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?
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?
5% - 5 day : [E® - 1.65 (std dev)] * Dollar portfolio
1% - 5 day : [E® - 2.33 (std dev)] * Dollar portfolio
2.5% 5 day - will be between it.
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.