Question

Suppose you invest 30% of your money in Security A and the rest in Security B

	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

A. What is the expected return of the portfolio?

B. What is the portfolio beta?

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?

D. What percentage of your portfolio variance comes from the “interaction” component of total risk?

Answer 1

Weight of portfolio A (W₁) = 0.3
Weight of portfolio B (W₂) = 0.7
a) expected return = W₁* Return of A + W₂ * Return of B = 0.3 * 15% + 0.7 * 10% = 11.5%
b) Portfolio beta = W₁* Beta of A + W₂ * Beta of B = 0.3 * 1.3 + 0.7 * 1.1 = 1.16
c)Variance of A = (standard deviation) = 0.25^2 = 0.0625
Variance of B = (standard deviation) = 0.17^2 = 0.0289

Portfolio variance = (W₁* ₁)² + (W₂* ₂)² + 2 W₁* ₁ * W₂* ₂ * ₁₂ =  (0.3* 0.25)² + (0.7* 0.17)² + 2* 0.3* 0.25 * 0.7* 0.17 * 0.5 = 0.028711 0r 2.87%

Portfolio variation is smaller because there correlation is 0.5 which gives diversification benefit.
d) Percentage of variance = 2 W₁* ₁ * W₂* ₂ * ₁₂/Total variance = 2* 0.3* 0.25 * 0.7* 0.17 * 0.5 /0.028711 = 31.086%

Best of Luck.God Bless