Stress TestingMedium

A risk model says what usually happens. A stress test asks what happens in the case the model has never seen — and the hard part is choosing the case rather than running it.

8 min read · 1 411 words

Why a second method exists at all

A risk measure such as value at risk answers a question about a distribution: on how many days, out of a hundred, would the loss exceed this figure? It is a statement about the ordinary, calibrated on data from a period that was mostly ordinary, and it is deliberately silent about the size of the losses beyond its own threshold. Risk measures sets out what it does and does not say.

Stress testing answers a different question, and it is a question rather than a measurement: if this particular thing happened, what would we lose, and could we survive it? There is no probability attached. That is not a weakness to be apologised for — attaching a probability to a scenario that has never occurred would be the least defensible number in the exercise.

The two are complements. One describes the middle of the distribution with statistical machinery; the other describes a specific corner of the tail with a story. A firm relying on either alone is looking at half the picture.

Four shapes of the exercise

• Sensitivity analysis — move one thing and see what happens. Rates up 200 basis points, spreads wider by 100, the currency down 15%. Cheap, fast, run daily, and blind to the fact that these things move together.
• Scenario analysis — move everything at once, coherently. A recession scenario has to say what happens to rates, spreads, equities, unemployment, house prices and defaults as one story, because a scenario whose parts contradict each other tests nothing. Building it is largely an exercise in internal consistency.
• Historical scenarios — replay an actual episode across today's positions. The advantage is that the moves genuinely happened together, so the internal consistency is free. The limitation is that today's portfolio was often built precisely to survive the last crisis.
• Hypothetical scenarios — construct an episode that has not happened. Necessary, because the next one will not be the last one, and much harder to defend, because every number in it is a judgement.

Reverse stress testing: the most useful version, and the least comfortable

Every exercise above starts with a scenario and computes a loss. Reverse stress testing inverts it: start with the outcome — the firm is no longer viable, the business model has failed — and work backwards to what would have to happen.

It is more useful for one specific reason. A forward exercise tests the scenarios somebody thought of, which means it systematically misses the ones nobody thought of. Starting from the failure and asking what could produce it forces a different search, and it usually surfaces concentrations and dependencies that no scenario library contains: a single funding source, one clearing relationship, a client base that is more correlated than the exposure report shows.

It is less comfortable for an obvious reason: the deliverable is a written description of how the firm dies, and it is read by people whose job it is to prevent that. The exercises that get diluted are diluted here.

Second-round effects: where the number stops being additive

The naive calculation revalues the current portfolio under the shocked inputs and stops. The interesting losses are in what happens next, and they are what turns a bad quarter into a failure:

• Forced selling. A loss triggers a margin call, the call is met by selling, the selling moves the price, the move produces another call. Margin and collateral is the mechanism, and it is the one that runs fastest.
• Funding withdrawal. Deteriorating results and a wider spread make lenders shorter-dated and then absent. Assets that were funded overnight have to be funded from somewhere else or sold.
• Liquidity evaporating in the same instant. The exit assumed in the revaluation is priced at calm-market spreads. In the scenario the spread is wider and the depth is thinner, so the loss is larger than the mark implied — liquidity covers why.
• Correlations moving to one. The diversification the position was sized against is a parameter, and it is the parameter least stable under stress. A hedge that works on average may not work on the day the scenario describes; hedging sets out the basis risk that remains.
• Everyone doing the same thing. If a scenario forces one firm to sell, it usually forces the firms holding similar positions to sell too, into each other. A single-firm test cannot see this by construction, which is one reason system-wide exercises exist.

Supervisory exercises, and what they are for

Supervisors run their own tests across many firms at once, with a common scenario and common methodology, and publish results. Three things about them are worth knowing:

• The comparability is the product. One firm's internal test says something about that firm. A common scenario applied to fifty balance sheets says something about the system, including where the same exposure sits in many places.
• The result feeds requirements. Outcomes inform capital guidance, so the exercise is not an academic one — see bank capital for what the requirement then does.
• The published scenario becomes an optimisation target. Once firms know what will be tested, positions drift towards surviving that test. This is not cheating; it is the intended effect, working in a way that also narrows what the exercise can discover next year.

Four reasons a stress test misses the thing that happens

• The scenario was chosen by people who had to imagine it. The search is bounded by memory and by what is defensible in a meeting.
• The exposure data is a snapshot. Portfolios change; a monthly test on a book that turns over weekly is describing a firm that no longer exists.
• The behavioural assumptions are the soft part. How fast deposits leave, how much of an undrawn facility gets drawn, whether a client posts collateral or defaults. Every one of these is an assumption, and in a real stress they all move the unhelpful way at once.
• Nobody wanted the answer. An exercise whose result would force an uncomfortable decision has a well-documented tendency to come back reassuring. This is a governance problem wearing a quantitative costume, and it is why the exercise is owned by risk and reviewed by internal audit rather than by the desk being tested.

The honest way to read a stress result

A stress number is a conditional statement, and it should be quoted as one: under this scenario, with these assumptions about behaviour, the loss would be this. Stripped of its conditions it becomes a forecast, and it was never that. The most valuable output of the exercise is usually not the loss figure at all — it is the list of assumptions somebody had to write down to produce it, because that list is where the firm's real beliefs about itself are recorded.

Every case study on this site is, read one way, a scenario somebody's exercise did not contain: LDI in 2022, Archegos in 2021, SVB in 2023. None of them was unimaginable afterwards.

What to take away

• A stress test is a conditional question, not a measurement, and it carries no probability on purpose.
• Sensitivities are cheap and blind to co-movement; scenarios are coherent and expensive to build.
• Reverse stress testing starts from failure and finds what forward exercises structurally miss.
• The second-round effects — forced selling, funding, liquidity, correlation — are where a bad quarter becomes a failure.
• Quote a stress number with its conditions, and read the assumption list before the loss figure.