[R-SIG-Finance] 130/30 Portfolio Optimization
Shlomo Katchmalik
katchmalik at gmail.com
Mon Apr 14 20:04:55 CEST 2008
Hi All,
Does anybody have an idea as to how one would find an optimal 130/30
portfolio using R?
More specifically, for a given return covariance matrix Q, vector of
expected security returns mu, and risk tolerance tau, the problem is
to find the portfolio vector x that minimizes
x' * Q * x - tau * mu' * x
subject to the following constraints:
A * x = b for given constraint matrix A and vector b,
x >= L,
x <= U,
the sum of the positive elements of x is 1.3,
the sum of the negative elements of x is -0.3,
If not for the last two nonlinear constraints, solve.QP in
library(quadprog) would be applicable. Unfortunately, these two
constraints are central to the problem.
I'd appreciate any help.
Thanks,
Shlomo.
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