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. 2. **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. 3. **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. 2. **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. 3. **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:** | Dimension | Parametric | Historical Simulation | |---|---|---| | Speed | Very fast | Moderate | | Non-linearity | Poor | Good | | Fat tails | Misses them | Captures them | | Regime changes | Misses them | Slow to adapt | | Data requirement | Means, vols, correlations | Full return history | | Ghost effects | None | Significant | **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.