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

Guy Yollin guy.yollin at rotellacapital.com
Mon Apr 14 20:34:34 CEST 2008

```Hi Shlomo,

On Feb 5th, David Basterfield gave a webcast on the differential
evolution algorithm (http://www.icsi.berkeley.edu/~storn/code.html) in
which he works through a few 115/15 portfolio optimization examples.
The webcast can be downloaded from the events area of the Insightful
website (www.insightful.com).

The DE algorithm is quite elegant and has been implemented in the
package DEoptim.

Best,

-- G

-----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 11:05 AM
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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