Basel II

[jyothi1965]

David

In your Basel II movie you mention that under the simple method, the risk weights of the collateral is substituted for the counterparty while the exposure itself is reduced in case of the comprehensive approach.

I think the Basel II document says that even under the comprehensive approach, if the volatility adjusted exposure is greater than the volatility adjusted collateral, the difference will be multiplied by the risk weight of the counterparty. This means that the methodology is still the same as simple method.

Secondly, under standard haircuts, the supervisor can specify the haircuts. Question - is this for exposure or for collateral or for both?

Grateful if you could reply

Jyothi
Bahrain

 

[David Harper CFA FRM]

Hi Jyothi,

Yes Basel II does say that and it's likely the typical scenario: volatility-adjusted exposure would typically be greater than (>) vol-adjusted collateral. It would be true even for a fully collateralized exposure due to the haircuts that are meant to widen the differen between the two. If $10 exposure were collateralized with $10, the adjusted exposure under the comprehensive approach would likely be positive = (10 + haircut) - (10 - haircut - fx).

But this is different than the simple approach. Say the exposure is $10 and it collateralized with $5.

Under Simple CRM, you still have a charge against all $10, it's just that you get to substitute the risk weight (subject to 20% minimum) for the $5 collateral.

But under comprehensive CRM, you get to reduce the $10 exposure to something between $5 and $10: (10 + haircut) - (5 - haircut - currency haircut). That "net" exposure is multiplied by the counterparty risk weight, of course, not the collateral (since the collateral's benefit is in the reduction).

On your 2nd question, frankly I have not addressed it, so I looked at the Basel docs. I just read the CRM section and, while I do not see they explicitly say, the implication (to me) is that the haircuts are *both* supervisor-supplied or *both* internal. (Come to think of it, I suppose the use of a single haircut table implies the standard haircut is same for exposure and collateral, but that's appears to be implied rather than stated...).

So, first, I'd stress the supervisor estimates are the default (not so much that "supervisors can specify" - by default, they do specify). Subject to several qualifying criteria, supervisors may *allow* banks to use internal haircuts. And my *interpretation* of the doc, but I'd love to hear from someone fresh from practice, is banks can get their own for both haircuts (e.g., it does use the plural 'haircuts').

I hope that helps. Thank you Jyothi for joining, given your background I am please to count you as a member! David

 

[jyothi1965]

David

Thanks. On the issue of whether the haircut in the B-II doc pertains to collateral or exposure or both:

1. It pertains to both. The logic is if your exposure is hedged by the same quality of the collateral(meaning the haircut is the same), in effect, the two haircuts will cancel out (assuming that it is in the same currency. This is logical.

2 If the exposure is hedged by a lower quality collateral (haircut is higher), then the two will not cancel out. The exposure will thus higher. and so will be the capital charges.

3 If the exposure is hedged by the highest quality collateral (cash), the haircut is zero and in effect this will be eqvt to the on-balance sheet netting.

Is this reasoning correct?

Jyothi

 

[David Harper CFA FRM]

Hi Jyothi,

1. Not cancel each other out. The formula is (Exposure + haircut) - (Collateral - haircut - currency mismatch). So if, for example, both happened to be 2-year A-rated, haircut is 6% and instead of canceling out they *increase* the difference by 12% (rounded, not exact!): (Exposure + 6%) - (Collateral - 6% - currency mismatch).

2. If applied as above, then yes, correct. Lower quality collateral -> higher collateral haircut = greater net exposure (net = adjusted exposure - adjusted collateral).

3. Similar but not the same, I think. First, CRM does allow for on-balance sheet netting. But under advanced approach above, if the exposure is instead "merely" collateralized with cash (e.g., lack of enforceable netting agreement), the exposure would still be volatility-adjusted (+ haircut) Cash as collateral has a haircut of "zero" so in that respect, it is like netting. (you could still have the currency haircut). So, by my logic, the economic difference between the two is the exposure haircut.

I would like to summarize where we are, just in case other FRM candidates read this, who might be new to Basel II (and don't need to know all the details):

1. Among the original Basel's many shortcomings, it takes a crude "all or nothing" approach to credit risk mitigants. Mitigants provide cushion/protection - they "mitigate" the exposure and include Collateral, Guarantees, Derivatives, and Netting.

2a. Basel II improves recognition of mitigants. Under the STANDARDIZED approach to credit risk, there are two routes: simple and comprehensive. Simple CRM replaces the counterparty's risk weight with the collateral's risk weight, for the secured portion. Under Simple CRM, capital is charged against the entire exposure, it just may get the benefit of a lower charge for the collateralized portion.

2b. Comprehensive CRM is nearer to treating the NET EXPOSURE, which is EXPOSURE - COLLATERAL. Except that there is a sort of basis risk between the two - their values do not track perfectly over time. So, Basel makes the bank INCREASE the EXPOSURE and DECREASE the COLLATERAL with haircuts (and further, if their is a currency mismatch). So the charge under comprehensive CRM is against the "net" exposure: (Exposure + haircut) - (Collateral - haircut - currency mismatch).

3. Under the IRB approach to credit risk, an FRM candidate does not need specific knowledge. Since the IRB is a function based on PD, LGD, EAD and Maturity, hopefully you see that it is natural to deal with collateral in the LGD (loss given default) parameter. Under IRB, CRM will reduce the LGD.

 

[jyothi1965]

Thanks David. That was helpful.

On the issue of the ASRF in Basel II, I wanted to bounce some ideas on the similarity between this approach in credit risk and market risk. Please let me know if my thinking is right

In market risk one way of simplfying the portfolio risk is to take a diagonal model approach (jorion), where in risk is attributable to a single factor (the market portfolio, if it is the stocks). That way it is possible to ignore stock specific factors and focus only on the systematic risk. The approach in the ASRF seems to be conceptually similar. But what exactly is the single risk factor?

Secondly, by taking conditional EL and then subtracting EL, we are in fact taking the eqvivalent of the concept of the worst case loss (WCL). This effectively means that in modelling credit risk we are better off estimating the tail using a WCL approach.

However, where the ASRF differs from the market risk approach is in in not taking correlations into account. Or rather the assumption that by taking a ASRF approach in a finely granular portfolio, correlations can be ignored seems to be a big simplification.

The subsequent models, especially the multifactor model (which is again conceptually similar in market risk) seems to do a better job especially the Pykhtin model and as corroborated by other researchers later.

Lastly when we talk of a paramteric approach in modelling credit risk, the BET model seems to be the choice according to the LO. But in what ways is the BET different from CSFB's CreditRisk+ portfolio model - both of them model only default risk and not deteriorations.

As I mentioned, these may not be directly relevant to the FRM, but recognizing similarities in concepts seems to be a great way of sticky learning!

Thanks

Jyothi

 

[David Harper CFA FRM]

Jyothi,

Sticky learning, fantastic! (It is the new BT mission statement...)

Yes, I think the parallel to market portfolio models is correct (somewhere I recall, in commentary around the regs, they acknowledge as much). The ASRF reminds me of the market model, too. But I think it also misled me into the question, what is the single risk factor (because, for CAPM, the factor is the market equity premium, and with multi-factor [fundamental] models, you know what the factors are!) When writing the notes, this question vexed me for over a week, and no one could tell me what the single factor was! But the answer is found in a careful reading of (assigned reading) “An Explanatory Note on the Basel II IRB Risk Weight Functions” (attached below as PDF). In words, they claim the systematic risk factor "reflects the global state of the economy" but mathematically there is no factor substance to this.

Above I put the IRB function. The clever folks at BIS don't really need to define the ASRF factor! They take a bank PD and transform into conditional PD with the above function. Mathematically, the "implementation of the ASRF framework" only requires a systematic confidence (99.9%) and a correlation between the bank exposure and the systematic factor (from 10 to 24%). If you look at the conditional PD above, it adjusts the PD based on (i) correlation and (ii) the 99.9% confidence. G() is the inverse normal, so the formula basically unpacks the PD then blends in adjustment, and recalculates the PD. It would be sort of like, it the company provided a beta in the CAPM, and increased exposure to the systematic risk factor were handled by a +x% to the beta. There is not fundamental factor per se in there, its implied behind the correlation & confidence.

If it helps to understand the above, imagine a zero correlation [between exposure and asset factor]. In that case, the left side of the PD adjustment is G(PD) and the right side, within the yellow highlight, is zero, and the adjusted PD is just PD. And you get zero for conditional EL - EL. That is appropriate to an instrument with only idiosyncratic risk! To understand this model is to see why it is perhaps too clever by half - can you imagine a better poster child for model risk?

Yes, I agree, conditional EL - EL is equivalent to WCL. You will see in the note, they introduce EL + UL as equal to VaR.

"However, where the ASRF differs from the market risk approach is in not taking correlations into account. Or rather the assumption that by taking a ASRF approach in a finely granular portfolio, correlations can be ignored seems to be a big simplification."

- Right, your first sentence above is backwards: the ASRF *ASSUMES* a well-diversified portfolio; i.e., it assumes idiosyncratic correlations are eliminated and that implicit correlations are captured in shared exposure to the "systematic risk factor." It is a indeed a HUGE simplification. BIS is clearly on defense over this. Over @ your prmia, Chris Walen has good notes from his meeting where this problem is cited (http://www.prmia.org/Weblogs/Regulation/ChristopherWhalen2/ )

"The subsequent models, especially the multifactor model seem to do a better job..." Well, I probably should have explained better, the subsequent models, as part of the LO are from the attached assigned reading. As such, they primary job is to fix the problem created by the assumption of granular portfolio - i.e., to handle name/sector concentrations that render the ASRF framework unrealistic.

Re BET vs. CSFB, I should probably defer to somebody with specific practical knowledge, but: the BET is very simple. I view it as corresponding to a component of the CreditRisk+ (i.e., the distribution of default frequency). The BET just takes a portfolio of exposures (say, n=100) and, owing to their histogram into sector buckets, gives you back a smaller portfolio of uncorrelated (independent) exposures. Say 100 with correlation becomes 60 uncorrelated. The the set of uncorrelated exposures can use the simple binomial function to compute default frequency. I see your point, because, CR+ only models defaults with a discrete process (Poisson, but I think that coverages will small p to binomial). So, they share in common a binomial/Poisson distribution for defaults. But the BET is a technique specifically designed to address the correlations by their sector commonality; where CreditRisk+ has no explicit way to treat correlations. It is handled through shared exposure to "background factors."

So, I would tentatively draw two differences: (1) explicit versus implicit treatment of correlation, and (2) BET only does a PD translation whereas CreditRisk+ is a model with other components

David

 

[jyothi1965]

David,

A huge thank you for this clarification.

The promptness is much appreciated. As I said before, there are opportunities for multi-dimensional learning in BT, and that is what is makes it so useful.

will go through the materials posted

Jyothi

 

[jyothi1965]

David

First of all welcome back from your much deserved vaccation...I think your really deserved a much longer one, but the way BT is attracting members.....I guess you had to come back.....

Well FRM or no FRM the committment to learn has to continue...... hope the opportunity to interact with you continues beyond the FRM mandate...please correct me if I am wrong.

I recently got time to read the documents that you has suggested on the IRB risk weight. (and I am trying to develop a worksheet on my own)

In your "Basel2 IRB Function" worksheet, you have used =(0.08451-0.05898*LN(C4))^2 (cell C9) to calculate an estimate of b, whereas the attached document (Basel IRB risk weight has a different formula as shown below.

b(PD) = (0.11852-0.05478*log(PD))^2

I am referring to the constants in the above eqn (11.852 and 5.478) - they are diffrent in the formaula in above worksheets.

Any inputs?

Thanks as always

best regards

 

[David Harper CFA FRM]

Jyothi,

Hello! Thanks for your kindness. And thanks for your previous debrief on the exam! I meant to reply, but I was going to ask you to give opinion (weigh-in) on my plan to offer an early-early-bird start (Jan 1st) for FRM 2008. The idea will be to ramp up new learners to key themes, so i'll really appreciate your feedback if you have a chance...

"....hope the opportunity to interact with you continues beyond the FRM mandate...please correct me if I am wrong" - of course, please, nothing would make me happier than if you hanged around a bit. Customers are easily my favorite people

On the IRB function. I used the function given in the (newly assigned) reading by Saidenberg & Schuermann (attached). The best of the assigned readings on Basel, btw, in my opinion. I did *not* think to check the source Basel document; I see your point, the parameters are different. Prima facie, I cannot explain the difference...as otherwise, the paper and the Accord seem to have the same IRB function...perhaps the paper is wrong, but i bet there is some difference. At first glance, I thought perhaps they refer to different exposure types but both here appear to refer to CORPORATE exposures, so I am stuck on the difference for moment

I wrote the authors (I know that's what you would do Jyothi!)...I'll update if/when i hear back...

Thanks again, David

 

[jyothi1965]

David

The attached paper is good as you say, but perhaps dated? (March 2003) ....The Basel IRB mentions that the Third consultative paper (first issued in 2003) had a different regression output then what was finally decided upon in the final accord (which was June 2004).

So I guess the authors Saidenberg & Schuermann must have taken it from the Third consultative paper (2003)....possible.

Otherwise there is no change for the regression output for a corporate /bank/sovereign or for SME and retail. The risk weight however undergoes a change.......

Thanks a ton David for those worksheets. Honestly it gave me such a great leg up in IRB. When I develop it fully I will mail you a copy.

J

 

[jyothi1965]

David

On your request to give an opinion on an early start - I had sent a longish private message but it seems that it is not reached you. Just to confirm once again that I would be most happy to give any feedback that you wanted.

J

 

[David Harper CFA FRM]

Jyothi,

Re: the IRB function. You must be right, the regression parameters likely changed and my XLS needs to be updated to reflect the latest Accord. Thanks for spotting this!

I got your PM. It's really excellent (I agree), will respond ASAP...Thanks again, David

 

[jyothi1965]

David

sent you the Basel 2 IRB worksheets as I had promised. Hope this is useful. As I mentioned, the risk weights tally with the B II document and therefore are correct. Please let me know if you need clarifications

I wrote to Kamkura's CEO to obtain the full study after reading your excellent article on CDOs. Hope to come up with some comments on that.

As I always maintained learning is central and passing the exams is incidental.

What ever the outcome of the FRM exam, I can confidently say that there is huge difference in my knowledge levels - pre-BT and post BT.

A huge thank you for all your efforts. Hoping to continue access FRM 2008 matls...on BT

Jyothi

 

[David Harper CFA FRM]

Jyothi,

Thank you so much for your email with the IRB function. I admit i have not had a chance to look at it, but really look forward to reviewing this weekend.

And for your kind feedback in yesterday's forum post...i am blushing....

Did you see Kamkura just published another study? - I asked to get it - looks very interesting. They say whole assumption about impact of correlation on equity tranche is utterly reversed (yikes!)....

David

 

[Andy]

Hi David and Jyothi,
Really some nice discussion on this thread, but here is something for which I couldn't find any concrete answer in Basel:-
Should we use currency mismatch haircut under Simple Approach for collaterals or not? I believe Basel is fairly silent on this point or does that mean to ignore currency mismatch under Simple Approach which everyone will understand is against general practice of risk management.
It will be really nice if you can provide some direct reference(Para No.) from Basel on this.

With regards,
Andy

 

[David Harper CFA FRM]

Andy,

Hi. I admit that hasn't come up for me, strangely?! Good point. If I had to guess an interpretation, which can be no better than yours, it *looks* to me that simple ignores currency mismatch. That's my guess only b/c para 184 seems to be at lease AWARE of currency mismatch w/in simple; ergo, by omission, I'd guess like you. But, agreed, it seems uncomfortably simple and I don't *really* know the answer...

David

 

[Andy]

Thanks David for clarification and now as we found our self on the same boat let me tell you that I work for a consultancy firm and suppose to answer my clients on this in couple of days.
So this takes us back to the basics and as the matter is fairly open possible solutions which I can think of goes like:-
1. As simple approach treat collateral also like guarantee but then again I doubt if a different currency collateral asks for a higher risk weight.
2. Fall back to age old concept of "conservatism" and apply a currency hair-cut on collateral in simple approach too, but then there's no mention of haircut in simple approach at all.

Can you suggest your take here, or is there any way of addressing this to committee directly via email or on some other forum?

With regards,
Andy

 

[David Harper CFA FRM]

Hi Andy,

It is always good to welcome folks with a real job

I took at look at the source framework (June 2006). Did you notice footnote 44 (page 36), in reference to cash as collateral:

"When cash on deposit, certificates of deposit or comparable instruments issued by the lending bank are held as collateral at a third-party bank in a non-custodial arrangement, if they are openly pledged/assigned to the lending bank and if the pledge/assignment is unconditional and irrevocable, the exposure amount covered by the collateral (after any necessary haircuts for currency risk) will receive the risk weight of the third-party bank."

This seems to be under collateral generally, not necessarily Comprehensive (do you agree?). Therefore, I would favor your (2), which also seems to me to be in the spirit of the CRM treatment.

On the other hand, i am a bit confused by Annex 11. Annex 11 para 43: 43. "Under the simplified standardised approach, only the simple approach from the standardised approach will apply, which, similar to the 1988 Accord, substitutes the risk weighting of the collateral for the risk weighting of the counterparty for the collateralised portion of the exposure (generally subject to a 20% floor). Partial collateralisation is recognised. Mismatches in the maturity or currency of the underlying exposure and the collateral will not be allowed. "

Confused as to Basel's treatment here, but either way, it seems to me the currency adjusting (haircut) the collateral (your #2) is consistent and, as you say, properly conservative.

Regarting committee/contacts, I don't know where to go for this frankly. The best person i know for this is Jyothi, given her background, maybe she will eventually weigh in but that won't help you in two days...

Thanks,
David

 

[Andy]

Thanks David,
And in the absence of any readymade feature I have to add one post just to acknowledge your help and pay my gratitude.
Will carry on this discussion in new light as and when it strikes.

With Regards,
Andy

 

[dphamhi]

Dear All, dear David,

it's a real pleasure to gather knowledge here.
Apparently, new light hasn't struck since June but I wish to point to a dark or shady zone :cheese:

It's the apparent divergence between Basel II relationship between correlation and probability of default ( should be smooth monotonic decreasing in exp (minus PD) ) and what comes out from many banks ' local observations ( India, France etc.) : the relationship is non monotonic and increasing most of the time.

Apparently, the dynamics in the low PD's is not what Basel II think it is ; either sampling problem (international vs local) or non-asymptotic, or even non-single factor .

Anyone has anything? either to corroborate this paradox or explain it away ?

Thanks and may the Bourse be with you !

Duc