2. Scenarios and stress: thinking about what is not in the data
Risk 6: The limits of the tools
If the previous module leaves one conclusion behind, it is that any measure estimated from recent history describes the world that has already happened. Scenarios cover the rest: they are the only part of risk analysis that can contain events absent from the sample.
What a scenario is, and how it differs from a statistical measure
A statistical measure summarizes a distribution. A scenario does the opposite: it fixes one specific event and works out what would happen to your portfolio if it occurred. It does not weight, it does not average and it does not need the event to be in your data. That is the whole of its advantage.
The practical difference is enormous. A 99% VaR tells you that a bad day costs 2.3%. A scenario tells you that if the index falls 35%, credit widens by 400 basis points and the safe haven turns illiquid all at once, you lose 41% and your broker calls for margin on Thursday. The second sentence is something you can act on.
Historical scenarios: replaying the past over today's portfolio
The cheap, sensible starting point is to take real episodes and apply their moves to the current composition of the portfolio. The three indispensable ones:
- 2008. The S&P 500 fell more than 55% from the October 2007 peak to the March 2009 trough, with high-quality government debt rising while almost everything else fell together.
- October 1987. An extraordinarily violent fall concentrated into a single day, with no preceding recession to explain it and no material time to react.
- March 2020. The S&P 500 fell by around a third in some twenty-three sessions, and for a few days not even US government debt traded normally.
They are not the same blow at different intensities: they are different ways of losing. In 2008 there was time, a long slide with rallies along the way. In 1987 there was none at all. In 2020 the problem was not only the price, but that liquidity vanished precisely where it was supposed to be infinite.
Applying this to a specific portfolio is elementary arithmetic and even so hardly anyone does it. A portfolio of 300,000 euros, 70% in global equities and 30% in long-dated bonds. A 2008 scenario, with equities falling 50% and bonds rising 8%: you lose 32.6%, some 98,000 euros. A 2022 scenario, with equities 18% down and bonds 15% down: you lose 17.1%, some 51,000. The first hurts twice as much in euros, but the second teaches something worse: the leg that was there to cushion the blow can fall at the same time as the other one, which is what level 5 warned about when it dealt with dependencies.
Hypothetical scenarios: what has never happened
Historical scenarios have an obvious ceiling: they contain only what has already occurred. And crises rarely come round again in the same costume, because after each one defenses get built against that exact way of breaking. That is why you need invented scenarios, invented with judgment: a partial default by a sovereign issuer regarded as a safe haven, a clearing house failing for two days, a 300 basis point rise in rates over six months with the stock market falling at the same time.
The usual objection is that there is no data with which to calibrate them. True, and that is precisely the reason to include them. The hypothetical scenario is not after a probability: it is after locating which assumption your portfolio depends on without you ever having written it down. If, on posing the default of the safe haven, you discover that half your construction rests on that asset rising when everything else falls, you have already learned what you needed to learn, whether or not the event ever happens.
The useful question is not what the probability is
Arguing over whether a scenario has a 2% or a 0.5% probability is a conversation nobody can win: nobody knows how to estimate that figure and it all ends in clashing opinions. The operational question is a different one: if it happens, do I survive?
And surviving is a concrete concept, one that comes down from earlier levels: that the loss does not throw you out before your time, does not force you to sell at the worst possible moment, does not trigger a margin call and does not leave you so far down that the arithmetic recovery is out of reach. None of that depends on getting the probability right; it depends on the size of your positions, your liquidity and your payment commitments.
The mistake that guarantees falling short
Calibrating stress with the worst case observed in your sample looks rigorous and is a logical failure. If you have twenty years of data and the worst fall was 34%, stressing at 34% amounts to asserting that the future is forbidden from beating the past. No market has ever respected that rule: every record loss was, the day before, a value that appeared in no sample at all.
The remedy is not sophisticated: multiply the sample's worst case by a factor, add combinations that never occurred together and, above all, do not let the harshest scenario you consider coincide with the harshest one you have already lived through.
A real case: October 19, 1987
That Monday the Dow Jones fell 22.6% in a single session, the largest daily percentage fall in its history, with no recession under way and no news to justify it. Given the typical volatility of that market, a move like it is, under the Gaussian bell curve, an event of more than twenty standard deviations: so improbable that no reasonable model would have included it in its most pessimistic scenario.
No sample predating 1987 contained anything like it. Anyone who had calibrated their stress with the worst day of the preceding decades would have regarded 12% or 13% as catastrophic, and would have fallen short by half. Part of the fall is attributed to automatic hedging strategies that sold futures as the market went down. It is the perfect example of this module's two ideas: the sample's worst case bounds nothing, and the next crisis came in through a different door.