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

ID: 2740531 • Letter: S

Question

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

What is the expected return of the portfolio? (20 points)

What is the portfolio beta? (20 points)

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)

What percentage of your portfolio variance comes from the “interaction” component of total risk? (20 points)

Security A 15% 0.25 1.3 Security B Expected return Standard Deviation Beta Correlation co efficient between A and B 0.17 1.1 0.5

Ans) 1) Expected return of the portfolio = weight of A* Expected return of A + weight of B * Expected of return of B

= 30% * 15% + 70% * 10%

= 0.045 + 0.07 = 0.115 = 11.5%

2) Portfolio Beta = Weight of A*Beta of A + Weight of B*Beta of B

= 30%*1.3 + 70%*1.1 = 0.39 + 0.77 = 1.16

3) Portfolio Variance = (weight of A)^2*variance of A + (weight of B)^2*variance of B + 2*weight of A*weight of B*Cov(A,B)

Variance of A = (Standard Deviation of A)^2 = 0.25^2 = 0.0625

Variance of B = (Standard Deviation of B)^2 = 0.17^2 = 0.0289

Portfolio Variance = (30%)^2*0.0625 + (70%)^2*0.0289 + 2*30%*70%*0.5

= 0.005625 + 0.014161 + 0.21 = 0.229786

4) The portfolio variances as compared to variances of A and B is larger

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