about time horizon effct of PD

[minnie]

hi,David
I have a wonder about time horizon effct of PD.
In handbook 4th, Jorion says with time horizon increasing, PD increases, but investment grade increases more greatly than non-investment. I see in schweser notes , however, the question is reversed.
What do you think about this question ?

Thanks.

 

[David Harper CFA FRM]

Hi minnie,

If it's on the exam, which I sort of doubt it will be, Jorion's answer will be correct. That's because (historically for the FRM) Jorion is agreeing with (in synch with) de Servigny, who is the relevant assigned text: cumulative PD increases with maturity, but more rapidly for lower initial PD (higher quality).

It's worth noting that Basel II IRB has a maturity adjustment.
Of course a higher charge for longer maturity, as you'd expect.
But maybe not as you'd expect, Basel's IRB maturity adjustment is more harsh/severe for low PDs; i.e., implying investment grade "increases more greatly" than speculative. So, since Basel II is consistent with Jorion, it's the safe bet. (although, it is my understanding that the Basel adjustment is not necessarily to reflect an empirical reality here, but rather simply to give insist on more "cushion" when the charge would otherwise be low. I don't mean to be confusing, but despite that Basel II is consistent with Jorion, it may simply be a kind of conservatism)

Couple of caveats. First, I wouldn't expect this question because GARP is pretty good about writing questions with decisive , unequivocal answers. Yet, there is a non-trivial definitional issue here: of course cumulative PD increases with maturity (it must), but what is *precisely* meant by increasing more rapidly? If 0.01% scales to 0.02% (low PD) and 1% grows to 1.5% (high PD), it's not obvious to me that, just because the low PD doubles, that it's increasing more rapidly. I just finished Altman's latest book, he has authority on this, and his research (based on moody's & S&P shows empirical anomalies; i.e., so you couldn't make a sweeping generalization with it. That's why i tend to think GARP would not ask this, because it can be argued.

The other thing I briefly wondered about refers to definitions. GARP will be good about definitions. I assume you mean "cumulative PD" but I wondered initially if you meant "marginal PD." As always, but esp. here, it may help to focus on the language of the questions. I don't have the schweser question/notes but it's possible they are also correct because they mean something different? hope that helps, interesting question for sure!

David