Value at Risk — Historical Method

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Maximum expected loss at a given confidence level over a horizon, computed from the empirical distribution of historical returns.

Details

• category: Risk Management
• formula: VaR_α = -Quantile(returns, α)
• formula latex: \text{VaR}_\alpha = -\text{Quantile}(R, \alpha)
• limitations: Backward-looking; misses regime shifts, No information about losses beyond VaR (use CVaR/Expected Shortfall), Assumes future losses look like historical sample
• related terms: var, expected-shortfall, cvar, tail-risk

Formula

VaR_α = -Quantile(returns, α)