VaR and confidence interval

CFA Level III
#1

In my understanding, as VaR = (Expected Return - Z score * standard deviation) * portfolio value

When the confidence interval increases, the Z score increases, so in my understanding the VaR is going to be smaller.

Am I right?

#2

(VAR - analytical method)

Nope if the overall equation is negative and generally it’s the case so that if Z goes up —> VAR gets larger.

Hope it helps,

#3

But I saw in a question in Schweser’s practice problems, it says when the confidence interval increases, the VaR gets smaller.

It does’t even give out number to plug in the formula. Just quite confused about this.

#4

confidence interval increases

z score actually DECREASES

When confidence interval is 5% - z score = 1.645

when confidence interval is 1% - z score = 1.96

so with a higher confidence interval - the score z-reduces - so VaR reduces…

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I think you are confusing yourself with the direction of movement of the z score as the confidence interval increases…

#5

So as you say, when confidence level is 95%, the confidence interval is 5%?

confidence level and confidence interval are two different things?

#6

They are two different things, but that’s not an accurate statement. A confidence level represents the long-run accuracy of the method, while the confidence interval itself represents a range of possible values for the true parameter value.

The confidence level increases as the magnitude of the critical values increase. It is the area under the curve beyond the critical values that decreases as the critical values get larger.

#7

As far as I the material I’ve come across the only two variables that get VAR smaller are :

  1. the E® which is in line with what I say above : Equation is usually negative as the second member (Z x Std Dev) is larger than E® BUT if the E® is larger hence VAR gets smaller (less negative).

  2. Time period VAR refers to. The smaller the temporal window VAR refers to, the smaller the VAR in itself.

Hope it helps,

#8

So when we refer VaR, it does mean the loss value. VaR increases, meaning the loss is going to greater?

#9

Yes. I intend “Value at Risk” as our “minimum” potential loss.

#10

Always 1% VaR value (loss)>=5% VaR loss