Rating transition matrix

[higaurav]

Hi David,

I came across one concept, that in the rating transition matrix, the credit ratings are more stable over one year horizon whereas the stability declines over the long horizon. How does this happen?

I thought that as we have seen the behavior of the assets/rated companies for a longer period, it should stabilize over the long period. Request your help in understanding this. Pls help.

Thnks,
OM

 

[phwdisse]

I'm also confused by this. It's question 31 from the first practice exam from 2007.

But agencies try to incorporate business cycles so the are trough-the-cycle and i thought credit rating would be more stable.

At-the-point-in-time is the credit quality over the near term and i thought there would be more changes in credit rating.

I my perspective answer A would be the correct answer on this question.

Dear David can you help us with this.

Regards,

Paul

 

[David Harper CFA FRM]

Hi OM and Paul,

I don't like the question (31) because I tend to think the meaning of a "stable matrix" needs more definition; what do we mean exactly?

Maybe the question means something that follows mathematically from a typical migration matrix which has high probabilities in the diagonal (i.e., high prob that an AAA will remain an AAA over a one year period, etc). If you compound these marginal (unconditional) probabilities matrices over several periods, the n-period matrix (i.e., the longer term migration matrix) must inevitably have lower probabilities in the diagonal and greater probabilities in the "extremes" like default. Put another way, if an AAA has a 90% chance of staying in AAA over one period, then it's two-period probability of remaining AAA reduces to 90%^2 (+ a bit of loose change) and the other options therefore increase. (But, it's hard to tell if this is instability or if this really should be the baseline against which instability is measured?! This is why i feel the question is not well-prepared)

Jorion (in the FRM handbook) has a different take on ratings stability, and well come to think of it, maybe this is what the question could mean. Jorion's point is that one-period (marginal, unconditional) ratings probably tend to mean-revert; e.g., a highly-rated credit (AAA) has statistical difficulty in maintaining the high rating over long periods of time. Something like "you can't be perfect forever." And conversely, junk bonds, if they survive a little while, may mean revert to better quality by virtue of surviving. This is different from, in contradiction with, the above in a way because it implicity assumes non Markov and, by definition, means the ratings are non-stable.

Either way, what the above have in common is: if a 1-period matrix says a certain rating has an 90%+ chance of remaining in the category for one year, then that probability is less applicable the further forward we go.

The assigned reading is de Servigny. He seems to support Jorion with the notion that a ratings matrix is volatile or time-varying. And, perhaps specifically to the question, "Schagen and Schuermann observe that the more the time horizon of an independent transition matrix increasese, the less monotonic the matrix becomes [i.e., PDs decreasing with higher rating]." My paraphrase of de Servigny on this: although a one-period matrix may be accurate, [due to path dependence] it starts to lose its predictive power as it extends thru time.

Paul: re point-in-time vs. through-the-cycle, I agree this further confuses this issue. But not because of the assigned de Serigny. I think in de Servigny (I could be wrong) he separates this issues such that, you may be right, TTC is less volatile than ATPIT, but *BOTH* rating approaches are still less stable for an n-period matrix than a 1-period matrix. My read in de Servigny is they are just different issues. However, the Aschcraft subprime case study adds a different view: their argument is that through-the-cycle actually is more volatile because it creates less frequent but more abrupt rating changes. In other words, one big change is less stable than a few small changes.

Sorry for length, the length just reflects i can't make immediate sense of the question either...rating stability has been an issue each of the last two years and i don't think we've perfected the intent here

David

 

[higaurav]

Thanks David for taking time for answering this and other questions, it really helps !!

Rgrds
OM

 

[phwdisse]

Thanks David,

The explanation from Jorion is the exact explanation GARP gives in question 99 from 2007 FRM Practice exam III. But the are referring to the Merton's Model and not to the rating transition matrix.

Is there any link between the Merton's Model and this explanation? The only one I can think of is that, if the PD is calculated with the Merton's Model the PD will changes immediately if the value of equity or dept of the firm changes. So the PD for a Aaa-rated firm will increase immediately if de value of the equity decreases and with maturity a Aaa-rated firm will often deteriorate.


Regards,

Paul

 

[David Harper CFA FRM]

Paul,

THANK YOU for pointing me to the 2007 practice question. The question is confused: the stated rationale is from Jorion, not de Servigny (least of all Ch 6) and the Merton reference is only really supported in Stulz!

I see your point that Merton, being "point-in-time", will give volatility to the implied PD (and, indeed, this is a weakness of structural models, they are prone to overreaction). But i don't see how this leads to a up/down bias...

However, there is indeed a link between Merton and the explain. I just took the Merton XLS (on the member page) and quicky tweaked to show two senarios.

Please take a look. All assumptions are the same in both sheets except the debt level.

Notice the "interesting" Merton dynamic (see red row at bottom): the low PD (highly rated) firm has marginal PDs which increase over time. The high PD (low rated) firm is the opposite.

But (i) it's not a fair question under our 2008 cirriculum [I really don't think we are burdened to know these Merton dynamics specifically] and (ii) I really doubt it's what the question meant given the explain...

David

 

[phwdisse]

David,

Thanks. Sheets explians the relation between maturity and PD in the Merton's model.

I'm not always happy with the practice questions.

Thank you for your time.

Paul