Modeling an Accounting-Based Rating System for Austrian Firms

Modeling an Accounting-Based Rating System for Austrian Firms eingereicht von Mag Evelyn Hayden Dissertation zur Erlangung des akademischen Grades Doctor rerum socialium oeconomicarumque (Dr rer soc oec.) Doktor der Sozial und Wirtschaftswissenschaften ¨ Wirtschaftswissenschaften und Informatik Fakult¨at fur Universit¨at Wien Erstgutachter: o.Univ.Prof Dr Josef Zechner Zweitgutachter: o.Univ.Prof Dr Engelbert Dockner Wien, im Juni 2002 Contents Introduction Model Selection 10 I Parameter Selection 11 II Choice of Input Variables 11 III Model-Type Selection 13 IV Default Definition 15 V Time Horizon 16 The Data Set 18 Methodology 25 I Selection of Candidate Variables 25 II Test of Linearity Assumption 33 III Univariate Logit Models 40 IV Derivation of the Default Prediction Models 43 Three Rating Models for Austria 46 Rating Models Based on Sector Information 56 I Choice of the Appropriate Sector Information 58 II Univariate Regression Results 59 III Multivariate Regression Results 60 A Rating Model for Germany 67 I The German Data 68 II The Rating Model for German firms 71 CONTENTS Testing for Rating Accuracy 78 I The Receiver Operating Characteristic 80 II 87 III Interpretation of the Area Under the ROC Curve ˆ Confidence Intervals for the Area A 88 IV Connection between ROC and CAP Curves 91 V Applying the Concept of ROC Curves to the Austrian Rating Models 93 Conclusion A 96 100 I The Data Set with Loan-Restructuring as Default Criterion 100 II The Data Set with 90-Days-Past-Due as Default Criterion 103 B 106 I C Program Code for the Implementation of the adjusted HodrickPrescott Filter in STATA 7.0 106 109 I D Correlations between Accounting Ratios of the Same Credit Risk Factor Group 109 114 I Correlations between Firm-Based and Sector-Based Accounting Ratios 114 To my Family Acknowledgements I would like to thank my supervisors Josef Zechner and Engelbert Dockner and my coauthors Bernd Engelmann and Dirk Tasche for their intellectual support In addition, Helmut Elsinger, Sylvia Fr¨uhwirth-Schnatter, Alfred Lehar, David Meyer, Otto Randl, Michaela Schaffhauser-Linzatti and Alex Stomper have made valuable comments I also thank participants of the doctoral seminars at the University of Vienna and at the European Financial Management Association 2001 in Lugano and participants of the conference of the Austrian Working Group on Banking and Finance 2001 in Vienna Besides, I gratefully ¨ acknowledge financial support from the Austrian National Bank ( ONB) under the Jubil¨aumsfond grant number 8652 and the contribution of three Austrian commercial banks, the Austrian Institute of Small Business Research, the Austrian National Bank, and the German Central Bank for providing the necessary data for this thesis Chapter Introduction In January 2001 the Basel Committee on Banking Supervision released the second version of its proposal for a new capital adequacy framework In this release the Committee announced that an internal ratings-based approach could form the basis for setting capital charges for banks with respect to credit risk in the near future For this reason it is one main purpose of this work to develop a simple and therefore practicable but efficient credit quality rating model applicable to the Austrian market that could be used by Austrian banks as a benchmark when adjusting their internal rating models Essentially, there are three main possible model inputs: accounting variables, market-based variables such as market equity value and so-called soft facts such as the firm’s competitive position or management skills As in Austria the market capitalization is very low, for most companies market-based variables are not observable, which also implies that models based on the option pricing approach originally proposed by Merton are not optimal for an application to Austria Besides, due to the inherent subjectivity of candidate variables and data unavailabil6 CHAPTER INTRODUCTION ity, soft facts were excluded from the model, too, leaving accounting variables as the main input to the statistical analysis based on logistic regressions However, as in the literature also some other factors such as the size or the legal form of the companies are reported to be helpful in predicting default, these variables are additionally included into the model building process Besides, in contrast to similar studies that can be found in the literature, this work extends the study beyond the analysis of accounting variables in comparing them to the respective median values in the appropriate sector or branch As it is common habit to evaluate the performance of a company by comparing it to similar firms operating in the same industry, this approach could also be used in estimating default-prediction-models The hypothesis would be that the worse a firm does compared to the typical firm of a sector, the higher its default probability should be For example lower net profits per assets than that of the mean or median firm should increase the default probability, while a lower debt ratio should decrease it What’s more, historically credit risk models were developed using the default criterion bankruptcy, as this information was relatively easily observable However, the Basle Committee on Banking Supervision (2001a) defined default as any credit loss event associated with any obligation of the obligor, including distressed restructuring involving the forgiveness or postponement of principal, interest, or fees and delay in payment of the obligor of more than 90 days According to the current proposal for the new capital accord banks will have to use this tight definition of default for estimating internal rating-based models Now an important question is whether “old” rating models that use only bankruptcy as default criterion are therefore outdated, or whether there is a possibility to adjust them in such a way that they perform just as well as models that were developed CHAPTER INTRODUCTION using a more complex default definition One of the main aims of this thesis is to answer this question, and therefore rating models using the default definitions of bankruptcy, loan restructuring and 90 days past due will be estimated and compared The data necessary for this analysis was provided by three major Austrian commercial banks, the Austrian National Bank and the Austrian Institute of Small Business Research By combining these data pools a unique data set on credit risk analysis for the Austrian market was constructed However, although the data was carefully inspected and harmonized, it is still advantageous to crosscheck the chosen methodology by applying it to a second, more homogeneous data set Therefore the analysis is repeated with the similar, but larger and homogeneous data pool of German firms gathered by the German Central Bank, where default is defined as hard insolvency As the economies in Germany and Austria are comparable in many aspects, similar results of the rating model building process for the German data set as for the Austrian one would further strengthen the Austrian model Finally, the performance of the estimated models has to be evaluated However, testing the accuracy of internal rating models by statistical methods is still an open question in the literature, even though Basel II further increases the need of banks and regulators for statistical validation procedures The validation techniques currently used in practice are the concepts of Cumulative Accuracy Profiles and Accuracy Ratios, which deliver a single number to judge upon the quality of internal rating models However, the reliability of such judgements is questionable if no confidence interval can be stated in addition to the Accuracy Ratio Therefore, by using the concept of Receiver Operating Characteristics and the U-test of Mann-Whitney, in the last chapter of this thesis confidence inter- CHAPTER INTRODUCTION vals for the area under the Receiver Operating Characteristic Curve are derived in an analytical and consequently simple way Besides, a relationship between this area and the Accuracy Ratio is proven, which demonstrates that the concepts derived for Receiver Operating Characteristic Curves can be applied to Cumulative Accuracy Profiles, too Hence different rating models can be compared by using confidence intervals instead of single numbers, which allows a sound decision-making about the superiority of one model, as will be demonstrated by comparing the performance of the models developed in this thesis The remainder of this work is composed as follows: In Chapter the model building strategy is chosen, while Chapter describes the data and Chapter details the applied methodology The derived Austrian rating models are depicted in Chapter and Chapter examines the estimation results when the accounting ratios are compared to the respective median values in the appropriate branch Chapter presents the German rating model Finally the power of the developed models is tested in Chapter Chapter concludes Chapter Model Selection As already mentioned in the introduction it is the aim of this study to develop a simple and therefore practicable but yet efficient model to derive a credit quality rating for Austrian firms from certain firm characteristics To this, the first step is to decide on the following five important questions: Which parameters shall be estimated? Which input variables are used? Which type of model shall be estimated? How is default defined? Which time horizon is chosen? In the following sections these questions will be answered for the work at hand 10 APPENDIX A 101 Figure A.1 Borrower Counts by Number of Observed Yearly Observations This figure shows the number of borrowers that have either one or multiple financial statement observations for different lengths of time Multiple observations are important for the evaluation of the extent to which trends in financial ratios help predict defaults 4000 Unique Firms 3000 2000 1000 Consecutive Annual Statements Figure A.2 Distribution of Financial Statements by Legal Form This figure displays the distribution of the legal form The test sample differs slightly from the estimation sample as its percentage of limited liability companies is a few percentages higher Development Sample 82% Limited Liability Companies 90% Limited Liability Companies 9% Limited Partnerships 6% Limited Partnerships 3% Single Owner Companies 2% Single Owner Companies 5% General Partnerships 2% General Partnerships Validation Sample APPENDIX A 102 Figure A.3 Distribution of Financial Statements by Sales Class This graph shows the distribution of the accounting statements grouped according to sales classes for the observations in the estimation and the test sample Differences between those two samples according to this criterion are only marginal 37% 5-20m ATS 36% 5-20m ATS 38% 20-100m ATS 40% 20-100m ATS 19% 100-500m ATS 19% 100-500m ATS 3% 500-1000m ATS 3% 500-1000m ATS 3% >1000m ATS 2% >1000m ATS Development Sample Validation Sample Figure A.4 Distribution of Financial Statements by Industry Segments This figure shows that the distribution of firms by industry differs between the development and the validation sample as there are less service companies in the test sample This provides a further element of out-of-universe testing Development Sample 33% Service 26% Service 33% Trade 36% Trade 23% Manufacturing 27% Manufacturing 11% Construction 11% Construction 1% Agriculture 1% Agriculture Validation Sample APPENDIX A 103 II The Data Set with 90-Days-Past-Due as Default Criterion Table A.2 Number of observations and defaults per year for the delay-in-payment data set This table shows the total number of the observed balance sheets and defaults per year The last column displays the yearly default frequency according to the delay-in-payment data set year 1992 1993 1994 1995 1996 1997 1998 1999 Total observations 353 776 1,469 2,605 3,486 3,459 2,918 1,731 16,797 in % 2.10 4.62 8.75 15.51 20.75 20.59 17.37 10.31 100.00 defaults 18 46 100 268 380 359 316 117 1,604 in % 1.12 2.87 6.23 16.71 23.69 22.38 19.70 7.29 100.00 default ratio in % 5.10 5.93 6.81 10.29 10.81 10.90 10.38 6.76 9.55 APPENDIX A 104 Figure A.5 Borrower Counts by Number of Observed Yearly Observations This figure shows the number of borrowers that have either one or multiple financial statement observations for different lengths of time Multiple observations are important for the evaluation of the extent to which trends in financial ratios help predict defaults Unique Firms 2000 1000 Consecutive Annual Statements Figure A.6 Distribution of Financial Statements by Legal Form This figure displays the distribution of the legal form The test sample is almost equal to the estimation sample Development Sample 91% Limited Liability Companies 91% Limited Liability Companies 5% Limited Partnerships 5% Limited Partnerships 1% Single Owner Companies 0% Single Owner Companies 3% General Partnerships 3% General Partnerships Validation Sample APPENDIX A 105 Figure A.7 Distribution of Financial Statements by Sales Class This graph shows the distribution of the accounting statements grouped according to sales classes for the observations in the estimation and the test sample Differences between those two samples according to this criterion are only marginal 47% 5-20m ATS 44% 5-20m ATS 37% 20-100m ATS 37% 20-100m ATS 13% 100-500m ATS 16% 100-500m ATS 2% 500-1000m ATS 3% 500-1000m ATS 1% >1000m ATS 1% >1000m ATS Development Sample Validation Sample Figure A.8 Distribution of Financial Statements by Industry Segments This figure shows that for the delay-in-payments data set also the distribution of firms by industry is similar for the development and the validation sample Development Sample 41% Service 39% Service 29% Trade 29% Trade 17% Manufacturing 19% Manufacturing 12% Construction 12% Construction 1% Agriculture 1% Agriculture Validation Sample Appendix B I Program Code for the Implementation of the adjusted Hodrick-Prescott Filter in STATA 7.0 capture program drop HP-Filter program define HP-Filter set matsize 100 local lambda = 0.005 mkmat N¨u local N = N tempname M Minv HP matrix ‘M’ = J(‘N’,‘N’,0) local i = while (‘i’ = ‘N’) local a1 = range[‘i’+2]-range[‘i’+1] local a2 = range[‘i’+1]-range[‘i’] 106 APPENDIX B 107 local a3 = range[‘i’]-range[‘i’-1] local a4 = range[‘i’-1]-range[‘i’-2] local ip1 = ‘i’ + local ip2 = ‘i’ + local in1 = ‘i’ - local in2 = ‘i’ - if ‘i’ == matrix ‘M’[‘i’,‘i’] = + ‘lambda’ * (1/(‘a2’2 )) matrix ‘M’[‘i’,‘ip1’] = ‘lambda’ * ((-1/(‘a2’2 ))-(1/(‘a1’*‘a2’))) matrix ‘M’[‘i’,‘ip2’] = ‘lambda’ * (1/(‘a1’*‘a2’)) else if ‘i’ == matrix ‘M’[‘i’,‘i’] = + ‘lambda’ * ((1/(‘a3’2 ))+(2/(‘a2’2 ))+(2/(‘a2’*‘a3’))) matrix ‘M’[‘i’,‘ip1’] = ‘lambda’ * ((-2/(‘a2’2 ))-(1/(‘a2’*‘a3’))-(1/(‘a1’*‘a2’))) matrix ‘M’[‘i’,‘ip2’] = ‘lambda’ * (1/(‘a1’*‘a2’)) matrix ‘M’[‘i’,‘in1’] = ‘lambda’ * ((-1/(‘a3’2 ))-(1/(‘a2’*‘a3’))) else if ‘i’ == ‘N’-1 matrix ‘M’[‘i’,‘i’] = + ‘lambda’ * ((1/(‘a3’2 ))+(2/(‘a2’2 ))+(2/(‘a2’*‘a3’))) matrix ‘M’[‘i’,‘ip1’] = ‘lambda’ * ((-1/(‘a2’2 ))-(1/(‘a2’*‘a3’))) matrix ‘M’[‘i’,‘in1’] = ‘lambda’ * ((-2/(‘a3’2 ))-(1/(‘a3’*‘a4’))-(1/(‘a2’*‘a3’))) matrix ‘M’[‘i’,‘in2’] = ‘lambda’ * (1/(‘a3’*‘a4’)) else if ‘i’ == ‘N’ APPENDIX B 108 matrix ‘M’[‘i’,‘i’] = + ‘lambda’ * (1/(‘a3’2 )) matrix ‘M’[‘i’,‘in1’] = ‘lambda’ * ((-1/(‘a3’2 ))-(1/(‘a3’*‘a4’))) matrix ‘M’[‘i’,‘in2’] = ‘lambda’ * (1/(‘a3’*‘a4’)) else matrix ‘M’[‘i’,‘i’] = + ‘lambda’ * ((2/(‘a3’2 ))+(2/(‘a2’2 ))+(2/(‘a2’*‘a3’))) matrix ‘M’[‘i’,‘ip1’] = ‘lambda’ * ((-2/(‘a2’2 ))-(1/(‘a2’*‘a3’))-(1/(‘a1’*‘a2’))) matrix ‘M’[‘i’,‘ip2’] = ‘lambda’ * (1/(‘a1’*‘a2’)) matrix ‘M’[‘i’,‘in1’] = ‘lambda’ * ((-2/(‘a3’2 ))-(1/(‘a3’*‘a4’))-(1/(‘a2’*‘a3’))) matrix ‘M’[‘i’,‘in2’] = ‘lambda’ * (1/(‘a3’*‘a4’)) local i = ‘i’ + matrix ‘Minv’ = inv(‘M’) matrix ‘HP’ = ‘Minv’ * N¨u svmat ‘HP’, names(HP) end Appendix C I Correlations between Accounting Ratios of the Same Credit Risk Factor Group In Appendix C the pairwise correlations between the accounting ratios of the ten credit risk factor categories leverage, debt coverage, liquidity, activity, productivity, turnover, profitability, firm size, growth rates and leverage development are depicted One can see that for some categories not all variables are highly correlated, but that there exist correlation sub-groups Due to space limitations inter-category correlations are not listed, especially as they are in general rather small, just as was expected 109 APPENDIX C 110 Table C.1 Correlations for leverage accounting ratios Leverage ar1 ar2 ar3 ar4 ar5 ar6 ar7 ar8 ar9 ar10 ar1 1.000 -0.798 -0.787 0.190 0.175 0.382 0.377 0.330 0.311 0.098 Leverage ar9 ar10 ar9 1.000 0.815 ar2 ar3 ar4 ar5 ar6 ar7 ar8 1.000 0.974 -0.239 -0.159 -0.343 -0.345 -0.320 -0.308 -0.114 1.000 -0.239 -0.159 -0.341 -0.351 -0.318 -0.313 -0.115 1.000 -0.179 -0.045 -0.048 -0.032 -0.036 -0.102 1.000 0.351 0.347 0.358 0.357 0.318 1.000 0.985 0.913 0.882 0.943 1.000 0.902 0.888 0.928 1.000 0.984 0.843 ar10 1.000 Table C.2 Correlations for debt coverage accounting ratios Debt Coverage ar11 ar12 ar11 1.000 ar12 0.365 1.000 Table C.3 Correlations for growth rate accounting ratios Growth Rate ar62 ar63 ar62 ar63 1.000 0.878 1.000 Table C.4 Correlations for leverage change accounting ratios Leverage Change ar64 ar65 ar64 1.000 ar65 0.252 1.000 APPENDIX C 111 Table C.5 Correlations for liquidity accounting ratios Liquidity ar13 ar14 ar15 ar16 ar17 ar18 ar19 ar20 ar21 ar22 ar23 ar24 ar25 ar26 ar13 1.000 0.699 0.886 -0.503 0.538 0.229 0.729 0.197 0.281 0.218 -0.141 0.412 0.999 0.785 ar14 ar15 Liquidity ar21 ar22 ar23 ar24 ar25 ar26 ar21 ar22 ar23 1.000 0.863 1.000 -0.004 -0.010 1.000 0.050 0.129 -0.084 0.280 0.216 -0.142 0.229 0.417 -0.117 ar16 ar17 ar18 ar19 ar20 1.000 0.742 1.000 0.019 -0.544 1.000 0.859 0.630 0.308 1.000 0.284 0.222 -0.034 0.220 1.000 0.626 0.778 -0.317 0.588 0.188 1.000 0.128 0.159 -0.145 0.046 0.730 0.049 1.000 0.246 0.259 -0.012 0.282 0.047 0.063 0.353 0.181 0.191 -0.031 0.188 0.125 0.004 0.420 0.019 -0.180 0.246 0.023 -0.022 -0.135 -0.037 0.252 0.338 -0.315 0.091 0.846 0.268 0.750 0.707 0.892 -0.501 0.548 0.231 0.736 0.195 0.559 0.696 -0.416 0.405 0.334 0.576 0.297 ar24 ar25 ar26 1.000 0.410 1.000 0.490 0.785 1.000 APPENDIX C 112 Table C.6 Correlations for activity accounting ratios Activity ar27 ar28 ar29 ar30 ar31 ar32 ar33 ar34 ar35 ar36 ar37 ar27 1.000 0.996 0.837 0.030 0.025 -0.233 -0.249 -0.109 0.058 0.251 -0.402 Activity ar35 ar36 ar37 ar35 1.000 0.699 0.124 ar28 ar29 ar30 ar31 ar32 ar33 ar34 1.000 0.837 1.000 0.034 0.037 1.000 0.024 0.031 0.988 1.000 -0.235 -0.255 0.650 0.662 1.000 -0.250 -0.264 0.584 0.596 0.957 1.000 -0.109 0.150 0.612 0.619 0.347 0.314 1.0000 0.061 0.251 0.188 0.185 -0.112 -0.122 0.4341 0.259 0.183 0.267 0.246 -0.040 -0.059 0.0657 -0.399 -0.335 0.318 0.320 0.340 0.335 0.4072 ar36 ar37 1.000 0.003 1.000 Table C.7 Correlations for productivity accounting ratios Productivity ar38 ar39 ar40 ar41 ar38 1.0000 ar39 -0.7042 1.000 ar40 -0.5621 0.700 1.000 ar41 -0.6605 0.505 0.001 1.000 Table C.8 Correlations for turnover accounting ratios Turnover ar42 ar43 ar44 ar42 1.000 ar43 0.969 1.000 ar44 0.992 0.963 1.000 APPENDIX C 113 Table C.9 Correlations for profitability accounting ratios Profitability ar45 ar46 ar47 ar48 ar49 ar50 ar51 ar52 ar53 ar54 ar55 ar56 ar57 ar58 ar45 1.000 0.989 0.755 0.721 0.956 0.964 0.891 0.803 0.780 0.779 0.778 0.614 0.615 0.744 Profitability ar53 ar54 ar55 ar56 ar57 ar58 ar21 1.000 0.715 0.707 0.838 0.841 0.678 ar46 ar47 ar48 ar49 ar50 ar51 ar52 1.000 0.738 0.709 0.950 0.960 0.907 0.814 0.769 0.774 0.784 0.604 0.605 0.741 1.000 0.898 0.722 0.720 0.652 0.689 0.846 0.629 0.623 0.698 0.694 0.596 1.000 0.774 0.717 0.696 0.726 0.843 0.634 0.629 0.703 0.705 0.603 1.000 0.950 0.920 0.828 0.773 0.781 0.779 0.616 0.618 0.747 1.000 0.905 0.808 0.822 0.818 0.816 0.653 0.655 0.780 1.000 0.904 0.733 0.735 0.747 0.582 0.584 0.702 1.000 0.703 0.670 0.680 0.558 0.560 0.640 ar22 ar23 ar24 ar25 ar26 1.000 0.992 0.806 0.808 0.947 1.000 0.796 1.000 0.799 0.995 1.000 0.942 0.760 0.762 1.000 Table C.10 Correlations for size accounting ratios Size ar59 ar60 ar61 ar59 ar60 ar61 1.000 0.984 1.000 0.833 0.833 1.000 Appendix D I Correlations between Firm-Based and Sector-Based Accounting Ratios In Appendix D the pairwise correlations between the “simple” accounting ratios and those compared to the median values of the appropriate branches are depicted This is done for the two cases when the companies are grouped by ¨ using either all six or only two digits of the ONACE-classification code One can see that for all variables the correlations between the traditional accounting ratios and the corresponding sector-based variables are extremely high, implying that it is not possible to integrate both types of information within one regression model 114 APPENDIX D 115 Table D.1 Correlations between Firm-Based and Sector-Based Accounting Ratios ar1 ar2 ar3 ar4 ar5 ar6 ar7 ar8 ar9 ar10 ar11 ar12 ar13 ar14 ar15 ar16 ar17 ar18 ar19 ar20 ar21 ar22 ar23 ar24 ar25 ar26 ar27 ar28 ar29 ar30 ar31 ar32 ar33 2-digit ratios 0.9805 0.9810 0.9766 0.9904 0.9425 0.9397 0.9439 0.9780 0.9755 0.9278 0.9994 0.9942 0.9663 0.8771 0.9694 0.9426 0.7723 0.9975 0.9772 0.9960 0.9691 0.9585 0.9995 0.9973 0.9582 0.9407 0.8975 0.8986 0.9391 0.9280 0.9279 0.9096 0.9215 6-digit ratios 0.9510 0.9624 0.9581 0.9805 0.9146 0.8944 0.9135 0.9631 0.9602 0.8854 0.9983 0.9887 0.9527 0.8593 0.9518 0.8990 0.7362 0.9926 0.9544 0.9916 0.9084 0.8870 0.9755 0.9939 0.9461 0.9099 0.8133 0.8035 0.8555 0.8825 0.8815 0.8568 0.8720 ar34 ar35 ar36 ar37 ar38 ar39 ar40 ar41 ar42 ar43 ar44 ar45 ar46 ar47 ar48 ar49 ar50 ar51 ar52 ar53 ar54 ar55 ar56 ar57 ar58 ar59 ar60 ar61 ar62 ar63 ar64 ar65 2-digit ratios 0.9646 0.9783 0.9901 0.9468 0.8264 0.9701 0.9709 0.6821 0.9304 0.9434 0.9333 0.9949 0.9952 0.9789 0.9830 0.9932 0.9922 0.9902 0.9909 0.9920 0.9928 0.9939 0.9946 0.9947 0.9946 0.9883 0.9848 0.9887 0.9972 0.9948 0.9999 0.9993 6-digit ratios 0.8726 0.9560 0.9745 0.8397 0.7616 0.9165 0.9557 0.6049 0.8362 0.8558 0.8417 0.9808 0.9821 0.9632 0.9601 0.9824 0.9791 0.9761 0.9796 0.9786 0.9858 0.9878 0.9880 0.9879 0.9888 0.9843 0.9771 0.9805 0.9927 0.9862 0.9998 0.9967