General VAR question and confidence Interval

Hi David,

I'm trying to grasp the big picture regarding var.

a) In general -- if there were NO exceedes in VAR (supposing you have a VAR model and evaluating the effectiveness of the model), then you would say that the model is not a very good one, and it's set too low, as you would expect there to be exceedences of var.

b) However, a higher VAR entails a GREATER degree of confidence interval (i.e. 95% is 1.645, 99% is 2.33) -- i.e. greater accuracy -- yet this would only make it even MORE difficult to exceed the VAR, no?

Generally -- we would want a higher confidence interval to map a greater level of accuracy -- isn't that true? Plus -- you don't want a VAR to be too low, so as to be UNDERSTATING your potential losses.

I'm trying to reconcile point a) and point b.

Thanks!
 

David Harper CFA FRM

David Harper CFA FRM
Staff member
Subscriber
Hi shi,

Let's use your example, say portfolio = $100 with volatility = 10%.
95% VaR = 100*10%*1.65 = $16.5
99% VaR = 100*10%*2.33 = $23.3

Now over one year (T=250), if both models are good (accurate), we expect:
5% * 250 = 12.5 days on which the daily loss is greater than $16.5, and
1% * 250 = 2.5 days on which the daily loss is greater than $23.3

Increasing the confidence increases the VaR threshold and decreases the number of days for which that threshold would be exceeded (if the model is accurate).

In regard to your statement (a), this is TRUE almost regardless; any confidence < 100% expects some exceedences (it is the nature of VaR that it is not trying to bound the extreme) … zero exceedences is suspicious, although less so as the confidence increases, because as the confidence increases we are expecting fewer exceedences to "clear the higher bar"

In regard to (b), this is true but hopefully you can see why it is appropriate? In this respect, think about regulatory or economic capital… if your goal were to minimize the odds of a default, which you prefer equity capital of $16.5 or $23.3? You would prefer, if safety was your, goal more cushion ("only make it even MORE difficult to exceed the VAR…")

Accuracy is a distinct idea: as the 1% VaR only expects 2.5 exceptions, it samples a smaller dataset, so ceteris paribus, the FRM generally says that as confidence increases (we are moving into the extreme tail), we are going to lose accuracy. In the extreme, it is very difficult to be "accurate" where we are trying to measure "once in a lifetime events."

Good luck on the exam, please share back your experience!!!

David
 
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