Stress Testing and Scenario Analysis

Statistical risk measures like Value at Risk (VaR) answer a probabilistic question, "how much might I lose on a normal-ish bad day?", and they estimate the answer from recent history. That's their weakness: recent history is usually calm, so the model has never seen the move that actually breaks you. Stress testing sidesteps probability altogether and asks a blunt, concrete question instead: if this specific event happened, what would I lose? No claim about how likely it is, just the raw damage.

There are two flavors. Historical scenarios replay an actual crisis, the 1987 crash, 2008, the 2020 COVID drop, the 2022 rate shock, applying those exact market moves to today's portfolio. Hypothetical scenarios are hand-built: a made-up but plausible shock like "equities −25%, credit spreads +300bp, the dollar +10%, oil −40%, all at once." Both bypass the statistical model and go straight to "what if."

How you actually run one

You don't need probabilities, you need a mapping from market shocks to portfolio profit and loss. Usually that comes through a factor model: express each position's sensitivity to a set of risk factors (equity beta, rate duration, credit spread, currency, commodity), then shock the factors and add up the losses.

$$\Delta P \;\approx\; \sum_{k} \beta_k \, \Delta f_k ,$$

where $\Delta P$ is the portfolio's profit-and-loss under the scenario, $\beta_k$ is the portfolio's sensitivity (its exposure) to factor $k$, and $\Delta f_k$ is the shock you impose on that factor. For a linear book this is a quick dot product; for a book with options you need to reprice with the shocked inputs because the exposures themselves ($\beta_k$) change as the market moves, that curvature is exactly what stress tests are for.

Worked example: a scenario table

Take a simple $100,000,000 book: 60% equities, 30% investment-grade credit, 10% gold. Run it through four scenarios by applying each asset's move and summing:

Scenario	Equity	Credit	Gold	Portfolio P&L
2008 crisis	−38%	−8%	+5%	−$24.7m
2020 COVID crash	−34%	−6%	−2%	−$22.6m
2022 rate shock	−18%	−13%	−1%	−$15.6m
Hypothetical stagflation	−25%	−10%	+15%	−$16.5m

Work the first row: equities contribute $0.60 \times (-38\%) = -22.8\%$, credit $0.30 \times (-8\%) = -2.4\%$, gold $0.10 \times (+5\%) = +0.5\%$, summing to $-24.7\%$ of $100m, a $24.7m loss. Notice what the table reveals that a single VaR number hides: the book is overwhelmingly an equity bet, gold barely cushions anything, and the 2008-style shock is the binding constraint. That is the actionable output, not a probability, but a ranked list of what actually hurts.

Reverse stress testing

The most useful variant flips the question. Instead of "what does scenario X lose?", ask "what scenario would wipe out X% of my capital?" Reverse stress testing searches for the combination of shocks that produces a target catastrophic loss, then asks whether that combination is plausible. It's powerful because it finds your hidden vulnerabilities, the specific pattern of moves you're most exposed to, rather than only testing the scenarios you already thought to worry about.

Where it fits

Stress testing is the qualitative complement to the quantitative tail measures. Expected Shortfall (CVaR) tells you the average loss in the worst statistical outcomes; a stress test tells you the loss under a named event you can reason about and act on. It feeds directly into Tail-Risk Hedging (which shocks should I insure against?) and into Robust Portfolio Optimization (build a book that survives the worst scenario, not just the average one). Regulators mandate it precisely because they learned, expensively, that a risk model calibrated on calm data is silent about the storm.