What are the main pitfalls of historical simulation VaR and how do ghost effects distort results?

Historical simulation (HS) is deceptively simple. You take the last N days of actual returns, apply them to today's portfolio, and find the relevant percentile. But several pitfalls make it less reliable than it appears.

How HS VaR Works:

1. Collect past 500 days of returns for each risk factor
2. Revalue today's portfolio under each historical scenario
3. Sort the 500 P&L outcomes from worst to best
4. 99% VaR = the 5th worst loss (500 x 1% = 5)

Pitfall 1: The Ghost Effect

This is the most counterintuitive problem. Suppose 501 days ago there was a massive market crash that generated the worst loss in your window. For 500 days, that crash sits in your dataset and keeps VaR high.

On day 501, that observation drops out of the window. Suddenly, VaR drops sharply — not because risk decreased, but because one extreme data point exited the rolling window. The market hasn't changed at all, but your VaR estimate jumps.

Even worse, the ghost effect works in reverse: if a calm period drops out and gets replaced by a volatile day, VaR spikes.

Example — Greystone Risk Analytics:

Greystone's 500-day HS window includes the March 2020 crash. Their 99% VaR = $4.2M. On the day the crash observation exits the window (day 501), VaR drops to $2.8M overnight. No portfolio change occurred — just a data rotation.

Pitfall 2: No Extrapolation Beyond the Window

HS can never produce a loss larger than the worst historical observation. If your window doesn't include a financial crisis, your VaR will never reflect crisis-level losses. This is especially dangerous for 99.9% confidence levels with only 500 observations — you'd need the single worst day, which is highly unstable.

Pitfall 3: Equal Weighting of All Observations

Standard HS gives equal weight to what happened 500 days ago and what happened yesterday. If volatility spiked last week, HS VaR barely moves because 499 other observations dilute the signal. This makes HS slow to react to regime changes.

Pitfall 4: Regime Dependence

If your 500-day window falls entirely within a low-volatility regime, VaR will be artificially low. The moment a crisis hits, the model is blindsided.

Mitigation Approaches:

Filtered Historical Simulation (Hull-White approach) rescales each historical return by the ratio of current volatility to historical volatility. If today's GARCH vol is 2x what it was a year ago, historical returns are scaled up by 2x. This makes HS responsive to current conditions.

For more on VaR methodology, check out our FRM Part II market risk materials.