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 5.6%. The probability distributions of the risky funds are:

	Expected Return	Standard Deviation
Stock fund (S)	17%	46%
Bond fund (B)	8%	40%

The correlation between the fund returns is 0.0600.

What is the Sharpe ratio of the best feasible CAL?

Answer 1

Return of Stock Fund (Rs) = 17%

Return of Bond Fund (Rb) = 8%

SDs = 46%

SDb = 40%

Correlation(s.b) R(s,b) = 0.0600

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

= 0.0600 * 46 * 40

= 110.4

Optimum weight of Bond (Wb) =

=

= 2005.6 / 3495.2

= 0.5738 OR 57.38%

Weight of Stock Fund (Ws) = 100 % - 57.38% = 42.62%

Expected Return = Ws * Rs  + Wb * Rb

= .4262 * 17% + .5738 * 8%

= 11.84%

SD =

=

=

= 31.07%

Sharpe ratio =  

= 11.84 - 5.6 / 31.07

= 0.2008

=