# 4-Factor Prepayment Model

In previous posts, I have covered CPR, PSA, and a spreadsheet that allows for any prepayment vector you might want to create. There have been many attempts to describe what the prepayment pattern for MBS will look like in the future. One of the models that has been used extensively, particularly with ALM (Asset / Liability Management) models, is the 4-Factor prepayment model. Some models have more than four factors, but I am hoping this spreadsheet with four factors, will give the user an idea of how the 4-Factor model might work. The model relies on historic data, but can be adjusted for the user’s personal expectations. The four factors I will consider are:

1. **Refinance Incentive**: This is the difference between the weighted average coupon (WAC) of the loans, and the current market yield that is an alternative for refinancing the loans. This is the base factor that determines what will happen to the CPR, under various changes in market yields.

2. **Burnout:** After the loans have gone through one or more interest rate cycles, and for various reasons still have not refinanced, the expectation is that the remaining loans might be less likely to refinance in the future.

3. **Seasoning: **Like the PSA model, it is assumed that newer loans are less likely to prepay than more seasoned loans. The PSA model assumes the CPR will start at 1/30th if the CPR, ramps up until it peaks at 30 months, and then assumes the full CPR for the rest of the life of the loans. This seasoning factor takes into consideration the base model to determine in what month the ramping of the expected CPR will peak. Unlike PSA, the seasoning factor is not dependent on only one CPR (6%).

**Seasonality:** Run virtually any data set and you will find that, for various reasons, people tend to sell or refinance their homes more often during certain months of the year. For this reason, the amortization schedule used to run the model, needs a starting date.

The Excel functions looks like this for **7/1/2017**:

**Base Factor (CPR)**

Assuming the spread is **-2.00%** (WAC – Market Rate)

=1-(1-VLOOKUP(-2.00%,CPR,2,FALSE)/100)^(1/12)

=1-(1-8/100)^(1/12)

**Base Factor = .006924**

*CPR = Base Factor Table

**Burnout**

Assuming a pool factor of **1.0**

=VLOOKUP(ROUND(CPB/OSB,1),Burnout,2,FALSE)

**Burnout = 1.000**

*CPB = Current Principal Balance

*OSB = Original Starting Balance

*Burnout = Burnout Table

**Seasoning**

Assuming the spread is **-2.00%** (WAC – Market Rate) & the payment number is **19**

=MIN(10/VLOOKUP(-2.00%,Seasoning,2,TRUE),1)

MIN(0.39583,1)

**Seasoning = 0.39583**

*Seasoning = Seasoning Table

**Seasonality**

Assuming the payment date is** 7/1/17**

=(VLOOKUP(MONTH(7/1/17),Seasonality,2,TRUE))

**Seasonality = 1.10**

*Seasonality = Seasonality Table

**SMM (Single Monthly Mortality Rate)**

SMM = .006924 *1.00* .39583* 1.10

**SMM for the 7/1/2017 payment = .003015**

On the right hand side of the amortization sheet I show the calculations for each factor, and for each payment:

Change the Market Yield (use the drop down box) to see how it effects the prepayment chart. Note the change of scale on the Y axis:

Download “4-Factor”

Phenomenal work you have done here and finding a site like yours is a rare pleasure indeed. Do your monthly seasonality adjustments seek to capture both day-count (as CPR tends to report monthly retro to current) or mainly is it weighted toward capturing the speedup in ‘moving around’ months. In any event, I very much like your adjustments and thank you for running such a site.

Thank you Andy,

The monthly seasonality is “weighted toward capturing the speedup in ‘moving around’ months.”

Don

Hi, Don. This is great work. I love this prepayment model. Could I download the model?

Maryann,

Yes. At the bottom of the post it says “Download 4-Factor”

Don

I have been asked to research “Agency Factors” in relation to the prepayment of loans for an interview. I am in finance and familiar with mortgage loans to the extent of amortization tables and P&I but have never heard of “Agency Factors”. Maybe its just a terminology thing, but your blog is the only thing that looks like its related. Is it?

Thank you!!

I am not sure what “Agency Factors” are either. The first thing that comes to mind are pool factors, that represent the percent of original principal remaining for MBS.

If they are asking about the factors go into the models that agencies like Fannie Mae, Freddie Mac, etc. use for prepayment assumptions, the agencies are not going to divulge that. Even if they did, the assumptions will most likely change over time.

I think your best bet is to ask the person that asked you the question to be more explicate in their request.

Sorry I could not be of more help.

Thanks for doing this blog. Your spreadsheets are the best on the web for this subject matter.

Thank you. It is nice to get feedback.