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| {{freeessay|isda|tail events|{{image|Tail event|jpg|}}}}{{quote| | | {{freeessay|isda|tail events|{{image|Tail event|jpg|}}}} |
| You asked me what’s my pleasure:<br>
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| A movie or a measure?<br>
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| I’ll have a cup of tea<br>
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| And tell you of my dreaming.
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| :—Blondie, ''Dreaming'' (1979)}}{{d|Tail event||n|}}{{nld}}
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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>
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| '''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.
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| </Ol>
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| ====The randomly distributed marketplace====
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| {{Drop|A|market, in the}} abstract, looks like a [[nomological machine]]. There is a bounded environment, a finite trading day, a limited number of market participants and a defined set of financial instruments with which one can engage in a limited range of transactions, whose outcomes will set the price for the traded instrument, which can be easily compared with the last traded price for that instrument (in that it will be higher, lower, or the same).
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| From this information we can ''derive'' a relationship between transactions — price went up, price stayed the same, price went down — and a ''trend''. A trend is a stab at extracting a [[signal]] from the [[noise]].
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| 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]].
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| =====The theory-dependence of signal=====
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| If given events are truly “independent” — in a first order sense, they are: the participants in the later trade do not know who or where the participants in the earlier even are, let alone what their motivations for trading were — then a “trend” we draw between them is, more or less, meaningless. All that is left is mathematics.
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| But we ''have'' a theory, so draw the line all the same. We make assumptions about the homogeneity of all market participants: we assume all have similar price information, and that all are propelled by the same essential economic rationalism: you don’t sell things you expect to do better than comparable investments, and you don’t buy things you expect to do worse.
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| =====Private narratives wash out=====
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| Each investor’s private motivation may be nuanced and personal — how is the rest of its portfolio positioned, what are the local macro risks to which it is especially sensitive — but largely these idiosyncrasies cancel themselves out in a large sample — they are [[Brownian motion]]; reversions to [[entropy]], which is baseline white noise — so we can disregard them.
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| Put another way, though the “interconnectedness” of similar transactions means they are ''not'' independent, as the probabilities of [[normal distributions]] require, most of the time it's close enough: the immediate transaction history is chaotic — as traders say, “noisy”— in the immediate term, here the dissimilarities between trader motivations are most pronounced, but over a large aggregation of trades these dissimilarities tend to cancel themselves out. A “signal” only emerges over time. If all traders are using market information, this immediate interdependence looks a lot like independence. So a “normal” probabilistic model<ref>I am working hard not to use the intimidating term [[stochastic]]” here by the way.</ref> works fairly well. It’s not a bad ''model''.
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| 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.
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| This is good: it gets our model out of the gate. If investors were not broadly homogeneous, our statistics would not work. “What is the average height of all things” is not a meaningful calculation. Which way the causal arrow flows — whether signal drives theory or theory determines what counts as a signal — is an open question.
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| 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, that informs price formation process: all can thereby infer the trend from prior trades — and use this abstract information to form their [[bid]] or [[ask]].
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| =====Nomological machines never quite work in the real world=====
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| 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 assumptions for Newton’s laws to hold are not present, so we let it pass when our bouncing ball never quite obeys them, but it is close enough and usually no one is counting in any case.
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| The same applies to the statistical techniques for we use to measure behaviour of the market. As we have seen, the occasional intervention of idiosyncratic behaviour is basically noise. Where the interdependence creates a persistent variance from the normal probability model over time we can model that, too, with measures like [[volatility]]. We use probabilistic techniques to model these second order corrections, too.
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| But there is a ''third'' order of dissimilarities. In times of stress in the market the behaviour of other people in the market ''directly'' and ''directionally'' affects your transaction, and yours affects others.
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| This is not just the crowded theatre phenomenon, when everyone stampedes for the exits at once, and the narrow aperture makes the stampede all the more urgent, and therefore dramatic — but second order features. An investor long “on margin” might wish to, and be able to, ride out a short term crash by meeting margin calls. In most dislocations this is the obvious and — if you can manage it, correct — thing to do. The market usually recovers, at least in the short term. But meeting your margin call means drawing on your revolving credit facility and your bank is experiencing a liquidity crisis and unexpectedly pulls you lines, or suspends withdrawals, as a result of its ''own'' market exposure to the crash. Your prime broker, usually patient with you and tolerant of peripheral looseness in your margin operations, is also under pressure, has told you today there is no flex, and for good measure, it is jacking up your IM.
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| All that near perfect information in the market evaporates — rather, other information, which the market ''didn’t'' have, but took for granted, such as the solvency of systemically important financial institutions, suddenly becomes much more important. And it dramatically impacts behaviour in the market. All at once no-one fancies taking a view on ''anyone’s'' credit.
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| Cash is suddenly King, Queen, Jack and Ace. There are people on the TV in sharp suits wandering dazedly around outside their buildings clutching [[Iron Mountain]] boxes full of personal effects.
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| All indicators are going one way, across the board, in all markets and all asset classes.
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| Now we find the model we were using has stopped being largely right, or broadly right, or even vaguely right. It is flat out wrong.
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| You will find at this stage limited tolerance for blaming a model. If you say things like, {{Viniarquote}}. This is not a good look for the CFO of a bulge bracket [[Vampire Squid]].
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| Using normal distributions as a heuristic to model interdependent events is generally effective if a few conditions pertain.
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| {{L1}}The market is generally diversified. If you carve out all the personal idiosyncrasies — stochastic modelling requires — that might explain why one rational person is prepared to sell what another is prepared to buy, it stands to reason that a buyer’s gain is a seller’s loss. In a diversified market, a sudden collapse in value for some traders means an appreciation for others, and all kinds of other effects. See: [[Brownian motion]]<li>
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| No individual participant, or group of participants with correlated interests dominate the market <li>
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| Information about the market, and any “crowded” positions in the market, is widely held. Of course individual positions are private, proprietary and confidential, so this last condition is usually satisfied by the general assumption of liquidity: in a sufficiently deep market, no-one is big enough to have such a concentrated position, so we can take it as a given that no-one does. (In some markets there are materiality thresholds over which positions must be reported too.)</ol>
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| But in the modern market, where scale and leverage are so important, these are not always safe assumptions. Lenders only know what they know.
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| ====Derivatives trading====
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| In the context of trading derivatives, things that (a) you didn't reasonably expect and that . (b) bugger up your contract.
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| =====Credit defaults=====
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| 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”.
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| 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.
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| Inability is the main player here: generally captured by insolvency, and correlative defaults under other agreements.
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| 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.
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| 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''.
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| 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,
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| 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.
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| =====Externalities=====
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| 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 discourage 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.
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| Secondary events of this kind — things that limit a dealer’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.”
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| Customers have less incentive to break trades if it means realising
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| {{sa}}
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| *[[The map and the territory]]
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