Risk Management foundations
Course 02 · Portfolio tail risk

Value at Risk &
Expected Shortfall

Move beyond per-trade stops and measure the loss distribution of an entire portfolio—especially the outcomes hiding in its left tail.

VaR

Threshold

ES / CVaR

Tail average

Horizon

Time window

Confidence

Coverage

Original visual

VaR marks the door.
ES looks through it.

VaR identifies a percentile boundary. It does not describe how severe losses become beyond that boundary. Expected Shortfall averages the observations inside the tail.

VaR boundary
Expected Shortfall averages this tail
Large lossesPortfolio returnsLarge gains

Value at Risk asks

“At this confidence level and horizon, what loss threshold should the portfolio cross only rarely?” A 95% one-day VaR still anticipates a breach on roughly one day in twenty.

Expected Shortfall asks

“When the threshold is breached, how large is the average loss?” That makes the severity of tail events visible instead of stopping at a single percentile.

THREE ESTIMATION LENSES

The method shapes the answer

Fast

Parametric

Uses volatility and a chosen distribution to estimate a percentile. Efficient, but highly dependent on its assumptions.

Useful for

Stable portfolios and rapid monitoring

Watch for

Normality can understate fat-tail risk

Observable

Historical simulation

Replays actual historical returns against today's portfolio and ranks the resulting gains and losses.

Useful for

Capturing nonlinear moves seen in the sample

Watch for

The future may not resemble the lookback window

Flexible

Monte Carlo

Generates many hypothetical paths from a chosen process, then measures the simulated loss distribution.

Useful for

Complex portfolios and scenario exploration

Watch for

A sophisticated engine can still have poor assumptions

Interactive lab

Parametric tail-risk estimator

Estimate loss thresholds from portfolio value and daily volatility under a normal-distribution assumption. This simplified model excludes drift, fat tails, changing correlations, and liquidity costs.

Volatility should come from consistent return data. Do not substitute the instrument's price change in points.

Model output

Value at Risk95% threshold

$2,468

Losses should exceed this threshold about 5% of periods under the model.

Expected Shortfallaverage tail loss

$3,093

Estimated average loss when the VaR boundary is breached.

Model governance

A risk number needs a challenge process

No single statistic is a safety guarantee. Pair the model with scenario analysis, exposure limits, and a record of actual breaches.

Backtest how often VaR is breached.
Stress correlations during market shocks.
Include spreads, gaps, and liquidation costs.
Compare calm and crisis lookback windows.
Run named scenarios outside historical data.
Escalate when risk limits are exceeded.

Lesson complete

Use thresholds and tails together

VaR supports limits. Expected Shortfall exposes the damage beyond them. Stress tests ask what neither model has seen.

Next: Drawdown analysis