Math behind pricing a CMBS loan
Hi guys,
I have been working on sizing loans. While I work on comps, cash flows, pre lim underwriting, I dont get to work on structuring/pricing a loan. So, I am trying to learn how CMBS loans get priced.
We have a break even spread in our model. Right now, its 180-185 bps for a lot of my loans sized. I get that it is market driven, but can anybody ELI5 the math behind how that is derived? or even what the break even spread is actually is? I am assuming this varies across product types?
Secondly, based on the break even spread of say 180-185, I think my structuring team comes up with the all in spread of 210-220 bps. I also see references to a "15 bps per point". I dont know what this is, but I think this helps the team come up with the 210-220 bps.
If somebody can walk me through the math behind this, I would really appreciate it, thank you!
To add to what some others have said, in CMBS business, Break-Even spread helps calculate the loan coupon at which the bank will neither make nor lose money after securitizing the loan. Most CMBS loans are 10 year loans these days. So the spread is a spread over 10 year swap rates. If 10 year swap rate is 3.00%, a break-even spread of 185 means that if teh bank makes a loan at 4.85% (3.00% + 1.85%), it will not make or lose money. If it makes the loan at a higher spread, it will make money. For 10 year loans, generally 14 basis points results in profit of 1 point or 1% on the loan amount. So, if the bank prices a 10 year loan at a spread of 213, it will make a profit of 2% (i.e. (213-185)/14). 7 year and 5 year loans are less common. For 7 year loans, 20 bps is 1%, and for 5 year loans 25 bps is one point.
To price a loan/debt with pass-through structure, the method proposed by David Lee has been widely used. You need to estimate a Hazard Rate Function and use it to derive the survival function, then simulate default and prepayment time.
The risk of default and prepayment will be well incorporated into the spread data in an efficient market, that's for sure. But it's been less welcomed to price MBS cash flow and a "macro" or aggregate level since the 2008 crisis. Both industry and academics have been making progress to model the cash flow at loan level, which requires tons of advanced math stuff.
I can't agree with you on this. The math is actually beyond 99.99% people's capability. There are very smart PhDs behind the models and data. I talked to Intex and they are well aware the models in the Intex system is only at very basic level and barely used by quants in big banks. Even the models in Intex can make most people rubbing head for days to understand. If you think MBS is easy, you're way behind time bro. As a CDO manager, I can say with confidence, you'll need a master's in physics to understand the newest models.
The starting point of predicting cash flow of a pool of loans has always been the survival function with Copula method. It's been widely criticized since the 2008 crisis but the academics have not come up with a new procedure that can completely replace Copula. Spreads are market pricing for credit risks that generated from default and prepayment probability distributions. It's like in ancient times people have priced options reasonably after years of trial and error trading, but Black and Scholes derived the mathematical form of it and it has been used ever since. Same goes for structured credit, David Li was the Black Scholes Merton in the structured area.
And please, educate me. I've personally led 7 CMBS deals and in charge of structured credit investment research for the largest bank in Asia, but I'm sure you know better.
I think there's a valid point to be made that CMBS outcomes are very binary, so the techniques used on granular pools of residential loans, which uses PD/LGD to derive an expectation of the pool's cash flow are unlikely to be realized for CMBS. As a result, a lot of CMBS investing is driven by property cash flow underwriting and valuation - esepcially for single asset exposures or even conduits where the pool is weighted heavily on the top 5 or 10 loans. I know of very few investors who weigh models heavily in their investment process, for better or worse.