Conditional VaR (Expected Shortfall)
The average loss in the worst (1 - alpha)% of cases — a coherent tail-risk measure.
Definition
Conditional Value at Risk (CVaR), also called Expected Shortfall (ES), is the expected loss given that the loss exceeds the VaR threshold. Where VaR says "you will not lose more than X with 95% confidence", CVaR answers "but if the worst 5% happens, how bad is the average outcome?" CVaR is mathematically coherent (sub-additive) and therefore preferred in modern portfolio risk frameworks and Basel III. It penalises fat-tailed strategies that hide loss potential beyond the VaR cutoff.
Formula
CVaR(alpha) = E[ L | L > VaR(alpha) ]
In practice from simulations:
CVaR(alpha) = mean of the (1-alpha) worst lossesWorked example
From 10,000 Monte Carlo simulations of a portfolio, the 500 worst daily P&L outcomes (the 5% tail) average -$48,000. The 95% one-day VaR might be -$24,000, but CVaR is -$48,000. The CVaR is roughly 2x VaR here — typical of equity-heavy portfolios with negative skew.
How ARIA Analyst uses it
ARIA reports CVaR alongside VaR in every Monte Carlo run and uses it as the constraint in the Risk Parity and Black-Litterman optimisation modes.
Related terms
Value at Risk (VaR)
The maximum loss expected over a given horizon at a given confidence level.
Monte Carlo Simulation
A probabilistic technique that simulates thousands of random scenarios to estimate the distribution of outcomes.
Maximum Drawdown
The largest peak-to-trough decline of equity over a given window.
Volatility (σ)
Standard deviation of returns — the most common dispersion-based risk measure.
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