Financial analysts specializing in credit markets are often interested in creati

Question

Financial analysts specializing in credit markets are often interested in creating models to predict whether a firm will go bankrupt within some fixed period of time. If there is a good chance that a particular firm will go bankrupt, then the firm will have to pay a very high interest rate on any debt (bonds) that it may issue. In practice, statistical models to predict bankruptcy are fairly difficult to construct. One of the variables that may be useful in distinguishing between firms that go bankrupt and firms that stay solvent is the return on assets (ROA). The accompanying file Bankruptcy.xls (Links to an external site.) contains financial data on 44 firms. Of these 44 firms, 20 firms went bankrupt within 1 year after the data were collected; the other 24 firms remained solvent after 1 year. For this assignment, ignore all financial measures other than ROA. As a first step, unstack the ROA variable (see Data Utilities menu in StatTools) using “Bankrupt” as the code variable (in the menu, set Bankrupt as the “cat” variable and ROA as the “Val”). Now you should have two columns of ROA data in a new worksheet. For the purpose of this exercise we will assume that firms’ ROA is, in general, normally distributed. Construct a 90% confidence interval for the average ROA of firms that remained solvent. Attach the StatTools output as Exhibit A. State the confidence interval in the form: point estimate ± margin of error. Test the hypothesis that the average ROA of firms that went bankrupt is less than -5%. Attach the StatTools output as Exhibit B. State the p-value for this hypothesis test. At the 10% level of significance, is the average ROA of firms that went bankrupt less than -5%? Yes or No

CASH_DEBT ROA CURRENT ASST_SLS BANKRUPT 0.58 0.04 5.06 0.13 No 0.12 0.11 1.14 0.17 Yes -0.23 -0.30 0.33 0.18 Yes 0.48 0.09 1.24 0.18 No 0.16 0.05 2.31 0.20 No 0.07 0.02 1.31 0.25 Yes -0.07 -0.09 1.45 0.26 Yes 0.14 -0.03 0.46 0.26 No 0.15 0.05 1.88 0.27 Yes -0.14 -0.07 0.71 0.28 Yes 0.20 0.08 1.99 0.30 No 0.19 0.05 2.25 0.33 No 0.07 -0.01 1.37 0.34 Yes 0.38 0.11 3.27 0.35 No -0.02 0.02 2.05 0.35 No 0.37 0.11 1.99 0.38 Yes 0.29 0.06 1.84 0.38 No 0.06 0.02 1.01 0.40 Yes -0.07 -0.06 1.37 0.40 Yes 0.22 0.08 2.35 0.40 No -0.08 -0.08 1.51 0.42 Yes -0.14 -0.14 1.42 0.43 Yes 0.56 0.11 4.29 0.44 No -0.45 -0.41 1.09 0.45 Yes 0.47 0.14 2.92 0.45 No -0.33 -0.09 3.01 0.47 No 0.54 0.11 2.33 0.48 No -0.28 -0.27 1.27 0.51 Yes 0.17 0.07 1.80 0.52 No 0.14 0.07 2.61 0.52 No 0.08 0.02 2.01 0.53 No 0.51 0.10 2.49 0.54 No 0.15 0.05 2.17 0.55 No 0.15 0.06 2.23 0.56 No -0.10 -0.01 2.50 0.58 No 0.01 0.00 1.26 0.60 Yes 0.32 0.07 4.24 0.63 No -0.28 -0.23 1.19 0.66 Yes -0.10 -0.09 1.56 0.67 Yes 0.31 0.05 4.45 0.69 No 0.12 0.05 2.52 0.69 No 0.01 0.00 2.15 0.70 Yes 0.04 0.01 1.50 0.71 Yes 0.05 0.03 1.68 0.95 Yes

Explanation / Answer

We shall provide the solution using the open source statistical package R

The complete R snippet is as follows

####

# read the data into R dataframe
data.df<- read.csv("C:\Users\586645\Downloads\Chegg oa.csv",header=TRUE)
str(data.df)

bankrupt <- data.df[which(data.df$BANKRUPT=="Yes"),]

## 90% confidence interval of mean , we use z = 1.645 for alpha = 0.1

mean(bankrupt$ROA) + 1.645*sd(bankrupt$ROA) # upper
mean(bankrupt$ROA) - 1.645*sd(bankrupt$ROA) # lower

# perform the test
t.test(bankrupt$ROA,mu=-0.05,alternative = "less",conf.level = 0.95)

t.test(bankrupt$ROA,mu=-0.05,alternative = "less",conf.level = 0.90)

###

The results are

> mean(bankrupt$ROA) + 1.645*sd(bankrupt$ROA) # upper
[1] 0.1580628
> mean(bankrupt$ROA) - 1.645*sd(bankrupt$ROA) # lower
[1] -0.2980628

> t.test(bankrupt$ROA,mu=-0.05,alternative = "less",conf.level = 0.95)

   One Sample t-test

data: bankrupt$ROA
t = -0.64514, df = 19, p-value = 0.2633 , as the p value is not less than 0.05 , hence we accept null hypothesis and conclude that average ROA of firms that went bankrupt is not less than -5%
alternative hypothesis: true mean is less than -0.05
95 percent confidence interval:
-Inf -0.01639542
sample estimates:
mean of x
-0.07

> t.test(bankrupt$ROA,mu=-0.05,alternative = "less",conf.level = 0.90)

   One Sample t-test

data: bankrupt$ROA
t = -0.64514, df = 19, p-value = 0.2633 , as the p value is not less than 0.10 , hence we accept null hypothesis and conclude that average ROA of firms that went bankrupt is not less than -5%
alternative hypothesis: true mean is less than -0.05
90 percent confidence interval:
-Inf -0.0288393
sample estimates:
mean of x
-0.07

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