Portfolio Optimization Using SPEA2 with Resampling

Proceeding of: Intelligent Data Engineering and Automated Learning – IDEAL 2011: 12th International Conference, Norwich, UK, September 7-9, 2011The subject of financial portfolio optimization under real-world constraints is a difficult problem that can be tackled using multiobjective evolutionary algorithms. One of the most problematic issues is the dependence of the results on the estimates for a set of parameters, that is, the robustness of solutions. These estimates are often inaccurate and this may result on solutions that, in theory, offered an appropriate risk/return balance and, in practice, resulted being very poor. In this paper we suggest that using a resampling mechanism may filter out the most unstable. We test this idea on real data using SPEA2 as optimization algorithm and the results show that the use of resampling increases significantly the reliability of the resulting portfolios.The authors acknowledge financial support granted by the Spanish Ministry of Science under contract TIN2008-06491-C04-03 (MSTAR) and Comunidad de Madrid (CCG10- UC3M/TIC-5029).Publicad

Evolutionary estimation of a Coupled Markov Chain credit risk model

There exists a range of different models for estimating and simulating credit risk transitions to optimally manage credit risk portfolios and products. In this chapter we present a Coupled Markov Chain approach to model rating transitions and thereby default probabilities of companies. As the likelihood of the model turns out to be a non-convex function of the parameters to be estimated, we apply heuristics to find the ML estimators. To this extent, we outline the model and its likelihood function, and present both a Particle Swarm Optimization algorithm, as well as an Evolutionary Optimization algorithm to maximize the likelihood function. Numerical results are shown which suggest a further application of evolutionary optimization techniques for credit risk management

Evolutionary multi-stage financial scenario tree generation

Multi-stage financial decision optimization under uncertainty depends on a careful numerical approximation of the underlying stochastic process, which describes the future returns of the selected assets or asset categories. Various approaches towards an optimal generation of discrete-time, discrete-state approximations (represented as scenario trees) have been suggested in the literature. In this paper, a new evolutionary algorithm to create scenario trees for multi-stage financial optimization models will be presented. Numerical results and implementation details conclude the paper

Statistical Properties of Cross-Correlation in the Korean Stock Market

We investigate the statistical properties of the correlation matrix between individual stocks traded in the Korean stock market using the random matrix theory (RMT) and observe how these affect the portfolio weights in the Markowitz portfolio theory. We find that the distribution of the correlation matrix is positively skewed and changes over time. We find that the eigenvalue distribution of original correlation matrix deviates from the eigenvalues predicted by the RMT, and the largest eigenvalue is 52 times larger than the maximum value among the eigenvalues predicted by the RMT. The $\beta_{473}$ coefficient, which reflect the largest eigenvalue property, is 0.8, while one of the eigenvalues in the RMT is approximately zero. Notably, we show that the entropy function $E(\sigma)$ with the portfolio risk $\sigma$ for the original and filtered correlation matrices are consistent with a power-law function, $E(\sigma) \sim \sigma^{-\gamma}$, with the exponent $\gamma \sim 2.92$ and those for Asian currency crisis decreases significantly

Dynamics of market correlations: Taxonomy and portfolio analysis

The time dependence of the recently introduced minimum spanning tree description of correlations between stocks, called the ``asset tree'' have been studied to reflect the economic taxonomy. The nodes of the tree are identified with stocks and the distance between them is a unique function of the corresponding element of the correlation matrix. By using the concept of a central vertex, chosen as the most strongly connected node of the tree, an important characteristic is defined by the mean occupation layer (MOL). During crashes the strong global correlation in the market manifests itself by a low value of MOL. The tree seems to have a scale free structure where the scaling exponent of the degree distribution is different for `business as usual' and `crash' periods. The basic structure of the tree topology is very robust with respect to time. We also point out that the diversification aspect of portfolio optimization results in the fact that the assets of the classic Markowitz portfolio are always located on the outer leaves of the tree. Technical aspects like the window size dependence of the investigated quantities are also discussed.Comment: 13 pages including 12 figures. Uses REVTe