When someone refers to something as an X% VaR, the X% refers to the probability of exceeding that loss. A 5% daily VaR of $10,000 means that 5% of the time the loss in one day will be $10,000 or greater. The X% is a significance level.

The thread you cited does not mention an X% VaR. It mentions a VaR with X% _ confidence _. Remember that the significance level = 1 − the confidence level. So to say that you have a daily VaR of $10,000 with 95% confidence is to say that you have a 5% daily VaR of $10,000: 5% of the time the daily loss will be $10,000 or greater, and 95% of the time it will be less than $10,000.

Your original post was:

As written, 95% is the significance level, so it means that 95% of the time the one-day loss will be $6.5 million or more, so 5% of the time the one-day loss will be less than $6.5 million.

Whoever wrote that question surely wrote it wrong – nobody ever talks about a 95% VaR – but as written, it means what I just described.

thanks, what you are saying about the confidence is exactly what I meant. I understand now that in the question the 95% was not intended as a confidence level but as a significance level. I was missing that.

I agree that nobody ever talks about a 95% VaR. For example in UCITS funds, the laws requires a calculation of a VaR of over 20 days with a confidence level of 95%. So if we get for example 15% as a result, it means that with a confidence of 95% in the next 20days we will expect a loss of max 15% of the portfolio.

If 95% value at risk (VaR) of $6.5 million means that five percent of the time, the portfolio can be expected to experience a loss of at least $6.5 million, then does 5% value at risk (VaR) of $6.5 million mean that ninety five percent of the time, the portfolio can be expected to experience a loss of at least $6.5 million?

If so, then why does Schwesser say that if, for example, monthly 5% VaR is $25,000, there is 5% probability of a loss of at least $25,000 in any given month? They both contradict then.

Sort of an aside: a 95% Confidence interval does not mean there is a 95% chance something falls within that interval, nor does it mean there is a 5% chance something falls outside the interval. This is a common incorrect interpretation of a confidence interval.

However, if I recall correctly, the VaR calculation uses a standard deviation not a standard error which would mean the interval is not a confidence interval. I believe it uses the percentiles, which has a different meaning than a confidence level, although it may look the same, superficially.

does 5% value at risk (VaR) of $6.5 million mean that ninety five percent of the time, the portfolio can be expected to experience a loss of at least $6.5 million?

A 95% (say, one-month) VaR of $6.5 million means that _ 95% _ of the time the portfolio can be expected to experience a 1-month loss of at least $6.5 million.

VaR is a straightforward probability statement: a 5% quarterly VaR of £60,000 means that there’s a 5% chance of a loss of more than £60,000 in any given quarter.

So, I haven’t looked at finance stuff since 2015, but the calculation for VaR, can you refresh my memory? As I said, I see people mentioning confidence levels, and I think I remember that VaR doesn’t use a standard error, but rather, a standard deviation. If it’s the latter, then I agree with the probability statement, but then talking about confidence levels is inappropriate. If it’s the former, then the interpretation of VaR is inaccurate in the context of a Frequentist confidence interval.

That was my thought, which is why I was saying it’s incorrect to refer to a confidence level or say “95% confident” when referring to these VaR topics.