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.
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- 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," Papers cond-mat/9801209, arXiv.org.
- 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.
- 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.
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