Given two risky assets and their corresponding covariance matrix, how do I compute the global minimum variance portfolio, its standard deviation and its expected return?

  • $\begingroup$ Are you like for Programming code or math? $\endgroup$ – Kyle Balkissoon Feb 19 '15 at 20:42

Assume the weights of the two assets are $w$,$1-w$ respectively;the expected returns and standard deviations are denoted by $\mu$,$\sigma$ with subscripts 1,2,p(for portfolio),i.e,we have $\mu_1$,$\mu_2$,$\mu_p$,$\sigma_1$,$\sigma_2$,$\sigma_p$.The correlation coefficent is $\rho$ Then

$$\sigma_p^2=w^2\sigma_1^2+(1-w)^2\sigma_2^2+2w(1-w)\sigma_1\sigma_2\rho \,\,\,\,...(1)$$ $$\mu_p=w\mu_1+(1-w)\mu_2 \,\,\,\,\,\,\,\,\,\,\,\,...(2)$$ $$\frac{d_{\sigma_p}}{dw}=0$$ $$w=\frac{\sigma_2^2-\rho\sigma_1\sigma_2}{\sigma_2^2+\sigma_1^2-2\rho\sigma_1\sigma_2}\,\,\,\,\,\,...(3)$$

Substituting(3) into (1) and (2) and simplify them will lead to the answer.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.