Abstract
This paper suggests a Robust Logit method, which extends the conventional logit model by taking outliers into account, to implement forecast of defaulted firms. We employ five validation tests to assess the in-sample and out-of-sample forecast performances, respectively. With respect to in-sample forecasts, our Robust Logit method is substantially superior to the logit method when employing all validation tools. With respect to the out-of-sample forecasts, the superiority of Robust Logit is less pronounced.
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Notes
- 1.
Atkinson uses \(k = +1\) as the number of parameters + 1 as the starting sample size. We do not adopt his suggestion because the small sample size often is full of zeros without one, invalidating the logit model.
- 2.
We could further repeat Step 1 to start different set of observations.
- 3.
We omit X 2 = retained earnings/total assets.
References
Altman, E. I. 1968 “Financial ratios, discriminate analysis and the prediction of corporate bankruptcy.” Journal of Finance 23(4), 589–609.
Altman, E. I. and A. Saunders 1998 “Credit risk measurement: developments over the last 20 years.” Journal of Banking & Finance 21(11–12) 1721–1742.
Atiya, A. 2001 “Bankruptcy prediction for credit risk using neural networks: a survey and new results.” IEEE Transactions on Neural Networks 12(4), 929–935.
Atkinson, A. C. 1985 Plots, transformations, and regression: an introduction to graphical methods of diagnostic regression analysis, Oxford University Press, New York.
Atkinson, A. C. 1994 “Fast very robust methods for the detection of multiple outliers.” Journal of the American Statistical Association 89(428), 1329–1339.
Atkinson, A. C. and T. -C. Cheng 2000. “On robust linear regression with incomplete data.” Computational Statistics & Data Analysis 33(4), 361–380.
Atkinson, A. C. and M. Riani 2001 “Regression diagnostics for binomial data from the forward search.” The Statistician 50(1), 63–78.
Atkinson, A. C. and M. Riani 2006 “Distribution theory and simulations for tests of outliers in regression.” Journal of Computational Graphical Statistics 15(2) 460–476.
Barrett, B. E. and J. B. Gray 1997 “Leverage, residual, and interaction diagnostics for subsets of cases in least squares regression.” Computational Statistics and Data Analysis 26(1) 39–52.
Cook, R. D. and S. Weisberg. 1982. Residuals and influence in regression, Chapman & Hall/CRC, London.
Dimitras, A. I., S. H. Zanakis and C. Zopoundis 1996 “A survey of business failures with an emphasis on prediction methods and industrial application.” European Journal of Operation Research 90(3), 487–513.
Doumpos, M. and C. Zopounidis 2002. “Multi-criteria classification and sorting methods: a literature review.” European Journal of Operational Research 138(2), 229–246.
Doumpos, M., K. Kosmidou, G. Baourakis and C. Zopounidis 2002 “Credit risk assessment using a multicriteria hierarchical discrimination approach: a comparative analysis.” European Journal of Operational Research 138(2), 392–412.
Flores, E and J. Garrido 2001 “Robust logistic regression for insurance risk classification.” Business Economics Universidad Carlos III, Departamento de Economía de la Empresa Working Papers wb016413.
Haslett, J. 1999. “A simple derivation of deletion diagnostic results for the general linear model with correlated errors.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 61(3), 603–609.
Lennox, C 1999 “Identifying failing companies: a reevaluation of the logit, probit and DA approaches.” Journal of Economics and Business 51(4), 347–364.
Levine, R. and S. Zervos 1998 “Stock markets, banks, and growth.” American Economic Review 88(3), 537–558.
Ohlson J. T. 1980 “Financial ratios and the probabilistic prediction of bankruptcy.” Journal of Accounting Research 18(1), 109–131.
Piramuthu, S. 1999 “Financial credit-risk evaluation with neural and neurofuzzy systems.” European Journal of Operational Research 112(2) 310–321.
Riani, M. and A. Atkinson 2007 “Fast calibrations of the forward search for testing multiple outliers in regression.” Advances in Data Analysis and Classification 1(2) 123–141.
Rousseeuw P. J. 1983 “Regression techniques with high breakdown point.” The Institute of Mathematical Statistics Bulletin 12, 155.
Rousseeuw, P. J. 1984 “Least median of squares regression.” Journal of the American Statistical Association 79(388), 871–880.
Rousseeuw, P. J. and A. Christmann 2003 “Robustness against separation and outliers in logistic regression.” Computational Statistics & Data Analysis 43(3) 315–332.
Rousseeuw P. J. and V. J. Yohai 1984 “Robust regression by means of S-estimators,” in Robust and nonlinear time series analysis, Vol. 26, W. H. Franke and R. D. Martin (Eds.). Springer, New York, pp. 256–272.
Sobehart, J. R. and S. C. Keenan 2004 “Performance evaluation for credit spread and default risk models,” in Credit risk: models and management Second Edition, D. Shimko (Ed.). Risk Books London, pp. 275–305.
Sobehart, J. R., S. C. Keenan and R. M. Stein 2000 “Rating methodology: benchmarking quantitative default risk models: a validation methodology.” Moody’s Investors Service, Global Credit Research, New York.
Stein, R. M. 2002 “Benchmarking default prediction models: pitfall and remedies in model validation.” Moody’s KMV, Technical Report, No. 030124.
Westgaard, S and N. Wijst 2001 “Default probabilities in a corporate bank portfolio: a logistic model approach.” European Journal of Operational Research, 135(2), 338–349.
Wu, C. and X. M. Wang 2000 “A neural network approach for analyzing small business lending decisions.” Review of Quantitative Finance and Accounting, 15(3), 259–276.
Zhu A. M. Ash and R. Pollin 2002 “Stock market liquidity and economic growth: a critical appraisal of the Levine/Zervos model.” International Review of Applied Economics 18(1), 1–8.
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Shen, CH., Chen, YK., Huang, BY. (2010). The Prediction of Default with Outliers: Robust Logistic Regression. In: Lee, CF., Lee, A.C., Lee, J. (eds) Handbook of Quantitative Finance and Risk Management. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-77117-5_62
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