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 5.8%. The probability distribution of the risky funds is as follows: Stock fund (S) Bond fund (B) Expected Return 19% 9 Standard Deviation 48% 42 The correlation between the fund returns is 0.18. 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 and round your final answers to 2 decimal places. Omit the "%" sign in your response.) Portfolio invested in the stock Portfolio invested in the bond Expected return Standard deviation

Answer 1

       Expected return       Standard deviation      
       Er              
Stock fund (s)        19 %   48 %   

Bond fund(B)       9 %   42 %  
T=bills rate (Rf) =       5.8   %          
Correlation between stock and bond fund = 0.18      
                      
Covariance (CoV SB) = r * σS * σB                      
       0.18*48*42=       362.880      

   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 ))  
  
(((19-5.8) * (42)^2 )- ((9-5.8) * 362.880))/ (((19-5.8) * (42)^2)+ ( (9-5.8) * (48)^2)- ((19-5.8+9-5.8) * 362.880))                       

       22123.584   /   24706.368      
                      
So, weight of S =           89.55%          
weight of B =           10.45%          
                     
Expected return = (weight of S * Expected return of S) + (Weight of B * Expected retun of B)                      
   (89.55%*19%)+(10.45%*9%)                  
   17.9546   %              
                      
expected retun of risky portolio is            17.9546   %      
                     
                      
Standard deviation formula                      
                      
(σp) =   ( (wS * σS ) ^2 + (wB * σB ) ^2 + (2 * wB* wS*σB *σS* rSB) )^(1/2)                  
= ((89.55%*48%)^2+(10.45%*42%)^2+(2*89.55%*10.45%*48%*42%*0.18))^(1/2)                  
= 43.9850   %              
                      
Standard deviation of risky portfolio is            43.9850 %