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# Credit risk for 2013

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi GP_2012,

Not exactly, but yes in a way of speaking: yes, when retired readings are consistent with concept continuity. As I understand GARP's methodology, questions are sourced from practitioners and subsequently vetted against the assignments (does the question have a reference? ... this frustrated me early on, I had really wished they would reverse this sequence and START with the assignment but frankly I have warmed to their approach b/c it is less susceptible to test gaming techniques). The method has pros and cons, but a unique challenge of the FRM (not wholly uncommon to other exams) is its want to meet goals somewhat in tension:
1. Update rapidly: this is often under-appreciated. For example, 2013 employs Tuckman's newest edition (arguably the finest reference on fixed income), Veronesi's fantastic MBS chapter only introduced last year, and many new Jon Gregory, who is to many, the best on his topic. Great great authors.
2. Be practical (not everybody thinks it succeeds on this criteria. Some harsh critics say it fails), and
3. Be testable to the readings; i.e., be a fair test of the assignments
So, if you study the historical database of practice questions published by GARP, I think you perceive a thread of evolving continuity; e.g., there is a pattern to value-at-risk questions. To answer your question, in my opinion, the most likely sort of question is one that is both referenced in a current reading and also in previous readings. Because it has, what i will call, concept continuity. Retired readings are not necessarily irrelevant; e.g., Gujarati econometrics Chapter 1 to 8 (in my humble opinion) remains a superior reference to prob and statistics than either the two replacements that have succeeded it (for example, Miller employs more calculus than will be tested!... i would love to see calculus tested but i think the Miller text will probably need to "season" a bit before we see any real calculus, is my guess).

The point is, the concepts are supported by the readings. Especially in Part 1, the bullet-point concepts have been very stable. So they are important, e.g., "Value-at-Risk (VaR): Applied to stock, currencies, and commodities; Applied to linear and non-linear derivatives; Applied to fixed income securities with embedded options; Structured Monte Carlo, stress testing, and scenario analysis; Limitations as a risk measure; Coherent risk measures; Volatility Models" ... but is Linda Allen Chapter 2 & 3 necessary (or even best) for these? I personally don't think so ...

(another example, due to reading switch, Bayes Theorem dropped from the 2012 AIMs only b/c Stock & Watson don't actually cover it ... but me and my informed customers nevertheless advised to still learn it ... and sure enough, Bayes was both included in last year's practice exam, and it's back on this year .... so the continuity trumped the particular reading. FWIW).

This is clearly frustrating to some candidates, but my impression is that it is less frustrating to those who are into the concepts and applications and maybe more frustrating to those who want to be able to predict what questions will be asked. I hope that is helpful, it's all just my opinion, nothing here is "endorsed" by GARP ... my conveyance of their approach was last checked by me near the end of 2012, I can't even promise they haven't updated their methodology, thanks,

#### Mark W

##### Active Member
Very informative post David - thanks.

#### RiskNoob

##### Active Member
Just going back to the initial discussion...

Hi RiskNoob,

Thanks! Yes, I have been thinking about this (because I really look forward to speaking with GARP about T6 at the next opportunity to ask, what were you thinking?). I can say with high confidence that for 2013 the "time-trap" lies in the technical (advanced) aspects of Jon Gregory: many of his technical concepts and discussion have very little chance of getting onto this year's exam. I do not refer to introductory counterparty risk concepts, which remain very testable; for example, you do want to spend time on the metrics (e.g., current exposure, EE, PFE), basic exposure profiles, conceptual MCS (e.g., what process might we assume for equities, FI?), and mitigants. But most of that is contained in the earlier portions of (to some extent Malz &) Gregory.

Where I would not get time-trapped is the technical/quantitative concepts in later Gregory: GARP has yet to produce a single question (sample or otherwise) to query this yet, I don't know why they assigned so much of Gregory, he is way over-assigned versus testability. For example, look at the GARP sample exams: I don't see a single Gregory question?! The counterparty questions are all squarely in the "introductory" segments.

CVA is the prime example: I frankly would not go deep (I mean, unless you want to out of intrinsic interest, Gregory is the best text although the organization is a bit woeful with overlaps, we totally supported it, we just had no idea that he'd show up this much but ...). In the notes, i included last year's Canabarro CVA because it's more accessible, quantitatively, and they have yet to test a simple calculation of CVA (to my knowledge), so the odds of a difficult CVA calculation have got to be pretty near zero (qualitative? yes, i would study it qualitatively, but that requires far less time).

That's my summary guidance: introductory/foundation counterparty risk (e.g., CVA) is clearly important, but as you go deeper into Gregory, you can increasingly tilt toward the qualitative/conceptual because the advanced counterparty quant has ~ zero chance of appearing (in 2013, we'll see if/how it seasons).

I'll definitely have more practical guidance in the videos, but I hope that helps, thanks!

Actually, I started/finishing Gregory's assigned core readings (week 7 in GARP's reading plan) - David's comment was really helpful to study it efficiently (less than 1 week) while reading entire sections in assigned Gregory readings.

In my opinion, Reading Jorion's Chapter 7 (Portfolio VaR, in T8) in advance would definitely help to understand the later readings (quantitative and pricing) in Gregory. The counterparty risk (exposure) quant terms in Gregory (quantile measures such as EE, PFE, or some measures involving calculus terms such as Marginal/component, incremental CVA) are very similar to the VaR-terms covered in Jorion's. And Jorion's Ch 7 reading is already extensively covered by BT.

I agree with David that several quant calculations in Gregory could be quite tedious which might have low testability (e.g. Complete bilateral CVA calculation) but most of quant sections are explained and complemented with great examples - graphs. It was not that time consuming than I thought and I definitely recommend read all of Gregory's readings if anyone has to read the core readings.

On the other hand, some of the readings in Malz (Don't get me wrong, it was one of my favorite readings in P2 so far) could be a time trap with low testability (e.g. Simulation using Copula, Some scenario analysis in Structured credit product).

RiskNoob

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Awesome share RiskNoob, thank you, I bookmarked your comment for future sharing, thanks!

#### RiskNoob

##### Active Member
No problem, there were several typos in the reply, most of them are corrected.

Also, I saw few AIMs in Malz readings are not included in the current 2013 T6 notes, yes, understandable, the calculations are quite tedious and long. Expect low testability.

RiskNoob

#### Johnson

##### New Member
Hi David,
I was going through the sample 2013 paper of GARP and found that it was quite heavy with questions on spread risk of Malz which is a new addition.So should we try to emphasize on the new additions or continue with the process as decided before of it being of low testability.
Also in Market risk(sorry changing the subject here) how relevant and important would be the new chapters of Tuckman on Science of term structure,Evolution of short rates and shape of term structure,Art of term structure modelsrift and volatility&distribution.
I hope to get your reply sooner with just couple of days remaining.
Thanks..

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi goal2013 - I did not think that I quite exactly said that Malz was low testability? I thought I said 80% of Malz/Gregory can't be tested (mathematically certain), the low testability among the new credit is almost surely the advanced Gregory, and some of the Malz is low testability (in May, due to high technicality). It's just a general point, please try not to put too fine a point on it, I have no special predictive powers, I am just applying history with common sense and making probabilistic assertions.

That's said, we've almost done writing new PQ for the new Malz (Suzanne is currently preparing Chapter 8 Malz).

In regard to the 2013 GARP sample paper, it is interesting: I count three Malz questions and none of them are uniquely new due to Malz. All three questions could have been asked last year, or the prior two years; i.e., they apply none of the new Malz (consistent with my "prediction"). They are:
• Apply the CDS valuation, which is that PV(premium payments by protection buyer) = PV(contingent payoff by seller). CDS valuation has been in the FRM for 5+ years
• The other two, to your point, are classic FRM questions (which barely depend on Malz) about using the no-aribitrage idea to find a probability of default; i.e., 1 + r = (1 - π) * (1 + y) + πR. This is classic FRM P2 credit risk, GARP loves to query this (questions 7 & 8)
So, yes, definitely prepare for the basic credit spread ideas. Question 7 in the sample is typical default-as-Bernoulli (classic!) but Question 8 is so predictably popular (i.e., you can expect to see it) that I am obliged to copy it here:
"Consider a 1-year maturity zero-coupon bond with a face value of USD 1,000,000 and a 0% recovery rate issued by Company A. The bond is currently trading at 80% of face value. Assuming the excess spread only captures credit risk and that the risk-free rate is 5% per annum, the risk-neutral 1-year probability of default on Company A is closest to which of the following?" --- Source GARP 2013 Sample Exam Part 2, Question 8 [cited due to very high testability]

Re: Tuckman on Term Structure: We've finished questions on those (it took has taken me a long time to write all the new term structure questions). It's relatively difficult material; I think it's hard to test on, frankly. I worry GARP over-assigned Tuckman and Gregory such that they'll have to retreat it later ... it is clearly a lot to absorb. But i really don't know about the newest Tuckman term structure material, to be honest, with respect to May testability. I won't be surprised if it shows up on the light side. Tuckman term structure and key rate had already been in the FRM before, with low testability to date, so i was surprised they basically doubled- or tripled-down on the this material (multi-factor) they weren't highly testing before which, to me, could have a meaning in either direction. It's a long way to say I don't know, please don't infer low testability (I spent > 100 hours writing questions for it, so i take that section seriously). Sorry for long response, I am short on time (editing PDFs) so my unedited answer. Thanks!

#### Johnson

##### New Member
Hi David,
I have few queries:
1.Can you plz elaborate on the sample question 8 mentioned above as they have used a second formula with recovery rate=0 and am unable to get the ans.And also like what would have been the change if the question had given recovery rate say 8%.(would b great as its imp concept)
2.In sample Q 6 on CDS valuation, I am unable to get the logic as to accrual premium.I think this is a silly query in my mind as if it is assumed that it will default halfway thru the year then we considered payoff leg with discounted 6 month payment from seller with default but in premium leg we should consider only 6 month accrual and why along with it 1 yr without default discounted pay is considered?Sorry for a basic question.
3.I was solving previous GARP papers in which, in Exotic options questions are asked like what will be vega for digital call,gamma for out of money digital call,and delta vega gamma for some other options.I am unable to answer it and I couldn't find it in the videos.Will b nice if you can tell the logic behind it or the link where I can find the answers to these.
4.In credit risk capital req standardized approach, while solving the example in the videos you had mentioned that we should know weight of 50% for A rating corporation. So there are 4 tables given for risk weights of sovereigns,bans (2 options) & corporations. So are these tables to be remembered for the exam?
Again my apologies for combining questions of different subjects here.I am in bit of a panic state with just few days for exam.
Thanks a lot.

#### Johnson

##### New Member
Hi David,can you plz reply to my post above.I understand you are short on time. But would be great if you can,will be of immense help.Thanks

#### Mark W

##### Active Member
Hi goal2013,

You might have to be a bit more precise about point 3 at the least...and probably points 1 and 2 as well. Try and make it as easy as possible for others to answer your questions (i.e. repost it or link to it) - if people have trawl PDFs to find it, they probably won't...though David being David will if he has time which he's no doubt very short of this week.

Re. point 4 - I doubt very much we are expected to know this...it's certainly a bit pointless. So it's up to you if you have the spare capacity amongst the grey matter with everything else.

Thanks - Mark

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi goal2013,
1. The second formula in the answer to 8 does not make sense to me, it looks like a typo, I do not recognize it. If the recovery is zero, then the first formula reduces not to the second formula but to the much simpler: 1 + r = (1 - π) * (1 + y), such that under recovery = 0, PD = 1 - (1+r)/(1+y).
Far more important is the logic of the first formula, which is expressed by Malz as:
1 + r = (1 - π) * (1 + r + z) + πR (Malz p 203); where yield (y) = risk-free rate (r) + spread for credit risk (z), such that we get the first formula in sample question 8:
1 + r = (1 - π) * (1 + y) + πR.

If recovery (R) = 0, you see how it simplifies. In the meantime, it is an extremely common pattern. On the left we have the riskfree return: $1.00 will grow to$1.05, guaranteed, under these assumptions. The premise of the "=" is that, on the right, the expected (average) return on the risky bond will get us to the same place, $1.05. Sort of like, if you don't care about risk, you would pay a certain$0.50 for a coin toss that paid you either $1.00 (heads) or zero (tails) because the expected value of the coin is$1*50% + 0*50% = $0.50. There can be two outcomes, default or not. The right-hand side is just a weighted average of the two outcomes, either the bond does not default and returns the yield (y) or it defaults and returns recovery. 2. It's a good question, not basic at all. Here is a way to look at it. We could add a "hidden" fourth term to the CDS valuation, so that we are assuming a fair deal between protection buyer and seller. Keep in mind that there are the same two outcomes for both parties, trigger (default) or not: [if default: protection buyer pays the 0.5 year accrued premium] + [if no default: buyer pays the full year's spread] = [if default: seller pays the LGD] + [if no default: seller pays zero] The fourth term [seller pays zero] is not shown, but to me, inserting it helps show how we are just computing a weighted average for both sides, symbolically: PD*(accrual, assumed 0.5 year) + (1-PD)*(premium) = PD*payoff + (1-PD)*0... mathematically little difference between buyer and seller ... both sides include the full spectrum of outcomes, PD or (1-PD) 3. You are painting a wide brush, sorry, i can't ably summarize exotic Greeks. I think they each require a look; further, they really depend highly on an accurate grasp of the Greeks. I've found that often the problem is not first grasping the meaning of delta/vega/gamma: it's almost impossible to get them in the exotics (e.g., barrier) without first grasping them in vanillas. However, honestly, I would not spend a a lot of extra time in exotics, i might give them a superficial look at this point, frankly. 4. I've evolved on this, years ago, I recommended memorizing these values, because we saw them tested, but today I agree with Mark: I would not bother, I think that with the addition of Basel III, their likelihood of being tested (e.g., 20%, 50%) is much lower than in the past. I agree with Mark, I would save your memorization for more important concepts. #### Mark W ##### Active Member Seconded. I have to admit I find the solution to Q8 in the 2013 P2 exam confusing...given the information supplied in the question my first inclination was to use Stulz's formula: $$z = spread = - \frac{1}{T} \ln (\frac{D_{mv}}{F}) - r$$ which is derived simply from $$D_{mv} = F e^{-(r+z)T}$$ which uses the information which is given. With no recovery, spread ($$z$$) and $$\pi$$ are ~ equivalent? On further reflection I think Stulz's and Malz's formula are almost the same allowing for continuous vs. discrete...but I'm bored of looking at this question now. #### Johnson ##### New Member Hi David, I have few queries listing those down. 1.Gregory, chapter: Quantifying Counterparty credit exposure 1: In the identification of PFE graphs, graphs for cross currency swap, options and credit derivative(@95%) looks same.Are their any differences or they r same. 2.In the same chapter its mentioned that Consider 2 Cross Currency swaps with same maturity, one pays higher interest rate and other receiving higher int rate.Swap paying this high rate has greater exposure than reverse swap. why?As the party receiving the higher rate should be at risk with higher exposure. 3.in the case of close out netting, what exactly happens when the counterparty becomes insolvent( basic idea) operational risk( sorry combining it here) 1. 2009 practice exam.: Due to rogue trader, we estimate over 1year period there is 10% chance we could loose between$0 to \$ 100mm(not writing the whole question)will b nice if you explain it as its in EL and UL.
2. 2011 practice exam: You are manager of renowned hedge fund and analyzing 1000 share position, current stock price 80(not writing the whole question)..I am unable to get in the calculation of LC.In var calculation z* sigma was multiplied by no of shares* their price but in LC calculation its calculated as (Spread*0.5/price of shares)*(no of shares* their price).I didn't understand why it was divided by price of shares in this calculation.
Sorry if these are very basic questions.
Thanks.

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
goal2013 we are only 1 week from the exam, can you break this out separately into their forums and try to give me some help (i.e., by asking good questions with detail; it will take me too long to decipher what you are asking in some of these. You aren't even giving me the question numbers on the GARP exams), some of these have been asked/answer before, it will be easier if i can pick these off (and cross reference where possible) one at a time

(sorry, I need to support this weekend plus edit the mock exam we are trying to publish. If it weren't one week away from the exam i could spend more time). Thanks,

#### djh2121

##### New Member
I'll volunteer to help with the OpRisk questions since they are more clear in what is being asked.

#1

There's a 10% chance of having a rogue trader where the loss due to the rogue trader is uniformly distributed between 0 and 100. There's also a 20% chance that due to model risk we suffer a loss that is normally distributed with a mean of 25 and a standard deviation of 5. Some simple calculation shows that .1 * 50 = .2 * 25 so that the expected loss of both OpRisks are equal. However, UL is concerned with losses in excess of EL, and this is where the different distributional characteristics come in. The model risk is distributed normally so that the probability of large losses becomes rapidly small. In fact we can be 99% sure that given that we suffer a model risk loss event the loss will be less than 25+2.33*5=36.65. However, fo r the uniformly distributed rogue trader the same can be said only at a loss of 99. The basic intuition is that there is much more mass in the probability density function far away from the mean of the uniform distribution than there is for this normal distribution. Therefore, the losses in the tail are likely to be much larger for the rogue trader (i.e. the UL is much greater.)

#2 This is question 13 on the 2011 GARP practice exam. This is an example of Dowd's exogenous constant spread (see page 74 in BT's P2 forumla sheet). Basically we are assuming that the spread is held constant and is unaffected by the trade we are going to make. In this situation the liquidity cost is directly related to the spread. For each unit we want to trade we'll have to pay half the spread. To get this into the form that GARP presents in the answer we can think of the spread as a percentage of the asset's value, and define the "asset's value to be the mid price. When we do that we can cast the expression as follows:
LC = (# of shares) * .5 * (spread as % of asset value) * (asset value) = (# of shares) * .5 * ( ( ask - bid) / asset value) * (asset value)

Both of these expressions give a dollar value for the liquidity cost.

#### Johnson

##### New Member
Hi David,
Apologies for not mentioning the question numbers of GARP exams.Will post in the forums separately..I understand how hectic it must be with just 1 week for exam..thanks
djh2121,
thanks a lot with both the questions.(posting the question as well as answer)..The basic intuition you said,just great...that cleared the doubt totally..thanks a lot...

#### Johnny Firpo

##### Member
Hi RiskNoob,

Thanks! Yes, I have been thinking about this (because I really look forward to speaking with GARP about T6 at the next opportunity to ask, what were you thinking?). I can say with high confidence that for 2013 the "time-trap" lies in the technical (advanced) aspects of Jon Gregory: many of his technical concepts and discussion have very little chance of getting onto this year's exam. I do not refer to introductory counterparty risk concepts, which remain very testable; for example, you do want to spend time on the metrics (e.g., current exposure, EE, PFE), basic exposure profiles, conceptual MCS (e.g., what process might we assume for equities, FI?), and mitigants. But most of that is contained in the earlier portions of (to some extent Malz &) Gregory.

Where I would not get time-trapped is the technical/quantitative concepts in later Gregory: GARP has yet to produce a single question (sample or otherwise) to query this yet, I don't know why they assigned so much of Gregory, he is way over-assigned versus testability. For example, look at the GARP sample exams: I don't see a single Gregory question?! The counterparty questions are all squarely in the "introductory" segments.

CVA is the prime example: I frankly would not go deep (I mean, unless you want to out of intrinsic interest, Gregory is the best text although the organization is a bit woeful with overlaps, we totally supported it, we just had no idea that he'd show up this much but ...). In the notes, i included last year's Canabarro CVA because it's more accessible, quantitatively, and they have yet to test a simple calculation of CVA (to my knowledge), so the odds of a difficult CVA calculation have got to be pretty near zero (qualitative? yes, i would study it qualitatively, but that requires far less time).

That's my summary guidance: introductory/foundation counterparty risk (e.g., CVA) is clearly important, but as you go deeper into Gregory, you can increasingly tilt toward the qualitative/conceptual because the advanced counterparty quant has ~ zero chance of appearing (in 2013, we'll see if/how it seasons).

I'll definitely have more practical guidance in the videos, but I hope that helps, thanks!

Hi goal2103,
Thanks for the kind words! First, I will have some new Credit videos (of course I won't be able to cover all of the new Credit before May ... by November, I will). I plan to hit the highlights in new videos. With respect to Canabarro, YES, he is relevant for CVA (in fact, his approach, in my opinion, is more testable for CVA than Gregory ... only because he gives relatively simple numerical examples .... while much of the Gregory will take significant time to manifest in a test question pattern of any reliable manner).
Second, with respect to May, I suggest do not over-rotate: GARP has dropped in massive new changes, 80%+ of Malz/Gregory will (frankly) never make the May test. That number is probably too low, by sheer arithmetic (For example, I don't think Canabarro even really made the exam in 2012 and his CVA is more accesssible, it takes time for new concepts to "season" a bit). Here is my hot tip: start with "calculate" AIMs, calculate AIMs suggest something concrete and more testable. After that, I would emphasize "shallow comprehension" rather than "deep dive" on individual AIMs, you will likely only need the key top-level ideas for May. Most of these AIMs have zero chance of being tested in May. I'm referring here to Credit. Current Issues (T9) is a different sort of animal, thanks,

Very useful thoughts David! Would you let these unchanged for May 2014 or do you have any updates/new recommendations on these? (especially the approach of dealing with Malz/Gregory!).

#### Johnny Firpo

##### Member
I know times are busy but a short update of BT opinionon this topic would be very helpful!

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