Does it mean VAR = 0 at a given probability over a given time period?
Thanks.
Not sure I understand your question… analytical VAR = [E® - Z(Std.Dev)] x Value
OP’s asking what happens if your formula returns a postive value. All examples I remember give negative, meaning loss.
I’m also curious what a positive value implies, guess it means technically there’s no value at risk?
EDIT: althought it seems highly unlikely that you’d get a expected return so large and risk so small that E® - z*standard dev > 0
A positive VAR of £10,000 at 5% significance means that there is an 95% probability that the portfolio will return £10,000 or higher. I suppose for a very low risk portfolio VAR could be positive.
if the calculated number is positive - then there is absolutely no probability that a loss would occur.
In CFAI parlance - VAR is a negative number - since it represents a loss - so treat it as such. VAR can never be positive. (in the CFAI world, and it helps to keep thinking about it that way). This helps you resolve questions where E® increases - and therefore VAR decreases…
if the calculated number is positive - then there is absolutely no probability that a loss would occur. Thus, VAR = 0?
Usually, expected return = 0, thus VAR must be negative.
What book have you been reading? If something was expected to return 0, I don’t think it would be something many people would be interested in investing in
Industry practice
the E® is made 0 only when you are trying to do daily VAR - and also that helps compare multiple companies in the same industry.
Exactly… for daily VAR, we can use 0 expected return. But, for cfa exam purposes, to say expected return is usually zero, is a little off the mark.
Sure, for CFA exam, always use the number exam given.
Curriculum:
Some approaches to estimating VAR using the analytical method assume an expected return of zero. This assumption is generally thought to be acceptable for daily VAR calculations because expected daily return will indeed tend to be close to zero. Because expected returns are typically positive for longer time horizons, shifting the distribution by assuming a zero expected return will result in a larger projected loss, so the VAR estimate will be greater. Therefore, this small adjustment offers a slightly more conservative result and avoids the problem of having to estimate the expected return, a task typically much harder than that of estimating associated volatility. Another advantage of this adjustment is that it makes it easier to adjust the VAR for a different time period. For example, if the daily VAR is estimated at $100,000, the annual VAR will be $100,000250‾‾‾‾√=$1,581,139 . This simple conversion of a shorter-term VAR to a longer-term VAR (or vice versa) does not work, however, if the average return is not zero. In these cases, one would have to convert the average return and standard deviation to the different time period and compute the VAR from the adjusted average and standard deviation.
Thanks all!
If E® is large, you’lre likely going to have a standard deviation that is also large which would also likely increase VAR.
to frank with ER at 0:
E® @ 0 just simply removes the E® benefit from the VAR equation - makes it a total loss versus netted against expected returns which is more conservative absolute VAR number.