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 rate of 4%. The probability distribution of the risky funds is as follows: 10 points Expected Return 24% 12 Standard Deviation 30% 19 Stock fund (S) Bond fund (B) eBook The correlation between the fund returns is 0.13. What is the Sharpe ratio of the best feasible CAL? (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.) Print References Sharpe ratio

Answer 1

Return of Stock Fund (Rs) = 24%

Return of Bond Fund (Rb) = 12%

SDs = 30%

SDb = 19%

Correlation(s.b) R(s,b) = 0.13

Cov(s,b) = R(s,b) * SDs * SDb

= 0.13 * 30 * 19

= 74.1

Optimum weight of Bond (Wb) =

SD32 - Cov(s,b) SDs2 + SD62 – 2 * Cov(s. b)

=

302 – 74.1 302 + 192 – 2 * 74.1

= 74.22 %

Weight of Stock Fund (Ws) = 100 % - 74.22% = 25.78%

Expected Return = Ws * Rs  + Wb * Rb

= .2578 * 24% + .7422 * 12%

= 15.09%

SD of Portfolio =

VSDs2 * W S2 + SD62 *W62 + 2 * Rſs, b) * SDs*W* SDb* W

=

10.302 * 0.25782 +0.192 * .74222 + 2*0.13*0.30 * 0.2578 * .19 * 0.7422

= 0.169420 OR 16.94

Sharpe ratio =

Expected Returnof Portfolio - Risk Free Return Standard Deviationof Portfolio

=

15.09 -4 16.94

= 0.65466 OR 65.47%   

Sharpe Ratio at best feasible CAL is 65.47%

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