Question

A portfolio consists of two shares: X and Y. Variance of returns for share X is 0,4 and for share Y is 0,5. Covariance of returns between X and Y is (-0,08). Calculate the proportion of share Y in the portfolio necessary to build a minimum-variance portfolio consisting only of these two shares. Describe what does minimum-variance portfolio means from the point of view of Markowitz theory

Please send me the answer with the steps and the equation

Answer 1

Minimum Variance portfolio according to Markowitz theory means that is that portfolio or composition of stock at whcih standard deviation or variance of portfolioi is minimum. Risk of portfolio in terms of variance or standard deviation cannot be reduced below that risk level which is at Minimum portfolio variance level.

Variance of X or (σX)^2 = 0.4

Variance of Y or (σY)^2 = 0.5

CoVariance of X and Y = -0.08

Formula for Minimum Variance Portfolio or equation to calculate proportion of Y (weight Y) = ((σX)^2 - CoV XY)/((σX)^2+(σY)^2-(2*Cov. XY))

((0.4 - (-0.08))/((0.4+0.5-(2*(-0.08)))

=0.4528301887 or 45.28%

So the proportion of share Y in the portfolio necessary to build a minimum-variance portfolio consisting only of these two shares is 45.28%