Conditional VaR and stress testing

VaR draws a line at the edge of the bad tail. The tools here look at what lives beyond that line — the part that actually ends accounts.

Conditional VaR (expected shortfall)

Conditional VaR (CVaR), also called expected shortfall, answers the question VaR ducks: when the loss does exceed the VaR threshold, how bad is it on average? It is the average of the losses in the worst tail, not just the cut-off point.

1-day 95% VaR        = US$2,000   (the threshold of the worst 5% of days)
1-day 95% CVaR       = US$3,500   (the average loss ON those worst 5% of days)

CVaR is always at least as large as VaR, and the gap between them tells you how fat the tail is — how nasty the rare bad days really are. A strategy can have a comfortable VaR and a frightening CVaR, and the CVaR is the number that warns you about ruin.

Stress testing

Statistics describe the normal past. Stress testing ignores probabilities and instead asks a blunt what-if: if a specific extreme event happened right now, what would my account do? You pick scenarios and recompute the damage by hand:

Scenario A: my main pair gaps 5% against me overnight  -> account effect?
Scenario B: a 2008-style crash, every position down together -> account effect?
Scenario C: my broker halts trading and I cannot exit for an hour -> account effect?

Why both beat VaR alone

CVaR and stress tests force you to confront the worst case rather than the typical one. If the answer to a plausible stress scenario is "I am wiped out," your position is too large regardless of how comfortable the everyday numbers look. Sizing to survive the stress case, not the average day, is the heart of survival.