VaR Calculation

[jihan w]

Hi @lushukai and All,
I am wondering if you could help me to find the solution for the VaR calcution from the graph posted in the forum: https://forum.bionicturtle.com/...feedback-postponed-2020-exam.23675/post-86852. i.e.,

Hello all –
The questions were fairly in line with Garp’s practice exam and at least 1-2 levels easier than BT mock questions. Some of the qualitative questions gave me a bit of difficulty since a few questions required having gone through some very specific concepts in the GARP books.

From what I can remember:
[I'll Edit this if I remember something else]

• 2 questions with on conditional probability and bayes theorem. 1 question provided a conditional probability table.
• A question on Expected shortfall and VaR calculation in a discrete setting. I think the data went something like that on a portfolio of 8M USD View attachment 3089
• 2 qualitative questions on the assumptions of OLS
• There were questions that were straightforward on Option pricing. N(D1) and N(D2) lookups were not required. [Edit : One of them I remember gave me a few difficulties due to it's ambiguity. We were given N(D1) and N(D2) with dividend but also the dividend amount and asked to calculate the price of the bond. I was initially confused by that wording]
• 1 question on key rates. I do not remember it exactly.
• 1 question on the interest futures. We were given the characteristics (maturity and duration I think) of the cheapest to deliver bond and asked to to infer whether the interest rates were above or lower 6% and whether the curve was upward or downward sloping
• 1 qualitative question on Solvency 2 which is a bit astonishing given that this is not a core focus of garp reading.
• There were a few questions about volatility. 1 question asked us to calculate volatility given EWMA assumptions. There were other questions, if I remember correctly, about the relationship between EWMA and GARCH (1,1) that were qualitative.
• There was a question about the assumptions underlying APT vs the CAPM
• We had 2 question asking us to rank portolios according to the sharp and the treynor ratio.The one with the Treynor ratio require a bit of attention, we were given the fact that the ranking was being done on well diversified portfolios but with the additional constraint of the sharpe ratio not being higher(or was it lower?) than 0.35
• 2 questions on the role of Senior management. One was the role of senior management vs the Board in the context of stress testing. I cannot remember the other one,unfortunately
• Barbell portfolio from a given bullet portfolio

Concerning the exam logistics:
[Edit : As per @Nicole Seaman request below - The test location was in Paris 17 eme Arrondissement ]
It was a mess!! We had a fair share of candidates in our exam venue that came without the correct calculator. Proctors were unsure to allow them to pass the exam without the use of their calculators or to send them on their way.
Moreover, several candidates, including me, were given the wrong exam booklet. ERP i/o FRM. We asked twice and the proctors told us it was the same thing...” you will see during the exam” was what I think they said. Given that this was my first sitting, I had a lot of doubt but let it pass at first.
I had to ask them a third time to cross check before they eventually asked their senior and realised that they made a mistake. The worse of it was that those who face that issue were not given additional time to enter fill in their candidate’s details. I was prepared and was able to finish with some time to spare but I think I lost a good 5-10 minutes not including the stress and loss of momentum that such situations create.
While I understand logistic issues are problematic with the covid, the fact that the proctors did not know their stuff was quite frightening and I would go further and say disrespectful given the cost and investment that the FRM requires.

Thank you.

 

[Lu Shu Kai FRM]

Dear @jihan w ,

I do not see a specific question on the graph but I can think of several (possible) ones. The graph also looks like an equally weighted loss distribution (which may not always be the case from BT's questions):

• 95% VaR = -5% * 8M USD = 0.4M USD
• 99% VaR = -15% * 8M USD = 1.2M USD (though I remember VaR has several interpretations ... ES has no discrepancy and is much more straightforward)
• 95% ES = [(-5%) + 3*(-10%) + (-15%)]/5 * 8M USD = 0.8M USD
• 99% ES = -15% * 8M USD = 1.2M USD

Maybe you can inquire more about the exact nature of the question? I read that most of the questions were of a qualitative nature so focusing on quantitative ones may not be the wisest decision.

 

[jihan w]

Hi @lushukai,

I really appreciate your feedback.
May it be possible to explain how do you select -5% for 95% and -15% for the 99% VaR ?

I will follow your advice and focus more on qualitative question.

Thank you again for your support.

 

[David Harper CFA FRM]

Dear @jihan w ,

I do not see a specific question on the graph but I can think of several (possible) ones. The graph also looks like an equally weighted loss distribution (which may not always be the case from BT's questions):

• 95% VaR = -5% * 8M USD = 0.4M USD
• 99% VaR = -15% * 8M USD = 1.2M USD (though I remember VaR has several interpretations ... ES has no discrepancy and is much more straightforward)
• 95% ES = [(-5%) + 3*(-10%) + (-15%)]/5 * 8M USD = 0.8M USD
• 99% ES = -15% * 8M USD = 1.2M USD

Maybe you can inquire more about the exact nature of the question? I read that most of the questions were of a qualitative nature so focusing on quantitative ones may not be the wisest decision.

I agree 100% with @lushukai 's calculations!

For the 95.0% ES, I get the exact same answer per habitual application (to the same end): (-15.0%*1.0% + -10.0%*3.0% + -5.0%*1.0%)/5% = -10.0%, because you only want 1.0% of the third worst outcome to get to a total of 5.0% of the tail.

@jihan w In regard to 95.0% VaR, notice that the worst two densities (in the tail) only get you to 4.0%: 1.0% is worst, then 3.0% is second worst. To get to the 5.0% quantile, you have to go "inside the third density which has probability 26%. Visually, you are barely "inside" that third bar if you want to get to the edge of the 5.0% tail.

In regard to 99.0% VaR, the first density is 1.0% such that you are exactly "in between" the worst outcome (-15%) and the second worst (-10.0%). As Lu Shu says, this is the ambiguous case. The best answer is -15.0% per Dowd, but -10.0% is acceptable (per Jorion) and so is an interpolation or average (e.g., -12.5%). Thanks,

 

[jihan w]

Thank you all for your feedback.

 

[Lu Shu Kai FRM]

Thank you David for the wonderful details and happy birthday @Nicole Seaman !!

 

[Eyram]

Hi, David
I need clarification on VaR in terms of percentage basis and the dollar value bases when it comes to
the tails of the distribution (on-tailed and two-tailed)

 

[Lu Shu Kai FRM]

Hi @Eyram,

I'm afraid we can't answer you because your question isn't specific enough. Perhaps you can narrow it down with an example?

 

[David Harper CFA FRM]

@Eyram I've answered thousands of VaR questions over 10+ years but @lushukai is right (thank you!): it's actually difficult to understand what you are asking, usually I can pluck out the essence of the the question, but yours is too vague. I will say: VaR is always one-sided. VaR is only concerned with the loss side of the distribution. Unlike volatility which is symmetrical (ie, counts jumps in both directions)--and this symmetry is a key criticism of volatility--value at risk (VaR) is a downside risk measure (another far less popular downside risk measure is the Sortino ratio, e.g). So in regard to the standard normal distribution, for example, a typical two-sided 95.0% confidence interval is bounded by quantiles/deviates at +/- 1.96 = NORM.S.INV(97.5%) because that put 2.5% in each (rejection region) tail, the 95.0% standard normal VaR is always =NORM.S.INV(95.0%) = 1.645 because we are only concerned with the loss tail; this quantile is multiplied by a raw standard deviation, of course, to retrieve the scaled VaR. It can be percentage(%) or dollars($) and it is widely understood (and often assumed, especially on FRM/CFA exams) that the normal distribution is not realistic in the tails. Hope that's helpful,

 

[Eyram]

Thanks David