# [R-SIG-Finance] 130/30 Portfolio Optimization

Christian Prinoth Christian.Prinoth at epsilonsgr.it
Tue Apr 15 11:03:40 CEST 2008

```A few days ago I have posted a link to a paper describing techniques to
do what you want with solve.QP. Please search in the archive, I do not
have the link handy right now.

Chris

-----Original Message-----
From: r-sig-finance-bounces at stat.math.ethz.ch
[mailto:r-sig-finance-bounces at stat.math.ethz.ch] On Behalf Of Shlomo
Katchmalik
Sent: Monday, April 14, 2008 20:05
To: r-sig-finance at stat.math.ethz.ch
Subject: [R-SIG-Finance] 130/30 Portfolio Optimization

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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