Testing Sample Bond Transition Matrices Against Agency Ratings

Summary

The question concerns whether a transition matrix estimated from a sample of bond rating histories is consistent with a published agency matrix. The response points readers to research on statistical comparison of rating transition matrices, including work that considers time dependence and comparisons across rating agencies.

No test statistic, calculation procedure, or empirical result is provided in the discussion itself. The suggested literature may be useful starting material, but the appropriate test depends on the available sample size and on whether the analysis must account for changes in transition behavior over time. The document therefore frames the inference problem and offers references rather than a ready-to-apply testing method.

Key ideas

• A sample transition matrix can be assessed against a published bond rating matrix using statistical tests.
• Available sample size may affect which testing approach is appropriate.
• Research on time-dependent stability and cross-agency comparisons may inform the analysis.
• The discussion supplies references but no test formula or worked example.

Tags

# How to perform significance test on transition matrices


# How to perform significance test on transition matrices












Say you have in your hand a transition matrix published by Moody, and you also collected the rating information for a sample of bonds, which you use to form your own transition matrix. How can we use our sample to test whether if Moody's transition matrix is correct?

## Answer by Jacob M. Morley (score 2, accepted)

https://quant.stackexchange.com/a/10588

Depending upon how much data you have, you might find Violi (2004) useful.

Nickell et al. (2000), while principally considering time-dependent stability tests, refers a bit to significance testing between the matrices of different agencies and might also provide some insight.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.