Your LVaR briefcast

[sridhar]

(I had trouble posting a comment on the briefcast page. I always get screwed by that word I am supposed to type that matches the one in the image. Don't know what I am doing wrong...) Anywho....

David: I just saw your screencast here...There might be a small boo-boo in your XLS. When you take into account the volatility of the spread, the critical z-value (at 5% significance) -- you have used the same z-value that you used for computing the absolute VaR, i.e. 1.64.

I've read in maybe Culp, that in the case where you are augmenting the absolute VaR, the critical z-value -- for the spread distribution -- should be the 2-tailed value and not 1-tailed value. Thus at 5% significance, your computation for adding the liquidity delta is:

0.5 * (1% + 1.96*0.8%)

and not the 1-tailed 1.64. Do you agree?

--sridhar

 

[David Harper CFA FRM]

Hi sridhar,

Thanks for your attention to detail (and for viewing the screencast). And thanks for f/back on the comment interface, I've got to fix that blasted CAPTHA...

I got three emails about the LVaR screencast, wanting to correct me on two issues with my LVaR vis a vis Culp.

In regards to the spread, Culp does not appear to explicitly say. John raised a question about the 2008 FRM sample exam question #36; but I think question #36 is incorrect. I think John is right to be confused by that answer. To my thinking, we want a one-tailed test (just like VaR) because our confidence only concerns the scenario where the spread widens. If we use 1.96 @ 95%, that implies we care about the other tail where the spread narrows. That doesn't make sense to me, as we are adding a "worst expected spread" to a "worst expected (VaR) loss." I'm totally open to be wrong, but so far a good source has not been identified that shows the contrary. If our only exception here is question #36, I am not so far not convinced I should budge on this but if we have a better source I will gladly investigate.

The other issue raised is the notation, where I don't use Culp's: mean - (critical value)(volatility) + (1/2)(spread).
I think this, too, is technically an error; the spread is offsetting the volatility when it should be augmenting it. I have seen sample questions get a wrong answer with this; for example, if mean is +10% and volatility is 20%, then you have 10% - (value)(20%) + (1/2)(spread) and your negative VaR is being increased to something less negative (?!)

That is why i like to follow Kevin Dowd's VaR formula:
-mean + (critical value)(volatility)

because notice how this does not leave sign errors (+/-) to chance. Because the VaR is always positive, and now we are always adding the spread:

LVaR = -mean + (critical value)(volatility) + (1/2)(spread); i.e., positive VaR increased by the spread.

David