Credit VAR (Calculating WCL) [Jorian FRM Handbook Example 23.5]

[mikey10011]

Could you flesh out a bit more how Jorian found the Worst Case Loss (WCL) at the 99.9% confidence level in FRM Handbook Example 23.5 (p. 534)?

Obviously because I don't really understand the "physics" (or "economics") but in computing Credit VAR or Unexpected Loss for the 99.9% confidence level, where is the 2.645 multiplier to the standard deviation?

 

[David Harper CFA FRM]

Mikey,

UL(confidence) = VaR(confidence) - Expected Loss (EL)

The tricky part is the VaR(99.9%). It's a bernoulli (bionomial) variable: one bond that will "no default" with 99.83 and default with (1-99.83%). To answer your question specifically, this is a binomial distribution with only 1 trial, that's why we don't use a normal deviate (e.g., 1.645, 2.33).

So, for a binomial with only two states [no default @ 99.83%, default @ 0.17%], what is the 99.9% VaR? It's 1.0. For any confidence <= 99.83, VaR = 0; for any confidence > 99.83, VaR = 1 (or 1 * $1MM, in this case). For what it's worth, the excel function would be CRITINBOM(1 Trial, 0.17% probability of sucess, 99.9% alpha) = 1.0. That's the issue, it's discrete and so VaR falls awkwardly on the entire amount or on zero (which, btw, is why VaR won't be coherent here)

David

 

[mikey10011]

Wow, your response was totally *awesome*!

I sort of understand what you are saying but per Jorian's example could you give a heuristic (rule of thumb) on "VaR falls awkwardly on the entire amount of or on zero? At this stage of cramming the last thing I need is to memorize the Bernoulli distribution.

Also, could you elaborate on your *coherence* (which I take to be the lack of diversification due to the lack of subadditivity)?

p.s., Consider this a low priority inquiry--just trying to understand. ;-)

 

[mikey10011]

Oops, one more (should be a trivial) thing. Could you create a PICT (and you agreed that you could do this by pasting it into EditGrid) of the symbolic math of Jorian Eq (23.10) [page 533] for the discrete Bernoulli distribution: aka CRITINBOM(1 Trial, 0.17% probability of sucess, 99.9% alpha) ?

 

[David Harper CFA FRM]

Hi Mikey,

The Bernouilli/binomial distribution is not assigned for 2008 FRM (the handbook is not necessarily relevant).

Here is a post about coherence that uses bonds to show why VaR is not subadditive (a binomial is used here, but individual VaR is generally not subadditive for any non gaussian/non eliptical distribution). For the exam, i doubt subadditive can be tested deeply, just remember: Individual VaR, or any generally unspecified VaR, is not subadditive (not coherent) but Component VAR (by definition) is subadditive.

Re the heuristic, I took that spreadsheet and made this simple illustration:
https://www.editgrid.com/bt/admin/example_23.5

Maybe this will clarify. It describes a single bond, par $100, with PD = 1%. Then the VaR for confidence levels. Please note: given only two outcomes, the VaRs are either 0 or $100. This is the issue: the distribution is discrete, so the VaR (%) falls into 0 or 1.

(Re the image, where would i put that? to what end?)

David

 

[mikey10011]

Re the image, where would i put that? to what end?
Two reasons: (1) alpha-numeric symbols are hard to read and understand; and (2) to do the *mental translation* of computing VaR under a *continuous* distribution in Jorian Eq (23.10) [page 533] to a *discrete* distribution.

I think that your EditGrid accomplished the latter. Thanks!


Re The Bernouilli/binomial distribution is not assigned for 2008 FRM (the handbook is not necessarily relevant).
I disagree. The binomial distribution is foundational in computing/manipulating PDs and as your EditGrid showed, its use in the FRM Handbook question was incredibly *trivial*--with the caveat of once you see it. ;-)

 

[David Harper CFA FRM]

Mikey,

"I disagree. The binomial distribution is foundational in computing/manipulating PDs and as your EditGrid showed,"

Right, good point. Yes, foundational indeed. But then don't you also think it (binomial) should be in the AIMs/Learning outcomes, otherwise the foundation is not set? Similar to, just to name one example of many examples I could cite, a transition/migration matrix is not formally introduced via assignments/AIMs (But, it too is foundational) I would be interested in your feedback as my #1 feedback for GARP this year is:

1. Be more consistent from the assignments & AIMs to the exam.
2. Try to develop consistent methodologies (e.g., compound frequencies) and points of view (e.g., procyclicality) where different readings may give different viewpoints (e.g., LVaR)
(3. Vet the sample questions for accuracy)

My program is based on adhering to assignments/AIMs but there seems to be a non-trivial concern, based on sample questions (a concern i frankly share) that exam may stray from the assignments. On this forum, there are a non-trivial number of topics that candidates are studying that are not strictly on the AIMs (e.g., b/c they are in handbook) because, well, maybe they will be tested but we are not sure (?). The issue is: limited time, candidates aren't lush with time to go down blind study alleys. Or, the other way to go is abolish AIMs. But it seems to me, either you use AIMs or you don't, but if you do they should be comprehensive and largely representative.

Thanks for any f/back you have on this, David