0
$\begingroup$

I solved attached question but I am not sure whether I did part a and c correctly. Is there a way to calculate weights of A and B by just knowing their standard deviation and correlation's value?

enter image description here

enter image description here

$\endgroup$
1
$\begingroup$

To find the weights in the question (a) you should write your portfolio expected excess return and variance as: $$ E[R_p^e] = w_A R_A + w_b R_B - R_f \\ \sigma^2[R_p^e] = \sigma^2[w_A R_A + w_b R_B - R_f] = w_A^2\sigma_A^2 + w_B^2 \sigma_B^2 + 2 \rho_{AB}\sigma_A\sigma_B $$ The sharpe ratio is given by: $$ S(w_A,w_B) = \frac{E[R_p^e]}{\sigma[R_p^e]} $$ So, to find the weights which maximize Sharpe ratio, you should solve the equation: $$ \nabla S |_{w_A+w_B=1} = 0 $$

$\endgroup$
  • $\begingroup$ Thank you for your response, @carbolymer. If you have a time, can you solve this question with given value? I am not sure that I understand. Should I solve weights like following way: WA=W, WB=1-W. W^2*(0.02)^2+(1-W)^2*(0.07)^2+2*(-0.5)*W*(1-W)*(0.02)*(0.07)=0 $\endgroup$ – auhan Dec 23 '15 at 1:02

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.