Parametric VaR vs. Historical Simulation VaR — when does each method fail?

Excellent question — understanding when VaR methods break down is arguably more important than knowing the formulas, and GARP loves testing this on the exam.

Parametric (Variance-Covariance) VaR

Formula: VaR = μ − zσ (or simply zσ if μ ≈ 0 for short horizons)

Strengths: Fast to compute, easy to decompose into component VaR.

Failure Modes:

1. Non-normality of returns. Real financial returns exhibit fat tails (excess kurtosis) and negative skewness. A portfolio with a 99% parametric VaR of $1.5M might actually face a $2.3M loss at the 99th percentile because the normal distribution underweights extreme events.

1. Non-linear positions. If Greenleaf Asset Management holds a portfolio of deep out-of-the-money put options, the delta-normal approximation dramatically underestimates risk. The option's payoff is convex — a 3% market drop might cause a 15% portfolio loss, not the 3% the linear model predicts.

1. Unstable correlations. Parametric VaR uses a fixed correlation matrix, but correlations spike toward 1.0 during crises. The method misses this regime change.

Historical Simulation VaR

Method: Apply each of the last N days' actual returns to today's portfolio and sort the resulting P&L.

Strengths: No distributional assumption needed, captures fat tails and non-linearity automatically.

Failure Modes:

1. Ghost effects. If you use a 500-day window, a single extreme event (say a flash crash) stays in your sample for exactly 500 days, then drops out suddenly. Your VaR can jump discontinuously on the day that observation exits the window — even though nothing changed in the market.

1. Backward-looking bias. Historical simulation assumes the future will resemble the past. If the last 2 years were unusually calm, your VaR estimate will be artificially low. This is exactly what happened at several banks in 2006–2007 — the historical window didn't contain a stress period, so VaR dramatically underestimated risk heading into the financial crisis.

1. Limited data for tail estimation. With 500 days and 99% confidence, you're relying on roughly 5 observations to define the tail. That's a tiny sample — your VaR estimate has high estimation error.

Side-by-Side Comparison:

Exam Tip: If a question describes a portfolio with significant option exposure and asks which VaR method is least appropriate, the answer is almost always parametric.

Dive deeper into VaR methodology with AcadiFi's FRM Part I practice questions — we have 50+ scenario-based items on this topic alone.