Rating frailty, Bayesian updates, and portfolio credit risk analysis*

Abstract

This paper studies how to utilize individual ratings and credit performance for portfolio credit risk analysis and surveillance. We model the default intensity of firms using a proportional form, with rating specific individual frailty to account for heterogeneity within a rating group, as well as rating specific exposure to observable macro covariates, industries and a latent mean-reverting macro frailty factor. To estimate the model, we take the Bayesian approach and develop a Markov chain Monte Carlo-based algorithm. This approach enables us to quantify parameter uncertainty which is crucial for forecasting and it also provides a convenient tool for performing updates. Using a large default dataset spanning a period of 45 years including the 2008 financial crisis, we provide strong evidence for the dependence of individual frailty and exposure to systematic risk factors on credit rating. In out-of-sample testing, we showcase the ability of our model to forecast the number of defaults through business cycles and particularly in the financial crisis. Furthermore, by monitoring a collateralized loan obligation (CLO), we show that our model can perform reasonably well for the surveillance purpose with timely updates, even if the data used for the initial calibration of the model does not contain the firms in the CLO.

Keywords:

• Portfolio credit risk
• Credit rating
• Frailty
• Surveillance

Acknowledgments

We thank the editor and the referees for their valuable comments that led to significant improvements in the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 CLOs are the dominant type of structured finance products in the CDO market after the 2008 financial crisis. The strikingly strong recovery of CLOs in recent years has prompted significant concerns over the market and its valuation. See, for example, ‘CLO surge prompts regulatory concerns’, Financial Times, September 8, 2014.

2 See p.3 of the paper, and in particular, footnote 5.

3 The importance of dealing with unlisted firms is further accentuated by the report in Stulz (2018) which documents a sharp fall in the number of listed stocks in the U.S. since 1997.

4 To apply our model to a new name outside the database, we use the estimated model for the rating class where the new name belongs.

5 We use Moody's definition of default; see Chava et al. (2011), p.1272.

6 Our result cannot be directly compared with the conclusion in Hilscher and Wilson (2017) which states that 1-year default probability of firms with lower ratings is more sensitive to changes in the median default probability across all firms. In contrast, we analyze the sensitivity of the instantaneous default intensity to changes in the macro factors, which are different things. Our finding is in line with those of Coval et al. (2009b) and Huang and Huang (2012) which consider the sensitivity of credit spreads to systematic factors.

7 Without rating specific exposure, the estimate of ν would be pulled down so that the common frailty process has to be more persistent in order to make up for the high default intensity levels in the data.

8 For simplicity, we do not show the results for the complete model as ν varies among rating classes. But those results are similar to what figure 3 shows.

9 The standard deviation of individual frailty of IG/SG firms is estimated using the frailty sampled from the Gibbs sampler for all the firms in IG/SG.

10 One can see from figure 1 that default cases surged in 2008 compared with the previous four years. This makes forecasting the number of defaults in 2008 challenging for all models, not just our models. Even if a model captures the main features of default behavior, it would still be difficult to predict the default number in 2008 given the low default numbers used for training the model.