Pricing Mortgage Notes

Whenever we receive a tape of mortgage notes or a set of tax liens or even a pool, it always comes with one important question: any interest in this?

As with most finance things, it depends.

For well capitalized investors, it depends almost entirely on whether the currently available information (and confidence in said info) suggests that the price of the note is less than its fair value. If it is, then feel free to offer to buy at a price that makes it worth your time. If it isn't... you probably should pass.

We decided we'd share our simple model for valuing a mortgage bond because we believe more transparency is better for the industry and sheds light onto some of the darker corners of finance. Unless you're a professional or an academic, you rarely read about fixed income pricing. Regardless, we like to think that pricing notes is far easier than pricing equities if you have a large enough pool of assets.

For complex assets, we build a one off model and add enough spread to account for small sample sizes, but for a mortgage pool, WE HAVE THE STATS. The model that we use can be crude as long as it returns a quick response and handles the major features of the distributions we've assumed/measured.

Back to School - First Principals

Regardless of the one-off model or building a systematic pricing engine, we start with the discounted cash flow (DCF). We won't actually derive any DCF equations in this post. Just imagine that you know there will be (hopefully) be a sequence of future payments from the borrower or from a foreclosure auction (hopefully not). You can derive a value for how much you would pay for these cashflows today based around some alternative investment or project.

Many asset managers like to use the 10y federal reserve note plus some arbitrary rate spread as a proxy for their mortgage notes. This largely is due to there being similar duration exposure between a 10y treasury and the 30y mortgage. Something about homeowners only staying in their home for 7-8 years on average before the refinance or sell.

With a discount rate (using the alternative investment), we just need to use the monthly payments in a DCF model to derive the net present value (NPV) of the cashflows. Let's call this modeled value fair value #1. This is the simplest model that is worth giving any thought to. Unfortunately, we can't use this model.

Pesky Mortgages

Mortgages have a couple properties that make standard DCF pricing models unsuitable:

• Mortgages don't have many proxies - 20 or 30 year U.S. treasury bonds have similar "term," but they don't amortize, they have differing tax consequences, and are unsecured obligations. I suppose technically the U.S. government has never defaulted. Never say never though
• Mortgages are very long dated - a 30-year fixed full-term amortization mortgage lasts for... 30 years. Because of this, the assumed discount rate may change dramatically over time
• Mortgage borrowers tend to pre-pay - homeowners tend to refinance every 7-8 years while the most popular owner occupied note has a 30 year term. This gives homeowners a massive option: if rates go up they probably won't refinance, and if rates go down, they will almost definitely refinance.
• Some borrowers DON'T pre-pay. when we say that borrowers "pre-pay," what we really should say is SOME borrowers pre-pay. the rest aren't paying attention or can't refinance or simply lack the financial literacy to know that they're getting free money to refinance lower when rates drop.
• Mortgage borrowers sometimes default - most people borrow money thinking they'll be able to repay. Mortgages are very long dated though, so it's hard to be 100% confident that nothing will come up in 15 years that could change things

To solve these issues, mortgage lenders incorporate all kinds of non-linear features that make mortgages pretty complicated compared to unsecured borrowing:

1. Lenders offer adjustable rate mortgages (ARMs). This mitigates the risk that the lender lends at X% and then a couple years in, the best alternative investment is yielding 2X%. There are several common shapes, but they generally have 30 year terms and amortization schedules, with a "fixed" period up front with a floating rate quoted after the fixed. For example, a 10/1 ARM is fixed for the first 10 years, then the interest rate adjusts once a year for the next 20 years.
2. Lenders have pre-payment penalties. Non-owner occupied properties, lenders often require borrowers to pay a penalty if they wish to pay down their loan sooner.
3. Lenders can foreclose. If a borrower defaults, the lender has the right to exercise certain options including foreclosure (taking title to). In a foreclosure, the lender usually is obligated to auction the property to the public at some reserve price. If the property sells at or above the reserve price, the lender is paid the balance out of the proceeds. If the property doesn't sell, the lender is stuck with the property. This is not a good outcome, but for the sake of argument let's not address it right now

Unfortunately, these mortgage features further complicate the answer to the question "How much is this mortgage note worth?"

Dealing with Complexity

In every one of the random properties that we mentioned above and the corresponding solutions, there are non-linearities, conditional logics, and correlations that make it tricky to come up with a single number for fair value. Enter Monte Carlo (MC) simulation.

Let's say you have different assumed scenarios with independent and identical distributed likelihood (i.i.d.) in the total space of possible outcomes (Ω). Given a scenario, you can confidently come up with a time-series of cashflows, interest rate changes, early payoffs, defaults, etc. Based on a basic DCF of cashflows, you can also compute the NPV of those assumed cashflows.

Since we said that the scenarios are i.i.d., that means that we can effectively find the expected value of outcomes by computing the mean of the outcomes.

In layman's terms: it's hard to come up with a clean answer so we estimate said answer by trying a bunch of different scenarios that we think have equal chance of happening and just averaging everything together.

Further academic exploration is outside the scope of this post, but happy to recommend more reading if there's any interest.

Now For Some Practical Use

We released a simple version of our pricing engine. We wouldn't begin to suggest that it's appropriate for pricing a portfolio of loans because we left off correlated default rates due to macro environment, extreme path dependency, the "burnoff" that we mentioned above, and a number of other features in our model, but we believe it's a good benchmark for a quick check on if a mortgage note is overpriced or not.

Check It Out