Abstract
We are interested in forecasting bankruptcies in a probabilistic way. Specifically, we compare the classification performance of several statistical and machine-learning techniques, namely discriminant analysis (Altman’s Z-score), logistic regression, least-squares support vector machines and different instances of Gaussian processes (GP’s)—that is GP classifiers, Bayesian Fisher discriminant and Warped GPs. Our contribution to the field of computational finance is to introduce GPs as a competitive probabilistic framework for bankruptcy prediction. Data from the repository of information of the US Federal Deposit Insurance Corporation is used to test the predictions.
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Notes
- 1.
The work by Estrella et al. (2000) has a similar scope to ours.
- 2.
Identifying a disease.
- 3.
Estimating the prospect of recovery.
- 4.
Some human remains discovered in a burial site in Egypt were required to be sexed, i.e. determined whether they belonged to female or male specimens (Fisher 1936).
- 5.
We recall that x is a vector of observed features obtained through indirect means whereas y is a canonical variable representing the class.
- 6.
The response function is the inverse of the link function used in statistics.
- 7.
We have omitted dependencies on x ⋆ to keep the notation uncluttered.
- 8.
As expressed by Rasmussen and Williams (2006), the characteristic length scales can be loosely interpreted as the distance required to move along each axes in order to have uncorrelated inputs.
- 9.
We thank the Centre for Computational Finance and Economic Agents (CCFEA).
References
Altman, E. I. (1968). Financial ratios, discriminant analysis and the prediction of corporate bankruptcy. Journal of Finance, 23(4), 589–609.
Atiya, A. F. (2001). Bankruptcy prediction for credit risk using neural networks: a survey and new results. IEEE Transactions on Neural Networks, 12, 929–935.
Back, B., Laitinen, T., Sere, K., & van Wezel, M. (1996). Choosing bankruptcy predictors using discriminant analysis, logit analysis, and genetic algorithms (Technical Report 40). Turku Centre for Computer Science, September 1996.
Beaver, W. H. (1966). Financial ratios as predictors of failures. Journal of Accounting Research, 4, 71–111.
Bishop, C. M. (1995). Neural networks for pattern recognition. Oxford: Oxford University Press.
Bishop, C. M. (2006). Pattern recognition and machine learning. Information science and statistics. New York: Springer.
Box, G. E., & Tiao, G. C. (1973). Bayesian inference in statistical analysis. Wiley classics library, published 1992. New York: Wiley.
Chen, S.-H. (Ed.) (2002). Genetic algorithms and genetic programming in computational finance. Dordrecht: Kluwer Academic.
Cortes, C., & Vapnik, V. V. (1995). Support vector networks. Machine Learning, 20, 273–297.
Efron, B. (1979). Bootstrap methods: another look at the Jackknife. The Annals of Statistics, 7, 1–26.
Estrella, A., Park, S., & Peristiani, S. (2000). Capital ratios as predictors of bank failure. Federal reserve bank of New York economic policy review, pp. 33–52, July 2000.
Fisher, R. A. (1936). The use of multiple measurements in taxonomic problems. Annals of Eugenics, 7, 179.
Grimmett, G., & Stirzaker, D. (2004). Probability and random processes (3rd ed.). Oxford: Oxford University Press.
Joos, P., Vanhoof, K., Ooghe, H., & Sierens, N. (1998). Credit classification: a comparison of logit models and decision trees. In 10th European conference on machine learning. Proceedings notes of the workshop on application of machine learning and data mining in finance (pp. 59–72). 24 April 1998, Chemnitz, Germany.
Credit Metrics—Technical Document (1997). JP Morgan. New York, April 1997.
Kimeldorf, G. S., & Wahba, G. (1970). A correspondence between Bayesian estimation on stochastic processes and smoothing by splines. Annals of Mathematical Statistics, 41(2), 495–502.
Krige, D. G. (1996). Two-dimensional weighting moving average trend surfaces for ore evaluation. Journal of the South African Institute of Mining and Metallurgy.
Mackay, D. J. C. (1995). Probable networks and plausible predictions—a review of practical Bayesian methods for supervised neural networks. Network: Computation in Neural Systems, 6(3), 469–505.
Mackay, D. J. C. (1998). Introduction to Gaussian processes. In C. M. Bishop (Ed.), NATO ASI Series: Vol. 168. Neural networks and machine learning (pp. 133–165). Berlin: Springer.
Mackay, D. J. C. (2003). Information theory, learning and inference algorithms. Cambridge: Cambridge University Press.
MacLachlan, G. J. (1991). Discriminant analysis and pattern recognition. New York: Wiley.
Minka, T. P. (2001). A family of algorithms for approximate Bayesian inference. PhD thesis, Massachusetts Institute of Technology.
Neal, R. M. (1996). Bayesian learning for neural networks. New York: Springer.
O’Hagan, A. (1978). Curve fitting and optimal design for prediction. Journal of the Royal Statistical Society, Series B (Methodological), 40(1), 1–42.
Park, C., & Han, I. (2002). A case-based reasoning with the feature weights derived by analytic hierarchy process for bankruptcy prediction. Expert Systems with Applications, 23, 255–264.
Peña Centeno, T., & Lawrence, N. D. (2006). Optimising kernel parameters and regularisation coefficients for non-linear discriminant analysis. Journal of Machine Learning Research, 7, 455–491.
Quintana, D., Saez, Y., Mochon, A., & Isasi, P. (2007). Early bankruptcy prediction using ENPC. Journal of Applied Intelligence, ISSN 0924-669X.
Rasmussen, C. E. (2004). Gaussian processes in machine learning. In O. Bousquet, U. von Luxburg, & G. Rätsch (Eds.), Lecture notes in computer science/artificial intelligence: Vol. 3176. Advanced lectures on machine learning. Berlin: Springer.
Rasmussen, C. E., & Williams, C. K. (2006). Adaptive computation and machine learning. Gaussian processes for machine learning. Cambridge: MIT Press. http://www.GaussianProcess.org/gpml.
Rätsch, G., Onoda, T., & Müller, K.-R. (1998) Soft margins for AdaBoost (Technical Report NC-TR-98-021). Royal Holloway College, University of London, London, UK.
Seeger, M. (2004). Gaussian processes for machine learning. International Journal of Neural Systems, 14(2), 69–106.
Serrano-Cinca, C., Martin, C. B., & Gallizo, J. (1993). Artificial neural networks in financial statement analysis: ratios versus accounting data. In 16th annual congress of the European accounting association, Turku, Finland, 28–30 Apr.
Shin, K.-S., & Lee, Y.-J. (2002). A genetic algorithm application in bankruptcy prediction modeling. Expert Systems with Applications, 23, 321–328.
Snelson, E., Rasmussen, C. E., & Ghahramani, Z. (2003). Warped Gaussian processes. In S. Thrun, L. K. Saul, & B. Schölkopf (Eds.), Advances in neural information processing systems 16. Cambridge: MIT Press.
Stone, M. (1974). Cross-validatory choice and assessment of statistical predictions. Journal of the Royal Statistical Society, 36, 111–147.
Suykens, J. A. & Vandewalle, J. (1999). Least squares support vector machines. Neural Processing Letters, 9(3), 293–300.
Suykens, J. A., Van Gestel, T., Brabanter, J. D., Moor, B. D., & Vandewalle, J. (2002). Least squares support vector machines. Singapore: World Scientific.
Thiele, T. N. (1931). Theory of observations. London: Layton. Reprinted in Annals of Mathematical Statistics, 2, 165–308.
Tsang, E. P. K., & Martinez-Jaramillo, S. (2004). Computational finance. In IEEE computational intelligence society newsletter (pp. 3–8). New York: IEEE Press.
Varetto, F. (1998). Genetic algorithms applications in the analysis of insolvency risk. Journal of Banking and Finance, 22, 1421–1439.
Wahba, G. (1990). CBMS-NSF regional conference in applied mathematics: Vol. 59. Spline models for observational data. Philadelphia: Society for Industrial and Applied Mathematics.
Williams, C. K. (1999). Prediction with Gaussian processes: from linear regression to linear prediction and beyond. In M. I. Jordan (Ed.), Behavioural and social sciences: Vol. 11. Learning in graphical models, D. Dordrecht: Kluwer Academic.
Williams, C. K., & Barber, D. (1998). Bayesian classification with Gaussian processes. IEEE Transactions, Pattern Analysis and Machine Intelligence, 20(12), 1342–1351.
Yip, A. Y. N. (2003). A hybrid case-based reasoning approach to business failure prediction (pp. 371–378). Amsterdam: IOS Press. ISBN 1-58603-394-8.
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Appendix
Appendix
A brief description of the financial ratios that compose the FDIC data follows.
Ratio 1. Net interest margin (NIM) is the difference between the proceeds from borrowers and the interest payed to their lenders.
Ratio 2. Non-interest income (NII) is the sum of the following types of income: fee-based, trading, that coming from fiduciary activities and other non-interest associated one.
Ratio 3. Non-interest expense (NIX) comprises basically three types of expenses: personnel expense, occupancy and other operating expenses.
Ratio 4. Net operating income (NOI) is related to the company’s gross income associated with its properties less the operating expenses.
Ratio 5. Return on assets (ROA) is an indicator of how profitable a company is relative to its total assets. ROA is calculated as the ratio between the company’s total earnings over the year and the company’s total assets.
Ratio 6. Return on equity (ROE) is a measure of the rate of return on the shareholders’ equity of the common stock owners. ROE is estimated as the year’s net income (after preferred stock dividends but before common stock dividends) divided by total equity (excluding preferred shares).
Ratio 7. Efficiency ratio (ER) is a ratio used to measure the efficiency of a company, although not every one of them calculates it in the same way.
Ratio 8. Non current assets (NCA) are those that cannot be easily converted into cash, e.g. real estate, machinery, long-term investments or patents.
Ratio 9. It is the ratio of cash plus US treasury and government obligations to total assets.
Ratio 10. Equity capital (EC) is the capital raised from owners.
Ratio 11. The capital ratio (CR) also known as the leverage ratio is calculated as the Tier 1 capital divided by the average of the total consolidated assets.
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Peña, T., Martínez, S., Abudu, B. (2011). Bankruptcy Prediction: A Comparison of Some Statistical and Machine Learning Techniques. In: Dawid, H., Semmler, W. (eds) Computational Methods in Economic Dynamics. Dynamic Modeling and Econometrics in Economics and Finance, vol 13. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16943-4_6
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