TASK 4 - Bankruptcy data

The data set contains profitability, leverage, and bankruptcy indicators for 84 US companies, 42 of which filed for Chapter 11 bankruptcy in 2001–2002 after the stock market crash in 2000. The bankrupt companies were matched with 42 surviving companies with the closest capitalisation and the same US industry classification codes.

The information for each company was collected from the annual reports for 1998–1999, i.e. 3 years prior to the defaults of the bankrupt companies. The data set contains profitability and leverage ratios calculated as the ratio of net income (NI) and total assets (TA) and the ratio of total liabilities (TL) and total assets (TA). Profitability and leverage ratios are considered as numerical variables, the bankruptcy status in 2001 is a categorical variable with levels 1 (the company filed for Chapter 11) and -1 (the company survived the market crash).

We want to test, whether there is a statistical evidence supporting a claim that the leverage and profitability ratios are different for companies that went bankrupt in the market crash and the companies that survived.

Let us assume that the elements of random vectors (with elements leverage and profitability ratio) are normally distributed.

We want to test the hypothesis \[ H_0: \mu_X = \mu_Y .\] For that we use the Hotteling’s \(T^2\) test

library(DescTools)
with(bankruptcy,
  HotellingsT2Test(cbind(lev, prof) ~ Bankruptcy), conf.level = 0.95, var.equal=FALSE)

## 
##  Hotelling's two sample T2-test
## 
## data:  cbind(lev, prof) by Bankruptcy
## T.2 = 8.7378, df1 = 2, df2 = 81, p-value = 0.0003663
## alternative hypothesis: true location difference is not equal to c(0,0)

As we can see, the test rejected the null hypothesis. There is therefore a statistically significant evidence to support the claim that the leverage and profitability ratios for bankrupt and survival companies were different already 2 years prior to the market crash.

We can also look at confidence intervals. As we can see, from the duality of confidence intervals and hypotheses testing we would also reject the null hypothesis. There appears to be a difference in profitability ratio with the surving companies having on average the profitability ratio bigger by 0.15 than the bankrupt companies.

	Lower Boundary	Upper Boundary	Mean Estimate
prof	0.0962078	0.2083351	0.1522714
lev	-0.1933795	0.0265612	-0.0834091