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Why do markets soar and crash? Part of the explanation lies in herding behavior. By herding behaviour I mean that banks or investors like to buy what others are buying, sell what others are selling, and own what others own. There are three main explanations for why bankers and professional money managers herd (Thaler, 1994, Persaud, 2000). First, in a world of uncertainty, one of the best ways of exploiting the unknown information that others possess is to copy what the competition is doing. Second, bankers and investors are often measured and rewarded by relative performance over short time frames (quarterly, annually), so it literally does not pay for a risk-averse player to stray too far from the pack. Third, professional money managers are more likely to be sacked for being wrong and alone than being wrong and in company.

The second part of the explanation lies in conventional quantitative risk management practices (Daily equity at risk or DEAR, and Value at Risk or VaR). Modern quantitative risk management, particularly for heavily leveraged financial institutions (banks), focuses on minimizing changes in equity for short term periods. This is accomplished by estimating potential equity declines over a specified period for a specific probability of occurence level, where the probability of occurence for an event is estimated from statistical models built from the recent historical record. In the heavily leveraged case, the significant time horizon for investment results becomes subordinated to equity maintenance concerns, particularly where loans are covenanted with DEAR or VaR limits.

The key to contagion is that market participants behave strategically – in relation to one another – but DEAR and VaR measure risks “statically” – without strategic considerations. Market prices can only be a random walk in an environment of unbridled liquidity and maximum diversity of goals. However, the tendency of professional money managers to herd into particular assets can lead to large distortions in the price forming process. Previous price volatility and asset price correlations that are measured over a period of time, when the herd gradually builds up ownership of an asset, are almost certain to underestimate future price
volatility and asset price correlations when a strategic event comes along that can cause many investors to want to sell the same asset at the same time. Such strategic events can give rise to constrained liquidity over the short term, which in turn promotes contagion and market crashes.

This contagion type of behaviour is not as irrational as it may seem at first glance and can be modelled more formally using game theory. In a sense, herd behavior in an environment of falling prices mimics that of the well known prisoner's dilemma, whose rational solution is to always "defect", "defect" here being analogous to "sell".

The prisoner's dilemma is the most well known and well publicized game in game theory. In the prisoner's dilemma, two partners in a crime are caught and interrogated separately. The police have enough evidence to convict the pair of a lesser crime, and they know that the pair has committed a serious crime, but the evidence isn't strong enough to convict either of them of the serious crime. Therefore, the police must get one of them to "defect" and provide evidence to the State in
order to get any conviction on the more serious crime. Each prisoner is offered the following deal separately: if the prisoner cooperates and his partner does not, then the one who cooperates gets to go free of all charges and the other partner gets a sentance of 20 years. If both prisoner's confess, they will each get 10 years. If neither prisoner cooperates, then they will both get 3 years on the lesser charge. At first glance the optimum solution for the prisoners would seem to be to refuse to cooperate, but again, this ignores any strategic considerations. Since most players in this type of game have a tendency to base their utility relative to the outcome for their partner, the rational solution becomes "always defect" because this ensures that the worst case differential punishment is zero (the same punishment) while
still leaving open the possibility that the outcome will be favorable (partner gets 20 years, you get zero, for a net of +20 years).

Professional market participants, when confronted by an environment of falling asset prices, often behave in the same way as the prisoner's dilemma, rationally, they always defect. This is reinforced in the case of highly leveraged investment, where DEAR or VaR covenants force participants, "to reduce exposure". Although the media often portrays such market action as irrational panic, in a world where performance is short term in orientation, and measured relative to a peer group, the
decision to sell by a manager is often quite rational as this ensures a minimum differential between their short term performance and those of their peers.

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Since most players in this type of game have a tendency to base their utility relative to the outcome for their partner, the rational solution becomes "always defect" because this ensures that the worst case differential punishment is zero (the same punishment) while
still leaving open the possibility that the outcome will be favorable (partner gets 20 years, you get zero, for a net of +20 years).


However, if both participants in the game operate under the philosophy of "Minimize the total jail time served by both parties", the rational response is to never cooperate. Sure, if your partner is untrustworthy, total jail time is 20 years, but you have the chance to get 6 years. Defecting ensures that total jail time will be 20 years.
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However, if both participants in the game operate under the philosophy of "Minimize the total jail time served by both parties", the rational response is to never cooperate.

yes you're right. that is why it is called the prisoner's dilemma. but that is the point. the prisoner's don't cooperate together, the marginal utility function tends to be relative to the other partner. that is why the police always separate their prisoners and interrogate them individually. there is just a huge body of evidence out there that suggests that most probable solution to the prisoner's dilemma is to always defect. and interestingly enough, in a re-iterated prisoners dilemma, the optimum strategy is "tit for tat" (see Axelrod, Univ. of Michigan).

on wall street this paradox particularly holds true among the hedge funds and trading desks where competition tends to be high. even within a firm competition is often nasty and brutish. the goal is to outperform everyone else and in my experience there is very little cooperation among participants.

tr
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However, if both participants in the game operate under the philosophy of "Minimize the total jail time served by both parties", the rational response is to never cooperate.

A strategy where every prisoner keeps mum, thereby satisfying the above requirement, can be successfully invaded by a cheater (defector), who avoids 3 years of jail time by tacking another 17 years on to his partner's sentence. It's no skin off his back.

When cheaters make up 25% of the population at large, your expected jail sentence from defecting is 0.75 * 0 + 0.25 * 10 = 2.5 years, still lower on average than the 3 years of mandatory time for the lesser charge. At a 50% incidence of cheating, the average sentence is 0.5 * 0 + 0.5 * 10 = 5 years, which is longer than 3, but shorter than the 0.5 * 3 + 0.5 * 20 = 11.5 average term for the non-cooperators.

At every point along this continuum of 0 to 100% defectors, defectors have shorter jail terms, on average, than non-cooperators. In behavioral ecology, this is referred to as an "evolutionarily stable strategy", or ESS. In essence, an ESS is a strategy that can not be unseated by alternative strategies once it has been adopted by the majority of players, even if the overall fitness of the population suffers as a result.

When cheaters are identifiable and subject to retaliation (which in the "prisoner's dilemma" game of ex-cons, is probably a given), then you can have other optima based on conditional probabilities (i.e. the "tit for tat" solution that solasis mentioned).

Buffett and Munger have repeatedly recommended Richard Dawkins' "The Selfish Gene" at their annual meetings. If you want a good, albeit simple, intro to this sort of thinking, I highly recommend it.

Obviously, Wall Street is way more complex than any simple game theory models. But you might think of passive indexing as the non-cooperation strategy, active investing to beat the index as the defector strategy, and frictional effects (translating into a drag on GDP) as the cost paid by everyone.

TA

P.S. to solasis: Hope I'm not behaving like an annoying stray dog following you over here. But you're producing these amazing sand-painting posts for nobody, and I feel compelled to comment before they get washed away. BTW, good call on USG--I've already written it down to 0.
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i need to read dawkins. "the selfish gene" is good?

i just finished a book by Strauss and Howe called "The Fourth Turning", which is a very interesting theory about generational time, and historical cycles relative to generations.

the central thesis is that time flows in cycles, each cycle is called a "turning", and lasts around 20-25 years, and the turnings are tied to generational demographics. turnings have a demonstrated progression (a cultural political/economic 'high' - followed by a social 'awakening' - followed by a social 'unraveling' - and ending in major political 'crisis') that occur within the context of the saeculum, which is a four turning, larger historical cycle of 80-100 years.

the book discusses the previous five saeculae in anglo-american history, from the war of the roses/victory of the stuarts to the present day. in their context of history, we are coming to the end of a third turning (an unraveling) and preparing to enter another fourth turning, which is a period of crisis.

it is interesting, and others, military historians, toynbee for example, have noticed this, that there is this clocklike precision to major political crisis in anglo american history on a 80-100 year period.

war of the roses
wars of reformation -spanish armada
glorious revolution - cromwell - scottish/irish subjugations
american revolution - 1770's 1780's
american civil war & emancipation - 1860's
great depression/WW II - 1930's, 1940's
??? 2010s, 2020s?

this is not to neglect the devestation caused by WWI, the boer war, the spanish-american war, the mexican -american war, the napoleonic wars, etc, but none of these wars changed the political landscape within anglo-america the way that the aforementioned did.

cyclical time has general appeal to me, but i think that the markets demonstrate a clear tendency towards aperiodic cycles, and even the elliot wave theorists acknowledge that cycles can on occasion "invert" and do the opposite of what might be expected, based on the long run "pattern".

here's to hoping for a cycle inversion in the fourth turning that provides us not with crisis, but unexpected unprecedented peace and economic prosperity.

tr
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TWA40 said:

P.S. to solasis: Hope I'm not behaving like an annoying stray dog following you over here. But you're producing these amazing sand-painting posts for nobody, and I feel compelled to comment before they get washed away. BTW, good call on USG--I've already written it down to 0.

Don't worry that no one is reading our friend's posts. Many lurk when they have nothing to add, and it's often hard to add to such good posts.

dan
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i need to read dawkins. "the selfish gene" is good?

If you were retired or back in grad school, I'd say "yeah, you should definitely read it." But I qualify "need to read" lists a little more carefully now. I've got bookmarks sitting in half a dozen books on the nightstand, and they're mostly the same ones that were there last winter. But I do get to re-read "The Grouchy Ladybug" and "Go Dog, Go!" almost every night, so I should count my blessings.

I read "Selfish Gene" back in grad school shortly after it came out, and it certainly rocked my boat. Maybe shook my universe would be a better description. My copy is dog-eared and taped together from lending it out so many times, but I haven't gone back to see if it's still got legs. I suspect it has.

Dawkins is a great popular writer, but he doesn't compromise on the science. And with respect to explaining how natural selection works, he takes you right up to the abyss and lets you peer in, unlike Gould for example.

FWIW, my views on evolution are strikingly similar to Jefferson's views on Christianity. The world will likely be a better place if most of humanity remains naive.

TA

PS: As a war, Vietnam is easy to dismiss in the grand scheme of global conflicts. But as an event that changed the Anglo-American political landscape, it seems to warrant more than just an inter-cycle blip?
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