Problem 6-06 Given: E(R1) = 0.13 E(R2) = 0.18 E(σ1) = 0.04 E(σ2) = 0.06 Calculate...

Problem 6-06

Given:

	E(R₁) = 0.13
	E(R₂) = 0.18
	E(σ₁) = 0.04
	E(σ₂) = 0.06

Calculate the expected returns and expected standard deviations of a two-stock portfolio having a correlation coefficient of 0.75 under the conditions given below. Do not round intermediate calculations. Round your answers to four decimal places.

w₁ = 1.00
Expected return of a two-stock portfolio:

Expected standard deviation of a two-stock portfolio:
w₁ = 0.80
Expected return of a two-stock portfolio:

Expected standard deviation of a two-stock portfolio:
w₁ = 0.55
Expected return of a two-stock portfolio:

Expected standard deviation of a two-stock portfolio:
w₁ = 0.30
Expected return of a two-stock portfolio:

Expected standard deviation of a two-stock portfolio:
w₁ = 0.05
Expected return of a two-stock portfolio:

Expected standard deviation of a two-stock portfolio:

Solutions

Expert Solution

E(R1)=0.13
E(R2)=0.18
E(σ1) = 0.04

E(σ2) = 0.06
Correlation =0.75

a) W1 =1; W2 =0
Expected Return =Weight of Stock 1*E(R1)+Weight of Stock 2*E(R2) =1*0.13+0*0.18 =0.13
Standard Deviation =((Weight of 1*E(σ1))^2+(Weight of 2*E(σ2))^2+2*Weight of 1*Weight of 2*E(σ1)*E(σ2)*r1,2)^0.5
=((1*0.04)^2+(0*0.06)^2+2*1*0*0.04*0.06*0.75)^0.5=0.0400

b) W1 =0.80; W2 =0.20
Expected Return =Weight of Stock 1*E(R1)+Weight of Stock 2*E(R2) =0.80*0.13+0.20*0.18 =0.14
Standard Deviation =((Weight of 1*E(σ1))^2+(Weight of 2*E(σ2))^2+2*Weight of 1*Weight of 2*E(σ1)*E(σ2)*r1,2)^0.5
=((0.80*0.04)^2+(0.20*0.06)^2+2*0.8*0.2*0.04*0.06*0.75)^0.5=0.0418

c) W1 =0.55; W2 =0.45
Expected Return =Weight of Stock 1*E(R1)+Weight of Stock 2*E(R2) =0.55*0.13+0.45*0.18 =0.1525 or 0.153
Standard Deviation =((Weight of 1*E(σ1))^2+(Weight of 2*E(σ2))^2+2*Weight of 1*Weight of 2*E(σ1)*E(σ2)*r1,2)^0.5
=((0.55*0.04)^2+(0.45*0.06)^2+2*0.55*0.45*0.04*0.06*0.75)^0.5=0.0459

d) W1 =0.30; W2 =0.70
Expected Return =Weight of Stock 1*E(R1)+Weight of Stock 2*E(R2) =0.30*0.13+0.70*0.18 =0.165
Standard Deviation =((Weight of 1*E(σ1))^2+(Weight of 2*E(σ2))^2+2*Weight of 1*Weight of 2*E(σ1)*E(σ2)*r1,2)^0.5
=((0.3*0.04)^2+(0.7*0.06)^2+2*0.3*0.7*0.04*0.06*0.75)^0.5=0.0516

e) W1 =0.05; W2 =0.95
Expected Return =Weight of Stock 1*E(R1)+Weight of Stock 2*E(R2) =0.05*0.13+0.95*0.18 =0.1775 or 0.178
Standard Deviation =((Weight of 1*E(σ1))^2+(Weight of 2*E(σ2))^2+2*Weight of 1*Weight of 2*E(σ1)*E(σ2)*r1,2)^0.5
=((0.05*0.04)^2+(0.95*0.06)^2+2*0.05*0.95*0.04*0.06*0.75)^0.5=0.0585

jeff jeffy answered 1 year ago

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