## Default probabilities and recovery rates

I’ve been kind of obsessed lately with the “big three” ratings agencies S&P, Moody’s, and Fitch. I have two posts (this one and that one) where I discuss the idea of setting up open source ratings models to provide competition to them and hopefully force them to increase transparency (speaking of transparency, here’s an article which describes how well they cope with one of the transparency rules they already have).

Today I want to talk about a technical issue regarding ratings models, namely what the *output* is. There are basically two choices that I’ve heard about, and it turns out that S&P and Moody’s ratings have different outputs, as was explained here.

Namely, S&P models the probability of default, which is to say the probability that U.S. bonds will go through a technical default, I believe within the next year; Moody’s, on the other hand, models the “expected loss”, which is to say they model the future value of U.S. bonds by modeling the probability of default combined with the so-called “recovery rate” once the default occurs (the recovery rate is the percent of the face value of the bond that bond-holders can expect to receive after a default).

The reason this matters is that, for U.S. bonds specifically, even if default occurs *technically*, few people claim that the bonds wouldn’t eventually be worth face value. So S&P is modeling the probability that, through political posturing, we could end up with a technical default (i.e. not beyond the realm of possibilities), whereas Moody’s models what the value of the bond would be if that happened (i.e. face value almost certainly). It makes more sense, considering this, that S&P has downgraded U.S. debt but that Moody’s hasn’t.

This isn’t the only time such issues matter. Indeed, various different “ratings” models claim to model different things, which end up being more or less crucial depending on the situation:

- S&P: probability of default
- Fitch: probability of default
- Moody’s: expected loss
- Altman’s Z-scores: probability of corporate default
- Credit Grades: probability of default of publicly traded companies
- credit default swaps: expected loss

I threw in Credit Grades, which is a product that is offered by MSCI. One of the inputs for the Credit Grades model is the market volatility of the company in question, whereas most of the other models’ inputs are primarily accounting measurements. In particular, if the market volatility of the company is enormous, then the probability of default is increased. I wonder what it is now rating Bank of America at?

Credit default swaps are not ratings models directly- but you can infer the market’s expectation of default and recovery rate from the price of the CDS, since the cashflow of a CDS works like this: the owner of the CDS pays quarterly “insurance payments” for as long as the bond in question hasn’t defaulted, but if and when the bond defaults the writer of the CDS pays the remainder of the face value of the bond after removing the recovery rate. In other words, if the bond defaults and the recovery rate turns out to be 63%, then the CDS writer is liable for 37% of the face value of the bond.

Not to unfairly single out one issue among many that is difficult, but recovery rates are pretty difficult to model- the data is secondary market data, i.e. it’s not traded on directly but rather inferred from market prices like CDSs that are traded, and often people just assume a 40% recovery rate even when there’s no particular reason to believe it.

For that reason it’s not necessarily better information (in the sense of being more accurate) to model default with recovery rate consideration than it is to model straight out default probability, which is already hard. On the other hand, modeling expected loss like Moody’s is probably a more intuitive output, since as we’ve seen with the uproar last week, S&P is getting lots of flak for their ratings change but Moody’s has been sitting pretty.

In fact, U.S. sovereign debt is an extreme example in that we actually *know* the recovery rate is almost surely 100%, but in general for corporate debt different guesses at the expected recovery rates will drastically change the value of the bond (or associated CDS).

I guess the moral of this story for me is that it’s super important to know exactly what’s being modeled – I am now ready to defend S&P’s ratings change – and it’s also important to choose your model’s output well.

One thing that really fascinates me is that recovery rates are a correlated variable. In particular, it’s well known that recovery rates go down in periods where default rates go up (in a recession more companies go under and at the same time they’re selling their inventory and assets into a buyer’s market). Always wondered how much hard analysis went into this point within risk departments…

This has virtually nothing to do with modeling and virtually everything to do with who is paying whom. Check out Bill Black on this.

link?