Geometric approach to static and dynamic measurements of risk, bankruptcy and market ranking

This thesis presents two new geometric techniques for empirical analysis of financial data with empirical application on bankruptcy risk prediction. Within these frameworks, we propose the use of new ratio representations (index), the Risk Box measure (RB) and the Dynamic Risk Space (DRS). We also demonstrate the application of these geometric approaches for variable transformation and data visualization at different stages of corporate bankruptcy prediction models based on financial balance sheet. The different stages involved are the selection of variables (predictors), accuracy of each estimation model and the representation of each model for the transformed and common ratios. We provide evidence of the extent to which changes in values of this index are associated with changes in each axis values and how this may alter our economic interpretation of the patterns and direction of risk components. Results of Multiple Discriminant Analysis (MDA), Logistic Analysis (LA) and Genetic Programming (GP) and Logistic Robust statistics are obtained and compared as different classification models. Empirical results show that these classifiers with common ratio are outperformed by the transformed ratios. The Risk Box (RB)and Dynamic Risk Space (DRS) methodologies would be a general methodological guideline associated with financial data, including solving some methodological problems concerning financial ratios such as non-proportion,non-symmetric, non-scaled as illustrated in this thesis for bankruptcy prediction. In this research, the first geometric methodology for financial risk measurement is developed for financial concepts, focusing on theoretical bases rather than isolated facts of financial risk management. Subsequently, this study provides the first graphical financial risk ranking software, named as Dynamic Geometric Risk Space Software (DGRSS). This software provides visualization of risk factors and market ranking. It is ideal for public and private investors, banks, market analysts, companies and stock markets and compatible with any country/sector dataset based on DRS method. Lastly in this research, the Logistic Robust Regression is applied to bankruptcy data for the first time to handle outliers and to obtain more accurate predictions.

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