Abstract
Assessing the ability of applicants to repay their loans is generally recognized as a critical task in credit risk management. Credit managers rely on financial and market information, usually in the form of ratios, to estimate the quality of credit applicants. However, there is no guarantee that a given set of ratios contains the information needed for credit classification. Decision rules under strict uncertainty aim to mitigate this drawback. In this paper, we propose the use of a moderate pessimism decision rule combined with dimensionality reduction techniques and compromise programming. Moderate pessimism ensures that neither extreme optimistic nor pessimistic decisions are taken. Dimensionality reduction from a set of ratios facilitates the extraction of the relevant information. Compromise programming allows to find a balance between quality of debt and risk concentration. Our model produces two critical outputs: a quality assessment and the optimum allocation of funds. To illustrate our multicriteria approach, we include a case study on 29 firms listed in the Spanish stock market. Our results show that dimensionality reduction contributes to avoid redundancy and that quality-diversification optimization is able to produce budget allocations with a reduced number of firms.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abdi H, Williams LJ (2010) Principal component analysis. Wiley Interdiscip Reviews Comput Stat 2(4):433–459
Adams W, Einav L, Levin J (2009) Liquidity constraints and imperfect information in subprime lending. Am Econ Rev 99(1):49–84
Altman EI (1968) Financial ratios, discriminant analysis and the prediction of corporate bankruptcy. J Financ 23(4):589–609
Altman EI, Iwanicz-Drozdowska M, Laitinen EK, Suvas A (2016) Financial and non-financial variables as long-horizon predictors of bankruptcy. J Credit Risk 12(4):49–78
Angilella S, Mazzù S (2015) The financing of innovative smes: a multicriteria credit rating model. Eur J Oper Res 244(2):540–554
Armor DJ (1973) Theta reliability and factor scaling. Sociol Methodol 5:17–50
Avery RB, Bostic RW, Calem PS, Canner GB (2000) Credit scoring: statistical issues and evidence from credit-bureau files. Real Estate Econ 28(3):523–547
Ballestero E (2002) Strict uncertainty: a criterion for moderately pessimistic decision makers. Decis Sci 33(1):87–108
Ballestero E (2006) Ranking alternatives from the decision maker’s preferences: an approach based on utility and the notion of marginal action. J Oper Res Soc Jpn 49(1):49–65
Ballestero E, Pla-Santamaria D (2004) Selecting portfolios for mutual funds. Omega 32(5):385–394
Ballestero E, Romero C (1998) Multiple criteria decision making and its applications to economic problems. Kluwer Academic Publishers, Dordrecht
Ballestero E, Günther M, Pla-Santamaria D, Stummer C (2007) Portfolio selection under strict uncertainty: a multi-criteria methodology and its application to the frankfurt and vienna stock exchanges. Eur J Oper Res 181(3):1476–1487
Bartlett MS (1937) Properties of sufficiency and statistical tests. Proc R Soc Lond Ser A Math Phys Sci 160(901):268–282
Bellman R (1957) Dynamic programming. Princeton University Press, New Jersey
Bravo M, Pla-Santamaria D (2012) Evaluating loan performance for bank offices: a multicriteria decision-making approach. Inf Syst Oper Res 50(3):127–133
Breeden JL (2016) Incorporating lifecycle and environment in loan-level forecasts and stress tests. Eur J Oper Res 255(2):649–658
Carmines EG, Zeller RA (1979) Reliability and validity assessment. Quantitative applications in the social sciences. SAGE, Thousand Oaks
Cerny BA, Kaiser HF (1977) A study of a measure of sampling adequacy for factor-analytic correlation matrices. Multivar Behav Res 12(1):43–47
Chen M-Y (2014) Using a hybrid evolution approach to forecast financial failures for taiwan-listed companies. Quant Financ 14(6):1047–1058
Conway JM, Huffcutt AI (2003) A review and evaluation of exploratory factor analysis practices in organizational research. Organ Res Methods 6(2):147–168
Doumpos M, Zopounidis C (2011) A multicriteria outranking modeling approach for credit rating. Decis Sci 42(3):721–742
Edelberg W (2006) Risk-based pricing of interest rates for consumer loans. J Monet Econ 53(8):2283–2298
Einav L, Jenkins M, Levin J (2012) Contract pricing in consumer credit markets. Econometrica 80(4):1387–1432
Einav L, Jenkins M, Levin J (2013) The impact of credit scoring on consumer lending. Rand J Econ 44(2):249–274
Elisabetsky R (1976) Um modelo matemático para decisões de crédito no banco comercial. PhD thesis, Dissertação (Mestrado)–Escola Politécnica, Universidade de São Paulo, São Paulo
Eriksson K, Jonsson S, Lindbergh J, Lindstrand A (2014) Modeling firm specific internationalization risk: an application to banks’ risk assessment in lending to firms that do international business. Int Bus Rev 23(6):1074–1085
Fabrigar LR, Wegener DT, MacCallum RC, Strahan EJ (1999) Evaluating the use of exploratory factor analysis in psychological research. Psychol Methods 4(3):272
Falangis K (2007) The use of MSD model in credit scoring. Oper Res Int J 7(3):481–503
Ford JK, MacCallum RC, Tait M (1986) The application of exploratory factor analysis in applied psychology: a critical review and analysis. Pers Psychol 39(2):291–314
Freeman L, Hamilton D (2002) A dream deferred or realized: the impact of public policy on fostering black homeownership in new york city throughout the 1990’s. Am Econ Rev 92(2):320–324
George W, Snedecor CWG (1989) Statistical methods. Iowa State University Press, Iowa
Jory SR, Ngo TN, Wang D (2016) Credit ratings and the premiums paid in mergers and acquisitions. J Empir Financ 39:93–104
Kaiser HF (1958) The varimax criterion for analytic rotation in factor analysis. Psychometrika 23(3):187–200
Kaiser HF (1974) An index of factorial simplicity. Psychometrika 39(1):31–36
Kanitz S (1974) Como prever falencias de empresas. Revista de Negocios Em Exame, Dezembro, pp 95–102
Kantardzic M (2011) Data mining: concepts, models, methods, and algorithms. Wiley, New York
Kealhofer S (1993) Portfolio management of default risk. KMV Corporation, San Francisco
Laplace P-S (1825) Essai philosophique sur les probabilités. H. Remy, Paris
Legault, J. and Score, A. (1987). Ca score. warning system for small business failures. Bilanas, June, pages 29–31
Li H, Hong L-Y, Zhou Q, Yu H-J (2015) The assisted prediction modelling frame with hybridisation and ensemble for business risk forecasting and an implementation. Int J Syst Sci 46(11):2072–2086
Magee S (2013) The effect of foreign currency hedging on the probability of financial distress. Account Financ 53(4):1107–1127
McQuown J (1993) Market versus accounting-based measures of default risk. KMV Corporation, San Francisco
Mencía J (2012) Assessing the risk-return trade-off in loan portfolios. J Bank Financ 36(6):1665–1677
Merton RC (1974) On the pricing of corporate debt: the risk structure of interest rates. J Financ 29(2):449–470
Mester LJ (1997) What’s the point of credit scoring? Bus Rev 3(Sep/Oct):3–16
Nunnally JC, Bernstein I (1994) Psychometric theory (McGraw-Hill Series in Psychology), vol 3. McGraw-Hill, New York
Saunders D, Xiouros C, Zenios SA (2007) Credit risk optimization using factor models. Ann Oper Res 152(1):49–77
Sengupta R, Bhardwaj G (2015) Credit scoring and loan default. Int Rev Financ 15(2):139–167
Shi J, Xu B (2016) Credit scoring by fuzzy support vector machines with a novel membership function. J Risk Financ Manag 9(4):13
Sirignano J, Giesecke K (2019) Risk analysis for large pools of loans. Manag Sci 65(1):107–121
Sirignano JA, Tsoukalas G, Giesecke K (2016) Large-scale loan portfolio selection. Oper Res 64(6):1239–1255
Spector PE (1992) Summated rating scale construction: An introduction, vol 82. Sage, Newbury Park
Springate GL (1978) Predicting the possibility of failure in a Canadian firm: a discriminant analysis. PhD thesis, Simon Fraser University
Thomas LC (2009) Consumer credit models: pricing, profit and portfolios: pricing, profit and portfolios. Oxford University Press, Oxford
Vasicek O (1984) The philosophy of credit valuation: the credit valuation model. KMV Corporation, San Francisco
Wald A (1950) Statistical decision functions. Wiley, New York
Wang J, Wang J (2015) Forecasting stock market indexes using principle component analysis and stochastic time effective neural networks. Neurocomputing 156:68–78
Weber O (2012) Environmental credit risk management in banks and financial service institutions. Bus Strate Environ 21(4):248–263
Woerheide W, Persson D (1992) An index of portfolio diversification. Financ Serv Rev 2(2):73–85
Yu P-L (1985) Multiple-criteria decision making: concepts, techniques, and extensions. Plenum Press, New York
Zeleny M (1973) Compromise programming. In: Cochrane JL, Zeleny M (eds) Multiple criteria decision making. University of South Carolina Press, Columbia, pp 262–301
Zeleny M (1982) Multiple criteria decision making. McGraw-Hill, New York
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Appendices
Appendix: Definition of criteria
Criterion | Definitions | |
|---|---|---|
1 | Return on invested capital (ROIC) | \(\frac{{\text {NOPAT}}}{{\text {EQUITY}}+\text {NET DEBT}}\) |
2 | Return on assets (ROA) | \(\frac{{\text {EBIT}}}{{\text {ASSETS}}}\) |
3 | Assets turnover | \(\frac{{\text {SALES}}}{{\text {ASSETS}}}\) |
4 | Return on equity (ROE) | \(\frac{{\text {NET INCOME}}}{{\text {EQUITY}}}\) |
5 | Pretax income-to-equity ratio | \(\frac{{\text {PRE-TAX INCOME}}}{{\text {EQUITY}}}\) |
6 | EBIT-to-sales ratio | \(\frac{{\text {EBIT}}}{{\text {SALES}}}\) |
7 | Net value added-to-sales ratio | \(\frac{{\text {NET VALUE ADDED}}}{{\text {SALES}}}\) |
8 | Quick ratio | \(\frac{{\text { ASSETS-INVENTORY}}}{{\text {LIABILITIES}}}\) |
9 | Current ratio | \(\frac{{\text {CURRENT ASSETS}}}{{\text {CURRENT LIABILITIES}}}\) |
10 | Accounts receivable net turnover | \(\frac{{\text {SALES}}}{{\text {AVERAGE RECEIVABLES}}}\) |
11 | Total accounts receivable turnover | \(\frac{{\text {REVENUE}}}{{\text {AVERAGE RECEIVABLES}}}\) |
12 | Working capital-to-assets ratio | \(\frac{{\text {WORKING CAPITAL}}}{{\text {ASSETS}}}\) |
13 | Cash ratio | \(\frac{{\text {CASH}}}{{\text {LIABILITIES}}}\) |
14 | Current liabilities-to-assets ratio | \(\frac{{\text {LIABILITIES}}}{{\text {ASSETS}}}\) |
15 | Trade payable turnover | \(\frac{{\text { REVENUE COST+OTHER EXPENSES}}}{{\text {AVERAGE TRADE PAYABLE}}}\) |
16 | Suppliers turnover | \(\frac{{\text {COST OF SALES}}}{{\text {AVERAGE SUPPLIERS}}}\) |
17 | Financial leverage | \(\frac{{\text {PRE-TAX INCOME}}}{{\text {EQUITY}}} \times \frac{{\text {EBIT}}}{{\text {ASSETS}}}\) |
18 | Assets-to-liabilities ratio | \(\frac{{\text {ASSETS}}}{{\text {LIABILITIES}}}\) |
19 | Liabilities-to-(Liabilities+equity) ratio | \(\frac{{\text {LIABILITIES}}}{{\text {LIABILITIES+EQUITY}}}\) |
20 | Liabilities-to-equity ratio | \(\frac{{\text {LIABILITIES}}}{{\text {EQUITY}}}\) |
21 | Equity-to-assets ratio | \(\frac{{\text { EQUITY}}}{{\text {ASSETS}}}\) |
22 | Retained earnings-to-equity ratio | \(\frac{{\text {RETAINED EARNINGS}}}{{\text {EQUITY}}}\) |
23 | Retained earnings-to-assets ratio | \(\frac{{\text {RETAINED EARNINGS}}}{{\text {ASSETS}}}\) |
24 | (Non-current liabilities + equity)-to-assets ratio | \(\frac{{\text {NON-CURRENT LIABILITIES+EQUITY}}}{{\text {ASSETS}}}\) |
25 | Non-current liabilities-to-liabilities ratio | \(\frac{{\text {NON-CURRENT LIABILITIES}}}{{\text {LIABILITIES}}}\) |
26 | Debt-to-liabilities ratio | \(\frac{{\text {DEBT}}}{{\text {LIABILITIES}}}\) |
27 | Non-current liabilities-to-assets ratio | \(\frac{{\text {NON-CURRENT LIABILITIES}}}{{\text {ASSETS}}}\) |
28 | Leverage ratio | \(\frac{{\text {DEBT}}}{{\text {EQUITY}}}\) |
29 | Debt average cost | \(\frac{{\text {INTEREST EXPENSE}}}{{\text {AVERAGE DEBT}}}\) |
30 | Short term debt-to-net operating cash flow ratio | \(\frac{{\text {SHORT TERM DEBT}}}{{\text {NET OPERATING CASH FLOW}}}\) |
31 | Debt-to-net operating cash flow ratio | \(\frac{{\text {DEBT}}}{{\text {NET OPERATING CASH FLOW}}}\) |
32 | Current liabilities-to-net operating cash flow ratio | \(\frac{{\text {CURRENT LIABILITIES}}}{{\text {NET OPERATING CASH FLOW}}}\) |
33 | Liabilities -to- net operating cash flow ratio | \(\frac{{\text {LIABILITIES}}}{{\text {NET OPERATING CASH FLOW}}}\) |
34 | EBIT-to-net operating cash flow before interest and taxes ratio | \(\frac{{\text {EBIT}}}{{\text {NET OPERATING CASH FLOW BIT}}}\) |
35 | NOPAT-to-net operating cash flow before interest ratio | \(\frac{{\text {NOPAT}}}{{\text {NET OPERATING CASH FLOW BI}}}\) |
36 | Net income-to-net operating cash flow ratio | \(\frac{{\text {NET INCOME}}}{{\text {NET OPERATING CASH FLOW}}}\) |
37 | Legault and Score (1987) | Bankruptcy predictive model |
38 | Elisabetsky (1976) | Bankruptcy predictive model |
39 | Kanitz (1974) | Bankruptcy predictive model |
40 | Springate (1978) | Bankruptcy predictive model |
41 | Altman (1968) | Bankruptcy predictive model |
42 | Merton (1974) | Bankruptcy predictive model |
43 | Credit rating | Bankruptcy predictive model |
44 | Earnings per share | \(\frac{{\text {NET INCOME}}}{{\text {NUMBER OF SHARES}}}\) |
45 | Sales per share | \(\frac{{\text {SALES}}}{{\text {NUMBER OF SHARES}}}\) |
46 | Book value per share | \(\frac{{\text {EQUITY}}}{{\text {NUMBER OF SHARES}}}\) |
47 | Price-to-sales ratio | \(\frac{{\text {PRICE}}}{{\text {SALES}}}\) |
48 | Price-to-cash flow ratio | \(\frac{{\text {PRICE}}}{{\text {CASH FLOW}}}\) |
49 | Price-to-book value ratio | \(\frac{{\text {PRICE}}}{{\text {EQUITY}}}\) |
50 | Price-to-earnings ratio (PER) | \(\frac{{\text {PRICE}}}{{\text {NET INCOME}}}\) |
51 | Enterprise Value (EV)-to-Ebitda ratio | \(\frac{{\text {ENTERPRISE VALUE}}}{{\text {EBITDA}}}\) |
52 | Cash flow per share | \(\frac{{\text {CASH FLOW}}}{{\text {NUMBER OF SHARES}}}\) |
53 | Dividends per share | \(\frac{{\text {DIVIDENDS}}}{{\text {NUMBER OF SHARES}}T}\) |
54 | Years from foundation | (Self-explanatory) |
55 | Expectations on the economic sector | (Self-explanatory) |
Appendix: Summary of criteria statistics
Key:
-
Mean: Average value.
-
Std: Standard deviation.
-
Max: Maximum value.
-
Min: Minimum value.
-
0.025-Pct: 0.025-Percentile value.
-
0.975-Pct: 0.975-Percentile value.
Criterion | Mean | Std | Max | Min | 0.025-Pct | 0.975-Pct |
|---|---|---|---|---|---|---|
1 | 0.08 | 0.07 | 0.36 | \(-\) 0.03 | \(-\) 0.01 | 0.25 |
2 | 0.07 | 0.06 | 0.32 | \(-\) 0.05 | \(-\) 0.02 | 0.23 |
3 | 0.60 | 0.55 | 2.92 | 0.02 | 0.11 | 1.93 |
4 | 0.13 | 0.23 | 1.07 | \(-\) 0.50 | \(-\) 0.24 | 0.66 |
5 | 0.20 | 0.30 | 1.56 | \(-\) 0.10 | \(-\) 0.06 | 0.95 |
6 | 0.25 | 0.28 | 0.95 | \(-\) 0.12 | \(-\) 0.05 | 0.63 |
7 | 0.42 | 0.25 | 1.03 | 0.08 | 0.10 | 0.75 |
8 | 0.99 | 0.78 | 4.68 | 0.08 | 0.25 | 1.46 |
9 | 1.17 | 0.80 | 4.68 | 0.08 | 0.39 | 1.82 |
10 | 918.72 | 4.792.10 | 26.275.89 | 1.59 | 1.81 | 72.03 |
11 | 23.08 | 84.50 | 466.61 | 0.79 | 0.92 | 36.41 |
12 | \(-\) 0.01 | 0.15 | 0.26 | \(-\) 0.43 | \(-\) 0.39 | 0.17 |
13 | 0.29 | 0.22 | 1.00 | 0.00 | 0.01 | 0.78 |
14 | 0.28 | 0.16 | 0.70 | 0.02 | 0.11 | 0.62 |
15 | 2.06 | 2.22 | 10.17 | 0.00 | 0.00 | 7.33 |
16 | 3.93 | 2.62 | 11.53 | 0.28 | 1.33 | 10.07 |
17 | 0.37 | 0.24 | 0.80 | \(-\) 0.09 | \(-\) 0.06 | 0.80 |
18 | 0.38 | 0.19 | 0.89 | 0.05 | 0.11 | 0.64 |
19 | 2.00 | 1.53 | 9.35 | 1.06 | 1.12 | 2.79 |
20 | 0.62 | 0.19 | 0.95 | 0.11 | 0.36 | 0.89 |
21 | 0.38 | 0.84 | 1.20 | \(-\) 3.59 | \(-\) 1.43 | 1.05 |
22 | 0.20 | 0.18 | 0.56 | \(-\) 0.20 | \(-\) 0.07 | 0.56 |
23 | 2.65 | 3.15 | 17.35 | 0.12 | 0.56 | 10.65 |
24 | 0.72 | 0.16 | 0.98 | 0.30 | 0.38 | 0.89 |
25 | 0.45 | 0.21 | 1.00 | 0.07 | 0.15 | 0.75 |
26 | 0.57 | 0.22 | 0.99 | 0.09 | 0.20 | 0.82 |
27 | 0.34 | 0.16 | 0.66 | 0.00 | 0.11 | 0.62 |
28 | 2.09 | 4.08 | 16.15 | \(-\) 12.79 | \(-\) 5.75 | 11.08 |
29 | 0.05 | 0.02 | 0.09 | 0.02 | 0.03 | 0.09 |
30 | 2.73 | 6.93 | 35.40 | \(-\) 6.26 | \(-\) 2.47 | 23.05 |
31 | 13.57 | 42.76 | 236.48 | \(-\) 18.95 | \(-\) 7.49 | 110.44 |
32 | 7.47 | 20.50 | 105.49 | \(-\) 30.45 | \(-\) 11.50 | 58.31 |
33 | 21.15 | 64.39 | 353.46 | \(-\) 47.85 | \(-\) 18.15 | 165.36 |
34 | 1.18 | 2.64 | 8.97 | \(-\) 9.63 | \(-\) 4.34 | 6.09 |
Criterion | Mean | Std | Max | Min | 0.025-Pct | 0.975-Pct |
|---|---|---|---|---|---|---|
35 | 1.43 | 3.30 | 12.28 | \(-\) 10.10 | \(-\) 5.31 | 8.91 |
36 | 2.86 | 5.71 | 27.05 | \(-\) 1.99 | \(-\) 1.81 | 21.11 |
37 | \(-\) 0.44 | 0.93 | 1.74 | \(-\) 1.98 | \(-\) 1.73 | 1.54 |
38 | \(-\) 0.13 | 1.02 | 1.43 | \(-\) 4.85 | \(-\) 2.48 | 0.51 |
39 | 7.23 | 4.98 | 28.28 | \(-\) 2.28 | \(-\) 0.21 | 9.62 |
40 | 0.78 | 2.73 | 12.95 | \(-\) 0.97 | \(-\) 0.82 | 1.24 |
41 | 2.52 | 2.41 | 12.95 | \(-\) 0.36 | 0.37 | 9.36 |
42 | 7.36 | 3.38 | 16.69 | 0.14 | 1.43 | 15.10 |
43 | 0.59 | 0.13 | 0.85 | 0.27 | 0.30 | 0.84 |
44 | 25.81 | 51.14 | 248.08 | \(-\) 60.73 | \(-\) 44.99 | 160.68 |
45 | 8.35 | 32.01 | 55.39 | \(-\) 150.65 | \(-\) 58.05 | 28.12 |
46 | 3.32 | 4.54 | 23.05 | 0.25 | 0.59 | 16.94 |
47 | 4.40 | 8.11 | 36.32 | 0.21 | 0.34 | 5.47 |
48 | 30.30 | 82.10 | 447.84 | 0.12 | 1.47 | 252.31 |
49 | 16.26 | 37.96 | 212.76 | 0.28 | 0.70 | 105.17 |
50 | 2.00 | 2.89 | 11.28 | \(-\) 5.14 | \(-\) 3.67 | 8.14 |
51 | 1.34 | 35.54 | 30.00 | \(-\) 162.17 | \(-\) 32.60 | 26.83 |
52 | 1.87 | 4.86 | 26.56 | \(-\) 2.06 | \(-\) 1.05 | 13.06 |
53 | 0.10 | 0.25 | 0.90 | 0.00 | 0.00 | 0.83 |
54 | 0.52 | 0.34 | 1.49 | 0.02 | 0.15 | 1.06 |
55 | 0.28 | 0.22 | 0.75 | 0.00 | 0.00 | 0.75 |
Rights and permissions
About this article
Cite this article
Pla-Santamaria, D., Bravo, M., Reig-Mullor, J. et al. A multicriteria approach to manage credit risk under strict uncertainty. TOP 29, 494–523 (2021). https://doi.org/10.1007/s11750-020-00571-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11750-020-00571-0