Analytics of Risk Model Validation (eBook)

George A. Christodoulakis, Stephen Satchell (Herausgeber)

eBook Download: PDF | EPUB

2007 | 1. Auflage
216 Seiten
Elsevier Science (Verlag)
978-0-08-055388-7 (ISBN)

Infos

Risk model validation is an emerging and important area of research, and has arisen because of Basel I and II. These regulatory initiatives require trading institutions and lending institutions to compute their reserve capital in a highly analytic way, based on the use of internal risk models. It is part of the regulatory structure that these risk models be validated both internally and externally, and there is a great shortage of information as to best practise. Editors Christodoulakis and Satchell collect papers that are beginning to appear by regulators, consultants, and academics, to provide the first collection that focuses on the quantitative side of model validation. The book covers the three main areas of risk: Credit Risk and Market and Operational Risk.

*Risk model validation is a requirement of Basel I and II
*The first collection of papers in this new and developing area of research
*International authors cover model validation in credit, market, and operational risk

Inhalt

Front Cover 1
The Analytics of Risk Model Validation 4
Copyright Page 5
Table of Contents 6
About the editors 8
About the contributors 10
Preface 14
Chapter 1 Determinants of small business default 16
Abstract 16
1. Introduction 16
2. Data, methodology and summary statistics 18
3. Empirical results of small business default 21
4. Conclusion 25
References 26
Notes 26
Chapter 2 Validation of stress testing models 28
Abstract 28
1. Why stress test? 28
2. Stress testing basics 29
3. Overview of validation approaches 32
4. Subsampling tests 33
5. Ideal scenario validation 37
6. Scenario validation 38
7. Cross-segment validation 39
8. Back-casting 39
9. Conclusions 40
References 40
Chapter 3 The validity of credit risk model validation methods 42
Abstract 42
1. Introduction 42
2. Measures of discriminatory power 43
3. Uncertainty in credit risk model validation 46
4. Confidence interval for ROC 48
5. Bootstrapping 56
6. Optimal rating combinations 56
7. Concluding remarks 57
References 57
Chapter 4 A moments-based procedure for evaluating risk forecasting models 60
Abstract 60
1. Introduction 60
2. Preliminary analysis 62
3. The likelihood ratio test 62
4. A moments test of model adequacy 63
5. An illustration 66
6. Conclusions 68
7. Acknowledgements 70
References 70
Notes 71
Appendix 72
1. Error distribution 72
2. Two-piece normal distribution 73
3. t-Distribution 73
4. Skew-t distribution 73
Chapter 5 Measuring concentration risk in credit portfolios 74
Abstract 74
1. Concentration risk and validation 74
2. Concentration risk and the IRB model 75
3. Measuring name concentration 78
4. Measuring sectoral concentration 80
5. Numerical example 84
6. Future challenges of concentration risk measurement 86
7. Summary 88
References 89
Notes 90
Appendix A.1: IRB risk weight functions and concentration risk 91
Appendix A.2: Factor surface for the diversification factor 92
Appendix A.3 93
Chapter 6 A simple method for regulators to cross-check operational risk loss models for banks 94
Abstract 94
1. Introduction 94
2. Background 96
3. Cross-checking procedure 97
4. Justification of our approach 99
5. Justification for a lower bound using the lognormal distribution 101
6. Conclusion 104
References 105
Chapter 7 Of the credibility of mapping and benchmarking credit risk estimates for internal rating systems 106
Abstract 106
1. Introduction 106
2. Why does the portfolio’s structure matter? 107
3. Credible credit ratings and credible credit risk estimates 109
4. An empirical illustration 112
5. Credible mapping 117
6. Conclusions 121
7. Acknowledgements 121
References 121
Appendix 122
1. Further elements of modern credibility theory 122
2. Proof of the credibility fundamental relation 122
3. Mixed Gamma–Poisson distribution and negative binomial 124
4. Calculation of the Bühlmann credibility estimate under the Gamma–Poisson model 125
5. Calculation of accuracy ratio 126
Chapter 8 Analytic models of the ROC curve: Applications to credit rating model validation 128
Abstract 128
1. Introduction 128
2. Theoretical implications and applications 129
3. Choices of distributions 135
4. Performance evaluation on the AUROC estimation with simulated data 138
5. Summary 144
6. Conclusions 145
7. Acknowledgements 145
References 146
Note 146
Appendix 146
1. The properties of AUROC for normally distributed sample 146
Chapter 9 The validation of the equity portfolio risk models 150
Abstract 150
1. Linear factor models 151
2. Building a time series model 152
3. Building a statistical factor model 153
4. Building models with known beta’s 155
5. Forecast construction and evaluation 157
6. Diagnostics 158
7. Time horizons and data frequency 160
8. The residuals 161
9. Monte Carlo procedures 162
10. Conclusions 162
References 163
Chapter 10 Dynamic risk analysis and risk model evaluation 164
Abstract 164
1. Introduction 164
2. Volatility over time and the cumulative variance 166
3. Beta over time and cumulative covariance 174
4. Dynamic risk model evaluation 179
5. Summary 182
References 183
Chapter 11 Validation of internal rating systems and PD estimates 184
Abstract 184
1. Introduction 184
2. Regulatory background 185
3. Statistical background 187
4. Monotonicity of conditional PDs 194
5. Discriminatory power of rating systems 197
6. Calibration of rating systems 206
7. Conclusions 211
References 211
Notes 211
Index 212

Textauszug

1

Determinants of small business default*

Sumit Agarwal†; Souphala Chomsisengphet‡; Chunlin Liu¶
† Federal Reserve Bank of Chicago, Chicago, IL
‡ Office of the Comptroller of the Currency, Washington, DC
¶ College of Business Administration, University of Nevada, Reno, NV

Abstract

In this paper, we empirically validate the importance of owner and business credit risk characteristics in determining default behaviour of more than 31 000 small business loans by type and size. Our results indicate that both owner- and firm-specific characteristics are important predictors of overall small business default. However, owner characteristics are more important determinants of small business loans but not small business lines. We also differentiate between small and large business accounts. The results suggest that owner scores are better predictors of small firm default behaviours, whereas firm scores are better predictors of large firm default behaviour.

1 Introduction

In this chapter, we develop a small business default model to empirically validate the importance of owner and the business credit bureau scores while controlling for time to default, loan contract structure as well as macroeconomic and industry risk characteristics. In addition, several unique features associated with the dataset enable us to validate the importance of the owner and business credit bureau scores in predicting the small business default behaviour of (i) spot market loans versus credit lines and (ii) small businesses below $100 000 versus between $100 000 and $250 000.

Financial institutions regularly validate credit bureau scores for several reasons. First, bureau scores are generally built on static data, i.e. they do not account for the time to delinquency or default.1 Second, bureau scores are built on national populations. However, in many instances, the target populations for the bureau scores are region-specific. This can cause deviation in the expected and actual performance of the scores. For example, customers of a certain region might be more sensitive to business cycles and so the scores in that region might behave quite differently during a recession. Third, the bureau scores may not differentiate between loan type (spot loans versus lines of credit) and loan size (below $100 K and above $100 K), i.e. they are designed as one-size-fits-all.

However, it is well documented that there are significant differences between bank spot loans (loans) and lines of credit (lines). For example, Strahan (1999) notes that firms utilize lines of credit to meet short-term liquidity needs, whereas spot loans primarily finance long-term investments. Agarwal et al. (2006) find that default performance of home equity loans and lines differ significantly. Hence, we assess whether there are any differences in the performance of small business loans and lines, and if so, what factors drive these differences?

Similarly, Berger et al. (2005) argue that credit availability, price and risk for small businesses with loan amounts below and above $100 K differ in many respects. Specifically, they suggest that scored lending for loans under $100 K will increase credit availability, pricing and loan risk; they attribute this to the rise in lending to 'marginal borrowers'. However, scored lending for loans between $100 K and $250 K will not substantially affect credit availability, lower pricing and lesser loan risk. This is attributed to the price reduction for the 'non-marginal borrowers'. Their results suggest that size does affect loan default risk.

Overall, our results indicate that a business owner's checking account balances, collateral type and credit scores are key determinants of small business default. However, there are significant differences in economic contributions of these risk factors on default by credit type (loans versus lines) and size (under $100 K versus $100 K–250 K). We find that the effect of owner collateral is three times as much on default for small business loans than for lines. This result is consistent with Berger and Udell's (1995) argument that a line of credit (as opposed to loan) measures the strength of bank–borrower relationship, and as the bank–firm relationship matures, the role of collateral in small business lending becomes less important. Our results also show that the marginal impact of a 12-month increase in the age of the business on lowering the risk of a small business defaulting is 10.5% for lines of credit, but only 5.8% for loans. Moreover, a $1000 increase in the 6-month average checking account balance lowers the risk of default by 18.1% for lines of credit, but only 11.8% for loans. Finally, although both owner and firm credit scores significantly predict the risk of default, the marginal impacts on the types of credits differ considerably. The marginal impact of a 10-point improvement in the owner credit score on lowering the risk of defaults is 10.1% for lines, but only 6.3% for loans. A similar 10-point improvement in the firm credit score lowers the risk of default by 6.3% for small business loans, but only 5.2% for small business lines. These results are consistent with that of Agarwal et al. (2006).

Comparing small businesses under $100 K (small) and those between $100 K and $250 K (large), we find that the marginal impact of a 10-point improvement in the owner credit score in lowering the risk of default is 13.6% for small firms, but only 8.1% for large firms. On the contrary, the marginal impact of a 10-point improvement in the firm credit score in lowering the risk of default is only 2.2% for small firms, but 6.1% for the larger size firms. Furthermore, a $1000 increase in the 6-month average checking account balance lowers the risk of default by 5.1% for small firms, but by 12.4% for large firms. These results suggest that smaller size firms behave more like consumer credits, whereas larger size firms behave more like commercial credits and so bank monitoring helps account performance. These results are consistent with that of Berger et al. (2005).

The rest of the chapter is organized as follows. Section 1.2 discusses the data, methodology and summary statistics. Section 1.3 presents the empirical results for small business defaults by type (Section 1.3.1) and size (Section 1.3.2). Section 4 provides concluding remarks.

2 Data, methodology and summary statistics

2.1 Data

The data employed in this study are rather unique. The loans and lines are from a single financial institution and are proprietary in nature. The panel dataset contains over 31 000 small business credits from January 2000 to August 2002.2 The majority of the credits are issued to single-family owned small businesses with no formal financial records. Of the 31 303 credits, 11 044 (35.3%) are loans and 20 259 (64.7%) are lines and 25 431 (81.2%) are under $100 K and 5872 (18.8%) are between $100 K and $250 K. The 90-day delinquency rate for our dataset of loans and lines are 1.6% and 0.9%, respectively. The delinquency rates for credits under $100 K and between $100 K and $250 K are 1.5% and 0.92%, respectively. It is worth mentioning some of the other key variables of our dataset. First, our dataset is a loan-level as opposed to a firm-level dataset. More specifically, we do not have information of all the loans a firm might have with other banks. Second, because these are small dollar loans, the bank primarily underwrites them based on the owners' credit profile as opposed to the firms credit profile. However, the bank does obtain a firm-specific credit score from one of the credit bureaus (Experian).3 The owner credit score ranges from 1 to 100 and a lower score is a better score, whereas the firm credit score ranges from 1 to 200 and a higher score is a better score.

2.2 Methodology

For the purpose of this study, we include all accounts that are open as of January 2000, and exclude accounts with a flag indicating that the loan is never active, closed due to fraud/death, bankruptcy and default.4 Furthermore, we also exclude all accounts that were originated before 1995 to simplify the analysis on account age. We follow the performance of these accounts from January 2000 for the next 31 months (until August 2002) or until they default.

We use a proportional hazard model to estimate the conditional probability of a small business defaulting at time t, assuming the small business is current from inception up to time t – 1. Let Di,t indicate whether an account i defaults in month t. For instance, the business could default in month 24, then Di,t = 0 for the first 23 months and Di,24 = 1, and the rest of the observations will drop out of the sample. We define default as two cycles of being delinquent, as most accounts that are two cycles delinquent (i.e. 60 days past due) will default or declare bankruptcy. Furthermore, according to the SBRMS report, 57% of banks use the two cycles delinquent as their standard definition of default and another 23% use one cycle delinquent as their definition...

Produkt-Details

• Erscheint lt. Verlag: 14.11.2007
• Sprache: englisch
• Themenwelt: Sachbuch/Ratgeber ► Beruf / Finanzen / Recht / Wirtschaft ► Geld / Bank / Börse
• Themenwelt: Naturwissenschaften
• Themenwelt: Wirtschaft ► Betriebswirtschaft / Management ► Allgemeines / Lexika
• Themenwelt: Wirtschaft ► Betriebswirtschaft / Management ► Finanzierung
• Themenwelt: Betriebswirtschaft / Management ► Spezielle Betriebswirtschaftslehre ► Bankbetriebslehre
• Themenwelt: Wirtschaft ► Volkswirtschaftslehre
• ISBN-10: 0-08-055388-5 / 0080553885
• ISBN-13: 978-0-08-055388-7 / 9780080553887