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Traderoid

VaR Node

Value at Risk - maximum loss at confidence level

StatisticalRiskQuantile

Overview

Value at Risk (VaR) is the maximum loss expected at a given confidence level over a time horizon. VaR 95% = "99 days out of 100, we won't lose more than this." VaR is the regulatory standard for bank capital requirements and internal risk management. It's the complement to CVaR: VaR is the threshold; CVaR is the average beyond that threshold.

VaR directly answers: "How much capital do I need to cover worst-case losses?" For traders, VaR -5% (95% confidence) means "one in 20 days could be worse than -5% loss." Combine with CVaR to understand severity of breaches.

Formula & Calculation

Historical VaR
VaR = Quantile(Returns, 1-confidence)
Sort historical returns, find the percentile
95% VaR = 5th percentile of returns
Normal VaR
VaR = μ + σ × Z(confidence)
Parametric approach assuming normality
95%: Z = -1.645, 99%: Z = -2.326

Parameters

ParameterDefaultDescription
lookback252-504Historical window
confidence95% or 99%Confidence level

Common Use Cases

1. Capital Requirement

Banks/funds use VaR to set minimum capital: Capital = Portfolio Value × VaR(99%). Ensures survival of 1-in-100 days loss.

2. Position Limits

Set max position size: Position = Capital × Risk Appetite / VaR. If VaR = -5% and capital = $1M, max loss per trade = $50k.

3. Scenario Planning

Model stress scenarios: "If this position hits VaR 95%, am I bankrupt?" Identify concentration risks requiring hedges.

4. Regulatory Reporting

Daily VaR disclosure required for hedge funds/banks. Track VaR trend as risk indicator. Rising VaR = increasing portfolio risk.

Advantages & Limitations

Advantages

  • Regulatory standard
  • Single intuitive number
  • Works across assets
  • Enables capital planning
!

Limitations

  • Ignores severity beyond threshold
  • Assumes stationarity
  • Backward looking
  • Wrong in tail events

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