Question

Consider the following table of the mortality rates of loans estimated by a F/I: For A-rated loans the yearly and cumulative loss in the first year is 0.5% and 0.5%, respectively; while for B-rated loans the yearly and cumulative loss in the first year is 1.0% and 1.0%, respectively. In the second year, for A-rated loans the yearly and cumulative loss is 0.5% and x%, for B-rated loans the yearly and cumulative loss is 1.25% and y%. What is the cumulative mortality rate of the A-rated and B-rated loans for year 2?

	Year One	Year Two
A Rated Loan - Yearly Loss	0.5%	0.5%
B Rated Loan - Cumulative Loss	0.5%	x%
B Rated Loan - Yearly Loss	1.0%	1.25%
B Rated Loan - Cumulative Loss	1.0%	y%

Answer 1

Cp = Cumulative probability of no loss = Probability of no loss in year 1 x Probability of no loss in year 2

= (1 - p1) x (1 - p2)

Hence, the cumulative mortality rate = 1 - Cp

For the A rated loans:

Cp = (1 - 0.5%) x (1 - 0.5%) = 0.990025

Hence, the cumulative mortality rate = 1 - 0.990025 = 0.009975 = 0.9975%

For the B rated loans:

Cp = (1 - 1%) x (1 - 1.25%) = 0.977625

Hence, the cumulative mortality rate = 1 - 0.977625 = 0.022375 = 2.2375%

(Please do round off your answers as per your requirement)