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The Core Factor: A fast and accurate factor reduction technique

by Christoff Gössl of Unicredit Markets and Investment Banking

December 2007

Summary:  In credit portfolio modelling the normal copula approach and multi-factor models have become an industry-wide standard to describe the asset correlation structure. To calculate the portfolio loss distribution for these models, due to its analytical intractability, in general Monte Carlo methods, non-trivial numerical integrations, or structural simplifications have to be applied. Still, for more than 3-4 factors especially determination of risk contributions and optimisation routines become a very time-consuming endeavour. Aim of this paper is to present a new factor reduction approach using a single underlying factor to calculate the portfolio loss distribution. Focusing on risk contributions rather than asset correlations it is shown that the portfolio correlation structure could be captured in just one factor to an astonishing degree of accuracy. The paper outlines the basic idea and calibration of this factor reduction approach, and for illustrative as well as realistic, heterogeneous portfolios the new model is applied in the calculation of loss distributions and risk contributions. The capabilities of this approach are further demonstrated when used in an optimisation setting.

Keywords: Factor models, factor reduction, correlation, optimisation.

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