# Calculation VaR on long term period

I'm calculating VaR numbers from historical data for a single instrument (it's plain vanilla, not a derivative) and receive such variables:

I could provide necessary data, and formulas but I guess anyone on QF understands what is historical VaR and how it's calculated

• Median: -0.02%
• Standart Dev: 3.45%
• Norm Dist 1%: -8.06%
• Last Price: 349,628
• VaR T+1: 325,671 / 28,556 / 8.06%

The only problem that when I'm trying to use it for calculation VaR for 365 days forward (or any long term period) I receive figures that seems a bit irrelevant.

So is it «fine» to calculate VaR for such long period? And if no what should I do to receive relevant-risk-data for my instrument? cVaR? Monte-Carlo VaR modeling?

By the way, I'm looking for a practice usage advice, not academic answer.

## 2 Answers

Any VaR calculated for such a long period is going to be fairly sensitive to the estimate of the drift or mean return. Unfortunately, there is often a very large error on any estimate of the drift. So, in one common recent scenario, if you are only using returns from a bull market to estimate VaR, then you will get high long-term returns and your VaR will seem very low.

People often impose restrictions on the drift term for the returns they use in practice so that they can return VaR estimates that seem fairly sensible. For example, The PRIIPS regulations use the risk-free rate as an estimate of the long-term drift. I am not sure that that is any better though!

Have you tried VaR from the PerformanceAnalytics package? You could also de-mean your time series before running it through VaR to assess the impact of drift on the VaR estimates.