[R-SIG-Finance] Optimization Question

[Guy Yollin]

Ian,

An excellent technique for general purpose non-linear optimization is the differential evolution algorithm:

http://www.icsi.berkeley.edu/~storn/code.html

It has been implemented in the DEoptim package available on CRAN; the algorithm is very flexible and you could readily implement an maximum drawdown or VaR optimization strategy using DE.

Back in February 2008, David Basterfield gave a webcast on the differential evolution algorithm with a number of non-linear portfolio optimization examples; it is still available on the Insightful website under events/finance:

        www.insightful.com

Note, a number of papers have shown the superiority of conditional-value-at-risk (CVaR) to VaR as a risk metric.  The CVaR portfolio optimization can be framed as a linear programming problem and you could then use a linear programming package (e.g. lpSolve or linprog) to find mean-CVaR optimum portfolios.  The books Portfolio Construction and Risk Budgeting by Bernd Scherer and Introduction to Modern Portfolio Optimization by Bernd Scherer and Douglas Martin provides some details on this and other non-standard portfolio optimization techniques; although both these books include S+NuOPT examples, the key points are transferrable to R.

Best,

-- Guy




-----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 ian.mcdonald at malbecpartners.com
Sent: Tuesday, December 30, 2008 7:49 AM
To: r-sig-finance at stat.math.ethz.ch
Subject: [R-SIG-Finance] Optimization Question

I am interested in doing a portfolio optimization, but I need to impose
non-linear, functional constraints (i.e Max Drawdown, or VaR, etc). I've
looked into several of the optimization routines (nlminb, constrOptim and
optim with SANN/L-BFGS-B) but it appears that all of them are geared to
linear constraints. Other than using a penalty function method, is anyone
aware of any other approaches available in  R?

Thanks
Ian McDonald
Malbec Partners

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