Question

3. Consider two stocks, A and B, with their expected returns and standard deviations, as follows: Stock Expected return Standard deviation 15% 10 10% What is the expected retum if the portfolio contains equal amounts of each security? What is the standard deviation for the equally weighted portfolio in a) if the correlation between the security retums is i) Cor +1.00. ii) Cors+0.50, and iii) Corras - -0.50? a) 12.5%; b) i. 9%; ii. 7.81%; iii. 4.58%
letter b please

Answer 1

A.

Weight A=1/2=       0.5  
          
Standard deviation of A (σA)=       10%  
          
weight B=1/2=       0.5  
Standard deviation (σB)=       8%  
Correlation between A and B=       1  
  
(σp)=   ((weigh A * σA ) ^2 + (weight B* σB )^ 2 + (2 * Weight A* Weight B*σA *σB* correlation))^(1/2)      
(((0.5*10%)^2+(0.5*8%)^2+(2*0.5*0.5*10%*8%*1)))^(1/2)          
9.00%
          
Standard deviation of portfolio is 9%          

B.

Weight A=1/2= 0.5

Standard deviation of A (σA)= 10%

weight B=1/2= 0.5

Standard deviation (σB)= 8%

Correlation between A and B= 0.5

(σp)= ((weigh A * σA ) ^2 + (weight B* σB )^ 2 + (2 * Weight A* Weight B*σA *σB* correlation))^(1/2)

(((0.5*10%)^2+(0.5*8%)^2+(2*0.5*0.5*10%*8%*0.5)))^(1/2)

7.81%

Standard deviation of portfolio is 7.81%

C.

Weight A=1/2=       0.5
      
Standard deviation of A (σA)=       10%
      
weight B=1/2=       0.5
Standard deviation (σB)=       8%
Correlation between A and B=       -0.5

(σp)=   ((weigh A * σA ) ^2 + (weight B* σB )^ 2 + (2 * Weight A* Weight B*σA *σB* correlation))^(1/2)  
(((0.5*10%)^2+(0.5*8%)^2+(2*0.5*0.5*10%*8%*-0.5)))^(1/2)      
4.58%      
      
Standard deviation of portfolio is   4.58%  
      

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