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

Where:

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:

http://www.pistulka.com/Excel_Shared/

Hi,

“Zero defaults for the first 2 years, followed by a 1% constant default rate (1% CDR) at a 40% loss severity over a 12-month recovery period with no prepayments during the lock-out and yield maintenance periods, followed by a prepayment in full. A default rate of 1% per year (or a CDR of 1%) implies a cumulative default rate of 9.5% after 10 years, which we view as a likely scenario.”

I’ve been modeling to figure out how to get to 9.5% cumulative default rate. Could you please help with this?

Hi,

I am confused. Are there two separate loans?

If your question is what CDR monthly rate would you need to get a cumulative (sum the default amounts) to get a total of $95,000.00 in defaults on a $1,000,000 loan (9.5%), over 10 years, the answer is it depends. The default rate is based upon the remaining principal after normal principal and prepayments. Therefore you need to know the interest rate, so that you can calculate the two principal payment first. A 6% loan would require a 1.8390097274% monthly CDR in order to sum the default amounts to $95,000 on a million dollar loan (with no CPRs) for 119 months (no defaults on the last month, because the loan is paid off. Since I am so confused, this may not have helped at all. Email me at blog@pistulka.com to continue this thread.

Thanks

Son

Hi, first of all, love the website… very helpful and your descriptions/examples are very detailed!

I was wondering, could you create something similar to your “Reverse Engineering CPR” but for reverse engineering CDR?

I work on an MBS trading desk and am looking to model historic CDR based on mortgage pool performance.

Thanks!

Hi Don,

Thank you for your blog. In this particular example I noticed you calculate defaults as CDR x Balance AFTER scheduled P&I and prepayments. Shouldn’t defaults be calculated as CDR x Balance BEFORE scheduled P&I and prepayments? The way I am thinking about it, if I get my schedule P&I then there’s nothing to default on in that particular month. Your thoughts?

Thank you,

Pavel

Hi Pavel, Thank you for your comment.

When you say “if I get my schedule P&I then there’s nothing to default on in that particular month”, you must remember that these are pools of individual mortgages, not one mortgage. The assumption is that some loans will pay P&I as scheduled and while others will default.

The sequence of how principal is applied is the same as how principal would actually be handled in real life. On the payment date, all loans that pay scheduled principal (from P&I) would be subtracted from the previous months balance. Then any prepayments (CPR) would be in applied to the remaining balance after scheduled principal. Then any defaults (CDR) would be applied, after the scheduled and prepaid principal balance.

Thanks again,

Don

Hello Don,

Great resource, just discovered it!

I have a question – do you have a calculator that provides CDR given a certain $ loss and all the other inputs. I am using a cumulative loss input to get losses, and from there want to derive the CDR in a consistent manner. I don’t think a simple x12 is correct.

Appreciate you sharing this. Thank you.

Hi Karan,

I looked at your website and it appears you are working with short-term personal loans, not mortgage pools. Please send me a spreadsheet example of what you are working with including initial balances, interest rates, prepayments (CPR), etc. to blog@pistulka.com

Thanks

Don

Hi do you have knowledge of other risk modelling topics also.please ping me on my email id if you have. I would love to buy your consultancy

Karan,

It is a coincidence that you ask about other risk modeling. I am just finishing up a spreadsheet based on Monte Carlo analysis for forecasting returns on the Treasury Yield curve. I will probably post the blog and the spreadsheet later today or over the weekend.

As far as new modeling involving Constant Default Rate, let me know what you had in mind and if I can help I will let you know.

Don

Thank you for blogging on this stuff! It helped me immensely with some modeling I had to do and couldn’t find examples of these things anywhere else…much appreciated!

You are welcome. Thanks for the comment.

[…] CPR. Next 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 […]