Also see this post: Comparing CDR Default Formulas to Industry Standard Default Formulas
Constant Default Rate (CDR) is an annualized rate of default on a pool of loans. The default rate on loans depends on a number of conditions, such as the age of the loans, seasonality, burnout levels, FICO, LTV, income, etc. Since this is not an academic blog, I will ignore all of the above. I just want to get across the concept and how the math works, with an actual amortization schedule. I am working on a spreadsheet for a future post that will allow a finance manager to calculate a “holding period return” or “horizon analysis” using an amortization schedule. I will need CDR for that calculation. Hopefully, it will be helpful in making the decision to sell mortgage production or keeping it.
Now back to CDR. I have seen more than one way to calculate a default rate, but I think the one in the spreadsheet CDR is the most common. Along with the constant default rate is the “Loss Severity”, which is defined as the percentage of lost principal when a loan has defaulted. Both CPR and CDR use a single monthly mortality rate (SMM) in their calculations:
P3 = (1-(1-CPR) ^ (1 / 12))*(P1-P2)
P4 = (1-(1 -CDR) ^ (1 / 12))*(P1-P2-P3)
Loss Severity = P4 * S
P1 = Starting Principal Balance
P2 = Principal Portion of Scheduled Loan Payment
P3 = CPR Principal Prepayment (SMM for CPR)
P4 = SMM for CDR
S = Loss Severity Percent
In addition to the sheet that assumes CPR and CDR remain constant throughout the term of the loan, I have included another sheet that allows for changes of both CPR and CDR each month. Both tables are yellow input cells. When you enter a month (must start with month 1) and a rate it will continue to use that rate until you enter another month and rate. The tables allow for twelve changes.
The cash flow used to determine the internal rate of return and the present value at a given discount rate is from the standpoint of the buyer. Each cash flow is as below:
Scheduled Payment + Prepayment + Defaults – Loss Severity -Servicing
Why are defaults added into the return to the pool owner? Only the portion of defaults that are Loss Severity are losses, the remainder (recovery) is treated as a prepayment and assumes to happen at the same time as the loss.
If this pool was original production, owned by the originator, there would be no servicing fee and the entry next to “Servicing” would be zero.
The default data entered in yellow cells are meant as examples only and do not represent any empirical or published data.
Download workbook “CDR” from: