Systematic Risk in Recovery Rates - An Empirical Analysis of U.S. Corporate Credit Exposures

TLDR: In this paper, the authors present an analytical and empirical analysis of a parsimonious model framework that accounts for a dependence of bond and bank loan recoveries on systematic risk and provide estimators of the parameters of the asset value process and their standard errors in closed form.

Abstract: This paper presents an analytical and empirical analysis of a parsimonious model framework that accounts for a dependence of bond and bank loan recoveries on systematic risk. We extend the single risk factor model by assuming that the recovery rates also depend on this risk factor and follow a logit?normal distribution. The results are compared with those of two related models, suggested in Frye (2000) and Pykhtin (2003), which pose the assumption of a normal and a log-normal distribution of recovery rates. We provide estimators of the parameters of the asset value process and their standard errors in closed form. For the parameters of the recovery rate distribution we also provide closed-form solutions of a feasible maximum-likelihood estimator for the three models. The model parameters are estimated from default frequencies and recovery rates that were extracted from a bond and loan database of Standard&Poor's. We estimate the correlation between recovery rates and the systematic risk factor and determine the impact on economic capital. Furthermore, the impact of measuring recovery rates from market prices at default and from prices at emergence from default is analysed. As a robustness check for the empirical results of the maximum-likelihood estimation method we also employ a method-of-moments. Our empirical results indicate that systematic risk is a major factor influencing recovery rates. The calculation of a default?weighted recovery rate without further consideration of this factor may lead to downward-biased estimates of economic capital. Recovery rates measured from market prices at default are generally lower and more sensitive to changes of the systematic risk factor than are recovery rates determined at emergence from default. The choice between these two measurement methods has a stronger impact on the expected recovery rates and the economic capital than introducing a dependency of recovery rates on systematic risk in the single risk factor model.

Figures

Table 6 Parameter Estimates Under Normally Distributed Recovery Rates

Figure 6. Density of LGD for the 99.9% Percentile of the Systematic Risk factor

Table 2 Tests of a Normal Distribution of Recovery Rates

Table 5 Parameter Estimates Under Logit–normally Distributed Recovery Rates

Table 10 Economic Capital without Systematic Risk in LGD, Based on Market Prices at Default

Figure 3. Sensitivity of Recovery Rates to the Systematic Risk Factor, Estimated from Market Prices at Default

Full text

Düllmann, Klaus; Trapp, Monika
Working Paper
Systematic Risk in Recovery Rates: An Empirical
Analysis of US Corporate Credit Exposures
Discussion Paper Series 2, No. 2004,02
Provided in Cooperation with:
Deutsche Bundesbank
Suggested Citation: Düllmann, Klaus; Trapp, Monika (2004) : Systematic Risk in Recovery
Rates: An Empirical Analysis of US Corporate Credit Exposures, Discussion Paper Series 2,
No. 2004,02, Deutsche Bundesbank, Frankfurt a. M.
This Version is available at:
http://hdl.handle.net/10419/19729
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Systematic Risk in Recovery Rates –
An Empirical Analysis
of US Corporate Credit Exposures
Klaus Dllmann
(Deutsche Bundesbank)
Monika Trapp
(Universitt Ulm)
Discussion Paper
Series 2: Banking and Financial Supervision
No 02/2004
Discussion Papers represent the authors’ personal opinions and do not necessarily reflect the views of the
Deutsche Bundesbank or its staff.

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Abstract
This paper presents an analytical and empirical analysis of a parsimonious model
framework that accounts for a dependence of bond and bank loan recoveries on sys-
tematic risk. We extend the single risk factor model by assuming that the recovery
rates also depend on this risk factor and follow a logit–normal distribution. The re-
sults are compared with those of two related models, suggested in Frye (2000) and
Pykhtin (2003), which pose the assumption of a normal and a log–normal distribu-
tion of recovery rates.
We provide estimators of the parameters of the asset value process and their
standard errors in closed form. For the parameters of the recovery rate distribution
we also provide closed–form solutions of a feasible maximum–likelihood estimator
for the three models.
The model parameters are estimated from default frequencies and recovery rates
that were extracted from a bond and loan database of Standard&Poor’s. We estimate
the correlation between recovery rates and the systematic risk factor and determine
the impact on economic capital.
Furthermore, the impact of measuring recovery rates from market prices at de-
fault and from prices at emergence from default is analysed. As a robustness check
for the empirical results of the maximum–likelihood estimation method we also em-
ploy a method–of–moments.
Our empirical results indicate that systematic risk is a major factor influencing
recovery rates. The calculation of a default–weighted recovery rate without further
consideration of this factor may lead to downward–biased estimates of economic
capital.
Recovery rates measured from market prices at default are generally lower and
more sensitive to changes of the systematic risk factor than are recovery rates de-
termined at emergence from default. The choice between these two measurement
methods has a stronger impact on the expected recovery rates and the economic cap-
ital than introducing a dependency of recovery rates on systematic risk in the single
risk factor model.
Keywords: asset correlation, New Basel Accord, recovery rate, LGD, recovery correla-
tion, single risk factor model
JEL Classification: G 21, G 33, C 13

Non–technical Summary
This paper analyses three credit risk models that account for systematic risk in
recovery rates of bonds or loans. The systematic risk is driven by a single unobserv-
able factor, similar to the single risk factor model that was used to derive the risk
weight function of the internal ratings based approach in Basel II. The three models
differ in the distributional assumption for the recovery rates. The model parameters
are estimated from default rates and recovery rates that were extracted from a bond
and loan database of Standard&Poor’s.
The following main conclusions can be drawn.
• The empirical analyses indicate that systematic risk is a major factor influenc-
ing recovery rates of bonds and loans. Ignoring it may lead to downward–
biased estimates of economic capital.
• Measuring recovery rates just after default or at emergence from default seems
to have a stronger impact on recovery rates and the economic capital than does
extending the single risk factor model to capture systematic risk in recovery
rates. Recovery rates measured at default are generally lower and more sen-
sitive to changes of the systematic risk factor than are recovery rates at emer-
gence from default.

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Systematic risk in recovery rates: an empirical analysis of us corporate credit exposures" ?

This paper presents an analytical and empirical analysis of a parsimonious model framework that accounts for a dependence of bond and bank loan recoveries on systematic risk. The authors extend the single risk factor model by assuming that the recovery rates also depend on this risk factor and follow a logit–normal distribution. The authors provide estimators of the parameters of the asset value process and their standard errors in closed form. For the parameters of the recovery rate distribution the authors also provide closed–form solutions of a feasible maximum–likelihood estimator for the three models. The results are compared with those of two related models, suggested in Frye ( 2000 ) and Pykhtin ( 2003 ), which pose the assumption of a normal and a log–normal distribution of recovery rates. Furthermore, the impact of measuring recovery rates from market prices at default and from prices at emergence from default is analysed. The calculation of a default–weighted recovery rate without further consideration of this factor may lead to downward–biased estimates of economic capital. 

Q2. What are the future works mentioned in the paper "Systematic risk in recovery rates: an empirical analysis of us corporate credit exposures" ?

In their example, these differences lead to deviations in economic capital in the range of 12 % –16 %, depending on the distributional assumption for recovery rates in the extended model. The following two aspects call for further research and can provide useful extensions of their analyses. Analysing what causes recovery rates derived from market prices at default to be so different from recovery rates derived from prices at emergence from default is a second interesting aspect requiring further research, especially as these differences have a strong impact on the economic capital. 

Q3. What are the main factors that affect recovery rates?

Apart from a potential influence by the macroeconomy, several contract–specific factors, for example, seniority and collateral, also seem to affect recovery rates. 

Q4. What is the sensitivity of the recovery rate to the systematic risk factor?

In the reference model that assumes a logit–normal distribution of recovery rates, the sensitivity depends not only on the product σ √ ω but also in a non–linear way on the recovery rate. 

Q5. What are the three distributional assumptions tested for the recovery rates?

Three distributional assumptions are tested for the recovery rates: a logit–normal distribution, a normal distribution and a log–normal distribution. 

Q6. How does the univariate model explain the variation in average recovery rates?

For the univariate model incorporating bond default rates as explanatory variables, they find that they can explain about 60% of the variation in average annual recovery rates. 

Q7. What are the three distributional assumptions used to explain the recovery rates?

In standard specification tests, the logit–normal distribution and the normal distribution are found to explain the observed recovery rates better. 

Q8. How are the parameters of the recovery rate distribution estimated?

In all three extended models parameter estimation is carried out in two steps: in the first step, the authors estimate the parameters of the asset value process, ρ and PD, and in the second step the three parameters of the recovery rate distribution. 

Q9. What is the relevant range from a risk management perspective?

The log–normal distribution yields the least systematic risk–sensitive estimate of the three models if X is smaller than −0.8 which is the most relevant range from a risk– management perspective.