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: Expected Return Standard Deviation Stock fund (S) 15 % 32 % Bond fund (B) 9 % 23 % The correlation between the fund returns is 0.15. What is the Sharpe ratio of the best feasible CAL?

0.296875

Explanation:

Given the following :

Probability distribution of risky funds :

- - - - - - - - - - - - - - stock fund(S) - - bond fund(B)

Expected return - - - 15% - - - - - - - - - - 9%

Std - - - - - - - - - - - - - 32% - - - - - - - - - - 23%

Correlation between funds return = 0.15

Sure rate = 5.5%

To calculate the Sharpe ratio we use the formula :

Sharpe Ratio = (Expected Return of Investment - Risk Free Rate) / Standard Deviation of excess return of investment

For the stock fund :

Expected return = 15%

Risk free rate = market sure rate = 5.5%

Standard deviation = 32%

Sharpe ratio of stock fund :

(15% - 5.5%) / 32%

= 9.5% / 32%

= 0.296875

For Bond fund :

Expected return = 9%

Risk free rate = market sure rate = 5.5%

Standard deviation = 23%

Sharpe ratio of bond fund :

(9% - 5.5%) / 23%

= 3.5% / 23%

= 0.1521739

Therefore the Sharpe ratio of the best feasible CAL is the higher of the two ratios which is 0.296875

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