American Institute of Mathematical Sciences

Advanced
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

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 & 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.  doi: 10.2307/2978933.  Google Scholar

[2]

E. I. Altman, J. Hartzell and M. Peck, Discriminant analysis and the Prediction of Corporate Bankruptcy,, Reprinted in, (1997).   Google Scholar

[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).   Google Scholar

[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.  doi: 10.1016/j.ejor.2004.02.018.  Google Scholar

[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.  doi: 10.1007/s10290-006-0077-5.  Google Scholar

[6]

M. A. Aziz and H. A. Dar, Predicting Corporate Bankruptcy: Where we stand?,, Corporate Governance, 6 (2006), 18.  doi: 10.1108/14720700610649436.  Google Scholar

[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.   Google Scholar

[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.   Google Scholar

[9]

P. Barnes, Methodological implications of non-normality distributed financial ratios,, Journal of Business, 9 (1982), 51.  doi: 10.1111/j.1468-5957.1982.tb00972.x.  Google Scholar

[10]

W. Beaver, Financial ratios for predictors of failure,, Journal of Accounting Research, 3 (1967), 71.   Google Scholar

[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.  doi: 10.1016/j.ejor.2004.03.023.  Google Scholar

[12]

A. Charitu, E. Neophytou and C. Charalambous, Predicting corporate failure: Empirical evidence of the UK,, European Accounting Review, 13 (2004), 465.  doi: 10.1080/0963818042000216811.  Google Scholar

[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.   Google Scholar

[14]

E. Deakin, On the nature of distribution of financial accounting ratios: Some empirical evidence,, The Accounting Review, 51 (1976), 90.   Google Scholar

[15]

L. Ding, X. Liu and Y. Xu, Competitive risk management for online bahncard problem,, Journal of Industrial and Management Optimization, 6 (2010), 1.  doi: 10.3934/jimo.2010.6.1.  Google Scholar

[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.   Google Scholar

[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.  doi: 10.1111/j.1468-5957.1990.tb00547.x.  Google Scholar

[18]

G. Foster, "Financial Statement Analysis,", Second edition, (1986).   Google Scholar

[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.   Google Scholar

[20]

J. M. Griffin and M. L. Lemmon, Book-to-market equity, distress risk, and stock returns,, Journal of Finance, 57 (2002), 2317.  doi: 10.1111/1540-6261.00497.  Google Scholar

[21]

Z. Gu, Analyzing bankruptcy in restaurant industry: a multiple discriminant model,, Hospitality Management, 21 (2002), 25.  doi: 10.1016/S0278-4319(01)00013-5.  Google Scholar

[22]

S. B. Jagdeep and L. A. Weiss, "Corporate Bankruptcy: Economic and Legal Perspectives,", Cambridge University Press, (1996).   Google Scholar

[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.  doi: 10.1111/1467-646X.00061.  Google Scholar

[24]

G. D. Kane, F. Richardson and N. Meade, "Rank Transformations and the Prediction of Corporate Failure,", Working paper, (1996).   Google Scholar

[25]

K. Keasey and R. Watson, Financial distress models: A review of their usefulness,, British Journal of Management, 2 (1991), 89.  doi: 10.1111/j.1467-8551.1991.tb00019.x.  Google Scholar

[26]

D. G. Kleinbaum, L. L. Kupper and K. E. Muller, "Applied Regression Analysis and Other Multivariate Methods,", Second edition, (1988).   Google Scholar

[27]

J. R. Koza, "Genetic Programming: On the Programming of Computers by Means of Natural Selection,", MIT Press, (1992).   Google Scholar

[28]

Y. Landskroner, D. Ruthenberg and D. Pearl, "Market to Book Value Ratio in Banking: The Israeli Case,", Bank of Israel banking, (2006).   Google Scholar

[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.  doi: 10.1111/j.1467-9876.2007.00610.x.  Google Scholar

[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.   Google Scholar

[31]

F. Modigliani and M. Miller, The cost of capital, corporation finance and the theory of investment,, American Economic Review, 48 (1958), 261.   Google Scholar

[32]

J. Ohlson, Financial ratios and the probabilistic prediction of bankruptcy,, Journal of Accounting Research, 18 (1980), 109.  doi: 10.2307/2490395.  Google Scholar

[33]

H. Ooghe, C. Speanjers and P. Vandermoere, "Business Failure Prediction: Simple-Intuitive Models versus Statistical Models,", Working Paper, (2005).   Google Scholar

[34]

H. Ooghe and C. Speanjers, "A Note on Performance Measures for Failure Prediction Models,", Working Paper, (2006).   Google Scholar

[35]

H. Ooghe and E. Verbaere, Some further empirical evidence on predicting private company failure,, Accounting and Business Research, 18 (1985), 57.   Google Scholar

[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.  doi: 10.1016/j.asoc.2007.02.001.  Google Scholar

[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.  doi: 10.1016/j.ejor.2006.08.043.  Google Scholar

[38]

T. Shumway, Forecasting bankruptcy more accurately: A simple hazard model,, Journal of Business, 74 (2001), 101.  doi: 10.1086/209665.  Google Scholar

[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.  doi: 10.1111/j.1468-5957.1987.tb00108.x.  Google Scholar

[40]

L. Sun and P. P. Shenoy, Using Bayesian networks for bankruptcy prediction: Some methodological issues,, European Journal of Operational Research, 180 (2007), 738.  doi: 10.1016/j.ejor.2006.04.019.  Google Scholar

[41]

M. Tippet, An introduced theory of financial ratios,, Accounting and Business Research, 21 (1990), 77.   Google Scholar

[42]

Ö. Uǧur and W. Weber, Optimization and dynamics of gene-enviroment networks with intervals,, Journal of Industrial and Management Optimization, 3 (2007), 357.   Google Scholar

[43]

C. J. Watson, Multivariate distribution properties, outliers and transformation of financial ratios,, Accounting Review, 65 (1990), 682.   Google Scholar

[44]

C. V. Zavgren, The prediction of corporate failure: The state of the art,, Journal of Accounting Literature, 2 (1983), 1.   Google Scholar

[45]

M. E Zmijewski, Methodological issues related to the estimation of financial distress prediction models,, Journal of Accounting Research, 22 (1984), 59.   Google Scholar

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.  doi: 10.2307/2978933.  Google Scholar

[2]

E. I. Altman, J. Hartzell and M. Peck, Discriminant analysis and the Prediction of Corporate Bankruptcy,, Reprinted in, (1997).   Google Scholar

[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).   Google Scholar

[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.  doi: 10.1016/j.ejor.2004.02.018.  Google Scholar

[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.  doi: 10.1007/s10290-006-0077-5.  Google Scholar

[6]

M. A. Aziz and H. A. Dar, Predicting Corporate Bankruptcy: Where we stand?,, Corporate Governance, 6 (2006), 18.  doi: 10.1108/14720700610649436.  Google Scholar

[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.   Google Scholar

[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.   Google Scholar

[9]

P. Barnes, Methodological implications of non-normality distributed financial ratios,, Journal of Business, 9 (1982), 51.  doi: 10.1111/j.1468-5957.1982.tb00972.x.  Google Scholar

[10]

W. Beaver, Financial ratios for predictors of failure,, Journal of Accounting Research, 3 (1967), 71.   Google Scholar

[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.  doi: 10.1016/j.ejor.2004.03.023.  Google Scholar

[12]

A. Charitu, E. Neophytou and C. Charalambous, Predicting corporate failure: Empirical evidence of the UK,, European Accounting Review, 13 (2004), 465.  doi: 10.1080/0963818042000216811.  Google Scholar

[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.   Google Scholar

[14]

E. Deakin, On the nature of distribution of financial accounting ratios: Some empirical evidence,, The Accounting Review, 51 (1976), 90.   Google Scholar

[15]

L. Ding, X. Liu and Y. Xu, Competitive risk management for online bahncard problem,, Journal of Industrial and Management Optimization, 6 (2010), 1.  doi: 10.3934/jimo.2010.6.1.  Google Scholar

[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.   Google Scholar

[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.  doi: 10.1111/j.1468-5957.1990.tb00547.x.  Google Scholar

[18]

G. Foster, "Financial Statement Analysis,", Second edition, (1986).   Google Scholar

[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.   Google Scholar

[20]

J. M. Griffin and M. L. Lemmon, Book-to-market equity, distress risk, and stock returns,, Journal of Finance, 57 (2002), 2317.  doi: 10.1111/1540-6261.00497.  Google Scholar

[21]

Z. Gu, Analyzing bankruptcy in restaurant industry: a multiple discriminant model,, Hospitality Management, 21 (2002), 25.  doi: 10.1016/S0278-4319(01)00013-5.  Google Scholar

[22]

S. B. Jagdeep and L. A. Weiss, "Corporate Bankruptcy: Economic and Legal Perspectives,", Cambridge University Press, (1996).   Google Scholar

[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.  doi: 10.1111/1467-646X.00061.  Google Scholar

[24]

G. D. Kane, F. Richardson and N. Meade, "Rank Transformations and the Prediction of Corporate Failure,", Working paper, (1996).   Google Scholar

[25]

K. Keasey and R. Watson, Financial distress models: A review of their usefulness,, British Journal of Management, 2 (1991), 89.  doi: 10.1111/j.1467-8551.1991.tb00019.x.  Google Scholar

[26]

D. G. Kleinbaum, L. L. Kupper and K. E. Muller, "Applied Regression Analysis and Other Multivariate Methods,", Second edition, (1988).   Google Scholar

[27]

J. R. Koza, "Genetic Programming: On the Programming of Computers by Means of Natural Selection,", MIT Press, (1992).   Google Scholar

[28]

Y. Landskroner, D. Ruthenberg and D. Pearl, "Market to Book Value Ratio in Banking: The Israeli Case,", Bank of Israel banking, (2006).   Google Scholar

[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.  doi: 10.1111/j.1467-9876.2007.00610.x.  Google Scholar

[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.   Google Scholar

[31]

F. Modigliani and M. Miller, The cost of capital, corporation finance and the theory of investment,, American Economic Review, 48 (1958), 261.   Google Scholar

[32]

J. Ohlson, Financial ratios and the probabilistic prediction of bankruptcy,, Journal of Accounting Research, 18 (1980), 109.  doi: 10.2307/2490395.  Google Scholar

[33]

H. Ooghe, C. Speanjers and P. Vandermoere, "Business Failure Prediction: Simple-Intuitive Models versus Statistical Models,", Working Paper, (2005).   Google Scholar

[34]

H. Ooghe and C. Speanjers, "A Note on Performance Measures for Failure Prediction Models,", Working Paper, (2006).   Google Scholar

[35]

H. Ooghe and E. Verbaere, Some further empirical evidence on predicting private company failure,, Accounting and Business Research, 18 (1985), 57.   Google Scholar

[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.  doi: 10.1016/j.asoc.2007.02.001.  Google Scholar

[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.  doi: 10.1016/j.ejor.2006.08.043.  Google Scholar

[38]

T. Shumway, Forecasting bankruptcy more accurately: A simple hazard model,, Journal of Business, 74 (2001), 101.  doi: 10.1086/209665.  Google Scholar

[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.  doi: 10.1111/j.1468-5957.1987.tb00108.x.  Google Scholar

[40]

L. Sun and P. P. Shenoy, Using Bayesian networks for bankruptcy prediction: Some methodological issues,, European Journal of Operational Research, 180 (2007), 738.  doi: 10.1016/j.ejor.2006.04.019.  Google Scholar

[41]

M. Tippet, An introduced theory of financial ratios,, Accounting and Business Research, 21 (1990), 77.   Google Scholar

[42]

Ö. Uǧur and W. Weber, Optimization and dynamics of gene-enviroment networks with intervals,, Journal of Industrial and Management Optimization, 3 (2007), 357.   Google Scholar

[43]

C. J. Watson, Multivariate distribution properties, outliers and transformation of financial ratios,, Accounting Review, 65 (1990), 682.   Google Scholar

[44]

C. V. Zavgren, The prediction of corporate failure: The state of the art,, Journal of Accounting Literature, 2 (1983), 1.   Google Scholar

[45]

M. E Zmijewski, Methodological issues related to the estimation of financial distress prediction models,, Journal of Accounting Research, 22 (1984), 59.   Google Scholar

[1]

Min Li, Jiahua Zhang, Yifan Xu, Wei Wang. Effects of disruption risk on a supply chain with a risk-averse retailer. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021024
[2]

Cicely K. Macnamara, Mark A. J. Chaplain. Spatio-temporal models of synthetic genetic oscillators. Mathematical Biosciences & Engineering, 2017, 14 (1) : 249-262. doi: 10.3934/mbe.2017016
[3]

Rafael Luís, Sandra Mendonça. A note on global stability in the periodic logistic map. Discrete & Continuous Dynamical Systems - B, 2020, 25 (11) : 4211-4220. doi: 10.3934/dcdsb.2020094
[4]

Jumpei Inoue, Kousuke Kuto. On the unboundedness of the ratio of species and resources for the diffusive logistic equation. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2441-2450. doi: 10.3934/dcdsb.2020186
[5]

Xu Zhang, Xiang Li. Modeling and identification of dynamical system with Genetic Regulation in batch fermentation of glycerol. Numerical Algebra, Control & Optimization, 2015, 5 (4) : 393-403. doi: 10.3934/naco.2015.5.393
[6]

Ardeshir Ahmadi, Hamed Davari-Ardakani. A multistage stochastic programming framework for cardinality constrained portfolio optimization. Numerical Algebra, Control & Optimization, 2017, 7 (3) : 359-377. doi: 10.3934/naco.2017023
[7]

Luke Finlay, Vladimir Gaitsgory, Ivan Lebedev. Linear programming solutions of periodic optimization problems: approximation of the optimal control. Journal of Industrial & Management Optimization, 2007, 3 (2) : 399-413. doi: 10.3934/jimo.2007.3.399
[8]

Reza Lotfi, Yahia Zare Mehrjerdi, Mir Saman Pishvaee, Ahmad Sadeghieh, Gerhard-Wilhelm Weber. A robust optimization model for sustainable and resilient closed-loop supply chain network design considering conditional value at risk. Numerical Algebra, Control & Optimization, 2021, 11 (2) : 221-253. doi: 10.3934/naco.2020023
[9]

Hong Yi, Chunlai Mu, Guangyu Xu, Pan Dai. A blow-up result for the chemotaxis system with nonlinear signal production and logistic source. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2537-2559. doi: 10.3934/dcdsb.2020194

2019 Impact Factor: 1.366

Tools

Metrics

  • PDF downloads (87)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences