Question

Moody’s has calculated that for the 1970-2013 period, a Ba rated issuer has cumulative default rates (%) of 1.110, 3.071 and 5.371 in years 1, 2 and 3. Calculate the average hazard rate during the third year for such an issuer. Show how you derived your answer.                     

Answer 1

Probability of default during year 3 = cumulative prob. in year 3 - cumulative prob. in year 2 = 5.371% - 3.071% = 2.3%

This probability is conditional upon the fact that the security does not default before year 3. The prob. that the stock does not default till year 2 is 1 - cumulative prob. of default in year 2 = 100-3.071 = 96.929%

So, the probability of default in year 3 conditional on the fact that it does not default before that = prob. of default in year 3/prob. of no default before year 3 = 2.3%/96.929% = 2.37%

This is the hazard rate for year 3.