Security A Security B Expected return 15% 10% Standard Deviation 0.25 0.17 Beta
ID: 2739316 • Letter: S
Question
Security A
Security B
Expected return
15%
10%
Standard Deviation
0.25
0.17
Beta
1.3
1.1
Correlation coefficient
between A and B
0.5
Suppose you invest 30% of your money in Security A and the rest in Security B
a) What is the expected return of the portfolio? (20 points)
b) What is the portfolio beta? (20 points)
c) What is the portfolio variance? Compare it with A and B variances. Is the portfolio variance larger or smaller than either A or B variances and why?
(40 points)
d) What percentage of your portfolio variance comes from the “interaction” component of total risk? (20 points)
Security A
Security B
Expected return
15%
10%
Standard Deviation
0.25
0.17
Beta
1.3
1.1
Correlation coefficient
between A and B
0.5
Explanation / Answer
Portfolio weights: WA=0.3 and WB=0.7:
E(RP) = 0.3 × 0.15 + 0.7 × 0.10 = 0.1150(11.50%)
2 = (0.30)2 (0.25)2 + (0.70)2 (0.17)2 + 2 (0.30) (.25) (0.70) (0.17) (0.5)
= 0.028711 or 2.9%
% of portfolio variance in total risk
= Portfolio variance / Total risk
= 0.028711 / 0.0287110.50
= 16.94%
c.
Variance of A = (Standard Deviation of A)2
= 0.252
= 0.0625 or 6.25%
and
Variance of B = (Standard Deviation of B)2
= 0.172
= 0.0289 or 2.89%
Variance of A is 6.25% which is higher than portfolio variance of 2.9%. However, variance of B is of 2.89% is almost close to variance of B which is 2.9% the reason being its standard deviation %. The more the standard deviation the more the variance would be.Hence, in the present question, the standard deviation (risk) is more for security A and therefore this variance is higher than portfolio variance. However, portfolio variance could be adjusted with the weights of security A and security B.