A new dynamic geometric approach for empirical analysis of financial ratios and bankruptcy

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October 2011, 7(4): 947-965. doi: 10.3934/jimo.2011.7.947

A new dynamic geometric approach for empirical analysis of financial ratios and bankruptcy

Alireza Bahiraie ^1, , A.K.M. Azhar ^2, and Noor Akma Ibrahim ^3,

1.	Institute of Mathematical Sciences, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Malaysia
2.	Graduate School of Management, University Putra Malaysia, 43400 Serdang, Selangor, Malaysia
3.	Institute for Mathematical Research, University Putra Malaysia, 43400 Serdang, Selangor, Malaysia

Received April 2009 Revised July 2011 Published August 2011

Abstract
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This paper presents a complementary technique for the empirical analysis of financial ratios and bankruptcy risk using financial ratios. Within this new framework, we propose the use of a new measure of risk, the Dynamic Risk Space (DRS) measure. We provide evidence of the extent to which changes in values for this index are associated with changes in each axis's values and how this may alter our economic interpretation of changes in patterns and directions. In addition, this model tends to be generally useful for predicting financial distress and bankruptcy. This method would be a general methodological guideline associated with financial data, solving some methodological problems concerning financial ratios such as non-proportionality, non-asymmetry and non-scaled. To test the procedure, Multiple Discriminant Analysis (MDA), Logistic Analysis (LA) and Genetic Programming (GP) are employed to compare results by common and modified ratios for bankruptcy prediction. Classification methods outperformed using the DRS approach.

Keywords: logistic regression, Bankruptcy, genetic programming., Finance, Risk Box.

Mathematics Subject Classification: Primary: 90B50 Secondary: 91B30, 91G40, 91B0.

Citation: Alireza Bahiraie, A.K.M. Azhar, Noor Akma Ibrahim. A new dynamic geometric approach for empirical analysis of financial ratios and bankruptcy. Journal of Industrial and Management Optimization, 2011, 7 (4) : 947-965. doi: 10.3934/jimo.2011.7.947

References:

[1]	E. I. Altman, Financial ratios, Discriminant analysis and the Prediction of Corporate Bankruptcy, The Journal of Finance, 23 (1967), 589-609. doi: 10.2307/2978933.
[2]	E. I. Altman, J. Hartzell and M. Peck, Discriminant analysis and the Prediction of Corporate Bankruptcy, Reprinted in "Emerging Market Capital Flows" (ed. R. Levich), Kluwer Publishing, Amsterdam, 1997.
[3]	E. I. Altman and E. Hotchkiss, "Corporate Financial Distress and Bankruptcy: Predict and Avoid Bankruptcy, Analyze and Invest in Distressed Debt," John Wiley and Sons, 2006.
[4]	J. D. Andres, M. Landajo and P. Lorca, Forecasting business profitability by using classification techniques: A comparative analysis based on a Spanish case, European Journal of Operational Research, 167 (2005), 518-542. doi: 10.1016/j.ejor.2004.02.018.
[5]	A. K. M. Azhar and Robert J. R. Elliott, On the Measurement of Product Quality in Intra industry Trade, Review of World Economics, 142 (2006), 476-495. doi: 10.1007/s10290-006-0077-5.
[6]	M. A. Aziz and H. A. Dar, Predicting Corporate Bankruptcy: Where we stand?, Corporate Governance, 6 (2006) 18-33. doi: 10.1108/14720700610649436.
[7]	A. Bahiraie, N. A. Ibrahim, A. K. M Azhar and M. Ismail, Robust Logistic regression to static geometric representation of ratios, Journal of Mathematics and Statistics, 5 (2009), 226-233.
[8]	A. Bahiraie, N. A. Ibrahim, M. Ismail and A. K. M Azhar, Financial ratios: A new geometric transformation, International Research Journal of Finance and Economics, 20 (2008), 164-171.
[9]	P. Barnes, Methodological implications of non-normality distributed financial ratios, Journal of Business, Finance and Accounting, 9 (1982), 51-62. doi: 10.1111/j.1468-5957.1982.tb00972.x.
[10]	W. Beaver, Financial ratios for predictors of failure, Journal of Accounting Research, 3 (1967), 71-111.
[11]	S. Canbas, A. Cabuk and S. B. Kilic, Prediction of commercial bank failure via multivariate statistical analysis of financial structures: The Turkish case, European Journal of Operational Research, 166 (2005), 528-546. doi: 10.1016/j.ejor.2004.03.023.
[12]	A. Charitu, E. Neophytou and C. Charalambous, Predicting corporate failure: Empirical evidence of the UK, European Accounting Review, 13 (2004), 465-497. doi: 10.1080/0963818042000216811.
[13]	X. Cui, X. Sun and D. Sha, An empirical study on discrete optimization for portfolio selection, Journal of Industrial and Management Optimization, 5 (2009), 33-46.
[14]	E. Deakin, On the nature of distribution of financial accounting ratios: Some empirical evidence, The Accounting Review, 51 (1976), 90-97.
[15]	L. Ding, X. Liu and Y. Xu, Competitive risk management for online bahncard problem, Journal of Industrial and Management Optimization, 6 (2010), 1-14. doi: 10.3934/jimo.2010.6.1.
[16]	H. Etemadi, A. A. Rostamy and H. Farajzadeh, A genetic programming model for bankruptcy prediction: Empirical evidence from Iran, Expert Systems with Applications, 6 (2008), 3199-3207.
[17]	M. Ezzamel and C. Mar-Molinero, The distributional properties of financial ratios in UK manufacturing companies, Journal of Business Finance and Accounting, 17 (1990), 1-29. doi: 10.1111/j.1468-5957.1990.tb00547.x.
[18]	G. Foster, "Financial Statement Analysis," Second edition, Prentice-Hall, Englewood Cliffs, NJ, 1986.
[19]	J. S. Grice and M. T. Dugan, The limitations of bankruptcy prediction models: Some cautions for the researcher, Review of Quantitative Finance and Accounting, 17 (2001), 151-166.
[20]	J. M. Griffin and M. L. Lemmon, Book-to-market equity, distress risk, and stock returns, Journal of Finance, 57 (2002), 2317-2336. doi: 10.1111/1540-6261.00497.
[21]	Z. Gu, Analyzing bankruptcy in restaurant industry: a multiple discriminant model, Hospitality Management, 21 (2002), 25-42. doi: 10.1016/S0278-4319(01)00013-5.
[22]	S. B. Jagdeep and L. A. Weiss, "Corporate Bankruptcy: Economic and Legal Perspectives," Cambridge University Press, 1996.
[23]	H. N. Joo and T. Jinn, Bankruptcy prediction: Evidence from korea listed companies during the IMF crisis, Journal of International Financial Management and Accounting, 11 (2000), 178-197. doi: 10.1111/1467-646X.00061.
[24]	G. D. Kane, F. Richardson and N. Meade, "Rank Transformations and the Prediction of Corporate Failure," Working paper, University of Delaware, Newark, DE, 1996.
[25]	K. Keasey and R. Watson, Financial distress models: A review of their usefulness, British Journal of Management, 2 (1991), 89-102. doi: 10.1111/j.1467-8551.1991.tb00019.x.
[26]	D. G. Kleinbaum, L. L. Kupper and K. E. Muller, "Applied Regression Analysis and Other Multivariate Methods," Second edition, The Duxbury Series in Statistics and Decision Sciences. PWS-KENT Publishing Co., Boston, MA, 1988.
[27]	J. R. Koza, "Genetic Programming: On the Programming of Computers by Means of Natural Selection," MIT Press, Cambridge, MA, 1992.
[28]	Y. Landskroner, D. Ruthenberg and D. Pearl, "Market to Book Value Ratio in Banking: The Israeli Case," Bank of Israel banking, Supervision Department, Research Unit, 2006.
[29]	M. Landajo, J. de Andrés and P. Lorca, Measuring firm performance by using linear and non-parametric quantile regressions, Journal of the Royal Statistical Society: Series C (Applied Statistics), 57 (2008), 227-250. doi: 10.1111/j.1467-9876.2007.00610.x.
[30]	S. McLeay and A. Omar, The senility of prediction models to the non-normality of bounded and unbounded financial ratios, British Accounting Review, 23 (2000), 213-230.
[31]	F. Modigliani and M. Miller, The cost of capital, corporation finance and the theory of investment, American Economic Review, 48 (1958), 261-297.
[32]	J. Ohlson, Financial ratios and the probabilistic prediction of bankruptcy, Journal of Accounting Research, 18 (1980), 109-131. doi: 10.2307/2490395.
[33]	H. Ooghe, C. Speanjers and P. Vandermoere, "Business Failure Prediction: Simple-Intuitive Models versus Statistical Models," Working Paper, Vlerick Leuven Gent, 2005.
[34]	H. Ooghe and C. Speanjers, "A Note on Performance Measures for Failure Prediction Models," Working Paper, Faculty of Economics and Business Administration, Ghent University, Belgium, 2006.
[35]	H. Ooghe and E. Verbaere, Some further empirical evidence on predicting private company failure, Accounting and Business Research, 18 (1985), 57-66.
[36]	V. Ravi, H. Kurniawan, P. Nweekok Thai and P. Ravikumar, Soft computing system for bank performance prediction, Applied Soft Computing Journal, 8 (2008), 305-315. doi: 10.1016/j.asoc.2007.02.001.
[37]	P. Ravikumar and V. Ravi, Bankruptcy prediction in banks and firms via statistical and intelligent techniques: A review, European Journal of Operational Research, 180 (2007), 1-28. doi: 10.1016/j.ejor.2006.08.043.
[38]	T. Shumway, Forecasting bankruptcy more accurately: A simple hazard model, Journal of Business, 74 (2001), 101-124. doi: 10.1086/209665.
[39]	S. J. So, Some empirical evidence on the outlier and non-normal distribution of financial ratios, Journal of Business Finance and Accounting, 14 (1987), 483-496. doi: 10.1111/j.1468-5957.1987.tb00108.x.
[40]	L. Sun and P. P. Shenoy, Using Bayesian networks for bankruptcy prediction: Some methodological issues, European Journal of Operational Research, 180 (2007), 738-753. doi: 10.1016/j.ejor.2006.04.019.
[41]	M. Tippet, An introduced theory of financial ratios, Accounting and Business Research, 21 (1990), 77-85.
[42]	Ö. Uǧur and W. Weber, Optimization and dynamics of gene-enviroment networks with intervals, Journal of Industrial and Management Optimization, 3 (2007), 357-379.
[43]	C. J. Watson, Multivariate distribution properties, outliers and transformation of financial ratios, Accounting Review, 65 (1990), 682-695.
[44]	C. V. Zavgren, The prediction of corporate failure: The state of the art, Journal of Accounting Literature, 2 (1983), 1-33.
[45]	M. E Zmijewski, Methodological issues related to the estimation of financial distress prediction models, Journal of Accounting Research, 22 (1984), 59-82.

show all references

References:

[1]	E. I. Altman, Financial ratios, Discriminant analysis and the Prediction of Corporate Bankruptcy, The Journal of Finance, 23 (1967), 589-609. doi: 10.2307/2978933.
[2]	E. I. Altman, J. Hartzell and M. Peck, Discriminant analysis and the Prediction of Corporate Bankruptcy, Reprinted in "Emerging Market Capital Flows" (ed. R. Levich), Kluwer Publishing, Amsterdam, 1997.
[3]	E. I. Altman and E. Hotchkiss, "Corporate Financial Distress and Bankruptcy: Predict and Avoid Bankruptcy, Analyze and Invest in Distressed Debt," John Wiley and Sons, 2006.
[4]	J. D. Andres, M. Landajo and P. Lorca, Forecasting business profitability by using classification techniques: A comparative analysis based on a Spanish case, European Journal of Operational Research, 167 (2005), 518-542. doi: 10.1016/j.ejor.2004.02.018.
[5]	A. K. M. Azhar and Robert J. R. Elliott, On the Measurement of Product Quality in Intra industry Trade, Review of World Economics, 142 (2006), 476-495. doi: 10.1007/s10290-006-0077-5.
[6]	M. A. Aziz and H. A. Dar, Predicting Corporate Bankruptcy: Where we stand?, Corporate Governance, 6 (2006) 18-33. doi: 10.1108/14720700610649436.
[7]	A. Bahiraie, N. A. Ibrahim, A. K. M Azhar and M. Ismail, Robust Logistic regression to static geometric representation of ratios, Journal of Mathematics and Statistics, 5 (2009), 226-233.
[8]	A. Bahiraie, N. A. Ibrahim, M. Ismail and A. K. M Azhar, Financial ratios: A new geometric transformation, International Research Journal of Finance and Economics, 20 (2008), 164-171.
[9]	P. Barnes, Methodological implications of non-normality distributed financial ratios, Journal of Business, Finance and Accounting, 9 (1982), 51-62. doi: 10.1111/j.1468-5957.1982.tb00972.x.
[10]	W. Beaver, Financial ratios for predictors of failure, Journal of Accounting Research, 3 (1967), 71-111.
[11]	S. Canbas, A. Cabuk and S. B. Kilic, Prediction of commercial bank failure via multivariate statistical analysis of financial structures: The Turkish case, European Journal of Operational Research, 166 (2005), 528-546. doi: 10.1016/j.ejor.2004.03.023.
[12]	A. Charitu, E. Neophytou and C. Charalambous, Predicting corporate failure: Empirical evidence of the UK, European Accounting Review, 13 (2004), 465-497. doi: 10.1080/0963818042000216811.
[13]	X. Cui, X. Sun and D. Sha, An empirical study on discrete optimization for portfolio selection, Journal of Industrial and Management Optimization, 5 (2009), 33-46.
[14]	E. Deakin, On the nature of distribution of financial accounting ratios: Some empirical evidence, The Accounting Review, 51 (1976), 90-97.
[15]	L. Ding, X. Liu and Y. Xu, Competitive risk management for online bahncard problem, Journal of Industrial and Management Optimization, 6 (2010), 1-14. doi: 10.3934/jimo.2010.6.1.
[16]	H. Etemadi, A. A. Rostamy and H. Farajzadeh, A genetic programming model for bankruptcy prediction: Empirical evidence from Iran, Expert Systems with Applications, 6 (2008), 3199-3207.
[17]	M. Ezzamel and C. Mar-Molinero, The distributional properties of financial ratios in UK manufacturing companies, Journal of Business Finance and Accounting, 17 (1990), 1-29. doi: 10.1111/j.1468-5957.1990.tb00547.x.
[18]	G. Foster, "Financial Statement Analysis," Second edition, Prentice-Hall, Englewood Cliffs, NJ, 1986.
[19]	J. S. Grice and M. T. Dugan, The limitations of bankruptcy prediction models: Some cautions for the researcher, Review of Quantitative Finance and Accounting, 17 (2001), 151-166.
[20]	J. M. Griffin and M. L. Lemmon, Book-to-market equity, distress risk, and stock returns, Journal of Finance, 57 (2002), 2317-2336. doi: 10.1111/1540-6261.00497.
[21]	Z. Gu, Analyzing bankruptcy in restaurant industry: a multiple discriminant model, Hospitality Management, 21 (2002), 25-42. doi: 10.1016/S0278-4319(01)00013-5.
[22]	S. B. Jagdeep and L. A. Weiss, "Corporate Bankruptcy: Economic and Legal Perspectives," Cambridge University Press, 1996.
[23]	H. N. Joo and T. Jinn, Bankruptcy prediction: Evidence from korea listed companies during the IMF crisis, Journal of International Financial Management and Accounting, 11 (2000), 178-197. doi: 10.1111/1467-646X.00061.
[24]	G. D. Kane, F. Richardson and N. Meade, "Rank Transformations and the Prediction of Corporate Failure," Working paper, University of Delaware, Newark, DE, 1996.
[25]	K. Keasey and R. Watson, Financial distress models: A review of their usefulness, British Journal of Management, 2 (1991), 89-102. doi: 10.1111/j.1467-8551.1991.tb00019.x.
[26]	D. G. Kleinbaum, L. L. Kupper and K. E. Muller, "Applied Regression Analysis and Other Multivariate Methods," Second edition, The Duxbury Series in Statistics and Decision Sciences. PWS-KENT Publishing Co., Boston, MA, 1988.
[27]	J. R. Koza, "Genetic Programming: On the Programming of Computers by Means of Natural Selection," MIT Press, Cambridge, MA, 1992.
[28]	Y. Landskroner, D. Ruthenberg and D. Pearl, "Market to Book Value Ratio in Banking: The Israeli Case," Bank of Israel banking, Supervision Department, Research Unit, 2006.
[29]	M. Landajo, J. de Andrés and P. Lorca, Measuring firm performance by using linear and non-parametric quantile regressions, Journal of the Royal Statistical Society: Series C (Applied Statistics), 57 (2008), 227-250. doi: 10.1111/j.1467-9876.2007.00610.x.
[30]	S. McLeay and A. Omar, The senility of prediction models to the non-normality of bounded and unbounded financial ratios, British Accounting Review, 23 (2000), 213-230.
[31]	F. Modigliani and M. Miller, The cost of capital, corporation finance and the theory of investment, American Economic Review, 48 (1958), 261-297.
[32]	J. Ohlson, Financial ratios and the probabilistic prediction of bankruptcy, Journal of Accounting Research, 18 (1980), 109-131. doi: 10.2307/2490395.
[33]	H. Ooghe, C. Speanjers and P. Vandermoere, "Business Failure Prediction: Simple-Intuitive Models versus Statistical Models," Working Paper, Vlerick Leuven Gent, 2005.
[34]	H. Ooghe and C. Speanjers, "A Note on Performance Measures for Failure Prediction Models," Working Paper, Faculty of Economics and Business Administration, Ghent University, Belgium, 2006.
[35]	H. Ooghe and E. Verbaere, Some further empirical evidence on predicting private company failure, Accounting and Business Research, 18 (1985), 57-66.
[36]	V. Ravi, H. Kurniawan, P. Nweekok Thai and P. Ravikumar, Soft computing system for bank performance prediction, Applied Soft Computing Journal, 8 (2008), 305-315. doi: 10.1016/j.asoc.2007.02.001.
[37]	P. Ravikumar and V. Ravi, Bankruptcy prediction in banks and firms via statistical and intelligent techniques: A review, European Journal of Operational Research, 180 (2007), 1-28. doi: 10.1016/j.ejor.2006.08.043.
[38]	T. Shumway, Forecasting bankruptcy more accurately: A simple hazard model, Journal of Business, 74 (2001), 101-124. doi: 10.1086/209665.
[39]	S. J. So, Some empirical evidence on the outlier and non-normal distribution of financial ratios, Journal of Business Finance and Accounting, 14 (1987), 483-496. doi: 10.1111/j.1468-5957.1987.tb00108.x.
[40]	L. Sun and P. P. Shenoy, Using Bayesian networks for bankruptcy prediction: Some methodological issues, European Journal of Operational Research, 180 (2007), 738-753. doi: 10.1016/j.ejor.2006.04.019.
[41]	M. Tippet, An introduced theory of financial ratios, Accounting and Business Research, 21 (1990), 77-85.
[42]	Ö. Uǧur and W. Weber, Optimization and dynamics of gene-enviroment networks with intervals, Journal of Industrial and Management Optimization, 3 (2007), 357-379.
[43]	C. J. Watson, Multivariate distribution properties, outliers and transformation of financial ratios, Accounting Review, 65 (1990), 682-695.
[44]	C. V. Zavgren, The prediction of corporate failure: The state of the art, Journal of Accounting Literature, 2 (1983), 1-33.
[45]	M. E Zmijewski, Methodological issues related to the estimation of financial distress prediction models, Journal of Accounting Research, 22 (1984), 59-82.

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