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 4.7%. The probability distributions of the risky funds are:

	Expected Return	Standard Deviation
Stock fund (S)	17%	37%
Bond fund (B)	8%	31%

The correlation between the fund returns is 0.1065.

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

Answer 1

Expected return of Stock fund (Er A) =17%  
standard deviation (σA) =37%  
Expected return of Bond fund (Er B) =8%  
standard deviation (σB) =31%  
risk free rate (rf)=4.7%  
correlation between both fund (r)= 0.1065
  
Covariance formula (CoV AB) = r * σA* σB  

0.1065*37%*31%

=0.01221555

  
Best feasible CAL will be made of optimal risky portfolio. We will calculate weight of A for optimal portfolio.  
  
Weight of Stock fund (weight A) in Optimal risky portfolio formula =(((Er A- Rf) * σB^2) - ( (Er B - Rf) * Cov AB )))/ (((Er A - Rf)*σB^2) + ( (Er B - Rf) * σA^2 )- ( (Er A - Rf +ErB-Rf)* Cov AB))  

=(((17%- 4.7%) * (31%)^2) - ( (8% - 4.7%) *0.01221555 ))/ (((17%-4.7%)*(31%)^2) + ( (8%-4.7%) * (37%)^2 )- ( (17%-4.7%+8%-4.7%)* 0.01221555 ))  

=0.7910816815

  
So weight of stock fund (wA)=0.7910816815

weight of Bond fund (B)= 1-0.7910816815 =0.2089183185

  
Expected return of ORP= (weight of A * Expected return A) + (Weight of B * Expected return of B)  

=(0.7910816815*17%)+( 0.2089183185*8%)

=0.1511973513

  
Standard deviation formula (σp) =√ ( (wA * σA ) ^2 + (wB * σB ) ^2 + (2 * wA* wB*σA *σB* rAB )  

=√((0.7910816815*37%)^2 + (0.2089183185*31%) ^2+ (2*0.7910816815*0.2089183185*37%*31%*0.1065))  

=0.3064402831
  
Sharpe ratio or Return to volatility ratio = (Expected return of portfolio - risk free rate of return) / Standard deviation  
=(0.1511973513-0.047)/0.3064402831

=0.3400249805

So Sharpe ratio of best feasible CAL is 0.3400