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{{L1}}'''Statistics''': Of a range of possible independent events, one whose frequency is three or more [[Normal distribution|standard deviation]]s from the mean. An event with a low [[probability]]. <li>
{{Nld}}
'''Work life''': An unwanted outcome to which you weren’t paying attention, which you didn’t expect and, therefore, for which you don’t think you should be blamed.
</Ol>
We are, as the JC frequently complains, in a swoon to the [[Reductionism|reducibility]] of all things.
 
This usually involves converting all the irreducible things that we do and that happen to us into numerical [[data]] points.
 
“Things that we do and that happen to us” are unique, four-dimensional, social constructions. They are [[ineffable]]. Converting them to words necessarily involves a loss of information. Converting them to numbers even more so. We cannot restore this loss of fidelity through statistical techniques. We can mimic it, but that is something different.
 
Data points, in themselves, are no more naturally [[effable]] than “odd things that happen to us” from which they are extruded, of course. But numbers have the quality of submitting easily to aggregation, symbolic manipulation and statistical techniques, in a way that “odd things that happen to us” do not.
 
This is the singular benefit of datafication. To simplify a complex artefact down to a number, or set of numbers, is to ''symbolise'' it. Symbols we can subject to ''symbol processing''. But we have switched domains: we have left the offline and gone online. We have left the domain of the signified and entered that of the signifier.
 
What one has rendered as data, one can use in calculations. With these one can generate abstract mathematical properties: a mean, a median, a mode. One can calculate probabilities.
 
Applying a number to an artefact is a linguistic operation, like assigning a noun. The calculations we perform with that number tell us about the mathematical properties of the number. They do not tell us about the artefact it signifies. This is easy to see with an average: the average height of the passengers in this train carriage tell us nothing about any of the passengers. Yet so much of the modern world measures against the average!
 
We say the average is an emergent property of the group, the the say that wetness is an emergent property of a group of water molecules. But is it?
 
We harvest information from artefacts, convert it into data, generalise it, manipulate it mathematically, and then apply it back to ''similar'' artefacts. A statistical method is legitimate if it applies to identical artefacts. We suppose it to be largely legitimate if it applies to similar artefacts.
 
Dice are not machined perfectly. But they are similar. The broad principles of probability apply to them generally, roughly.
 
But “similar” is a word, and therefore a value judgment. It exists in the domain of signifiers, not signified. We are similar in that we are all homo sapiens. But that signifier of similarity is not enough to determine breakfast preferences.
 
In the same way that we can calculate the probability of rolling consecutive sixes so, it seems, can we calculate the probability of rain tomorrow, a cut in stamp duty in the spring, or a thirty-point intraday drop in the NASDAQ.
 
This is an invalid move, unless the artefacts were in the first place sufficiently and relevantly similar. The sides of a dice are to a large degree. Clouds and weather patterns are, to a small degree. The conditions propelling the NASDAQ — humans — are not relevantly identical.
 
But numbers are alluring. They are under our control. They ''behave''. They bend to the spreadsheet’s will. The spreadsheet’s will is our will.
 
Except, as [[David Viniar]]’s immortal words remind us, the events these numbers represent — the territory for which they are a map — are wont to have other ideas.
 
{{quote|{{viniarquote}}<ref>explaining why the [[vampire squid]]’s flagship hedge funds lost over a quarter of their value in a week, in 2008.</ref>}}
 
Rolling dice are not like the stock market.
====The map and the territory====
Mr Viniar’s model, he hoped, would tell him something about the market’s behaviour. The model is the ''map'', the market is the ''territory''. We judge the success of a model by how close its prediction is to our subsequent [[lived experience]]. There is a natural dissonance: models are drawn from past experience, and that is singular, static and unalterable. It is dead.  Our future experience is, as far as we know, none of these things.
 
You would not expect a “twenty-five sigma” day once in several lifetimes of the universe. Goldman’s model was in effect saying, this kind of event ''will not happen''.
 
This would be the equivalent of all the molecules in a cup of tea spontaneously jumping to the right at the same moment. The molecules are bouncing around randomly — Brownian motion, right? — and so conceptually they could all jump left at once<ref>it may be that, conceptually, they couldn't — Brownian motion depends on collisions. For all I know, this implies that half the molecules are jumping the other way.</ref> but the sheer odds of every single atom doing do at once are so infinitesimally small that it would never happen in several billion lives of the universe. Neither the cup or the tea in it would last that long, of course.
 
But that is the scale of likelihood of a twenty-five sigma event.
 
That Mr Viniar thought there were several such days ''in a row'' — in a market history measured in decades, not universe lifetimes — must mean the model was wrong.<ref>It was, for reasons we explore elsewhere.</ref>
 
Now here is the thing. When we calculate probabilities — when we roll dice — we are situations of known risk. That average means something. It is not just that on some some dice the probability is more like ⅐, on others now like ⅕, but on average the dice work out at all about ⅙. It must be true of every individual die..
Rolling dice to ''determine'' an outcome is is quite
different. We do not build a statistical model that predicts a ⅙ probability: we build the dice to yield the that outcome. The dice are what [[Nancy Cartwright]] calls a “[[nomological machine]]”: a carefully designed, constrained, hermetically-sealed device, designed to generate a specific theoretical outcome. If over time the dice don’t yield a ⅙ outcome we don't chuck out our statistical model: we chuck out the ''dice''.
 
The “map” and territory ” are transposed: the dice are the map, the theoretical ⅙ probability is the territory. The map is, as far as engineering permits, ''identical'' to the territory. We could, indeed, generate the outcome we wanted without dice, by running the model with a random number generator.
 
The machined dice, the flat, constrained surface — these are a representation of the reality, which is the hypothetical model, and not the other way around.  A loaded die is a ''flawed'' machine. You don't chuck out the theory: you chuck out the equipment.
 
Likewise, if, inside your nomological machine there is a mischievous imp who catches and places the die as it sees fit, the conditions for your probabilistic calculation do not prevail. There is an interfering causal agent.
 
“Nomological machines” are highly constrained, artificial environments. If all their conditions are not satisfied, we can expect the world to behave differently without validating the machine. This is how, as [[Nancy Cartwright]] put it “the laws of physics lie”.
 
In any case, these are the circumstances in which the rules of probability prevail. Should the universe “misbehave” then the conditions required for the nomological machine cannot be present.
 
Boy did I get sidetracked.
 
Normal distributions standard deviations, and confident probabilities require a complete nomological machine where all potential events are known, are independent, and there is no intervening agency that can upset the observed behaviour of the system. If you have all that all risks can be calculated and probabilities assigned.
 
Markets, in the abstract, look just like such a machine. There is a bounded environment, a finite trading day and a limited number of market participants and financial instruments which one can buy or sell. In the modern days of computerised trading everything is very clean, tidy observable, unitary and discrete.
 
====Derivatives trading====
In the context of trading derivatives, things that (a) you didn't reasonably expect and that . (b) bugger up your contract.
=====Credit defaults=====
A swap being a private, bilateral affair, the most obvious category of tail events is “things which mean your counterparty cannot, or will not, or has not, performed its end of the deal”.
 
Straight out refusal to — repudiation — is rare, at least without the cloak of some kind of dispute as to whether the party was under such an obligation in the first place.
 
Inability is the main player here: generally captured by insolvency, and correlative defaults under other agreements.
 
Much of financial services being a play on [[leverage]] — the name of the game being to earn more, with other people’s money, than it costs you to borrow it — many market participants flirt with various formulations of [[insolvency]] as a basic business model, so there tend to be some pushback on the parameters of these correlative failures and “ostensible inabilities” to perform. Much of a [[negotiator]]’s life is spent haggling about them.
 
Where refusal or inability to perform cannot be proven, actual failure to pay or deliver ends all arguments. If you ''actually'' haven’t performed, it no longer matters ''why''.
 
There is therefore a sort of hierarchy of these events. Actual default is the safest, and most common, default trigger. Bankruptcy is the next — though there is more looseness around some of its limbs, an administrator actually being appointed, or a petition actually being filmed is clean, public and unlikely to prompt many arguments. Default Under Specified Transaction — that transaction being one to which you are directly a party,
 
The remaining events are sketchy and unpopular, depending as they do on private information you most likely won't have about thresholds you can't easily calculate. We may argue till we are hoarse about Cross Default. We will not invoke it.
 
=====Externalities=====
There are a category of events which make it impossible even for a solvent counterparty to perform. Change in law, for example — it is not beyond possibility that certain kinds of swaps might be restricted or outlawed altogether<ref>Not long ago the European Union proposed restricting the carbon market to “end users” to discouraged financial speculation, for example. This would have rendered certain forward contracts in {{euaprov|Allowances}} involving delivery to non-users illegal.</ref> or Tax events that make the transaction uneconomic as originally envisaged.
 
Secondary events of this kind — things that limit a delaer’s ability to hedge, or materially increase its  costs of doing so, tend not to be Termination Events partly this reflects a fact not often stated, but nonetheless true: there is a price at which the parties will agree to terminate any swap. Just because a party doesn't have an economic option to terminate the trade doesn't mean it can't terminate the trade. It always has an “at market” option. In liquid markets during times of fair weather this is a source of great comfort; in illiquid markets and at times of stress, less so. A dealer will say, “I will always show you a price. You just might not mind the price, is all.”
 
Customers have less incentive to break trades if it means realising
 
 
{{sa}}
*[[The map and the territory]]

Latest revision as of 17:46, 14 September 2024

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You asked me what’s my pleasure:
A movie or a measure?
I’ll have a cup of tea
And tell you of my dreaming.

—Blondie, Dreaming (1979)

Tail event
/teɪl ɪˈvɛnt/ (n.)

  1. Statistics: Of a range of possible independent events, one whose frequency is three or more standard deviations from the mean. An event with a low probability.
  2. Work life: An unwanted outcome you didn’t expect, to which you weren’t paying attention, and, therefore, for which you don’t think you should be blamed.

The randomly distributed marketplace

Amarket, in the abstract, looks like what Nancy Cartwright calls a “nomological machine”. A simplified model of the real world having defined boundaries and simplified operating conditions: a finite trading day, a limited number of market participants and a defined set of fungible financial instruments with which participants engage in a limited range of transactions, whose outcomes deterministically set observable prices for that set of traded instruments, which prices bear quantifiable relationships with previously traded prices for the same instruments (in that they will be higher, lower, or the same).

But the real world these instruments represent is intractable. It does not have boundaries. It is inchoate, and our knowledge about it less so: The “instruments” of the real world are not “fungible” — 2 shipments of the same commodity have indefinable idiosyncratic impurities and characteristics — abd the range of possible events that can occur to physical commodities in undefined in a way that the range of events that might occur to financial instruments is not.

“A portfolio of asset-backed securities cannot,” a commodities trader would say, “suffer water damage. They do not rust.”

Not having to deal with rust, water damage or manufacturing defect simplifies the business of investing in the financial instruments. The effects of these events are supposed to play out in the information layer, and translate efficiently into the prices at which related instruments trade. If an oil company’s tanker is wrecked, its share price declines.

It is tempting to infer information from price: to put a drop in the market down to “soft non-farm payroll data”. People make a living reading tea-leaves in this way.

From price information we can derive a relationship between transactions — the price went up, stayed the same, went down — and a trend. A trend is a stab at extracting a signal from the noise.

The signal depends on a theory of the game: otherwise the “relationship” between the two discrete transactions is arbitrary.

Without a theory, everything is noise.

The theory-dependence of signal

If events are truly “independent” then any “trend” we draw between them beyond their distribution is, more or less, meaningless. In a first order sense, market events are independent: the participants in the later trade do not know who or where the participants in the earlier are, let alone what were their motivations for trading. All we have is a theory and some mathematics. But we draw the line all the same.

We make assumptions: the market is homogeneous; all participants have similar price information; all are propelled by the same rationale. No trader sells things she expects to do well, nor buys things she expects to do badly.

Private narratives wash out

Given these assumptions, individual investors’ private motivations, opinions, theories and idiosyncrasies cancel each other out, so we can disregard them. They are like the Brownian motion of molecules in a nice hot cup of tea: reversions to the entropic mean; baseline white noise. This is just as well, because otherwise our models would not work. We can ignore individual sentiments because they don’t matter. Until they do.

Put another way: although the “interconnectedness” of similar transactions means they do not have the quality of independence that a normal distribution requires, most of the time they pretty much do: information is chaotic in the immediate term, here the dissimilarities between trader motivations are most pronounced, but over a large aggregation of trades and a longer period a “signal” emerges. This is what Black-Scholes, volatility and convexity models track: as long as all traders all use the same aggregated market information — and the market works hard to ensure they do — a “normal” probabilistic model works fairly well. It’s not a bad model.

So we treat professional market participants as a largely homogenous group from which emerges, over time, a signal. Almost like, you know, like an invisible hand is guiding the market. This gets our model out of the gate. If investors were not broadly homogeneous, our models would not work. “The average height of every item in this shed” is not a particularly useful calculation. Which way the causal arrow flows — whether signal drives theory or theory determines what counts as a signal — is an open question.

But there is a second-order sense in which the earlier and later trades are related, in practice: the later participants know about the earlier trade and its price — it is part of that universal corpus of market information, deemed known by all, it informs price formation process: all can thereby infer the trend from prior trades — and use this abstract information to form their bid or ask.

Nomological machines never quite work in the real world

When you bounce a ball, friction, energy loss, structural imperfections, impurities in the rubber and environmental interference frustrate the conditions needed to satisfy the “nomological machine”: the required conditions for Newton’s laws to hold are not present so, when our bouncing ball never quite conserves momentum, we let it pass. It is close enough and usually no one is counting in any case.

This is the sense in which, as Nancy Cartwright puts it, the laws of physics lie. They don’t represent what happens in the real world.

The same applies to the statistical techniques we use to measure market behaviour. Much of the non-homogenous behaviour cancels itself out. Where it doesn’t — where it creates a persistent variance from how a normal distribution would behave over time, we can model that, too, with measures like volatility. We use probabilistic — that is, independence-assuming —techniques to model these second-order corrections like volatility, too.

Why do we assume independence and homogeneity of events? Because otherwise, we could not predict at all. A human being with free will and moral agency does not obey laws of probability. She can put a coin down heads up every time. She can go out of her way to deliberately frustrate any prediction or suggestion her husband another person makes.

“Oh, you predicted heads? Well, I say tails.”

It’s not just that individual humans can do that: they like doing that. Likewise, you can’t draw models that predict the behaviour of dissimilar objects. Statistical rules require homogeneity. The odds of rolling a six hold true for fair dice, but not for carpet slippers or fish.

But this is the magic, so claimed, of big data. All those idiosyncrasies cancel themselves out and leave us with a set of basically homogenous participants. You night not like rice pudding or lentils but over a whole population, a fairly reliable proportion of the population does. We can ignore individuals. The variances they represent are noise. It is our dystopian lot that our institutions and social systems increasingly are configured to ignore us.

BRIAN: “You’re all individuals!”
CROWD: “Yes! We’re all individuals!”
BRIAN: “You’re all different!”
CROWD: “Yes! We’re all different!”
(small voice at the back): “I’m not.”

—Monty Python’s Life of Brian

Our agency and our idiosyncrasies average out. We all want to eat, be warm and dry and have rewarding careers. That we all go about this in subtly different ways doesn’t, to a data aggregator, much matter. Until it does.

For there is a third order of dissimilarities. In times of market stress, other people’s behaviour directly and directionally affects you and your transactions, and your behaviour affects theirs. This is not the irrationality of panic — if each decision were irrational, the effect would be random and the Brownian cancellation effect would come into play and everything would be fine — but an instinctive imitation of whatever it is the surrounding community is doing. THOSE GUYS ARE RUNNING AWAY. I DO NOT KNOW WHY BUT I MUST PRESUME THEY HAVE A REASON. THEREFORE I AM RUNNING AWAY.

This is “memesis”. Most of the time, thanks to the Dunning-Krueger-by-proxy[1] effect or otherwise, we presume the perspective we can bring to the information we have gives us an edge over the crowd, and we are happy to make our own decisions, whose individual variances boil off into Brownian randomness that can be neatly fitted to a standard deviation from the mean. But there are moments — by nature unexpected — when that confidence vanishes. Suddenly our conscious models, theories and nomological machines are less valuable than the tacit information we gather from the changed behaviour of everyone around us. There is something important we don’t know. It is better to mimic the behaviour of those around us. We presume they know — or that they are imitating the behaviour of someone else who knows.

This is the extraordinary behaviour of fish when a shark bursts through the school. This is the bewitching murmuration of starlings over a twilight meadow. In an instant that entropic, Brownian normalcy disappears and every particle darts the same way at once, as if by magic.

We are mesmerised but not surprised to see starlings perform their aerial magic. We would be gobsmacked if a cup of tea did this.

When the planet has unexpectedly gone into lockdown as a result of a global pandemic, buying habits for toilet paper and, oddly, lentils suddenly change. The fact that there are only three tins of lentils left on the shelf leads you to grab them. The fact that there are none leads to a nationwide run on tinned pulses people don’t, in normal times, much like. The Contrarian household still groans under the weight of tinned borloiti beans years after the last new variant.

There are not just these “cry fire in a crowded theatre” effects whereupon everyone stampedes for the exits at once, but second-order effects. You might not wish to head for the exit: you might be strong-willed enough to rise above the madding crowd — but you might still have no choice. You are not independent when your asthma inhaler is in your spouse’s rucksack.

If you are long “on margin” you might wish to ride out a sudden correction by meeting your margin calls. In most dislocations this is the obvious and — if you can manage it, correct — thing to do. You might, per your own books and records, be solvent, well-capitalised and in good standing with your banks, so why not?

But meeting the margin call means drawing on your standby revolving credit facility — you don’t keeps a yard of spare cash off the table for emergencies, right? — but it turns out your bank is, like everyone else, suffering a liquidity squeeze. It evokes some obscure market conditions CP buried in the docs and suspends drawdowns on the RCF as a result. This is nothing to do with you: the bank is managing its own cash position. It needs the money more than you.

At the same time your margin lenders — usually so patient with you, generally genial, good for a knees-up at Ascot and tolerant of peripheral looseness in your margin operations — have had a sense of humour failure. They are apologetic, but they are shipping a shower of grief from the head of risk and have been told to tell you that you today there is no flex. Today the money must be there on time without fail — and for good measure they are jacking up your IM.

You say this is absurd, that everything is fine, but appeals to their better nature and your solid, five-year track record fall upon deaf ears. Today they don’t know what to believe. Normal conditions of trust and amity are suspended. This could be the final round of the prisoner’s dilemma.[2] Anything they can’t see unaided with their own naked eyes could be fake news. The one thing they can see is that everyone else is running for the door.

The value of all that near-perfect market information evaporates and other information, which the market doesn’t have, but until now took for granted — such as the essential viability of systemically important financial institutions and the strength of the commercial imperative — is suddenly much more important. All at once, no-one fancies “taking a view” on anyone’s credit.

Cash is King, Queen, Jack and Ace. There are dazed people in sharp suits wandering around Canary Wharf clutching Iron Mountain boxes.

All indicators are going one way, across the board, in all markets and all asset classes.

Now we find our model has stopped being largely right, or broadly right, or even vaguely right. It is flat-out wrong.

Twenty-five sigma events

If a coin lands tails a hundred times in a row it is either a unique moment in the life of the cosmos or a dicky coin.

If you are the CFO of a bulge bracket Vampire Squid you will earn limited sympathy if you blame your losses on a statistical model, but absolutely none if you blame it on the misbehaviour of the universe. Do not say things like:

“We were seeing things that were 25-standard deviation moves, several days in a row”

Twenty-five sigma events do not happen once, let alone several days in a row. Your model did not work.

This is a tail event. This is what all the meaningful terms in your legal agreements are designed to protect you against.

See also

References

  1. I just made this up but it seems, for reasons I cannot now articulate, like a good and possibly profound idea. Possibly that reason is that I suffer from Dunning-Krueger-by-Proxy Syndrome
  2. According to game theory it is rational to cooperate in non-zero sum games as long as you expected them to repeat. If you expect them not to repeat, it is rational to defect. This is the traitor’s dilemma.