# which VaR smaller?

for a given portfolio,

5-day 5% VaR vs 5-day 2.5% VaR

other things the same.

which one is smaller?

2.5% VaR has higher z score and thus has smaller VaR? wrong?

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I think you got it mixed up.

5% VaR has smaller VaR than 2.5%

As you said, VaR 2.5% has higher z-score and is more extreme than 5% VaR.

Think about is this way: if you have a \$100m portfolio, is it more probable to incur \$5m loss or \$15m loss?

It ain't what you don't know that gets you in trouble. It's what you know for sure that just ain't so.

5% - 5 day : [E(r) - 1.65 (std dev)] * Dollar portfolio

1% - 5 day : [E(r) - 2.33 (std dev)] * Dollar portfolio

2.5% 5 day - will  be between it.

"You could not live with your own failure. Where did that bring you? Back to me." (Thanos - Endgame)

5% VaR is the min loss you can expect to exceed with a probability of 5%

2.5% VaR is the min loss you can expect to exceed with a probability of 2.5%

Are you more likely to run late for work, or get struck by lightning?

The loss is greater the lower the probability threshold.