(Parts I, II and III of this series are also available.)
One of the comments to part II of this series asked about recovery assumptions, observing that a 40% static recovery assumption would cause a 60-100% tranche to always be worth par, since it would never take damages. That’s correct and raises an issue I will dance around in part three: recoveries constitute another unobserved input to the copula model.
When issuers default, they do not drop completely out of the picture – there is a some recovery level assumed, on the premise that in bankruptcy there will be enough assets to cover some portion of the debt owed. It could be anywhere from 0% to 100%. If the issuer recovers 100%, the CDO takes no damage (as there is no need to pay out insurance).
The most simple way to address recovery assumptions is to take them as exogenous static inputs. They don’t necessarily have to be 40% (widely accepted as the long-run average recovery rate). Recovery assumptions could be based on an analyst’s estimate, implied from CDS, taken from a market quote (recoveries are traded quantities), spit out of a random number generator, etc. It doesn’t matter in an exogenously-specified static model.
The second way of dealing with them is to model them as stochastic quantities, which may or may not be correlated with default intensities. A simple (and hardly stochastic) method would be to lower recoveries as more issuers default, on the assumption that in such a scenario the business environment must be very bad. This would have the effect of compounding losses – not only are issuers defaulting, but the surviving issuer recoveries are falling over time. Alternatively, you could get very fancy and let the recoveries dance as random variables – incorporating a gamma process, for example. However, that’s a little beyond the scope of my series (for the moment).
There is generally enough information about recoveries available through research and market information that an exogenous model provides satisfactory results. One question we must ask is whether it is “bad” that 40% recoveries would cause a senior tranche to never take damages. Honestly, I think it isn’t because that’s a scenario that could easily be reflected in reality: if it really happened, then the tranche wouldn’t take damages. It might trade down, however, as people fear recoveries would drop – and that is where the model specification comes into play. It is the role of the model caretaker, not the model itself, to make sure its input parameters and dynamics are reflective of reality.
There’s nothing wrong with creating a risk free bond – and to take this example to extreme, the 99-100% tranche is most likely risk-free under any recovery assumptions. The only problem is to expect to get paid for holding it. Moreover, even a 60-100% tranche with 40% recoveries could trade under par depending on interest rates and (in some cases) prepayment probabilities. But that’s another chapter.
{ 2 comments… read them below or add one }
Thanks for the great write-up.
But I’m a bit confused by your last two paragraphs. To me, the more relevant question is whether it is “bad” for a model to assume that recoveries are unchanging quantities. I think the answer is very clearly yes. A model that prices a 60-100 tranche as a risk-free bond (even absent prepayment risk) is not representative of reality, and its caretakers should get wise to this if they haven’t already. Not that I’m claiming some special insight here, as I suspect most shops that use SFGC models have long since fixed the static recovery assumption.
I think it would be interesting to compare two implied volatility surfaces: one using static recovery and one using some kind of dynamic recovery model. Maybe run the comparison both today and as-of some interesting historical dates–say, May 2007 and October 2008–to see if the differences in the surfaces are any more/less stark nowadays. Unfortunately, I don’t have access to the horsepower to run it myself.
I think we need to make a distinction between bad inputs/assumptions and bad models. I don’t see the SFGC as being a bad model even if someone is plugging constant 40% recoveries into it; that is more a case of bad analysis (to the extent that 40% recovery is unrealistic). That said, I agree with you that some sort of dynamic recovery is probably going to give a more informed answer – I question, however, whether the impact will be dramatically better than a well-informed (that is to say, regularly updated) set of static recovery assumptions. I think you hit the nail on the head when you note it comes down to a matter of horsepower. Can you afford to spend a few more cycles working through recovery distributions? Do you feel comfortable having your model decide how recoveries will behave in the future (or even specifying those distributions)? Of course, I’m always playing devil’s advocate in favor of simplicity.