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A Hybrid Genetic-Quantitative Method for Risk-Return Optimisation of Credit Portfolios

by Frank Schlottmann of the Institute AIFB, and
Detlef Seese of the University Karlsruhe

October 25, 2001

Abstract: This paper proposes a new combination of quantitative models and Genetic Algorithms for the task of optimising credit portfolios. Currently, quantitative portfolio credit risk models are used to calculate portfolio risk figures, e. g. expected losses, unexpected losses and risk contributions. Usually, this information is used for optimising the risk-return profile of the portfolio. We show that gradient-like optimisation methods based on risk contributions can lead to inefficient portfolio structures. To avoid this local optima problem, our optimisation method combines quantitative model features with Genetic Algorithms. The hybrid approach in this paper consists of a task specific Genetic Algorithm that uses special variation operators reflecting portfolio credit risk model knowledge. The method presented here is compatible with any model providing a loss or profit/loss distribution for credit portfolios, e. g. CreditMetrics, CreditRisk+, Wilson's model, and others. As a consequence, it can be used with any risk measure based on such profit-loss distributions like Credit-Value-at-Risk, Expected Shortfall etc. We show how different additional constraints like economic and/or regulatory capital limits can be included in the optimisation process. The results of a test series with different portfolio sizes and structures in a CreditRisk+ General Sector Analysis model framework running on a standard Personal Computer are provided within this paper. They indicate that the hybrid Genetic Algorithm leads to better convergence than a standard Genetic Algorithm approach while not suffering from the local optima problem, and calculates efficient portfolio structures within reasonable time.

JEL Classification: G11, G20, G31, G33.

Keywords: Credit risk, Portfolio credit risk model, Portfolio optimisation, Genetic Algorithm, Credit-Value-at-Risk, Economic capital, Regulatory capital.

Published in: Quantitative Methods in Finance (2001) Conference Proceedings, University of Technology, Sydney, Australia, 2001, p. 55.

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