Dowd and normalization

[shanlane]

Hello,

I am reading Dowd right now. He seems to normalize everything without actually stating that he does so and this seems like a really strange thing to do, especially when discussing a non-parametric approach. For instance, figure 4.1 shows a histogram for a historical sim that is obviously normalized, because he keeps comparing his 95% VaR with the "true" VaR of 1.645.

My questions is, when asked for a historical VaR (or any VaR, for that case), should it be in $ terms or normalized terms?

If I am missing something here could you please explain what it is that I am overlooking?

Thanks,

Shannon

 

[David Harper CFA FRM]

Hi Shannon,

Great point, I had forgotten that his tendency to standardize challenged me, when i first read the book. (I have a preference for referring to this as standardization rather than normalization, if i can impersonate a pedant for a second)

Exam-wise, you won't be asked for the standardized/normalized answer: to you point, as an ANSWER, it's awkward. Instead, the standard normal is used as an input; e.g., what is 95% VaR if vol is 10%, answer 1.645*10%. For us, standard normal (or whatever) is used as an input to get to the VaR.

The more common choice is between a (non-standardized) dollar VaR or return VaR; e.g., in the above, if current value is $100, we can look for either 16.45% return VaR or $16.45 dollar VaR
... the final practical sub-distinction is between relative VaR and absolute VaR: $16.45 and 16.45% are RELATIVE VaRs, which are simplifications of the better ABSOLUTE VaR. That is, assume a +10% drift, and now we can refer either a relative VaR of $16.45 / 16.45% or an absolute VaR of $6.45 or 6.45%.

So, imo, the most general (useful) normal VaR (and this is from Dowd): VaR = -drift + volatility*(deviate; e.g., Z), in either $ or % terms, which is an absolute VaR that reduces to relative assuming drift is 0.

The reference to historical sim (a non-parametric approach!) is interesting: the exam, to my knowledge, does not do it (and maybe never has). This is for a good reason: to standardize a historical set is to "impose normality" (or whatever is the distribution). This is really data fitting. We don't want to get confused about that. A primary advantage of HS over parameteric methods is that we don't need to be limited by the specification of a distribution (e.g., we don't need to be limited to non-heavy normal tails). So, to standardize a HS VaR runs the risk of creating the misunderstanding that we think the data is distributed according to a distribution. We can use the historical dataset to inform the parameters of a parametric VaR; but that is a parametric approach that is not historical simulation. I hope that's helpful, thanks! David

 

[shanlane]

It is!

Thank you,
Shannon