Question

Asset A has expected return of 16% and variance of 12.98%. Asset B has an expected return of 8%, and a variance of 5.29%. The correlation coefficient between the two assets is 0.6. Portfolio X is composed 50% of portfolio A and 50% of portfolio B. Variance of portfolio X is? Answer percent.

Answer 1

Given the following information,

	Expected return	variance	Portfolio Weights	Assets A and B
Asset A	16%	0.1298	0.5
Asset B	8%	0.0529	0.5
Correlation Coefficient				0.6

Where Variance of asset A = (σA)^2 = 12.98% = 0.1298

  Variance of asset B = (σB)^2 = 5.29% = 0.0529

Weightage of asset A = wA = 50% = 0.5

  Weightage of asset B = wB = 50% = 0.5

Correlation Coefficient of asset A and asset B in a portfolio X =Corr(xA,xB) = 0.6

and σA = squareroot of 0.1298 = 0.36

  σB = squareroot of 0.0529 = 0.23

We need to find out the value of variance of portfolio of assets A and B which is given by (σP)^2 where

(σP)^2 = ((wA) ^2 * (σA)^2) + ((wB) ^2 * (σB)^2)) + 2*wA*wB*σA*σB*Corr(xA,xB)

Sustituting the above values in this equation, we get

(σP)^2 = (((0.5) ^2) * (0.1298)) + (((0.5) ^2) * (0.0529)) + 2*0.5*0.5*0.36*0.23*0.6

(σP)^2 = ((0.25)*(0.1298)) + ((0.25)*(0.0529)) + 0.025

(σP)^2 = (0.032) + (0.013) + 0.025

(σP)^2 = 0.071 = 7.1%

(σP)^2 = 7.1%

Therefore the variance of portfolio X ( Asset A and Asset B) = (σP)^2 = 7.1%