Question

For IBM, its expected return is 10% and its standard devidation is 20%. For Google, its expected return is 15% and its standard devidation is 30%. The return correlation between IBM and Google is 0.2. The risk-free rate is 5%. What is the expected return of the minimum variance portfolio (MVP) constructed from the two stocks?

Answer 1

Given for IBM,

expected return E(I) = 10%

standard devidation SD(I) = 20%

Given for Google,

expected return E(G) = 15%

standard devidation SD(G) = 30%

The return correlation between IBM and Google Corr(I,G) = 0.2

Weight of IBM Wi in Minimum variance portfolio is given by

Wi = (SD(I)^2 - SD(I)*SD(G)*Corr(I,G))/(SD(I)^2 + SD(G)^2 - 2*SD(I)*SD(G)*Corr(I,G))

So, Wi = (20^2 - 20*30*0.2)/(20^2 + 30^2 + 2*20*30*.2) = 0.1818 or 18.18%

So, weight of google in the portfolio = 1-0.1818 = 81.82%

Expected return of this portfolio is

Wi*E(I) + Wg*E(G) = 0.1818*10 + 0.8182*15 = 14.09%