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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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