Spin Glasses and Nonlinear Constraints in Portfolio Optimization
We discuss the portfolio optimization problem with the obligatory deposits constraint. Recently it has been shown that as a consequence of this nonlinear constraint, the solution consists of an exponentially large number of optimal portfolios, completely different from each other, and extremely sensitive to any changes in the input parameters of the problem, making the concept of rational decision making questionable. Here we reformulate the problem using a quadratic obligatory deposits constraint, and we show that from the physics point of view, finding an optimal portfolio amounts to calculating the mean-field magnetizations of a random Ising model with the constraint of a constant magnetization norm. We show that the model reduces to an eigenproblem, with 2N solutions, where N is the number of assets defining the portfolio. Also, in order to illustrate our results, we present a detailed numerical example of a portfolio of several risky common stocks traded on the Nasdaq Market.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Gábor, Adrienn & Kondor, I, 1999. "Portfolios with nonlinear constraints and spin glasses," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 274(1), pages 222-228.
- Galluccio, Stefano & Bouchaud, Jean-Philippe & Potters, Marc, 1998.
"Rational decisions, random matrices and spin glasses,"
Physica A: Statistical Mechanics and its Applications,
Elsevier, vol. 259(3), pages 449-456.
- Stefano Galluccio & Jean-Philippe Bouchaud & Marc Potters, 1998. "Rational decisions, random matrices and spin glasses," Science & Finance (CFM) working paper archive 500054, Science & Finance, Capital Fund Management.
- Stefano Galluccio & Jean-Philippe Bouchaud & Marc Potters, 1998. "Rational Decisions, Random Matrices and Spin Glasses," Papers cond-mat/9801209, arXiv.org.
When requesting a correction, please mention this item's handle: RePEc:arx:papers:1311.2511. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.