Question

Ad A z 1 Fonts 5 Paragraph Styles AD11423456 Voice LE TRAIL 5. (35 pts) There are two stocks: A and B, and Treasury Bill (TB). The parameters of these securities are following: Expected Return Standard Deviation Correlation with Stock A Stock A 10% 20% Stock B 15% 0.2 TB 0% 25% (20 pts. If you need an expected retum of 12% and you only have the access to the three securities above, what is your optimal portfolio composition? What is the standard deviation of your portfolio?

Answer 1

Answer.(5)

Investment Option	Stock A	Stock B	TB
Expected Return	10%	15%	5%
Standard Deviation	20%	25%	0%

Correlation Cofficient between Stock A and Stock B(Cor(A,B))= 0.20 (Given)

Expected Rate of Return is 12%

As we know that for optimal porfoli composition there should be least risk for the expected level of return.

So, Firstly we have to calculate the optimal composition between Stock A and Stock B

Weightage of Investment in Stock A(WA)= ((σB)^2- Cor(A,B)*σB*σA )/((σA)^2+(σB)^2-2*Cor(A,B)*σB*σA)

= ((25)^2- 0.20*20*25)/((20)^2+(25)^2-2*0.20*20*25)= (625-100)/(400+625-200)

= 525/825= 0.6364 i.e. 63.64%

Weightage of Investment in Stock B(WB)= 1-0.6364= 0.3636 i.e. 36.36%

Now Expected Return from the Optimal Portfolio of Stock A and Stock B(RAB) = WA*RA+WB*RB

= .6364*10+.3636*15=11.82%

Return on optimal composition= 11.82%

Which is below the expected rate of return so for getting expected rate of return we have to calculate optimal composition at said rate of return.

Let the Weightage of Stock A(WA)= p so, Weightage of Stock B(WB)=1- p

So,

12= p*10+(1-p)15

12= -5p+15

5p= 15-12

p= 3/5= 0.60 i.e. 60%

1-p= 1-0.60=0.40 i.e.40%

So, Investment in Stock A= 60% and Stock B= 40%

Standard Deviation of the portfolio= ((WA *σA)^2+(WB *σB)^2+ 2*Cor(A,B)*WA *σA*WB *σB)^1/2

= ((0.60*20)^2+(0.40*25)^2+2*0.20*0.60*0.40*20*25)^1/2

= (144+100+48)^1/2= 17.09% (Ans)

Note :- As we have already seen that at optimal portfolio composition rate of return from portfolio is below expected return so if we choose any combination of any other 2 or all three, resulting portfolio woluld not be the optimum at expected rate of return so we have taken only stock A and Stock B