Question

Problem 7-7 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 6%. The probability distribution of the risky funds is as follows: Expected Return 21% Standard Deviation 28% Stock fund (5) Bond fund (B) 12 18 The correlation between the fund returns is 0.09. Solve numerically for the proportions of each asset and for the expected return and standard deviation of the optimal risky portfolio. (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.) Portfolio invested in the stock Portfolio invested in the bond Expected return Standard deviation

Answer 1

       Expected return       Standard deviation  
       Er          
Stock fund (s)        21   %   28   %
Bond fund(B)       12   %   18   %
T=bills rate (Rf) =       6   %      
Correlation between stock and bond fund               0.009  
                  
Covariance (CoV SB) = r * σS * σB                  
       0.009*28*18       4.536  
                  
                  
Weight of stock=           ( 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          
                  
           [(21-6) * (18)^2 ] - [ (12-6) * 4.536)      
       _______________________________________________          
       [ (21-6) * (18)^2] + [ (12-6) * (28)^2] - [ (21-6+12-6) * 4.536]          
                  
       4832.784   /   9468.744  
                  
So, weight of Stock fund =           51.04%      
weight of bond fund =           48.96%      
                  
Expected return = (weight of S * Expected return of S) + (Weight of B * Expected retun of B)                  
   (51.04%*21)+(48.96%*12)              
   16.59   %          
                  
So, expected retun of portolio is 16.59%                  
                  
                  
Standard deviation formula                  
                  
(σp) =   ( (wS * σS ) ^2 + (wB * σB ) ^2 + (2 * wB* wS*σB *σS* rSB) )^(1/2)              
   ((51.04%*28)^2+(48.96%*18)^2+(2*51.04%*48.96%*28*18*0.009))^(1/2)              
   16.86   %          
                  
So, Standard deviation of portfolio is 16.86%.