Question

A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term bond fund, and the third is a money market fund that provides a safe return of 7%. The characteristics of the risky funds are as follows:

Expected Return Standard deviation

Stock fund (S) 22% 32%

Bond fund (B) 12 19

The correlation between the fund returns is 0.11.

What is the Sharpe ratio of the best feasible CAL? (Do not round intermediate calculations. Enter your answer as a decimal rounded to 4 places.)

Answer 1

		Expected return		Standard deviation
		Er
Stock fund (s)		22	%	32	%
Bond fund(B)		12	%	19	%
T=bills rate (Rf) =		7	%
Correlation between stock and bond fund				0.11
Covariance (CoV SB) = r * σS * σB
		0.11*32*19		66.8800

Weight of stock A as per Optimal Risky portfolio formula= ( ( Er S - Rf) * σB^2 - ( (Er B - Rf) * Cov SB )) / ((Er S - Rf)*σB^2 + ((Er B - Rf) * σS^2 )- ((Er S - Rf +ErB-Rf)* Cov SB ))

(((22-7) * (19)^2 )- ((12-7) * 66.88))/ (((22-7) * (19)^2)+ ( (12-7) * (32)^2)- ((22-7+12-7) * 66.88))

So, weight of S =			55.24%
weight of B =			44.76%
Expected return = (weight of S * Expected return of S) + (Weight of B * Expected retun of B)
	(55.24%*22%)+(44.76%*12%)
	17.5240	%
expected retun of risky portolio is			17.5240	%
Standard deviation formula
(σp) =	( (wS * σS ) ^2 + (wB * σB ) ^2 + (2 * wB* wS*σB *σS* rSB) )^(1/2)
	((55.24%*32%)^2+(44.76%*19%)^2+(2*55.24%*44.76%*32%*19%*0.11))^(1/2)
	20.4417	%
Standard deviation of risky portfolio is			20.4417	%
Return to volatility ratio = (Expected return of portfolio - risk free rate of return) / Standard deviation
	(17.524%-7%) / 20.4417%
	0.514827697
So, return to volatility or sharpe ratio of best feasible cal is				0.5148