Transition Matrices

[IAmEric]

Hi,



We've had what I think is an interesting and useful discussion of perturbing transition matrices over [url=/Show%20Post.aspx?PostIDKey=96461]here[/url].



One question I have is the nature of the ratings transition matrix. And even the nature of ratings themselves.



I understand to a certain degree that ratings get assigned to individual securities. As a result, the same issuer can have securities of various ratings depending on subordination and things like that.



On the other hand, in the news and in conversations you'll hear things like "Did you hear that XYZ got downgraded?"



I'm trying to reconcile the two points and asking here rather than create a distraction in that other thread.



Johnny is suggesting that the ratings transition matrix is computed from security ratings rather than issuer ratings. I have no reason to disagree, but am confused and am looking for some clarification. I was under the impression that the ratings transition matrices represented migrations of issuer ratings. The distinction between issuer ratings and individual security ratings is significant because a single issuer with lots of outstanding bonds that got downgraded would have different impacts on the "ratings universe" depending on which approach you were considering.



Of course, the answer is (as filthy often points out) "It depends".



I'm not sure if I even asked a question, but am throwing this out there in hopes of gaining some wisdom through whatever may come back Smiley



Eric

[Johnny]

I agree with IAE, there are interesting questions here. However, my main point wasn't to focus on the difference between issuer ratings and security ratings. Just for clarification, here's what I actually wrote on the other thread:



Yay, I'm glad that we're in agreement. Or almost, anyway. You wrote that the model is trying to model a given set of issuers, but that's not quite true. What a credit ratings transition matrix does is to model the proportion of issues at each rating next period (week, month, year &c) given the proportion of issues at each rating this period. The set of bonds next period is different from the set of bonds considered this period. By allowing the set of bonds to change from one period to the next, the model places no restriction on issuance by new as well as by existing issuers. It also implicitly allows bonds to come back from default. It's a Markov model, it doesn't remember that a bond ever defaulted if it's currently alive.



However, as you wrote, this is not the way in which they tend to be used. In simulations, default is usually treated as an absorbing state and issuance is not explicitly modelled. This all means that there is a disparity between the way that the models are set up (as in my first paragraph) and they way in which they are used, e.g. in simulations. I think it's as well to be clear about this disparity.

[tristanreid]

Memorized CFA definition (for what it's worth): A bond rating is an issuer's ability to repay their senior obligations with a maturity in excess of one year.  Issues with support mechanisms such as letters of credit or other indemnity are specifically excluded, but those issues may be explicitly rated.



So for each issuer, there can be a collection of interdependent ratings. An issuer will have seperate ratings for senior bonds and for preferred stock, for example.  Does that fit your mental image?  More importantly (to all y'all others) did what I said make sense?



-t.

[kr]

First, there are indeed issuer ratings and issue ratings. To be really honest I don't quite understand what is meant to be captured by issuer ratings, other than the fact that in some cases, all debt defaults at the same time through cross-acceleration clauses. But for any practical purpose I think it's pretty useless. The fact is that nearly any company that has debt claims will have different types of debt claims with different credit risks, and those credit risks might even be pretty tenuously connected with the operating performance of the business. If you are modelling, you shouldn't be comparing bank tier-1's with general unsecured, you shouldn't compare bank loans with senior sub debts, and you definitely shouldn't consider real estate securitisation debt for the corporate branch network with corporate financing for 'general corporate purposes.'



I think J's thrust is a bit different though, and I don't think I agree. Moody's ratings analysis is very cohort-specific. They publish empirical results by year and horizon. In practice people take explicit averages over the year parameter, and implicit averages over the underlying universe. This last bit is a lot of trouble to define properly, and just as an example people talk about defaults in number vs. defaults in size. These can be pretty different b/c credit cycle is often about the rapidly expanding amount of debt that can be raised on weaker and weaker terms, leading to a skew of the size-based numbers to defaults in a few headlines names. On the other hand if you are a portfolio manager, those big deals got done b/c everybody was buying them, and you're more likely to have gotten dinged by those same megadeals-turned-megadogs.



On the year-averaging thing, rating agencies claim they 'rate through the cycle'. I don't know what bank loan officers claim. In fact I don't know what this phrase is supposed to mean. In a very narrow context, mortgage deal tranche attachment moves around when the ratings people get nervous - see news on US subprime for example, where this is leading to the downgrade of recent deals through their moving of the goalposts. Is this 'rating through the cycle?' That's a rhetorical question, because any year-averaging scheme is a lowpass filter which more-or-less denies the existence of cyclical factors in downstream application.



On the 'universe' component, I think it's pretty commonly accepted that some sectors are more cyclical than others. I am thinking about cycles a lot right now, but for credit I'm not totally convinced. Yes, you do see big default waves that hit sectors, but the anecdotal reasons for downturn are not primarily from the operating profits diffusion wandering into the bad half-plane. From recollection:



- telecom... huge CAPX plans not fully financed at initiation and a sudden change in competitive landscape due to technological evolution (mobile phones)

- airlines... 9-11 related downturn in flight demand

- auto parts... competition structure and spike in steel prices

- energy... unregulated trading platforms collided with imaginative financial engineering followed by counterparty credit contagion?



I don't see any of these as a result of some hidden sinusoidal driver. But, it does highlight that just studying transition matrices will not result in a model that is qualitatively complete. In terms of this thread, my point is that the procedure used to construct these matrices in the first place has some bad assumptions baked into it from the get-beginning, which explains why 'it depends' is probably the best answer.



Some nice economics notes that fit into this discussion can be found here (compare 'horizontal', 'vertical'):

http://cepa.newschool.edu/het/essays/cycle/moneycycle.htm

[IAmEric]

Thanks kr.



I'm still a noob at all this, but the way I'm starting to think about it (which may be totally bogus) is that a credit is a credit and there should be some underlying credit profile that determines how much you should be paid for taking on various kinds of risks from a particular issuer. Acknowledging that its like driving by the rearview mirror, I think the transition matrix gives some indication of a rough first order approach to modelling a credit's migration.



As far as why ratings agencies rate different securities from the same issuer differently, that is still kind of a mystery to me. The differences among the various securities should be accounted for by some kind of recovery rating. Is that the way we should think of subordinated ratings?



It seems like there should almost be two separate ratings. One to denote the risk of the issuer getting into trouble and a second rating denoting the seniority or recovery risk in the event the issuer does get into trouble. Maybe that is the right way to think of the security ratings, but then we need to somehow divorce that from the ratings transition matrix if we're trying to use it as a credit migration model.



To incorporate information from financial statements or the credit cycle, I think that is where Martingale's question about perturbaing transition matrices may be helpful. At the moment, I'm still so far down the learning curve that I'm happy with what I can learn from a transition matrix. Once I learn more, I'd like to incorporate more specific firm-level information, and finally information about the credit cycle.



Thanks for the comments. This certainly adds to the NP knowledge base and I'm sure I'll be referring back to this stuff as I progress.



Cheers Beer

Eric

[kr]

"Recovery ratings" are part of the game now, which is helpful, but apart from that, it really is possible that different securities have different default times, even if they are 100% correlated. For instance, bank tier 1's can get wiped out without creating an event on the more senior capital - that's why they are tier 1 after all. Corporate bank loans could pay right through bankruptcy because of 'adequate protection' clauses and the idea that the bankers are basically in the driver's seat. Whether second lien could default separately from first lien is a function of the intercreditor documentation which is bespoke and might leave such a possibility open. Finally, WBS-type arrangements and other securitisation or asset-based loan structures have this exact logic behind them - that without the specific asset secured by that particular piece of debt, the operating company is toast, and moreover there may be a fallback user for the asset that is structured into the loan... point here would be to separate the operating company from the asset performance. You can see how this is very clear-cut for subprime loan originators who just flow-through the cash, and if they blow up, somebody else steps in to ensure that the cash goes through.



From a modelling perspective, it's absolutely fine to use 100% correlation in a copula-type approach - this just ensures that the default events would have to occur in a certain order and nothing more.



On your first point, the problem comes from taking an averaged piece of data and using it for a specific underlying. It can serve as a benchmark but all caveats apply. You see this at its worst in the whole Rock-Bottom Spreads idea - i.e. that one should find some kind of 'arbitrage' by taking names that trade cheap to their rating. Of course a whole industry has grown from this (single-tranche CDO)... but the premise is really that 'a rating is a rating', which is simply false.



Beyond all that, disagreement of opinion is what makes a market - what you get paid to take risks isn't necessarily where the market clears, hence all the shuddering about things being too tight (what I would call 'negative real credit carry').

[IAmEric]

Worship



You've managed to put a crack in my ignorance. I'm now convinced that the way I've been thinking is wrong. Now let's see if I can take that and turn it into something useful. Thanks. I'll get the hang of this stuff eventually Beer