Question

An investor invests 40 per cent of her funds in Company A's shares and the remainder in Company B's shares. The standard deviation of the returns on A is 20 per cent and on B is 10 per cent. Required: Calculate the variance of return on the portfolio assuming the correlation between the returns on the two securities is:

A) +1.0

B) +0.5

C) 0

D) -0.5

What do your answers show?

Answer 1

Let the weights be denoted by w and standard deviation by σ

Given,

w_A = 0.40

w_B = 0.60

σ_A = 0.20

σ_B = 0.10

Correlation = ρ

Standard deviation of the portfolio = √ w_A²σ_A² + w_B²σ_B² + 2w_Aw_Bσ_Aσ_Bρ

(a) ρ = 1

=> Standard Deviation of the portfolio = √ 0.4²0.2² + 0.6²0.10² + 2*0.4*0.6*0.2*0.1*1 = 0.14 or 14%

(b) ρ = 0.5

=> Standard Deviation of the portfolio = √ 0.4²0.2² + 0.6²0.10² + 2*0.4*0.6*0.2*0.1*0.5 = 0.12 or 12%

(c) ρ = 0

=> Standard Deviation of the portfolio = √ 0.4²0.2² + 0.6²0.10² + 2*0.4*0.6*0.2*0.1*0 = 0.1 or 10%

(d) ρ = -0.5

=> Standard Deviation of the portfolio = √ 0.4²0.2² + 0.6²0.10² + 2*0.4*0.6*0.2*0.1*(-0.5) = 0.07 or 7%

We can see that as the correlation between the stocks reduces, the standard deviation (risk) of the portfolio also reduces.