Main question
Can we use bankruptcy models to predict supplier bankruptcies?
But first:
Does the Altman Z-score [still] pick up bankruptcy?
Learning objectives
- Theory:
- Academic research
- Application:
- Predicting bankruptcy over the next year for US manufacturing firms
- Extend to credit downgrades
- Predicting bankruptcy over the next year for US manufacturing firms
- Methodology:
- Logistic regression
- Models from academic research
Where does the model come from?
- Altman 1968, Journal of Finance
- A seminal paper in Finance cited over 15,000 times by other academic papers
Bankruptcy in the US
- Chapter 7
- The company ceases operating and liquidates
- Chapter 11
- For firms intending to reorganize the company to “try to become profitable again” (US SEC)
Common outcomes of bankruptcy
- Cease operations entirely (liquidated)
- In which case the assets are often sold off
- Acquired by another company
- Merge with another company
- Successfully restructure and continue operating as the same firm
- Restructure and operate as a new firm
Z vs credit ratings, 1973-2017
df %>%
filter(!is.na(Z),
!is.na(bankrupt)) %>%
group_by(bankrupt) %>%
mutate(mean_Z=mean(Z,na.rm=T)) %>%
slice(1) %>%
ungroup() %>%
select(bankrupt, mean_Z) %>%
html_df()| bankrupt | mean_Z |
|---|---|
| 0 | 3.939223 |
| 1 | 0.927843 |
Z vs credit ratings, 2000-2017
df %>%
filter(!is.na(Z),
!is.na(bankrupt),
year >= 2000) %>%
group_by(bankrupt) %>%
mutate(mean_Z=mean(Z,na.rm=T)) %>%
slice(1) %>%
ungroup() %>%
select(bankrupt, mean_Z) %>%
html_df()| bankrupt | mean_Z |
|---|---|
| 0 | 3.822281 |
| 1 | 1.417683 |
Types of errors
This type of chart (filled in) is called a Confusion matrix
Type I error (False positive)
We say that the company will go bankrupt, but they don’t
- A Type I error occurs any time we say something is true, yet it is false
- Quantifying type I errors in the data
- False positive rate (FPR)
- The percent of failures misclassified as successes
- Specificity: \(1 - FPR\)
- A.k.a. true negative rate (TNR)
- The percent of failures properly classified
- False positive rate (FPR)
Type 2 error (False negative)
We say that the company will not go bankrupt, yet they do
- A Type II error occurs any time we say something is false, yet it is true
- Quantifying type I errors in the data
- False negative rate (FNR): \(1-Sensitivity\)
- The percent of successes misclassified as failures
- Sensitivity:
- A.k.a. true positive rate (TPR)
- The percent of successes properly classified
- False negative rate (FNR): \(1-Sensitivity\)
Useful equations
Let’s plot TPR and FPR out
- Two ways to plot it out:
ROC curves
- The previous graph is called a ROC curve, or receiver operator characteristic curve
- The higher up and left the curve is, the better the logistic regression fits.
- Neat properties:
- The area under a perfect model is always 1
- The area under random chance is always 0.5
- This is the straight line on the graph
ROC AUC simplest interpretation
AUC is the probability that our model assigns a higher estimated probability to a randomly selected 1 than to a randomly selected 0.
Where does the model come from?
- Merton 1974, Journal of Finance
- Another seminal paper in finance, cited by over 12,000 other academic papers
- About Merton
Model specification
\[ DD = \frac{\log(V_A / D) + (r-\frac{1}{2}\sigma_A^2)(T-t)}{\sigma_A \sqrt(T-t)} \]
- \(V_A\): Value of assets
- Market based
- \(D\): Value of liabilities
- From balance sheet
- \(r\): The risk free rate
- \(\sigma_A\): Volatility of assets
- Use daily stock return volatility, annualized
- Annualized means multiply by \(\sqrt{253}\)
- Use daily stock return volatility, annualized
- \(T-t\): Time horizon
Who uses it?
- Moody’s KMV is derived from the Merton model
- Common platform for analyzing risk in financial services
- More information
DD vs credit ratings, 1973-2017
df %>%
filter(!is.na(DD),
!is.na(bankrupt)) %>%
group_by(bankrupt) %>%
mutate(mean_DD=mean(DD, na.rm=T),
prob_default =
pnorm(-1 * mean_DD)) %>%
slice(1) %>%
ungroup() %>%
select(bankrupt, mean_DD,
prob_default) %>%
html_df()| bankrupt | mean_DD | prob_default |
|---|---|---|
| 0 | 0.6096854 | 0.2710351 |
| 1 | -2.4445081 | 0.9927475 |
DD vs credit ratings, 2000-2017
df %>%
filter(!is.na(DD),
!is.na(bankrupt),
year >= 2000) %>%
group_by(bankrupt) %>%
mutate(mean_DD=mean(DD, na.rm=T),
prob_default =
pnorm(-1 * mean_DD)) %>%
slice(1) %>%
ungroup() %>%
select(bankrupt, mean_DD,
prob_default) %>%
html_df()| bankrupt | mean_DD | prob_default |
|---|---|---|
| 0 | 0.8379932 | 0.2010172 |
| 1 | -4.3001844 | 0.9999915 |
ROC Curves
dfDD <- df %>% filter(!is.na(DD), !is.na(bankrupt))
pred_DD <- predict(fit_DD, dfDD, type="response")
ROCpred_DD <- prediction(as.numeric(pred_DD), as.numeric(dfDD$bankrupt))
ROCperf_DD <- performance(ROCpred_DD, 'tpr','fpr')
df_ROC_DD <- data.frame(FalsePositive=c(ROCperf_DD@x.values[[1]]),
TruePositive=c(ROCperf_DD@y.values[[1]]))
ggplot() +
geom_line(data=df_ROC_DD, aes(x=FalsePositive, y=TruePositive, color="DD")) +
geom_line(data=df_ROC_Z, aes(x=FP, y=TP, color="Z")) +
geom_abline(slope=1)
ROC Performance on this task
## Z DD
## 0.6465042 0.5847885Out of sample ROC performance
## Z DD
## 0.8134671 0.7420213ROC Performance on this task
## Combined Z DD
## 0.8151596 0.8134671 0.7420213