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Rational informational herding

It can be rational for traders to buy with rising prices and sell with falling prices. In particular, this should be the case if traders possess private information suggesting that “something big” is coming and that prices may move significantly, even if direction is not certain (e.g. “make-or-break” situations). Experiments confirm such rational informational herding.

Park, Andreas and Daniel Sgroi (2016), “Herding and Contrarian Behavior in Financial Markets: An Experimental Analysis”, Centre for Economic Theory and its Applications, Department of Economics, University of Warwick, Discussion Paper No. 17, January 2016

The below are excerpts from the paper. Headings, links and cursive text have been added. Some acronyms and technical terms have been replaced by simplified language.

Informational herding

“[If securities are traded through market makers] the general movement of prices captures the majority or ‘crowd’ action: rising prices indicate that there are more buyers than sellers, falling prices indicate that there are more sellers than buyers. We will define herding and contrarianism against this yardstick…

  • We thus say that a trader engages in herding behavior if he switches from selling to buying in the face of rising prices, or if he switches from buying to selling in the face of falling prices…
  • The counterpart situation, contrarianism, arises when a trader switches from selling to buying in the face of falling prices or if he switches from buying to selling in the face of rising prices…

There is symmetry in the definitions, making herding the intuitive counterpart to contrarianism.”

Switching behavior is triggered by observational learning, which is a core feature of informational herding, and from this perspective it is thus justified to label switching with the crowd as ‘herding’.”

The theory

“[Previous academic research] provides a theoretical insight showing that switching behavior [i.e. selling and buying in response to past price moves] can be fully rational even with efficient prices and…admits both rational herding and rational contrarian behavior.”

“The key hidden parameter that defines informational herding theory is the private information held by traders…There are three key types of [private] signals: monotonic, hill-shaped and U-shaped…

  • Recipients of a signal with an increasing likelihood function [greater likelihood of higher prices] will always buy, those with a decreasing likelihood function [greater likelihood of lower prices] will always sell…
  • Recipients of “U-shaped” signals [greater likelihood of significant market moves either way] will buy if prices rise a lot but sell if prices fall a lot…they “follow the trend”.
  • A signal with a “hill-shaped” likelihood function [greater likelihood of market stability] will buy if prices fall a lot and sell if prices rise a lot …[Investors with such signals will] “buck the trend” and act as contrarians…”

“Is it possible that a trader sells, even though his private signal alone tells him that [a security] is worth [more than the market price]? The answer is yes: for sufficiently many sales, the private information of any trader [in respect to the ‘fair’ value of a security] is swamped by the negative information derived from observing [the market]

  • An investor sells after bad news and buys after good news, if and only if, compared to the market, his private information is such that he puts more weight on the extreme outcomes Such a type… herds in the sense that he acts like a momentum trader, buying with rising and selling with falling prices.
  • Similarly, an investor buys after bad news and sells after good news, if and only if, he puts less weight on the extreme outcomes…Such a type…trades contrary to the general movement of prices.”

The experiment

“We analyze and confirm the existence and extent of rational informational herding and rational informational contrarianism in a financial market experiment…

  • In the setting used in this experiment, a buy increases the price, a sale decreases the price. Traders can thus perfectly infer past actions from prices and they can compute every type’s optimal action at any point in the past…
  • The financial asset in every treatment can take one of three possible liquidation values…which correspond to the true value of the asset. The traders were typically made up of 15-25 experimental subjects, plus a further 25% noise traders, with a central computer acting as the market maker. Noise traders…have a useful practical role in the experiment, simulating a degree of uncertainty about the usefulness of any observed actions…
  • “Prior to each treatment subjects were provided with an information sheet detailing the prior probability of each state, a list of what each possible signal would imply for the probability of each state, and the likelihood of each signal being drawn…The information on the sheets was common knowledge to all subjects. After being given the opportunity to study this [public] information, each subject received an informative private signal, described to them as a “broker’s tip”…The nature of the compensation system was also made clear in advance, and in particular that it directly implied that they should attempt to make the highest possible virtual profit in each round.”

Only traders with U-shaped signals can rationally herd as only their…expectation can be above the price after prices have risen. Similarly, only traders with hill-shaped signals can act rationally as contrarians.”

The findings

“We analyze whether receiving a U or hill-shaped signal affects the chance of acting as a herder and contrarian significantly relative to any other signal. We find that this is indeed the case…. 69% of trades conformed to the rational choice. This is in line with other experimental studies.

  • Compared to receiving any other signal, recipients of U-shaped signals are significantly more likely to herd….While the contrarian tendency of traders is strong enough to prevent some of the herding that should arise, U-shaped signals are still the relevant source of herding.
  • We observe that the marginal effect of receiving a U-shaped signal on the chance of herding is significantly stronger for the more rational subjects.
  • If contrarianism arises, it is most likely to be caused by someone with contrarian information; receiving a hill-shaped signal increases the probability of acting as a contrarian by 50% relative to receiving any other signal.”

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