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 5.6%. The probability distribution of the risky funds is as follows:

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

The correlation between the fund returns is 0.16.

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)        17 %   46 %
Bond fund(B)       8 %   40%
T=bills rate (Rf) =       5.6%      
Correlation between stock and bond fund = 0.16  
                  
Covariance (CoV SB) = r * σS * σB                  
       0.16*46*40=       294.400  
      

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 ))

=(((17-5.6) * (40)^2 )- ((8-5.6) * 294.4))/ (((17-5.6) * (40)^2)+ ( (8-5.6) * (46)^2)- ((17-5.6+8-5.6) * 294.4))

          17533.44   /   19255.68  
                  
So, weight of S =           91.06%      
weight of B =           8.94%      
                  
Expected return = (weight of S * Expected return of S) + (Weight of B * Expected retun of B)                  
= (91.06%*17%)+(8.94%*8%)              
   16.1950 %          
                  
expected retun of risky portolio is            16.20 %  
                  
                  
Standard deviation formula                  
                  
(σp) =   ( (wS * σS ) ^2 + (wB * σB ) ^2 + (2 * wB* wS*σB *σS* rSB) )^(1/2)              
= ((91.06%*46%)^2+(8.94%*40%)^2+(2*91.06%*8.94%*46%*40%*0.16))^(1/2)              
= 42.6048   %          
                  
Standard deviation of risky portfolio is 42.60 %          

Portfolio invested in the stock	91.06%
Portfolio invested in the bond	8.94%
Expected return	16.20%
Standard deviation 42.60%