Question about Jorion Chapter 5 (Var) Figure 5-2

[hsuwang]

Hello David,
For Figure 5-2 in Jorion's chapter 5 (JP Morgan's Daily Revenue), the Value-at-risk (obtained by reading the quantile off the empirical distribution) happens to be $-9.6M, but if we want to get the absolute dollar loss, we subtract the mean ($5.1M) from the $-9.6M to get $-14.7M. I'm not really getting the reason as to why this extra step is needed. I tried to think this through, but still can't figure out why the VAR is not $9.6M but rather $14.7M (why subtracting 5.1M?)

My only guess is that VAR needs to make its mean=0 (like a standard normal distribution). Can you please help me clarify the ideas that I'm missing? Thanks!

 

[David Harper CFA FRM]

Hi Jack,

(I moved the thread, if you don't mind. I see why you posted in Full Exam, but I meant that board to be the annotated practice Questions from the sample Full Exam I). I am grateful for your uncanny knack for spotting key issues, yet again here....

The logic is: the expected profits mitigate (offset) your loss. Jorion calls the difference absolute/relative but it amounts to: do you care about (do you count) loss compared to your initial position or your expected final (terminal) position?

In this case, if you invest the portfolio at $100 million (making this up), and the 95% VaR is realized, what is your loss? Relative VaR says loss is $14.7 (i.e., relative to the $105 MM portfolio you expected at the end of the day/period). Absolute VaR says your loss is $9.6 relative to the $100 you invested. See how this is about "relative to start-of-period wealth" versus end-of-period wealth?

Which is correct?

My view is that most experts would say absolute VaR (e.g. $9.6). When I have used relative VaR, I am not kidding, I have been flamed by practitioners with far more experience than me, telling me I cannot use relative VaR. Further, I would cite Carol Alexander (Vol IV) who says, basically, use absolute (i.e., include the expected return). There is more nuance here: if the expected return is riskless, omitting is okay b/c you are effectively merely discounting the worst expected loss to PV.

Treating the absolute as correct also has the following advantage: relative is the appropriate special case (absolute collapses to relative; mean drops out) for short periods (daily) when the assumption of zero mean return is a fine simplification. And this follows Wilmott who, btw, was assigned for this last year.

But, last year, I prepared a list of items, that i sent to GARP, for clarification, where the readings are not entirely in agreement. I am including this absolute/relative VaR item, this year, because there is arguably not an "exam consensus." Dowd and strict theory suggests absolute VaR; Jorion, on the other hand, while open-minded in Ch 5, later suggests Relative VaR is better (because, giving the larger number, it is more "conservative). And note this sample question Full E1.01 implicitly used relative VaR (where, of course, it should at least be explicit)

Hope that sheds light, if only into a deeper area of more questions for all of us! David

 

[hsuwang]

Hello David,
Sorry about posting in the wrong section (I was in a hurry and pressed "new post" on a random BT forum page that I had opened up at the time).

Thank you for the detailed explanation. Knowing absolute loss is used more common (and also how it assumes loss relative to the 100M initial investment), now comes another confusion- on the next few pages following figure 5-2, Jorion discusses the standard deviation approach to VAR, where VAR= stdev (9.2M) x 95%alpha (1.65) = 15.2M (and this approach looks natural to me from studying FRM thus far), now this seems more to me like a relative loss, but as you said, absolute loss is the more common interpretation. Does this mean for the FRM exam, we are leaning more towards relative loss?

Thanks!

 

[David Harper CFA FRM]

Hi Jack,

"for the FRM exam, we are leaning more towards relative loss?" Yes, I think you phrase it perfectly (this seems to be the default assumption). Supported by Jorion (even later) and, I suppose, the sample exam question cited. I think that is a good default assumption, unless told otherwise (though I still think we should seek clarification from GARP...frankly, they may not have addressed it internally yet).

David

 

[harifrm1980]

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