dstefan
03-22-2008, 01:26 PM
Chapter 8, Problem 2:
Assume that you can trade four assets (and that it is also possible to short the assets). The expected values, standard deviations, and correlations of the rates of return of the assets are:
\begin{array}{ccl}\mu_1 ~=~ 0.08; & \sigma_1 ~=~ 0.25; & \rho_{1,2} ~=~ -0.25; \\\mu_2 ~=~ 0.12; & \sigma_2 ~=~ 0.25; & \rho_{2,3} ~=~ -0.25; \\ \mu_3 ~=~ 0.16; & \sigma_3 ~=~ 0.30; & \rho_{1,3} ~=~ 0.25; \\ \mu_4 ~=~ 0.05; & \sigma_4 ~=~ 0.20; & \rho_{i,4} ~=~ 0, ~~\forall~ i=1:3.\end{array}
(i) Find the asset allocation for a minimal variance portfolio with 12% expected rate of return;
(ii) Find the asset allocation for a maximum expected return portfolio with standard deviation of the rate of return equal to 24%.
Solution:
a
Assume that you can trade four assets (and that it is also possible to short the assets). The expected values, standard deviations, and correlations of the rates of return of the assets are:
\begin{array}{ccl}\mu_1 ~=~ 0.08; & \sigma_1 ~=~ 0.25; & \rho_{1,2} ~=~ -0.25; \\\mu_2 ~=~ 0.12; & \sigma_2 ~=~ 0.25; & \rho_{2,3} ~=~ -0.25; \\ \mu_3 ~=~ 0.16; & \sigma_3 ~=~ 0.30; & \rho_{1,3} ~=~ 0.25; \\ \mu_4 ~=~ 0.05; & \sigma_4 ~=~ 0.20; & \rho_{i,4} ~=~ 0, ~~\forall~ i=1:3.\end{array}
(i) Find the asset allocation for a minimal variance portfolio with 12% expected rate of return;
(ii) Find the asset allocation for a maximum expected return portfolio with standard deviation of the rate of return equal to 24%.
Solution:
a