Predicting recovery rates using logistic quantile regression with bounded outcomes

Abstract

Logistic quantile regression (LQR) is used for studying recovery rates. It is developed using monotone transformations. Using Moody’s Ultimate Recovery Database, we show that the recovery rates in different partitions of the estimation sample have different distributions, and thus for predicting recovery rates, an error-minimizing quantile point over each of those partitions is determined for LQR. Using an expanding rolling window approach, the empirical results confirm that LQR with the error-minimizing quantile point has better and more robust out-of-sample performance than its competing alternatives, in the sense of yielding more accurate predicted recovery rates. Thus, LQR is a useful alternative for studying recovery rates.

Keywords:

• Expanding rolling window approach
• Inverse Gaussian regression
• Logistic quantile regression
• Recovery rate

JEL Classification:

• C53
• G21

Acknowledgements

The authors thank the reviewers for their valuable comments and suggestions that have greatly improved the presentation of this study. This research is supported by the Ministry of Science and Technology, Taiwan, Republic of China.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ The recovery rates have high concentrations at 0 and 1. The logit transformed recovery rate ln{y/(1 – y)} required in LQR is not defined when the recovery rate equals 0 or 1.

² The partition rule used in the third approach can also be based on the values of two or more predictor variables. However, under our real datasets in section 3, some resulting partitions of the estimation sample have small sizes; thus, their associated local quantile points are not suitable for predicting recovery rates for debts in those partitions.

³ For simplicity of presentation, the estimation results for the other models are not reported here, but are available on request.

⁴ The twelve values of ε in [10⁻¹¹, 0.5) include 10⁻¹¹, 0.0001, 0.0005, 0.001, 0.005, 0.01, 0.05, 0.08, 0.1, 0.2, 0.3 and 0.4999. These values of ε with 0.4999 replaced by 0.5 have been used in Qi and Zhao (2011) for determining the optimal value of ε for the given sample.

⁵ Although over-fitting can be a problem for all methods, it is more of a concern for nonparametric methods, including the regression tree (Qi and Zhao 2011).