Maximum Return/Risk Portfolio for multiple covariance matrices and expected returns

edgetrading · July 1st, 2012, 9:45 am

Hello,In normal maximum return/risk portfolio optimisation, we minimiseby taking the natural log and then differentiating.I would like to perform a simular operation, but adding another term, using a different \Sigma_1 and \mu_1. i.e.Following that, I would like to generalise for any number of \Sigma_i's and \mu_i's.Does anyone know how to do this? I am unable to take the natural log in this case, as log(a+b) does not have a nice identity.

Alan · July 1st, 2012, 1:41 pm

So, don't take the log -- just differentiate w.r.t. each w(i) and lambda, and then numerically solve for a soln. Alternatively, in say Mathematica, you could just use FindMaximum[...] on the expressions without the Lagrange multiplier term, maximizing over the {w(i)} with the constraint that they summed to 1. p.s. I have no idea if there are multiple local maxima or an unbounded maximum, so either procedure may potentially have problems.