130/30 Portfolio Optimization

[Shlomo Katchmalik]

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.

_______________________________________________
R-SIG-Finance@... mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-finance
-- Subscriber-posting only.
-- If you want to post, subscribe first.

[Guy Yollin-2]

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@...
[mailto:r-sig-finance-bounces@...] On Behalf Of Shlomo
Katchmalik
Sent: Monday, April 14, 2008 11:05 AM
To: r-sig-finance@...
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.

_______________________________________________
R-SIG-Finance@... mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-finance
-- Subscriber-posting only.
-- If you want to post, subscribe first.

_______________________________________________
R-SIG-Finance@... mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-finance
-- Subscriber-posting only.
-- If you want to post, subscribe first.

[Attiglah, Mama]

This is a simple non-linear optimisation with linear constraints in a
convex set. Go to www.r-project.org, download the package Rdonlp2, and
use the optimiser donlp2.
I would advise you to start with initial values being half way through
the feasible set of each of the control variables( the weights), then
reuse the optimal weights as the initial values in order to secure st
stability of the optimum.
Hope this will help.


-----
Mama Attiglah, PhD
Quantitative Research analyst
Advanced Research Center
State Street Bank
[phone] (Direct Line)
[phone] (Direct Fax)
Please visit our Web site at
www.ssga.com

-----Original Message-----
From: r-sig-finance-bounces@...
[mailto:r-sig-finance-bounces@...] On Behalf Of Guy Yollin
Sent: 14 April 2008 19:35
To: Shlomo Katchmalik; r-sig-finance@...
Subject: Re: [R-SIG-Finance] 130/30 Portfolio Optimization

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@...
[mailto:r-sig-finance-bounces@...] On Behalf Of Shlomo
Katchmalik
Sent: Monday, April 14, 2008 11:05 AM
To: r-sig-finance@...
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.

_______________________________________________
R-SIG-Finance@... mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-finance
-- Subscriber-posting only.
-- If you want to post, subscribe first.

_______________________________________________
R-SIG-Finance@... mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-finance
-- Subscriber-posting only.
-- If you want to post, subscribe first.

_______________________________________________
R-SIG-Finance@... mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-finance
-- Subscriber-posting only.
-- If you want to post, subscribe first.

[Christian Prinoth]

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@...
[mailto:r-sig-finance-bounces@...] On Behalf Of Shlomo
Katchmalik
Sent: Monday, April 14, 2008 20:05
To: r-sig-finance@...
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.

_______________________________________________
R-SIG-Finance@... mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-finance
-- Subscriber-posting only.
-- If you want to post, subscribe first.

DISCLAIMER:\ L'utilizzo non autorizzato del presente mes...{{dropped:16}}

_______________________________________________
R-SIG-Finance@... mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-finance
-- Subscriber-posting only.
-- If you want to post, subscribe first.