Question

Conestego and Fallen, Inc. are two firms that are being considered for a risky two-asset portfolio. Their performances are as described below:

a. What are the expected return and standard deviation of the return of Conestego and Fallen, Inc.?

b. An investor creates a two-asset portfolio consisting of 60% of Conestego and 40% Fallen, Inc. If the correlation coefficient of Conestego and Fallen, Inc’s return is 0.33, what is expected to be the expected return and standard deviation of the return of the two-asset portfolio?

Conestego, Inc.		Fallen, Inc
Return	Probability	Return	Probability
4%	.20	-2%	.4
12%	.50	5%	.2
14%	.30	10%	.4

Answer 1

Expected return =

where P = probability

R = rate of return

Conestego:

Expected return = 11%

Standard deviation = [P*(C - C')^2]^(1/2)

= (13)^1/2

= 3.61%

Fallen Inc.

Expected return = 4.2%

Standard deviation = (28.96)^1/2

= 5.38%

b)

expected return of a portfolio = Wc*Rc + Wf*Rf

where Wc and Wf = weights of conestego and fallen

expected return on a portfolio = 0.6*11% + 0.4*4.2%

= 8.28%

standard deviation of portfolio = [(Wc*stand.dev C)^2 + (Wf * stand.dev.F)^2 + 2*Wc *Wf * stand.dev C*stand.dev.F*correlation]^(1/2)

= [(0.6*3.61)^2 + (0.4*5.38)^2 + 2*0.6*0.4*3.61*5.38*0.33]^(1/2)

= (12.39)^1/2

= 3.52%