Default probabilities and default correlations

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Erlenmaier, Ulrich; Gersbach, Hans

Working Paper

Default probabilities and default

correlations

Research notes in economics & statistics, No. 01-5

Provided in cooperation with:

Deutsche Bank Research

Suggested citation: Erlenmaier, Ulrich; Gersbach, Hans (2001) : Default probabilities

and default correlations, Research notes in economics & statistics, No. 01-5, http://

hdl.handle.net/10419/40256

Editor:

Ann-Charlotte Eliasson

+49 69 910-31832

ann-charlotte.eliasson@db.com

Deutsche Bank Research

Frankfurt am Main

Germany

E-mail

: marketing.dbr@db.com

Fax

: +49 69 910-31877

Managing Directors

Axel Siedenberg

Norbert Walter

Research Notes

in Economics & Statistics

December 3, 2001

Quantitativ

e Analysis

Economics

Default Probabilities and Default

Correlations

Starting from the Merton framework for firm defaults, we provide the

analytics and robustness of the relationship between default

probabilities and default correlations. We show that loans with higher

default probabilities will not only have higher variances but also higher

correlations with other loans. As a consequence, portfolio standard

deviation can increase substantially when loan default probabilities rise.

This result has two important implications. First, relative prices of loans

with different default probabilities should reflect the differential impact

on portfolio standard deviation. Second, the standard deviation of loan

portfolios and of default rates, as well as the required economic capital

will vary significantly over the business cycle.

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Std. Returns of Firm 2

Std. Returns of Firm 1

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