Why Long-Horizon Historical VaR Is Sensitive to Drift Estimates
Summary
The document considers whether historical VaR for a single instrument can be extended to a one-year horizon. The main answer warns that long-horizon estimates are highly sensitive to the assumed or estimated mean return. Since drift is difficult to estimate precisely, a sample drawn mostly from a rising market can imply strong future returns and produce an implausibly low risk estimate. The horizon extension can therefore magnify uncertainty in the mean rather than provide a stable view of risk.
The response notes that practitioners sometimes constrain the drift used in long-term VaR calculations; PRIIPS, for example, uses the risk-free rate as a long-term drift assumption. It does not endorse this assumption as superior. Another suggestion is to remove the mean from the return series and compare the resulting VaR to the original estimate, or use a VaR function from a performance analysis package. These are practical checks, not a complete prescription: the document offers no instrument-specific validation, and it does not establish that conditional VaR or Monte Carlo modeling would resolve the underlying drift uncertainty.
Key ideas
- Long-horizon VaR can be highly sensitive to the estimated mean return.
- Drift estimates based on a bull-market sample can make projected long-term risk appear unusually low.
- Some practices constrain drift assumptions, though the cited risk-free-rate convention is not claimed to be better.
- Comparing VaR before and after de-meaning returns can show how much drift affects the estimate.
- The discussion does not establish a universally appropriate method for long-horizon VaR.
Tags
Full text
# Calculation VaR on long term period # 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 - Norm Dist 1%: `-8.06%` - 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. ## Answer by Tim Wilding (score 1) https://quant.stackexchange.com/a/40512 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! ## Answer by Rod Morley (score 1) https://quant.stackexchange.com/a/40520 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.
Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.