# Isn't VAR time scalable?

If so why doesnt this work? Annual E® = 14.4% Annual std dev = 21.5% So annual VaR at 5% is 14.4 - (1.65)(21.5) = -21.075% Convert to monthly = -21.075/ sq rt(12) = -6.0838% But thats wrong. You have to convert the E® and std dev to monthly first So monthly E® = 1.2% (14.4/12) Std dev monthly = 6.2065% (21.5/sq rt (12)) Var = 1.2% - 1.65(6.2065) = -9.0407% Why can’t I time scale VaR?

As far as I recall, VAR can only be time-scaled if the expected return is zero.

If our exptd return = close to zero, you can do that. i.e. annual var = monthly var * sq rt of 12 why it doesnt work for +ve return numbers … i dont know. anyone else.

VAR is NOT time scalable. Return and standard deviation scale differently. For return you simply divide by the number of periods (ie to get monthly return divide annual return by 12). For standard deviation you have to divide by the sqrt of the number of periods (ie to get monthly standard deviation divide annual standard deviation by the sqrt of 12). Since VAR is a product of both of numbers you CAN NOT scale VAR.

weren’t there EOC questions asking us to do just this? I seem to remember getting annual return and std deviation figures and being asked to compute monthly and daily var’s at different confidence levels.

After some more reading I have to agree with tiddly. When expected return is zero you can scale VAR without scaling the components separately and recalculating VAR. Use the same method as I discussed above for standard deviation. However, if expected return is not equal to zero you CAN NOT scale it. Does anyone have an example of this in the CFAI text? I want to see if they scale expected return back arithmetically or geometrically.

The example is from Schweser Vol 2 #1 PM. They found monthly by dividing by 12 for E®.

The above posters are correct. VAR can only be scaled if expected return is 0.

and if you’re taliking analytical var which assumes a normal distn.

Quick question about VAR: VAR decreases as the time period used to calculate it increases, right?

VAR increases with an increase in the time period or confidence interval.

You mean size of sample data increases? You’d expect so I guess because the std deviation would decrease. But if you’re using daily s.d. and scaling it up for a bigger period, you’re miltiplying that s.d by root(target time period) so in that respect var increases.

I think a lot of you are spot on. Just look at the formula VAR = E® - sigma*scaling So if you divide VAR by sqrt(time) then you are dividing both return and standard deviation by time, but you can only adjust standard deviation by the square root of time. Return is divided by the actual number of months, days, weeks, etc. This is why it only works if time is equal to zero; there is no return element in the formula.

As you said, it’s not hard to rescale it, at least if you are doing analytical VAR, but you can’t just multiply by a scaling factor and be done. E® increases proportional to t (or arguably e^t) Sigma increases proportional to SqRt(t) The critical Z value stays the same, assuming that you are still looking at the same lower limit 5% VAR, 1% VAR or whatever.