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# Exam FeedbackMay 2019 Part 2 Exam Feedback

#### nikic

##### Active Member
@nikic regarding ES, we do not "consider losses beyond the VaR threshold." Averaging losses is called a conditional VaR (or less often, tail conditional expectation, TCE) which has never been assigned and is ambiguous when the VaR is ambiguous. We use expected shortfall (ES) which is never ambiguous and is delimited by the probability not the quantile.

So, for example, if T = 252 trading days and let's say the worst 10 losses were conveniently sorted and given by {-10, -9, -8, -7, -6, -5, -4, ...}, then the 98.0% ES wants the conditional average of the 2.0% tail, so it's neither the average of the worst five or six but rather it is: [1/252*(10 + 9 + 8 + 7 * 6) + ([2% - 5/252]*5)] / 2.0% = 7.976.

@Jaskarn & @nikic are you sure it was 98.0% and T = 252? because that would require a more difficult calculation than simple average of worst 5 or 6? Much easier is 98.0% ES and T= 250 because that is "squarely" the simple average of the worst five ...
Thanks David. In that case I’m not sure most people are even aware of the method you explained to calculate the ES.

I’m 100% positive it was 98% ES for 252 trading days.

#### chiru696

##### New Member
and a question to find joint probability of default when 2 probabilities and correlation was given. Straight formula.
394 starting population , over 3 years 19, 6 and 4 defaulted. what is the conditional probability for the last year? 1.2 or 1.5? I think b is the answer

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Thank you @nikic really appreciated, were the choices only average of worst 5 or 6? Because I want to contact GARP if they did this incorrectly. If it was 98% with 252 Trading days, it seems unlikely to me they offered the correct solution ....

#### yang.yorku

##### New Member
Thanks David. In that case I’m not sure most people are even aware of the method you explained to calculate the ES.

I’m 100% positive it was 98% ES for 252 trading days.
My understanding to this question is 2% of 252 day is 5.04, ES takes the weighted average beyond the significant level. Therefore start from 5 and then 4,3,2,1 are points beyond the significant level of 5.04 which should be added to take the average.

#### amit.m.sharma

##### New Member
Subscriber
Thank you @nikic really appreciated, were the choices only average of worst 5 or 6? Because I want to contact GARP if they did this incorrectly. If it was 98% with 252 Trading days, it seems unlikely to me they offered the correct solution ....
Hi David, it was definitely 252 days. The 5 worst losses were -2.8%, -2.6%, -2.5%, -2.4% and -2.3%. I remember this clearly because I was stuck on this for a long time.

#### jkowalonek

##### New Member
there was a question on unsmoothing returns
I think it was basically asking whether Sharpe ratio and volatility would be higher or lower with if they smoothed the returns on illiquid assets.

#### amit.m.sharma

##### New Member
Subscriber
Hi David, it was definitely 252 days. The 5 worst losses were -2.8%, -2.6%, -2.5%, -2.4% and -2.3%. I remember this clearly because I was stuck on this for a long time.
I was wondering if you have to convert 98% ES to 99.x %VAR to get an estimate....is this approach absolutely flawed?

#### ziminli1228

##### Member
Subscriber
Should not you take LGD into account as well, like LGD*EE*PD?

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
@amit.m.sharma it looks like you were stuck for good reason: the 98.0% here is neither the average of worst 5 or 6.

You didn't provide the 6th worst, but let's say it is 2.20% such that the six worst are:
-2.8%, -2.6%, -2.5%, -2.4%, -2.3% and -2.2%

Then the 98.0% ES is the average of the 2.0% tail (always, ES is never ambiguous) which is a bit challenging because it is:
[1/252*(2.80 + 2.60 + 2.50 + 2.40 + 2.30) + ([2% - 5/252]*2.2%)] / 2.0% = 2.5175%

@yang.yorku In regard to ...
My understanding to this question is 2% of 252 day is 5.04, ES takes the weighted average beyond the significant level. Therefore start from 5 and then 4,3,2,1 are points beyond the significant level of 5.04 which should be added to take the average.
.... that's essentially correct but, because 5/252 < 2.0% and we want the conditional average of the 2.0% tail, we need a small slice of the sixth worst loss to contribute to the average (to be exact, it contributes 2.0% - 5/252 = 0.0159%). In the example above (i.e., -2.8%, -2.6%, -2.5%, -2.4%, -2.3% and -2.20%), the average of the worst 2.0% is the average of the worst 5.04 which is tedious: the 2.20% contributes only 0.040 * 2.2 = 0.08800, such that (2.8 + 2.6 + 2.5 + 2.4 + 2.3 + 0.0880)/5.04 = 2.5175. Again, while VaR is ambiguous in the discrete distribution, ES never is, it is the conditional average as delimited by the probability not the quantile. Delimiting by quantile is convenient (e..g, average of 5 or 6) however it is ambiguous, delimiting by the probability is never ambiguous because we can always average the tail of a distribution (although it can be tedious if not lined up conveniently).

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#### kylian.mbappe

##### Member
@amit.m.sharma it looks like you were stuck for good reason: the 98.0% here is neither the average of worst 5 or 6.

You didn't provide the 6th worst, but let's say it is 2.20% such that the six worst are:
-2.8%, -2.6%, -2.5%, -2.4%, -2.3% and -2.2%

Then the 98.0% ES is the average of the 2.0% tail (always, ES is never ambiguous) which is a bit challenging because it is:
[1/252*(2.80 + 2.60 + 2.50 + 2.40 + 2.30) + ([2% - 5/252]*2.2%)] / 2.0% = 2.5175%

@yang.yorku In regard to ...

.... that's essentially correct but, because 5/252 < 2.0% and we want the conditional average of the 2.0% tail, we need a small slice of the sixth worst loss to contribute to the average (to be exact, it contributes 2.0% - 5/252 = 0.0159%). In the example above (i.e., -2.8%, -2.6%, -2.5%, -2.4%, -2.3% and -2.20%), the average of the worst 2.0% is the average of the worst 5.04 which is tedious: the 2.20% contributes only 0.040 * 2.2 = 0.08800, such that (2.8 + 2.6 + 2.5 + 2.4 + 2.3 + 0.0880)/5.04 = 2.5175. Again, while VaR is ambiguous in the discrete distribution, ES never is, it is the conditional average as delimited by the probability not the quantile. Delimiting by quantile is convenient (e..g, average of 5 or 6) however it is ambiguous, delimiting by the probability is never ambiguous because we can always average the tail of a distribution (although it can be tedious if not lined up conveniently).

#### nikic

##### Active Member
Thank you @nikic really appreciated, were the choices only average of worst 5 or 6? Because I want to contact GARP if they did this incorrectly. If it was 98% with 252 Trading days, it seems unlikely to me they offered the correct solution ....
Two of the answers directly and exactly corresponded to the average of the worst five and average of the worst six. The other two answers...I am not sure what they corresponded to, but they were very "nice" numbers too.

#### nikic

##### Active Member
I think it was basically asking whether Sharpe ratio and volatility would be higher or lower with if they smoothed the returns on illiquid assets.
I believe the answer would have been lower Sharpe ratio / higher volatility. Correct me if I am wrong. I can't recall the verbiage of the answers but it should have been along these lines.

#### nikic

##### Active Member
and a question to find joint probability of default when 2 probabilities and correlation was given. Straight formula.
394 starting population , over 3 years 19, 6 and 4 defaulted. what is the conditional probability for the last year? 1.2 or 1.5? I think b is the answer
1) If I'm not mistaken, they actually gave the joint default probablity and the individual default probabilities. You had to calculate the correlation. Direct application of formula really.

2) For this, what's the method? I can't even recall what the question wanted. Is it taking PDcum3yrs - PDcum2yrs? Or is it just (1 - survive at 3 / survive at 2)? I did it the latter way but I figured I got it wrong.

#### yang.yorku

##### New Member
Two of the answers directly and exactly corresponded to the average of the worst five and average of the worst six. The other two answers...I am not sure what they corresponded to, but they were very "nice" numbers too.
It the other two answers are all nice number, I would say they must be all wrong. because the most accurate figure should be only 0.0025% away from the average of 5 worst right?

#### a_ishrat1973

##### New Member
Subscriber
Thanks David. In that case I’m not sure most people are even aware of the method you explained to calculate the ES.

I’m 100% positive it was 98% ES for 252 trading days.
Yes it was 98% ES for 252 trading days what I thought was 2% of 252 days which is 5.04 but the answer was not tallying with this calculation

#### AHoekstra

##### New Member
Subscriber
Market Risk:
1. Lognormal VAR calculation - given annual volatility, compute daily VAR
2. 95% ES
3. 98% ES of 252 trading days
4. Mean reversion, long-run mean rate -> Answer = 0.26/0.72 = 0.36
5. Ho-Lee model computation - two period down -> Answer = apply formula, use square root for the volatility
6. Vasicek model computation -> Answer excluded the second term, i.e. dw = 0 (it was 2.08% or 4.08% or something to that effect)
7. News of merger complete or fail – shape of implied volatility -> Answer = volatility frown
8. Implied volatility of equity options (i.e. smirk) -> Answer = at the money call and deep out of the money call
9. Weighted historical simulation approaches - age, corr, vol, filtered -> Answer = filtered
10. Regresssion hedge - obtain beta value from the table -> Answer incorporated the beta provided, then direct application of the formula
11. Duration / Cash flow / Principal mapping -> Answer = Cash Flow VAR < Duration VAR (incorrect?)
12. Historical Simulation vs Bootstrapping - normal/non-normal
13. Answer = "ES at least VAR"
14. Model backtesting question at 99% -> Answer = Reject model
15. Mapping, where one of the answer was mapping long term to 6-months -> Answer = ?????

Credit Risk:
1. Stressed loss -> Answer = (stressed pd – non-stressed pd) * EE * LGD (incorrect?)
2. CreditRisk+, KMV, CreditMetrics -> Answer = CreditMetrics (incorrect?)
3. Given loan equivalency ratio, compute the Exposure at Default -> Answer = Apply formula, use LEQ on the undrawn portion
4. TRS swap - bank enters into a swap as the TRS payer to hedge counterparty risk -> Answer = When default, bank receives Par minus mkt value (incorrect?)
5. Distressed company, high volatility - impact on the value of senior debt / subordinated debt
6. Collateral – threshold, remargin period etc -> Answer = high threshold (incorrect?)
7. Securitization of auto loan pool, where auto loan pool has higher rating than the bank's balance sheet -> Answer = funding benefit (incorrect?)
8. Credit VAR at 95%, 6 defaults from binomial model -> Answer = 6*2 - 2*68*0.04 = 6.56mil
9. Risk neutral / real world default probabilities -> Answer = higher CVA when using risk neutral default probabilities (incorrect?)
10. Number of defaults given a table showing the number of surviving companies
11. Hazard rate of 0.12, probability of survival in Y1 and death in Y2 -> Answer = (1 - e^-0.12(2)) - (1 - e^-0.12) = 10.0%
12. Group of 10 (G10) meeting following the financial crisis - what changed?
13. Can't recall but one question provided a credit spread of 450 basis point annually

Operational Risk:
1. AML - Correspondent Banking
2. Compute RAROC -> Answer = direct application of formula, ignoring the figure provided for Unexpected Loss completely
3. Loss due to floods - which is an operational risk loss?
4. New CDO, assesses data quality, which is the biggest issue? -> Answer = different business units have different formats of risk data (option D)
5. Threshold of 75 million, losses that exceed the threshold – GEV / generalized pareto -> Answer = generalized pareto dist for loss severity (incorrect?)
6. Calculate endegenous liquidity -> Answer = 1.08 bil
7. Specials spreads, i.e. is specials rate above/below GC rate, and the nature of the spread before/after auction -> Answer = ????
8. Bank has identified the Business Indicator, what's next? Answer -> internal loss data for the internal loss multiplier
9. Answer = "4 exceptions is within green zone"

10. Outsourcing risk for IT -> Answer = outsourced party must receive same attention as if it is done in-house
11. Many operational errors, what must be done? -> Answer = maker-checker controls (option D)
12. Answer = "declaring cash dividend will reduce Tier 1 capital"
13. Answer = "increase in operational risk capital charge" (Question was on swap transaction, the bank gained, so there would have been increase in gross profits)
14. LTCM -> Answer = VAR horizon (incorrect?)
** A possible question on Risk Appetite Framework - let me know if there was such a question
** A possible question on Adjusted RAROC - let me know if there was such a question

Investment Risk:
1. Fama French 3 factor model -> Answer = small minus big
3. Hedge fund -> Answer = merger arbitrage and large downside tail risk like equities
4. Hedge fund -> Answer = profit from dedicated short bias strategy
5. Hedge fund, on the changes following institutional investors joined
6. Risk budgeting, 80mil US equities portfolio -> Answer = Add 50 mil of US bonds to portfolio
7. Define Incremental / Marginal / Component VAR
8. Maximize sharpe ratio -> Answer = Option A, increase allocation to the stock with the highest excess return and lowest volatility, going by ratio of excess return to volatility (incorrect?)
9. On selecting the manager with the best performance, options were alpha, mogdiliani etc -> Answer = alpha (incorrect?)
** A possible question on Portfolio VAR - let me know if there was such a question

Current Issues:
1. SOFR rate derived from? -> Answer = Large banks (incorrect?)
2. Answer = "Clustering, to detect fraud"
3. Central counterparty -> Answer = initial/variation margin introduces liquidity risk
4. Cyber risk -> Answer = sharing information with law enforcement, supervisors, regulators and private sector
Hi Nikic,

Thanks for the impressive recollection. Some additions/comments from my side which may help out

Market Risk

Similar answers, as I recall, as you. Some deviations; For Vasicek I applied formula 13.23 (page 217). Didnt spend much time on reading this question fully so maybe I got tricked on that somewhere.
On 11. Duration / Cash flow / Principal mapping -> I dont recall the answer, but I vaguely recall an option that stated that cash flow mapping had lower VaR than Principal mapping. I marked this one.
15. Mapping, where one of the answer was mapping long term to 6-months -> I believe this question provided 4 option types and asked which was mapped correctly. I marked something with a delta approach on short options? Pretty much just becaused I believed the other three to be misstated.

These are exactly the 15 questions I recalled, sorry no additions.

Credit Risk

Too boost your confidence a bit, I screwed up the first two questions as well

4. TRS swap - bank enters into a swap as the TRS payer to hedge counterparty risk -> Dont recall what I marked. Basically asked if you have a defaulted exposure that is still worth 20m; do you get par or par - 20m?
5. Believe the correct answer was that it necessarily decreases the value of senior debt. For subordinated debt this can be ambiguous.
7. I vaguely recall this. Why wouldnt a funding benefit be correct? I think it said somewhere that the assets in the SPV were of higher quality than the balance sheet of the bank. Hence, I think a funding benefit makes perfect sense.
11. I reread this one a couple of times but the question specifically stated a conditional PD under constant hazard rate I think. Answer I marked was 11.3
12. Group of 10 (G10) meeting following the financial crisis - Central risk repository for OTC trades.

+ There was a question on the friction between arranger and asset manager --> arranger has to add credit enhancement to overcome AS.
+ CVA/DVA question where two companies where shown (their CVA/DVA) in a table and there were some statements on what happened to them (e.g. credit Q decreased/increased)
+ Calculated a BCVA somwhere. Wasnt sure on it, recall marking 40,000.

Yes, there was a question on ARAROC. But this may have been integrated into another question (as part of a larger table) where it was only 1 or 2 of the options related to this? Anyways, believe that my calculated disproved the ARAROC answer and I went for something else.

++ I believe there was a question on best practices where a possible answer was spreading an annual operational risk losses charge in 4 equal parts over the year. Believe I marked this, havent actually checked if that is correct.
+++ There was an OpRisk question where the correct answer I think was legal payments required to rebuild a damaged office (or something like that?).

Operational Risk

++ I believe there was a question on best practices where a possible answer was spreading an annual operational risk losses charge in 4 equal parts over the year. Believe I marked this, havent actually checked if that is correct.
+++ There was an OpRisk question where the correct answer I think was legal payments required to rebuild a damaged office (or something like that?).

Investment Risk:

2. Portfolio construction techniques ->Fairly confident the answer was stratification.
5. Hedge fund, on the changes following institutional investors joined; Was there something along the lines of that larger HF remained (vaguely recall).
6. Risk budgeting, 80mil US equities portfolio -> Do you recall whether it was ~14 or ~16m?
8. I used E/(beta) like in the book Table 6-5 page 114. WHich were equal and hence I marked dont change anything. (not at all sure)
9. Yeah weird question. I marked Treynor ratio because it stated the pension fund was highly diversified.

Current Issues:

SOFR was something with Treasury repos the answer.
Agree with other 3.

+ A Fintech question where I believe the correct answer was that it really benefit (integration of) personal finances.

#### AHoekstra

##### New Member
Subscriber
1) If I'm not mistaken, they actually gave the joint default probablity and the individual default probabilities. You had to calculate the correlation. Direct application of formula really.

2) For this, what's the method? I can't even recall what the question wanted. Is it taking PDcum3yrs - PDcum2yrs? Or is it just (1 - survive at 3 / survive at 2)? I did it the latter way but I figured I got it wrong.
1.) Yes, handled that one similarly.
2.) I believe it was (Cumulated PD YR3 - Cumulated PD YR2)/Initial (t=0) in pool.

#### nikic

##### Active Member
Hi Nikic,

Thanks for the impressive recollection. Some additions/comments from my side which may help out

Market Risk

Similar answers, as I recall, as you. Some deviations; For Vasicek I applied formula 13.23 (page 217). Didnt spend much time on reading this question fully so maybe I got tricked on that somewhere.
On 11. Duration / Cash flow / Principal mapping -> I dont recall the answer, but I vaguely recall an option that stated that cash flow mapping had lower VaR than Principal mapping. I marked this one.
15. Mapping, where one of the answer was mapping long term to 6-months -> I believe this question provided 4 option types and asked which was mapped correctly. I marked something with a delta approach on short options? Pretty much just becaused I believed the other three to be misstated.

These are exactly the 15 questions I recalled, sorry no additions.

Credit Risk

Too boost your confidence a bit, I screwed up the first two questions as well

4. TRS swap - bank enters into a swap as the TRS payer to hedge counterparty risk -> Dont recall what I marked. Basically asked if you have a defaulted exposure that is still worth 20m; do you get par or par - 20m?
5. Believe the correct answer was that it necessarily decreases the value of senior debt. For subordinated debt this can be ambiguous.
7. I vaguely recall this. Why wouldnt a funding benefit be correct? I think it said somewhere that the assets in the SPV were of higher quality than the balance sheet of the bank. Hence, I think a funding benefit makes perfect sense.
11. I reread this one a couple of times but the question specifically stated a conditional PD under constant hazard rate I think. Answer I marked was 11.3
12. Group of 10 (G10) meeting following the financial crisis - Central risk repository for OTC trades.

+ There was a question on the friction between arranger and asset manager --> arranger has to add credit enhancement to overcome AS.
+ CVA/DVA question where two companies where shown (their CVA/DVA) in a table and there were some statements on what happened to them (e.g. credit Q decreased/increased)
+ Calculated a BCVA somwhere. Wasnt sure on it, recall marking 40,000.

Yes, there was a question on ARAROC. But this may have been integrated into another question (as part of a larger table) where it was only 1 or 2 of the options related to this? Anyways, believe that my calculated disproved the ARAROC answer and I went for something else.

++ I believe there was a question on best practices where a possible answer was spreading an annual operational risk losses charge in 4 equal parts over the year. Believe I marked this, havent actually checked if that is correct.
+++ There was an OpRisk question where the correct answer I think was legal payments required to rebuild a damaged office (or something like that?).

Operational Risk

++ I believe there was a question on best practices where a possible answer was spreading an annual operational risk losses charge in 4 equal parts over the year. Believe I marked this, havent actually checked if that is correct.
+++ There was an OpRisk question where the correct answer I think was legal payments required to rebuild a damaged office (or something like that?).

Investment Risk:

2. Portfolio construction techniques ->Fairly confident the answer was stratification.
5. Hedge fund, on the changes following institutional investors joined; Was there something along the lines of that larger HF remained (vaguely recall).
6. Risk budgeting, 80mil US equities portfolio -> Do you recall whether it was ~14 or ~16m?
8. I used E/(beta) like in the book Table 6-5 page 114. WHich were equal and hence I marked dont change anything. (not at all sure)
9. Yeah weird question. I marked Treynor ratio because it stated the pension fund was highly diversified.

Current Issues:

SOFR was something with Treasury repos the answer.
Agree with other 3.

+ A Fintech question where I believe the correct answer was that it really benefit (integration of) personal finances.
Thanks so much for adding with more stuff!

For Vasicek, what formula did you apply? Wasn’t the formula already provided?

On the hazard rate, yeah if it was conditional pd then I got it wrong.

Yes I marked the option which said spreading ops risk loss into 4 quarters.

For risk budgeting, my answer was 14mil.

Same answer as you for the fin tech question.

For TRS swap, it should be Par minus 20 million, rather than the full par...no?

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#### nikic

##### Active Member
Guys, I seem to recall a question that asked for the quarterly BCVA or DVA or CVA or something? I calculated 240000 and divided by 4 to get 60000.

#### a_ishrat1973

##### New Member
Subscriber
A risk analyst estimated hazard rate is 0.12 per year. Assuming a constant hazard rate model, what is the probability that the company will survive in the first year and default before end of second year. The answer was 10.03. Does anybody remember this! is the answer correct.