[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.


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