My last post and spreadsheet concerned the Constant Default Rate (CDR) on a pool of loans. As the name implies, the CDR uses the same default rate for the complete term of the loan. It does not allow for the probability of default, depending upon the age of the loan.

The SDA curve was developed by “The Bond Market Association”. It is expressed in terms of CDR, but allows for different default rates, based upon a normal housing market. The premise is that the probability of default is low during the first months, peaks between 30 and 60 months, and then ramps down. During the housing crisis starting in 2007, it was the early months of the loan that had the highest probability of default, not the lowest. Like any curve, its usefulness will depend upon your outlook for the market.

The curve has some resemblance to the PSA prepayment model. The base curve is expressed as 100, but can be changed to increase or decrease the default rate. The base case for SDA assumes an initial CDR of .02% for the first month. It ramps up by .02% each month until the 30^{th} month where it reaches a CDR of .6%. It remains at .6% until the 60^{th} month. Then it starts decreasing at .0095% each month until it reaches month 120 at a CDR of .03% and stays at that level until the 360^{th} month.

Like the CDR, SDA requires a Loss Severity percentage.

Below is a chart of the SDA curves at 50, 100, 200, and 300 SDA:

My formula for the SMM for SDA allows for pools that have a WAM lower than 360 months, by adjusting the curve to fit the age of the loan.

Download Workbook SDA

Why does the y-axis of SDA chart use “CPR”?

“The base curve is expressed as 100, but can be changed to increase or decrease the default rate. The base case for SDA assumes an initial CDR of .02% for the first month. It ramps up by .02% each month until the 30th month where it reaches a CDR of .6%. It remains at .6% until the 60th month. Then it starts decreasing at .0095% each month until it reaches month 120 at a CDR of .03% and stays at that level until the 360th month.”

Rachel,

CPR or Constant Prepayment Rate (aka Conditional Prepayment Rate) is the base calculation for virtually all prepayment and default models. More precisely SMM (Single Monthly Mortality), which is the monthly equivalent of CPR.

Since defaults and prepayments use CPR as their base calculation, expressing the results graphically as CPRs makes it more comparable to other models.

I hope this answers your question.

Don

Hi, Don

Thanks for your reply!

[…] down is the default assumptions, either CDR or SDA. See these links for descriptions of CDR or SDA. To the right of each is your assumption rates. Next is the loss severity. That is the percent of […]