Dowd: [(significance% * n) + 1]th

[ARwin]

Hi David.

Im a newbie here. I would like to clarify the percentile computation using Dowd's [(significance% * n) + 1]th.

if N = 260 and the significance is 99% what should be the percentile VAR be?

Is it (1% * 260) + 1 = 3.6th worst?

Others interpret it as 3th worst due to rounding of the 2.6 to 3.0 ?

Thanks for your time.

 

[Suzanne Evans]

Hi @ARwin

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If you know the specific topic, I can move this for you. Thanks!

 

[David Harper CFA FRM]

Hi @ARwin

I don't perceive a "controversy" under that scenario as the quantile seems to be unambigious: it occurs at the 3rd worst (without any rounding required). Think of it this way, working from the tail:

• worst loss = 1/260 = 0.385%
• 2nd worst = 1/260 = 0.385% and cumulatively 0.769%; and 1 - 0.769% = 99.23%
  
• 3rd worst = 1/260 = 0.385% and cumulatively 1.154%; and 1 - 1.154% = 98.85%

So, the 99% VaR falls squarely "within" the 3rd worst loss

The ambiguity arises under a discrete distribution (like this) when the VaR quantile falls right in between two losses; e.g, the 99% VaR when n = 100. When n = 260, the analog to an "ambigious" scenario would be (for example) a 98.85x% VaR where Dowd's method would imply 4th worst loss but it would be reasonable, alternatively, to use the 3rd worst. I hope that helps!