is .15.
What is the Sharpe ratio of the best feasible CAL? (Do not round intermediate calculations. Round your answer to 4 decimal places.)
Sharpe ratio
Expected Return Standard Deviation Stock fund (S) 15% 32% Bond fund (B) 9% 23%Explanation / Answer
From the standard deviation and correlation we will develop Covariance Matrix Bonds Stock Bonds 23 x23 0.15 x 32 x 23 Stocks 0.15 x 32 x 23 32 X 32 Bonds Stock Bonds 529 110.4 Stocks 110.4 1024 proportions of Stock in the optimal risky portfolio Portfolio weight Stock= ^2B - COV(B,S)/^2S+ ^2B - 2COV(B,S) Portfolio weight Stock= (529 -110.4)/(1024 + 529 - 2 x 110.4) 31.42% Portfolio weight Bond Wb = (1- 31.42%) 68.58% Expected Return of the portfolio = 15% x 31.42% + 9% x68.58% 10.89% Standard deviation of portfolio =sqrt (68.58%^2 x529 +31.42^2 x 1024 + 2 x 68.58% x 31.42 %x 110.4) 19.94 % Sharpe ratio of the best feasible CAL =( E(R) - Rf)/SD(P) Sharpe ratio of the best feasible CAL = (10.89% - 5.5%)/19.94% 0.002701
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