Downgrade Risk versus Default Risk

[brian.field]

Gregory treats Default Risk as separate and distinct from Downgrade risk. This seems appropriate for higher rated bonds. However, if CCC is the lowest rating, i.e., with no rating below CCC except for Default, it seems that the Default Risk should equal the Downgrade Risk - this is not the case according to Gregory. Under Figure 14.6 in his text (Chapter 10), he states that, based on table 14.1, the probability of upgrade and downgrade for a A rated bond are 2.91% and 5.76% respectively (These probabilities exclude the Default probabilities.) He then states that the probability of upgrade and downgrade for a CCC are 12.2% and 0% respectively. It seems strange to me that someone would say a CCC bond has 0% probability of downgrade since it can be downgraded to default. (There is a default probability of 19.23% for CCC bond).....I suppose it is nothing more than semantics.

 

[David Harper CFA FRM]

Hi @brian.field in looking at the underlying exhibit (http://www.cvacentral.com/wp-content/uploads/2014/05/Chapter10.xlsm) while I do tend to agree with you that his semantics are awkward here, to me also, I see that he's done the multi-year matrix slightly different than I'd be inclined to do: he's excluded the default column from the matrix multiplication (probably to the same effect, I am sure; I would include the default column but also make it a row with 0% chance of migration).

But then again, it gets me thinking: maybe he's being very precise. First, his point in your quote is essentially about the "mean reversion" tendencies in upgrade/downgrades that are illustrated in Figure 10.5 (14.5?). Really, he's saying investment grade cumulative PD functions tend to be convex--that is, f''(x)>0--while junk tends to be concave (both are increasing). And he produces this by multiplying the 1-year matrix on itself. In this way, long-term upgrade/downgrade "mean reversion" (his phrase) is solely a function of the transition matrix excluding default (that's a terminal state). In this context, I do see why he would say downgrade for a CCC has a 0% probability. It's part of a mean reversion point; i.e., because CC cannot be downgraded, and can only be upgraded, their cumulative PD function must be concave.

and, then too, isn't it also true that a default is not a special case of downgrade. In the transition matrix they are co-located, so it gives a sort of optical illusion that default is "one notch below" CCC. But a default is a contractual legal event (following a financial event) whereas a downgrade is a market participant opinion. In these ways, his semantics make some sense. I hope that's interesting!

 

[brian.field]

Absolutely interesting! Thanks for the thoughtful response David!