How does non-parametric (historical simulation) VaR work, and what are its strengths and weaknesses?

Historical simulation (HS) is the most widely used VaR methodology in practice. It computes VaR directly from the empirical distribution of past portfolio returns, with no distributional assumptions.

The Mechanics:

1. Collect the last N days of historical returns for all risk factors
2. Apply each historical scenario to the current portfolio (full revaluation)
3. Sort the resulting P&L from worst to best
4. The VaR at confidence level c% is the (1-c) x N-th worst loss

Example — Ridgemont Trading Desk, 500-day window, 99% VaR:

• Sort 500 daily P&Ls from worst to best
• 99% VaR = the 5th worst loss (since (1-0.99) x 500 = 5)
• If the 5th worst loss is -$4.2M, then 1-day 99% VaR = $4.2M

Strengths:

1. No distributional assumption: Automatically captures fat tails, skewness, and non-normality
2. Captures correlations: Historical returns embed the actual dependency structure
3. Non-linear exposures: Full revaluation handles options and other non-linear instruments
4. Transparent and intuitive: Easy to explain to senior management and regulators
5. No parameter estimation error: No need to estimate volatilities or correlations

Weaknesses:

1. Backward-looking: Assumes the future will look like the past. If the last 500 days were calm, HS misses potential volatility spikes.
2. Ghost effects: A single extreme event enters the window and stays for exactly N days, then drops out — causing a sudden VaR change.
3. Sample size limitations: For 99% VaR with 500 observations, you're relying on just 5 data points in the tail.
4. Equal weighting: All observations carry the same weight, whether from yesterday or 2 years ago.
5. Stale data: Recent market conditions may be more relevant than distant ones.

Practical Impact — Clearmont Risk Management during COVID-19:

• On March 15, 2020, HS VaR using a 250-day window still reflected the calm 2019 market
• VaR was $8M, but the desk lost $32M in one day
• By April 2020, HS VaR jumped to $28M (now including March data) — but the worst was over
• The model was 'always one crisis behind'

FRM Key Points:

• HS is the baseline method tested on the exam
• Know how to identify ghost effects and explain why VaR jumps
• Understand that HS works well for liquid portfolios with stable market regimes
• Basel's IMA (Internal Models Approach) requires backtesting — HS often produces clustered exceptions

Practice HS VaR problems in our FRM Part II question bank.