In: Finance
A portfolio consists of 60% of Security A (expected return of 0.10 and standard deviation of 0.03) and 40% of Security B (expected return of 0.20 and standard deviation of 0.05) and the correlation coefficient between A and B is -0.0012.
a) Calculate the expected return and standard deviation of the portfolio.
b) Calculate the standard deviation of the portfolio if there was no diversification benefit.
Part A:
Expected Ret :
Portfolio Return is the weighted avg return of securities in that portfolio.
Stock | Weight | Ret | WTd Ret |
Security A | 0.6000 | 10.00% | 6.00% |
Security B | 0.4000 | 20.00% | 8.00% |
Portfolio Ret Return | 14.00% |
Portfolio SD:
Particulars | Amount |
Weight in A | 0.6000 |
Weight in B | 0.4000 |
SD of A | 3.00% |
SD of B | 5.00% |
r(A,B) | -0.0012 |
Portfolio SD =
SQRT[((Wa*SDa)^2)+((Wb*SDb)^2)+2*(wa*SDa)*(Wb*SDb)*r(A,B)]
=SQRT[((0.6*0.03)^2)+((0.4*0.05)^2)+2*(0.6*0.03)*(0.4*0.05)*-0.0012]
=SQRT[((0.018)^2)+((0.02)^2)+2*(0.018)*(0.02)*-0.0012]
=SQRT[0.0007]
= 0.0269
= I.e 2.69 %
Part B:
Particulars | Amount |
Weight in A | 0.6000 |
Weight in B | 0.4000 |
SD of A | 3.00% |
SD of B | 5.00% |
r(A,B) | 1 |
Portfolio SD =
SQRT[((Wa*SDa)^2)+((Wb*SDb)^2)+2*(wa*SDa)*(Wb*SDb)*r(A,B)]
=SQRT[((0.6*0.03)^2)+((0.4*0.05)^2)+2*(0.6*0.03)*(0.4*0.05)*1]
=SQRT[((0.018)^2)+((0.02)^2)+2*(0.018)*(0.02)*1]
=SQRT[0.0014]
= 0.038
= I.e 3.8 %