Econometric Default Modeling using Linear Discriminant Analysis

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Research Presentation I made for Summit Consulting giving a high level overview of Linear Discriminant Analysis, with application in Default Modeling (Altman's Z-score)

Data & Analytics

Altman's Z-score: a
Precursor to Modern
Default Modeling
Vivek Jha
July 25, 2014

Models through the years
Some popular modern models:
1. Merton Risk Model (D-D model)
2. Logistic Regression
3. Survival Analysis
4Jha

Linear Discriminant Analysis (LDA)
• LDA is a statistical technique used to classify an observation into 1 of
several a priori categorical groups given characteristics vector.
• Common assumptions: X1,…,Xn are normally distributed,
homoscedasticity, identical class covariances
Procedure:
1. Establish group classifications.
2. Collect data for objects in groups.
3. Discriminant coefficient vector determined by “best” maximizing
discrimination between groups.
8Jha

Results 2 Years prior to Bankruptcy
12Jha

Long-Range Predictive Accuracy
13Jha
20406080
100
CorrectClassificationofBankruptSample(%)
1 2 3 4 5
Years until Bankruptcy
Predictive Power of Altman Z-Score

Robustness through the ages
 Original model surveyed only public manufacturing
firms.
 Subsequent models estimated coefficient vectors and
new characteristic vectors for private/non-
manufacturing firms as well (Z’ and Z” respectively).
 From 1968-1999 model was approximately 80-90%
accurate in predicting bankruptcy 1 year before
event.
 Type II error was approximately 15-20%.
14Jha

Disadvantages
While seemingly effective, Altman’s Z-score has its downsides:
1. Not effective for financial firms.
2. Not significant after 2 years.
3. Financial ratio analysis often fails normality assumption.
4. Cut-offs for groups may alter within a particular industry.
16Jha

Final Remarks
 Altman’s Z-score provides a simple
model to judge financial health.
 Great for an initial guess!
 Popularized discriminant analysis in
the business field.
 Sparked insight into more powerful
statistical financial tools.
17Jha

References
1. Altman, E. I. Financial Ratios, Discriminant Analysis and the Prediction of
Corporate Bankruptcy. The Journal of Finance, 23, 589-609.
2. Altman, E. PREDICTING FINANCIAL DISTRESS OF COMPANIES:
REVISITING THE Z-SCORE AND ZETA® MODELS . Journal of Finance, 578-
585.
3. Burns, W. (2003). Discriminant Analysis. Applied Statistical Methods ().
4. Waide, J. (Director) (2006, January 25). Discriminant Analysis. Lecture.
Lecture conducted from , Innsbruck.
18Jha

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Over the past several years, financial analysts have been contributing significantly to society in the field of predicting bankruptcy. Corporate managers spend a lot of time understanding and changing policies to avoid bankruptcy, especially after the global meltdown in the year 2008. Post Covid-19 there is a growing interest in the corporate world to understand and assess the implications and fallout in the aftermath of global business disruptions. Serious issues arise when a company goes bankrupt, it hampers the interest of all stakeholders including investors and promoters. It is imperative to check and review the financial performance of a business regularly to take prompt actions before the occurrence of any unforeseen events. Bankruptcy of companies can be predicted based on ratio analysis; proven by studies conducted on several such cases. A case in point is Altman’s Z score. To achieve this study Altman’s Z score model is applied and concluded that the sample companies are Healthy and stable for the coming two to three years. For this purpose, researchers have taken 10 listed unicorn startup companies in India from the year 2019 to 2023.

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Econometric Default Modeling using Linear Discriminant Analysis

1. Altman's Z-score: a Precursor to Modern Default Modeling Vivek Jha July 25, 2014

2. Presentation Overview 2Jha

3. Default Modeling 3Jha

4. Models through the years Some popular modern models: 1. Merton Risk Model (D-D model) 2. Logistic Regression 3. Survival Analysis 4Jha

5. Presentation Overview 5Jha

6. Ratio Analysis Review 6Jha

7. Altman’s Original Model (1968) 7Jha

8. Linear Discriminant Analysis (LDA) • LDA is a statistical technique used to classify an observation into 1 of several a priori categorical groups given characteristics vector. • Common assumptions: X1,…,Xn are normally distributed, homoscedasticity, identical class covariances Procedure: 1. Establish group classifications. 2. Collect data for objects in groups. 3. Discriminant coefficient vector determined by “best” maximizing discrimination between groups. 8Jha

9. Discriminant Function Strength 9Jha

10. Discriminant Function Properties 10Jha

11. Presentation Overview 11Jha

12. Results 2 Years prior to Bankruptcy 12Jha

13. Long-Range Predictive Accuracy 13Jha 20406080 100 CorrectClassificationofBankruptSample(%) 1 2 3 4 5 Years until Bankruptcy Predictive Power of Altman Z-Score

14. Robustness through the ages  Original model surveyed only public manufacturing firms.  Subsequent models estimated coefficient vectors and new characteristic vectors for private/non- manufacturing firms as well (Z’ and Z” respectively).  From 1968-1999 model was approximately 80-90% accurate in predicting bankruptcy 1 year before event.  Type II error was approximately 15-20%. 14Jha

15. Presentation Overview 15Jha

16. Disadvantages While seemingly effective, Altman’s Z-score has its downsides: 1. Not effective for financial firms. 2. Not significant after 2 years. 3. Financial ratio analysis often fails normality assumption. 4. Cut-offs for groups may alter within a particular industry. 16Jha

17. Final Remarks  Altman’s Z-score provides a simple model to judge financial health.  Great for an initial guess!  Popularized discriminant analysis in the business field.  Sparked insight into more powerful statistical financial tools. 17Jha

18. References 1. Altman, E. I. Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy. The Journal of Finance, 23, 589-609. 2. Altman, E. PREDICTING FINANCIAL DISTRESS OF COMPANIES: REVISITING THE Z-SCORE AND ZETA® MODELS . Journal of Finance, 578- 585. 3. Burns, W. (2003). Discriminant Analysis. Applied Statistical Methods (). 4. Waide, J. (Director) (2006, January 25). Discriminant Analysis. Lecture. Lecture conducted from , Innsbruck. 18Jha

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