# Constant Default Rate (CDR): Definition, How They Work, and Risks

## What Is the Constant Default Rate (CDR)?

The constant default rate (CDR) is the percentage of mortgages within a pool of loans in which the mortgagors (borrowers) have fallen more than 90 days behind in making payments to their lenders. These pools of individual outstanding mortgages are created by financial institutions that combine various loans to create mortgage-backed securities (MBS), which they sell to investors.

### key takeaways

• The constant default rate (CDR) refers to the percentage of mortgages within a pool of loans for which the mortgagors have fallen more than 90 days behind.
• The CDR is a measure used to analyze losses within mortgage-backed securities (MBS).
• The CDR is not a standardized formula and can vary, sometimes including scheduled payments and prepayment amounts.
• CDR is related to the constant payment rate (CPR), which estimates MBS prepayment risk rather than default risk.

## Understanding the Constant Default Rate (CDR)

The constant default rate (CDR) evaluates losses within mortgage-backed securities. The CDR is calculated on a monthly basis and is one of several measures that those investors look at in order to place a market value on an MBS.

The method of analysis emphasizing the CDR can be used for adjustable-rate mortgages as well as fixed-rate mortgages.

## Constant Default Rate Formula & Calculation

The CDR can be expressed as a formula:

\begin{aligned} &\text{CDR} = 1 - \left ( 1 - \frac{ \text{D} }{ \text{NDP} } \right ) ^n \\ &\textbf{where:} \\ &\text{D} = \text{Amount of new defaults during the period} \\ &\text{NDP} = \text{Non-defaulted pool balance at the} \\ &\text{beginning of the period} \\ &n = \text{Number of periods per year} \\ \end{aligned}

The constant default rate (CDR) is calculated as follows:

1. Take the number of new defaults during some period and divide that by the non-defaulted pool balance at the start of that period, and subtract it from 1.
2. Raise this result from to the nth power, where n = the number of periods in the year.
3. Take this figure and subtract it from 1.

It should be noted, though, that the constant default rate (CDR)'s formula can vary somewhat. Some analysts also include the scheduled payment and prepayment amounts.

## Examples Using the Constant Default Rate

Gargantua Bank has pooled residential mortgages on houses located across the U.S. into a mortgage-backed security. Gargantua’s Director of Institutional Sales approaches portfolio managers at the Trustworthy Investment Company in hopes that Trustworthy will purchase an MBS to add to its portfolios that hold these types of securities.

After a meeting between Gargantua and his firm’s investment team, one of Trustworthy’s research analysts compares the CDR of Gargantua’s MBS with that of a similarly rated MBS that another firm is offering to sell to Trustworthy. The analyst reports to his superiors that the CDR for Gargantua’s MBS is significantly higher than that of the competitor’s issue and he recommends that Trustworthy request a lower price from Gargantua to offset the poorer credit quality of the underlying mortgages in the pool.

Or consider Bank ABC, which saw $1 million in new defaults for the fourth quarter of 2019. At the end of 2018, the bank’s non-defaulted pool balance was$100 million. Thus, the constant default rate (CDR) is 4%, or:

\begin{aligned} &1 - \left ( 1 - \frac{ \1 \text{ million} }{ \100 \text{ million} } \right ) ^4 \\ \end{aligned}

## Special Considerations

In addition to considering the constant default rate (CDR), analysts may also look at the cumulative default rate (CDX), which reflects the total value of defaults within the pool, rather than an annualized monthly rate. Analysts and market participants are likely to place a higher value on mortgage-backed security that has a low CDR and CDX than on one with a higher rate of defaults.

Another method for evaluating losses is the Standard Default Assumption (SDA) model created by the Bond Market Association. However, this calculation is best suited to 30-year fixed-rate mortgages. During the subprime meltdown of 2007-2008, the SDA model vastly underestimated the true default rate even as the number of foreclosures hit multi-decade highs.

## Is Constant Default Rate the Same as Conditional Default Rate?

Yes Both conditional and constant default rate, abbreviated CDR, refer to the same thing: CDR measures the portion of mortgages that default in a pool of mortgage loans on an annualized basis and is used to measure the riskiness of various MBS.

## What is the Constant Prepayment Rate (CPR)?

The constant (conditional) prepayment rate (CPR) is similar to the CDR, except instead of estimating annualized defaults in a pool of mortgage loans, CPR estimates the prepayment rate in an MBS.

## What Is Single Month Mortality (SMM)?

Single month mortality (SMM) is a similar MBS measure to CPR in that it measures estimated prepayments in a pool of mortgages; however, it is a monthly metric while CPR is annualized.

Article Sources
Investopedia requires writers to use primary sources to support their work. These include white papers, government data, original reporting, and interviews with industry experts. We also reference original research from other reputable publishers where appropriate. You can learn more about the standards we follow in producing accurate, unbiased content in our editorial policy.
1. Fabozzi, Frank J., ed. Investing in Asset-Backed Securities. Vol. 75. John Wiley & Sons, 2001. P. 325.

2. The Bond Market Association. "Chapter SF Standard Formulas for the Analysis of Mortgage-Backed Securities and Other Related Securities."

3. Federal Reserve History. "Subprime Mortgage Crisis."