Question

There are 3 assets. The following information is available about the assets:

Asset	Expected return	Expected standard deviation	Beta
A	.10	.04	1.1
B	.14	.06	1.5
C	.04	0.0	0

a. (5 points) What is the expected return on a portfolio that is 1/3 invested in each asset?

b. (5 points) What is the Beta of a portfolio that is 50% A and 50% C?

c. (5 points) If you wanted to have a portfolio with a Beta of 1.04 and had 20% in asset C, what percentages would you invest in A and B?

Answer 1

Answer A)

Expected Return = W(A) * R(A) + W(B) * R(B) + W(C) * R(C)

= 1/3* 10% + 1/3 * 14% + 1/3 * 4%

= 9.33%  

Answer B) Beta is weighted Average

Beta of Portfolio with A & C = 50% * 1.1 + 50% * 0

= 0.55

Answer C)

let weight of A is X, then Weight of B becomes 1 - X - 0.2

beta of portfolio =  1.1 * X + 1.5* (1-X-0.2) + 0 * 20%

1.04 = 1.1X + 1.5 - 1.5 X - 0.3

1.04 = 1.2 - 0.4 X

X = (1.2 - 1.04) / 0.4

X = 40%

Invest in A = 40%

Invest in B = 100 - 40%-20% = 40%

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