Duncan Pratt is the management accountant at Jade Bank, where the data science department is leading an initiative to predict whether loans will default or repay. The default rate in the training set

is $20\%.$ After building a model on the training set that predicts whether a loan will default or repay, the data scientist applies it to the validation set of $2,000$ observations to evaluate its performance.

Read the

Requirement $1.$ Help the data scientist complete the confusion matrixes below for different model thresholds.

Start by completing the confusion matrix for the cutoff point $0\mathrm{.}40.$

Complete the confusion matrix for the cutoff point $0\mathrm{.}55.$

Requirement $2.$ Assume that Jade Bank has $$1,000$ to invest in each loan of the validation sample. If Jade Bank does not invest in a loan, it keeps the money in a risk$-$free investment at $3\%$ a year

for $3$ years $($ignore the time value of money$).$ If Jade invests in a loan that eventually repays, it receives $12\%$ a year for $3$ years. If Jade invests in a loan that eventually defaults, Jade loses $55\%$ of

the amount of the loan. Fill in the payoff matrix below. Which model threshold should Duncan and the data scientist use?

Start by construting the payroll matrix. $($Enter a loss amount with a minus sign or parentheses.$)$