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 |
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 =
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%
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