Question

1)An investor is considering investing an equally weighed portfolio of two (2) stocks namely X and Y. You have been given the following information about these two stocks in terms of risk, return and correlation, as shown below:

2)Based on this calculate
a) portfolio return
b) portfolio risk
c.)Compare portfolio risk with the individual stock risks and identify the benefit of the diversification of the portfolio.

Stock	X	Y
E(R)	10%	8%
σ	20%	15%
Correlation between A and B	-0.25

Answer 1

A) Portfolio Return is the weighted average return of stock in the portfolio.

Portfolio Return = W1 X R1 + W2 x R2

Portfolio Return = .50 x 10% + .50 x 8%

Portfolio Return = 9%

Where,

W1= Weight in Security X i.e. 50%

W2= Weight in Security Y i.e. 50%

R1= Return of Security X i.e. 10%

R2= Return of Security Y i.e. 8%

B) Portfolio Risk i.e. Standard Deviation is calculated as-

Standard Deviation =

  

(W1 x 01)2 + (W2 x 02)2 + 2 x W1 XW2 X01 X 02 x corr (A,B)

(0.5 x 20 )2 + (0.5 X 15 )2 + 2 x 0.5 x 0.5 x 20 x 15 x -0.25)

Portfolio Risk =10.90%

Where,

W1= Weight in Security X i.e. 50%

W2= Weight in Security Y i.e. 50%

σ1 = Standard Deviation of Security X i.e. 20%

σ2 = Standard Deviation of Security Y i.e. 15%

Corr(X,Y) = Correlation Coefficient between Security X and Security Y i.e. -0.25

Note- In the given question correlation between A and B is given i.e. -0.25 assuming it is the correlation between X and Y

C) Portfolio Risk i.e.standard Deviation of Portfolio is 10.90% ,whereas standard Deviation of Security A is 20% and Standard Deviation of Security B is 15%, Due to diversification i.e. equal investment in both the security overall risk has been reduced which is equal to 10.90% lesser than the 20% and 15%