SAS Forum International Copenhagen 2004 15-17 June The estimate of default probability in Internal Rating Systems Americo Todisco University of Siena, Faculty of Economics Doctorate Program in Law & Economics I.R.E.F. - Institute for Research in Economics and Finance
CONTENTS An overview on Basle II. The analysis: objectives, data, tools. Construction of the samples. Characteristics of the sample. Development of the model: selection of the ratios; selection of the model. From the score to default probability. The definition of classes of rating. Mapping of default probability. Final comments.
AN OVERVIEW ON BASEL II (1) Safety and soundness in the financial system Minimum Capital Requirement Supervisory Review Market Discipline Three Pillars of The New Capital Adequacy Framework
AN OVERVIEW ON BASEL II (2) Minimum Capital Requirement Credit Risk Measurement approaches Market Risk Operational Risk Standardised Internal Ratings Pillar One External ratings by rating agencies Ratings estimated by internal system
THE ANALYSIS OBJECTIVE The estimate of default probability DATA Company accounts for Italian firms TOOLS The SAS/STAT software by SAS The LOGISTIC procedure The FASTCLUS procedure
CONSTRUCTION OF THE SAMPLE (1) DATA BASE: BALANCE SHEET PROFIT & LOSS SOLVENT FIRM SOLVENT FIRM SOLVENT FIRM SOLVENT FIRM DEFAULT FIRM DEFAULT FIRM DEFAULT FIRM DEFAULT FIRM CONSTRAINTS SECTOR TOTAL ASSETS YEARS OF ACCOUNTS GEOGRAPHICAL AREA
CONSTRUCTION OF THE SAMPLE (2) D D D D DATA SET: 50 MATCHED SAMPLES S1 S1 Si Si S50 S50 S1 S1 Si Si S50 S50 SAMPLE n.1 SAMPLE n. i SAMPLE n. 50
THE SAMPLE - (by firm size) TOTAL_ASSET - (000) EURO TOTAL_ASSET Frequency Percent Cumulative Frequency Cumulative Percent 50-250 369 0.66 369 0.66 250-500 1654 2.95 2023 3.60 500-1000 6183 11.02 8206 14.62 1000-1500 9220 16.43 17426 31.05 1500-2000 6740 12.01 24166 43.06 2000-2500 4916 8.76 29082 51.82 2500-3500 7111 12.67 36193 64.49 3500-5000 6524 11.62 42717 76.11 5000-7500 5312 9.47 48029 85.58 7500-10000 2207 3.93 50236 89.51 10000-25000 4364 7.78 54600 97.29 25000-50000 1038 1.85 55638 99.14 > 50000 484 0.86 56122 100.00 The sample is dominated by SMEs: about 90% of the sample has total assets below 10 million Euro.
THE SAMPLE - (by firm sales) TURNOVER - (000) EURO TURNOVER Frequency Percent Cumulative Frequency Cumulative Percent 0-250 8347 14.87 8347 14.87 250-500 927 1.65 9274 16.52 500-1000 1242 2.21 10516 18.74 1000-1500 3278 5.84 13794 24.58 1500-2000 7376 13.14 21170 37.72 2000-2500 5838 10.40 27008 48.12 2500-3500 7705 13.73 34713 61.85 3500-5000 6717 11.97 41430 73.82 5000-7500 5636 10.04 47066 83.86 7500-10000 2956 5.27 50022 89.13 10000-25000 4360 7.77 54382 96.90 25000-50000 1148 2.05 55530 98.95 > 50000 592 1.05 56122 100.00
THE SAMPLE - (sector) SECTOR SETT Frequency Percent Cumulative Frequency Cumulative Percent com 22636 40.33 22636 40.33 ind 29124 51.89 51760 92.23 ser 4362 7.77 56122 100.00
THE SAMPLE - (period) ANNO ANNO Frequency Percent Cumulative Frequency Cumulative Percent 1995 74 0.13 74 0.13 1996 497 0.89 571 1.02 1997 4628 8.25 5199 9.26 1998 17650 31.45 22849 40.71 1999 19264 34.33 42113 75.04 2000 7344 13.09 49457 88.12 2001 6506 11.59 55963 99.72 2002 159 0.28 56122 100.00 90% of balance sheets covers the period 1998-2002
VARIABLES SELECTED We computed 6 sets of ratios: PROFITABILITY AND CASH FLOW ACTIVITY (EFFICIENCY) LEVERAGE LIQUIDITY ALTMAN (1977) (Classic study on estimating probability of default)
DEVELOPMENT OF THE MODEL SELECTION OF THE RATIOS ECONOMIC VALUATION DEVELOPMENT OF THE MODEL The LOGISTIC Procedure by SAS/STAT software SELECTION OF THE MODEL BEST PERFORMANCE
DEVELOPMENT OF THE MODEL: selection of the ratios (1) Variable N 50 complete samples Logit forward with 23 ratios 50 estimation models Proc logistic with model statement option: selection=forward More frequent indicators I3 I4 I5 I8 I10 I11 I14 I16 I21 I24 I29 I39 I42 I43 I44 I49 I50 I60 I61 I63 I64 I65 I67 50 12 2 11 4 22 25 50 6 1 50 2 1 5 3 2 1 8 1 1 0 28 4
DEVELOPMENT OF THE MODEL: selection of the ratios (2) Four ratios emerged as most frequent and significant: they represent all relevant areas characterizing activity of firms Cash flow/total debt EBIT (Earnings before interest and tax)/total debt Net Equity/total debt Net financial position/total assets
DEVELOPMENT OF THE MODEL: selection of the model 50 learning samples Logit with 4 ratios 50 estimation models 50 control samples Best classification in the control sample Proc logistic with models estimated only in learning samples
Predictive power of the model (goodness-of-fit in sample and out of sample prediction) In the tables the cut-off point is equal to a probability of 0.5. State 1 = default State 2 = solvent. STATO Frequency Row Pct Frequency Row Pct Learning sample 1 596 81.98 2 150 20.63 stato_pred 1 2 131 18.02 577 79.37 Total 727 727 Total 746 708 1454 Best classification in the control sample STATO Frequency Row Pct Frequency Row Pct Control sample 1 582 80.50 2 145 20.06 stato_pred 1 2 141 19.50 578 79.94 Total 723 723 Total 727 719 1446
CAPABILITY OF THE MODEL TO DISCRIMINATE THE ROC CURVE Area under the ROC curve: 0.885
CAPABILITY OF THE MODEL TO DISCRIMINATE SIGNIFICANCE TESTS SIGNIFICANCE TESTS Cash flow/total debt <0.0001 Ebit/total debt <0.0001 Net Equity/total debt <0.0001 Net financial position/total assets 0.0063
CAPABILITY OF THE MODEL TO DISCRIMINATE A DEEPER VIEW CLASSES by STATE STATE Total 1 2 Frequency 35 454 489 A Col Pct 2,4% 31,3% 16,9% Frequency 15 139 154 B Col Pct 1,0% 9,6% 5,3% Frequency 27 140 167 C Col Pct 1,9% 9,7% 5,8% Frequency 74 199 273 D Col Pct 5,1% 13,7% 9,4% Frequency 120 219 339 E Col Pct 8,3% 15,1% 11,7% CLASSES Frequency 260 162 422 F Col Pct 17,9% 11,2% 14,6% G H I L Total Frequency 1450 1449 2899 Col Pct 100,0% 100,0% 100,0% Frequency Frequency Frequency Frequency 215 143 125 436 81 29 10 16 296 172 135 452 Col Pct Col Pct Col Pct Col Pct 14,8% 9,9% 8,6% 30,1% 5,6% 2,0% 0,7% 1,1% 10,2% 5,9% 4,7% 15,6% Error 7,2% 9,7% 16,2% 27,1% 35,4% 38,4% 27,4% 16,9% 7,4% 3,5% ERROR ERROR
CAPABILITY OF THE MODEL TO DISCRIMINATE THE WHOLE DATASET STATO Frequency Row Pct Frequency Row Pct Whole dataset 1 1468 81.8 2 11854 21.8 stato_pred 1 2 327 18.2 42424 78.2 Total 1795 54278 Total 13322 42751 56073 The table reports the power of discrimination computed for all 50 samples at t-1.
FROM THE SCORE TO DEFAULT PROBABILITY (1) Shall we use the probability estimated through the model directly as a probability of default of the firm?
FROM THE SCORE TO DEFAULT PROBABILITY (2) Expected default frequency score Two methods default probability Modifying the intercept of the model
FROM THE SCORE TO DEFAULT PROBABILITY (3) CLASSES by state state Total Frequency Probability 1 2 Default Corrected A Frequency 47 16534 16581 Col Pct 2,6% 30,5% 29,6% 0,3% 0,1% B Frequency 20 5667 5687 Col Pct 1,1% 10,4% 10,1% 0,4% 0,6% C Frequency 37 5670 5707 Col Pct 2,1% 10,4% 10,2% 0,6% 1,1% D Frequency 86 6521 6607 Col Pct 4,8% 12,0% 11,8% 1,3% 1,8% CLASSI E Frequency 137 8032 8169 Col Pct 7,6% 14,8% 14,6% 1,7% 2,7% F Frequency 300 7295 7595 Col Pct 16,7% 13,4% 13,5% 3,9% 3,9% G Frequency 278 2515 2793 Col Pct 15,5% 4,6% 5,0% 10,0% 5,8% H Frequency 188 831 1019 Col Pct 10,5% 1,5% 1,8% 18,4% 9,1% I Frequency 170 485 655 Col Pct 9,5% 0,9% 1,2% 26,0% 16,5% L Frequency 532 728 1260 Col Pct 29,6% 1,3% 2,2% 42,2% 59,4% Total Frequency 1795 54278 56073 Col Pct 100,0% 100,0% 100,0% 3,2% 3,3%
FROM THE SCORE TO DEFAULT PROBABILITY (4) Expected Default Frequency vs. Probability Corrected 60,0% 50,0% 40,0% 30,0% 20,0% 10,0% 0,0% A B C D E F G H I L EDF 0,3% 0,4% 0,6% 1,3% 1,7% 3,9% 10,0% 18,4% 26,0% 42,2% PC 0,1% 0,6% 1,1% 1,8% 2,7% 3,9% 5,8% 9,1% 16,5% 59,4%
THE DEFINITION OF CLASSES OF RATING (1) OK! Now i have the right PD for each class. This is enough to call my 10 classes scheme a rating scale?
THE DEFINITION OF CLASSES OF RATING (2) Number of classes The FASTCLUS Procedure by SAS/STAT software classes 7 10 15 Upper and lower limits of each class
THE DEFINITION OF CLASSES OF RATING (3) Equal size classes vs. Cluster analysis 45% 40% 35% 30% 25% 20% 15% 10% 5% 0% A B C D E F G H I L M N O P Q EQUAL SIZE 0,28% 0,34% 0,35% 0,58% 0,99% 1,36% 1,59% 2,46% 4,48% 8,98% 15,70% 18,33% 24,29% 32,36% 44,13% CLUSTER 0,24% 0,41% 0,37% 0,38% 0,54% 0,95% 1,29% 1,56% 1,77% 3,07% 5,11% 10,23% 18,00% 25,87% 42,68%
MAPPING OF DEFAULT PROBABILITY (1) STANDARD & POOR'S AAA / AA+ / AA 0,00% AA- 0,02% A+ 0,06% A 0,05% A- 0,04% BBB+ 0,32% BBB 0,34% BBB- 0,46% BB+ 0,64% BB 1,15% BB- 1,97% B+ 3,19% B 8,99% B- 13,01% CCC / C 30,85% I.R.E.F. A 0,24% B 0,41% C 0,37% D 0,38% E 0,54% F 0,95% G 1,29% H 1,56% I 1,77% L 3,07% M 5,11% N 10,23% O 18% P 25,87% Q 42,68%
MAPPING OF DEFAULT PROBABILITY (2) VS. bonds Way of financing banks multinational size SME high creditworthiness differentiated
FINAL COMMENTS Hypothesis on practical consequences of implementing an Internal Rating Systems Lack of methods to estimate credit risk properly Correct implementation of Internal Rating Systems Higher interest rates Interest rates reflect risk of enterprises Credit rationing Improved lending
Thank you for your attention. Questions, suggestions and comments are welcome! Americo Todisco todisco@unisi.it