 # VaR exercise CFAI

Anyone who could explain me why answer C is wrong?

The Index Plus Fund has a one-day 95% value at risk (VaR) of \$6.5 million.

B Five percent of the time, the portfolio can be expected to experience a loss of at least \$6.5 million.

C Ninety-five percent of the time, the portfolio can be expected to experience a one-day loss of no more than \$6.5 million.

I knew that for example with a 95% confidence level the VaR is X then:

• 95% of the time the max loss is X or

• 5% of the time the min loss is X

it states a loss of no more than… VaR gives you the minimum loss…

Don’t confuse maximum and minimum…think about it this way:

Traders are the most that use VaR to limit their trading risks:

say the currency desk is highly risky and the Max VaR assigned to this desk would be \$1,000,000 i.e. a min loss of \$1,000,000 would trigger VaR

Sorry but it’s still not clear.

They are stating exactly the same I am. I am not saying answer B is wrong, but to me also answer C is right.

Anyone else could help?

Taytus - ignore the above post.

The CFAI said it’s the minimum so if you want to pass the exam - just go with the statement that its the minimum loss.

yes but…mathematically speaking, to me it’s not correct!

no more opinions on that?

Respectfully, no they’re not.

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.

Hi S2000magician,

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.

This question was taken from the CFAI Curriculum books (question nr 3 at the following link): https://www.cfainstitute.org/programs/cfaprogram/exams/Documents/measuring_managing_market_risk_practice.pdf

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?

That _ isn’t _ what it means.

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.

No.

Read what I just wrote, and what I wrote on 3/15/17.

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.

Yes: standard deviation.

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.

VaR’s pretty straightforward. You need three values:

1. A probability
2. A time period
3. An amount (which might be an absolute currency amount, or a percentage of a portfolio or investment amount)

A 5% daily VaR of \$10,000 means that the probability of losing \$10,000 or more in one day is 5%.

A 10% monthly VaR of €500,000 means that the probability of losing €500,000 or more in one month is 10%.

A 3% annual VaR of 20% (of your portfolio) means that the probability of losing 20% or more of your portfolio’s value in one year is 3%.

And so on.

Thank you for confirming-- this is how I remembered it. This also confirms that the concept of VaR has zero to do with confidence levels.