Beginning in 2004, Kamakura Corporation began publishing the Kamakura Troubled Company Index on a monthly basis. Beginning in 2009, the index was made available to subscribers to the KRIS default probability service on a daily basis. The index is based on the Kamakura Risk Information Services public firm default probabilities for 29,400 companies in the 33 countries. The index is the percentage of these public firms for which the annualized 1 month default probability is more than one percent. With each new version of the KRIS default models, the troubled company index is updated and its history is restated. This blog discusses the upgrade of the troubled company index from the KRIS version 4.1 default probability models to the KRIS version 5 default probability models.
Kamakura Corporation announced the release of its long-awaited version 5 default probability models in this September 30 press release, which shows the dramatic increases in accuracy that the new models deliver:
The increases in accuracy compared to the version 4.1 models were significant at all maturities, but they were most impressive in the intermediate and long maturity default probabilities. Another area of improvement was the consistency between actual and expected defaults. The graph below shows the actual monthly number of default events (blue line) in the KRIS data base from January 1990 to December 2008 plotted against the expected number of defaults (red line) for the version 5 models:
Note the consistency of actual and expected defaults on the right hand of the graph, when the credit crisis peaked with the failures of Lehman, FNMA, FHLMC, and AIG. The following table compares the differences in correlation between actual and expected defaults for KRIS version 5 and version 4.1, which was estimated over the period from January 1990 to October 2004:
Note that the expected number of defaults (green line) on the right hand side of the graph, which is “out of sample,” substantially overshot the actual number of defaults at the peak of the credit crisis. Because of this, the KRIS version 5 models have a much higher degree of consistency between actual and expected defaults. The author and Dr. Xiaoming Wang of Kamakura Corporation suggested quantifying this consistency by comparing the adjusted R-squared on the linear regression
Actual defaults= A + B (Expected Defaults)
Those results are reported in the table below.
Version 5.0 KRIS models explain more than 74% of the monthly variation in the number of defaults. The version 4.1 models explained 66% of the monthly variation in defaults on an in-sample basis.
When we apply the models to calculate the troubled company index, we should then expect to see the following results:
- The average level of the troubled company index over the 1990-2010 period should be lower for the version 5 models, because the version 4.1 version of the index “overshot” the number of defaults toward the end of the crisis
- Recent values of the version 5 implementation of the troubled company index should be dramatically lower than they are using the version 4.1 of the index for the same reason
That is exactly what we see when we plot both versions of the troubled company index over the period from January 1990 to mid-October 2010:
Over the full history of the index, the two versions show a 95.1% correlation and their high and low values are nearly identical. We present a summary here:
The two versions are nearly identical in their peaks and valleys. The dates of the all time low are very different, however, between the two versions. The version 4.1 index all time low was in April 2006, while the version 5 all time low was in July 1994. This masks the fact that the version 5 index was 5.33 in April 2006, only 6 basis points away from being an all time low at that time. The key difference to note is in the “post credit crisis low,” where the version 4.1 index is much higher. This again stems from the model’s tendency to overshoot actual defaults in recent years that we saw in prior graphs.
Kamakura will officially report the troubled company index using version 5.0 models from November 1, 2010 onward. The graphic below shows the revised values of the index from 2006 to the present:
Comments and questions are welcome at firstname.lastname@example.org.
Donald R. van Deventer
Honolulu, November 4, 2010