Security A Security B Expected return 15% 10% Standard Deviation 0.25 0.17 Beta

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.

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