Americo Todisco. The estimate of default probability in Internal Rating Systems. SAS Forum International Copenhagen June

Transcription

1 SAS Forum International Copenhagen 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

2 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.

3 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

4 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

5 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

6 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

7 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

8 THE SAMPLE - (by firm size) TOTAL_ASSET - (000) EURO TOTAL_ASSET Frequency Percent Cumulative Frequency Cumulative Percent > The sample is dominated by SMEs: about 90% of the sample has total assets below 10 million Euro.

9 THE SAMPLE - (by firm sales) TURNOVER - (000) EURO TURNOVER Frequency Percent Cumulative Frequency Cumulative Percent >

10 THE SAMPLE - (sector) SECTOR SETT Frequency Percent Cumulative Frequency Cumulative Percent com ind ser

11 THE SAMPLE - (period) ANNO ANNO Frequency Percent Cumulative Frequency Cumulative Percent % of balance sheets covers the period

12 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)

13 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

14 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 I

15 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

16 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

17 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 stato_pred Total Total Best classification in the control sample STATO Frequency Row Pct Frequency Row Pct Control sample stato_pred Total Total

18 CAPABILITY OF THE MODEL TO DISCRIMINATE THE ROC CURVE Area under the ROC curve: 0.885

19 CAPABILITY OF THE MODEL TO DISCRIMINATE SIGNIFICANCE TESTS SIGNIFICANCE TESTS Cash flow/total debt < Ebit/total debt < Net Equity/total debt < Net financial position/total assets

20 CAPABILITY OF THE MODEL TO DISCRIMINATE A DEEPER VIEW CLASSES by STATE STATE Total 1 2 Frequency A Col Pct 2,4% 31,3% 16,9% Frequency B Col Pct 1,0% 9,6% 5,3% Frequency C Col Pct 1,9% 9,7% 5,8% Frequency D Col Pct 5,1% 13,7% 9,4% Frequency E Col Pct 8,3% 15,1% 11,7% CLASSES Frequency F Col Pct 17,9% 11,2% 14,6% G H I L Total Frequency Col Pct 100,0% 100,0% 100,0% Frequency Frequency Frequency Frequency 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

21 CAPABILITY OF THE MODEL TO DISCRIMINATE THE WHOLE DATASET STATO Frequency Row Pct Frequency Row Pct Whole dataset stato_pred Total Total The table reports the power of discrimination computed for all 50 samples at t-1.

22 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?

23 FROM THE SCORE TO DEFAULT PROBABILITY (2) Expected default frequency score Two methods default probability Modifying the intercept of the model

24 FROM THE SCORE TO DEFAULT PROBABILITY (3) CLASSES by state state Total Frequency Probability 1 2 Default Corrected A Frequency Col Pct 2,6% 30,5% 29,6% 0,3% 0,1% B Frequency Col Pct 1,1% 10,4% 10,1% 0,4% 0,6% C Frequency Col Pct 2,1% 10,4% 10,2% 0,6% 1,1% D Frequency Col Pct 4,8% 12,0% 11,8% 1,3% 1,8% CLASSI E Frequency Col Pct 7,6% 14,8% 14,6% 1,7% 2,7% F Frequency Col Pct 16,7% 13,4% 13,5% 3,9% 3,9% G Frequency Col Pct 15,5% 4,6% 5,0% 10,0% 5,8% H Frequency Col Pct 10,5% 1,5% 1,8% 18,4% 9,1% I Frequency Col Pct 9,5% 0,9% 1,2% 26,0% 16,5% L Frequency Col Pct 29,6% 1,3% 2,2% 42,2% 59,4% Total Frequency Col Pct 100,0% 100,0% 100,0% 3,2% 3,3%

25 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%

26 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?

27 THE DEFINITION OF CLASSES OF RATING (2) Number of classes The FASTCLUS Procedure by SAS/STAT software classes Upper and lower limits of each class

28 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%

29 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%

30 MAPPING OF DEFAULT PROBABILITY (2) VS. bonds Way of financing banks multinational size SME high creditworthiness differentiated

31 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

32 Thank you for your attention. Questions, suggestions and comments are welcome! Americo Todisco