Stress Testing and Scenario Analysis

Every method you've met so far — historical simulation, variance-covariance, Monte Carlo VaR and Expected Shortfall — is built from statistics of normal times: a historical window of returns, a fitted covariance matrix, a simulated model. That's precisely their weak point. A model trained on the last two years of calm trading has no way to imagine a day the market has never behaved like before — and the days that matter most to a risk manager are exactly the ones no model saw coming. Stress testing is the deliberate, unapologetically unstatistical complement: pick a genuinely extreme scenario, apply it to today's book by hand, and ask one blunt question — could we survive this?

Two flavours of scenario

Historical scenarios — replay the actual market moves from a real past crisis onto today's positions: Black Monday (October 1987), the 2008 financial crisis, the March 2020 COVID crash. The scenario needs no modelling at all — it already happened once.
Hypothetical scenarios — construct a plausible-but-unprecedented combination of shocks that hasn't literally occurred: interest rates jumping 300 basis points while equities fall 30% while credit spreads triple, say. These let a risk manager probe combinations that history hasn't yet handed them.

Crucially, a stress scenario carries no probability attached to it. VaR and Expected Shortfall both answer "how bad, at such-and-such a confidence level" — a stress test simply asks "if this happens, what does it do to us?" and reports the number, full stop.

Worked example: when the stress number dwarfs the VaR number

A trading book has a net long exposure to equities worth \$400{,}000 of loss per 1% the market falls, and its desk reports a comfortable 1-day 99% VaR of \$2{,}500{,}000, computed from the last year of (fairly calm) daily returns. Now apply three real historical single-episode equity shocks to that same \$400{,}000-per-1% sensitivity:

Scenario	Equity move	Stress P&L
Black Monday, Oct 19 1987 (single day)	−22.6%	−$9,040,000
2008 financial crisis (peak to trough)	−40%	−$16,000,000
COVID crash, Feb–Mar 2020	−34%	−$13,600,000

Every single stress scenario dwarfs the reported VaR — the mildest of the three is already 3.6\times the VaR figure, and the worst is 6.4\times. Nothing about the VaR calculation was wrong; it correctly summarized a year of calm markets. It simply never saw a Black Monday in its sample, so it had no way to warn about one. That gap is the entire reason stress testing exists as a mandatory, separate discipline rather than an optional extra.

October 19, 1987 remains the worst single-day percentage fall in the history of major equity indices, and much of the damage was self-inflicted by risk management itself. A strategy called portfolio insurance — automatically selling more stock index futures as prices fell, meant to synthetically replicate a protective put — was mechanically programmed into a large share of institutional money. As prices dipped, the programs sold; the selling pushed prices down further; the further fall triggered more automatic selling. A hedging technique designed to protect individual portfolios became, in aggregate, a feedback loop that helped crash the whole market — a story Module 13 picks up in more depth, with a cast of famous names who each, in their own way, learned this lesson the hard way.

Stress tests are still limited by human imagination. A scenario library built from the crises we've already lived through is exactly what its name suggests — a look backward. It can miss an entirely new kind of shock nobody has yet conceived of, which is why risk managers are sometimes accused of perpetually "fighting the last war."
Correlations you relied on can vanish exactly when you need them. A diversified book often assumes some assets will move independently, or even oppositely, of others. In a genuine systemic crisis, correlations across almost every asset class tend to spike toward 1 — everything sells off together — right when diversification was supposed to be protecting you. A stress test that only shocks one risk factor at a time can miss this; the best ones shock several factors together, correlated the way a real crisis correlates them.

Not optional: a regulatory mandate

Bank regulators no longer treat stress testing as a nice-to-have. Since the 2008 crisis, the Federal Reserve's annual CCAR / DFAST stress tests and equivalent Basel Committee exercises require every major bank to demonstrate, with regulator-specified adverse and severely adverse scenarios, that it would remain solvent through a hypothetical severe recession — a direct institutional descendant of exactly the exercise in the worked example above, now run at the scale of the entire global banking system.