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The One-in-a-thousand-day Problem
Summary:
This column argues that such drastic behavioural changes render statistical analyses based on normal times ineffective.
In times of extreme stress, banks instinctively prioritise self-preservation to weather the storm. Whereas this is understandable from their perspective, it leads to perhaps the most significant harm caused by financial crises.
Milton Friedman's controversial criterion states that a business's objective is to make money for its owners (see Kotz 2022). When applied by a bank CEO, this principle manifests in two distinct behavioural regimes.
Most of the time – perhaps 999 days in a thousand – banks focus on maximising profit through regular borrowing and lending activities.
However, on that rare one day in a thousand, when a major upheaval strikes and a crisis unfolds, short-term profit takes a backseat to survival. Banks halt the provision of liquidity and start hoarding it, triggering runs, fire sales, and a denial of credit to the real economy. This is usually the main economic damage of crises. It is difficult to predict or prevent – and impossible to regulate – because it arises from self-preservation.
These two vastly different behavioural regimes frustrate investors and regulators, not least because statistical models based on normal times fail to capture them.
The one-in-a-thousand-day problem
The buildup to a crisis and the recovery afterwards are prolonged processes that can span years or even decades. But the actual crisis erupts suddenly, catching almost everyone off guard. It is as if we go to bed one night and wake up the next morning to find ourselves in a crisis.
Fortunately, crises are rare. According to Laeven and Valencia's (2018) financial crises database, the typical OECD country experiences a systemic crisis once every 43 years. Given that the high-intensity phase of a crisis is relatively short, it is reasonable to say that a country is not in an acute crisis 999 out of a thousand days, but in crisis on that one remaining day.
The intense phase of a crisis is driven by banks striving to survive. Profit becomes irrelevant because they are willing to incur significant losses if it means securing their future. Critical decisions are made for entirely different reasons than usual – and often not by the usual people.
Survival hinges on having as much liquidity as possible. Banks minimise liquidity outflows and convert their liquidity into the safest assets available – historically gold; today, central bank reserves. When investors ‘went on strike’ in August 2007, they were motivated by survival.
This drive for self-preservation leads to fire sales and runs. Entities dependent on ample liquidity face hardship or even collapse, while the real economy suffers as credit lines are cancelled and banks refuse to lend. These outcomes constitute the main damage from crises and explain why central banks inject liquidity during such times.
Collectively, this indicates two distinct states: the usual 999 days when banks maximise profit, and that critical last day when they focus on survival. Roy's (1952) criterion aptly describes this behaviour – maximising profit while ensuring they do not go bankrupt. Thus, these two behavioural regimes are a direct consequence of aiming to maximise shareholder value.
Speed is essential
The shift from pursuing short-term profits to survival happens almost instantaneously. Once a bank decides it needs to weather a storm, acting quickly is crucial. The first bank to withdraw liquidity from the system stands the best chance of survival. Those who hesitate will suffer, and even fail.
This was evident when the Hong Kong family office Archegos Capital Management could not meet margin calls. Two of its prime brokers – Morgan Stanley and Goldman Sachs – acted almost immediately and mostly avoided losses. The other two – Nomura (which lost about $2 billion) and Credit Suisse (which lost about $5.5 billion) – hesitated, held lengthy meetings, and hoped for the best.
Implications for risk measurement
The one-in-a-thousand-day problem signifies a complete structural break in the financial system's stochastic processes because the 999-day regime differs fundamentally from the crisis regime.
Each 999-day regime also differs from others. Crises occur when risks are ignored and accumulate to a critical point. Once a crisis happens, that particular risk will not be overlooked again, and new hedging constraints will alter how prices evolve. This means we have a limited ability to predict price movements after a crisis.
Consequently, models based solely on the 999 normal days – an almost unavoidable practice – cannot forecast the likelihood of a crisis or its developments. Attempting to do so leads to what I have termed ‘model hallucination’ (Danielsson 2024).
This also explains why market risk techniques such as value-at-risk (VaR) and expected shortfall (ES), which focus on relatively frequent events (for VaR, one in a hundred days; for ES, one in forty days), are inherently uninformative about crises.
After the 2008 crisis, I organised an event with senior decision makers from that period. Tellingly, one of them remarked: "We used the models until we didn't".
Policy consequences
The one-in-a-thousand-day problem leads to significant misunderstandings about crises.
Excessive leverage and reliance on ample liquidity are the underlying causes of crises. But the immediate crisis trigger and the ensuing damage result from financial institutions simply trying to survive.
Therefore, when analysing crises, we must consider both factors: leverage and liquidity as the fundamental causes, and self-preservation as the immediate cause, which influences the likelihood and severity of a crisis.
We can regulate leverage and liquidity through macroprudential measures. However, we cannot regulate self-preservation. Banks’ behaviour during a crisis is not misconduct or excessive risk-taking – it is the instinct to survive.
In fact, financial regulations can inadvertently exacerbate the one-in-a-thousand-day problem.
Imagine all financial institutions prudently adhere to regulatory demands. Regulators increasingly instruct them on how to measure and respond to risk. When an external shock occurs – such as a virus outbreak or war – all these prudent institutions perceive and react to the risk similarly because they are following the same instructions from the authorities. The result is collective selling in a declining market and uncontrollable fire sales. These prudent banks are not permitted to put a floor under the market and halt the fire sales. Only central bank liquidity injections do so.
This is the fallacy of composition in financial regulations: making all institutions prudent can actually increase the likelihood and severity of crises.
The impact of artificial intelligence
The growing use of artificial intelligence (AI) exacerbates the one-in-a-thousand-day problem (Danielsson and Uthemann 2024).
In banks, one of the primary users of AI and advanced computing is the treasury function – the division that manages liquidity. When the treasury AI detects rising uncertainties, it swiftly decides whether to profit by supplying liquidity and stabilising the market, or to withdraw liquidity, which might trigger systemic stress.
Here, AI's strengths – speed and decisiveness – can be detrimental.
In a crisis, the treasury AI acts swiftly. Stress that might have unfolded over days or weeks now escalates in minutes or hours. AI's ability to handle complexity and respond rapidly means future crises are likely to be much more sudden and vicious than those we have experienced so far.
Conclusion
A common belief holds that one stochastic process governs how banks and other financial institutions behave, regardless of the underlying conditions – maximising short-term profits within set constraints. If this were true, we could use data from normal times to model not only bank behaviour during stress but also the likelihood of crises.
However, this view is incorrect.
There are two states: routine profit maximisation for about 999 days out of a thousand, and self-preservation on that one critical day.
In crises, banks disregard short-term profits to focus on survival. This means that normal-time behaviour cannot predict actions during a crisis or the likelihood of one occurring. It also implies that post-crisis behaviour and market dynamics will differ from previous patterns.
The survival instinct explains why crises can be so suddenly triggered and become so severe.
As we increasingly adopt AI for liquidity management, future crises may become particularly swift and intense, unfolding in minutes or hours rather than days or weeks.
Recognising the one-in-a-thousand-day problem allows authorities to mitigate the damage caused by crises and enables investors to hedge risks or even profit. Otherwise, they risk being blindsided, exacerbating the resulting harm.
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