Behavioural insights into financial bubbles

Financial bubbles is one of the topics in economics that are intuitive to most people, except for economists. A financial, or speculative bubble, is characterized by a rapid increase in prices of an asset, without much consideration for its intrinsic value, followed by a burst, that is, a sudden reduction in prices. Seems simple enough, no?

For economists, however, that strikes a nerve. Economic orthodoxy (traditional, mainstream) has consistently based itself on the fact that even if not all people are rational, a few such could wash away most market distortions – inefficiencies such as bubbles – through arbitrage.

The idea of bubbles, however, is not inconsistent with rationality. For example, the price of the stock of a company is usually thought as the present discounted value of future dividends. This means that a stockholder is entitled to receive payments proportional to the profits of a company, where the term discounted implies that future earnings are valued less than present earnings. Basically, only the prospect of dividends should matter. However, if a rational person expects the price to go up regardless of dividends, they might be tempted to ‘ride the trend’. Given the choices of others, one might expect a price to go up just because others also expect it to. But if everyone is rational, there shouldn’t be a trend to ride!

THE P-BEAUTY CONTEST

To understand this better, we shall introduce the concept of a p-beauty contest. In a simple beauty contest, each of the participants is asked to determine the most beautiful face in a given group of people, and they can’t interact or ask each other’s opinions. The participants who vote for the elected face are eligible for a prize. Clearly, there is an incentive to vote not only based on one’s personal taste, but also on who they believe others will vote for.

In a p-beauty contest, things differ slightly. Here, the payoff depends on your choice and on the average choice of others. In fact, we assume that the maximum payoff is given to a player who chooses p times the average chosen by everyone else. For example: in a community of traders that own a certain asset for which the price is currently going up, but everyone expects to go down in the future, a certain smart trader might try to calculate the optimal time for selling. If they sell too early, they might miss out on growth, but if they run late, prices may drop too much. In the p-beauty contest, this ideal time to sell is captured by p (between 0 and 1) times the average selling time among all traders.

Nonetheless, if everyone is smart, they are all trying to aim for a selling time slightly under the average. But if everyone is trying to sell before others, in the end they should all sell at time 0. That is, immediately! This is the “Nash equilibrium” of the game, where everyone is rational and believes others are too.

In real life, laboratory studies that asked people to participate in such p-beauty games [Nagel (1995)] have found evidence in stark contrast with what has just been described. Most people wait a few periods before selling, and this time varies with p. It could be that some people don’t believe others will think that much about the game, and therefore delay their own selling time. This, in turn, creates an incentive for everyone else to do so too, since the average is now different from zero. In fact, the mere suspicion of imperfection in the reasoning of others might be enough for rational people to wait a bit before selling.

What has been described translates to speculative bubbles quite naturally, at least in how bubbles keep momentum: given an initial forecast of unsustainable growth, expectations of what others will do and the mistakes they will make can give bubbles a friendly push. In fact, even in the absence of actual mistakes, but in a scenario where everyone believes others are making mistakes, the mechanism still works. But there is still a big problem to answer. How can a forecast of unsustainable growth be formed? Why does this idea appear in the first place?

REPRESENTATIVENESS HEURISTIC

Robert Schiller, in his paper From Efficient Markets Theory to Behavioral Finance, suggests how behavioral economics can give us some hints as to which biases might be at play. Take, for instance, the representativeness heuristic (Kahneman & Tversky, 1972). It is used when evaluating the probability of A belonging to B based on how much A resembles B, without considering the raw probability of B. In the context of bubbles, this would mean that we judge the likeliness of an asset being an exceptional investment based on how much it looks like it is. That is, we observe a trend of growth and tend to think it will continue (because it seems indeed exceptional), but we don’t take into account that the probability of extraordinary returns is slim – we ignore all the other occasions in which assets have surges in prices but then go down, and focus on those which kept going up. Take, for instance, the tulip market in Holland, from 1634 to 1637. In this period, Turkish tulips which contracted a non-fatal virus that made ‘flames’ appear in their petals were rising in price very rapidly. People seemed to believe that past growth could mean nothing less than future growth. They assumed that the spectacular trend implied a spectacular investment, and tulips were eventually sold at the price of houses! Of course, the price then collapsed dramatically, to the point that tulips were basically worthless after the burst.

SELF-ATTRIBUTION BIAS

 Another factor might be the self-attribution bias. Identified by Daryl Bem in 1965, it is the individual’s systematic belief that good things happen to them because of their own effort and aptitudes, whereas bad events are viewed as bad luck or sabotage. This pattern of human behavior could promote a false sense of legitimacy to speculative bubbles. Afterall, the first comers would consider the initial astonishing success not to be a fluke, but a product of their talent – and their bragging stories could spread like a wildfire, attracting more and more people to the endeavor.

Both these phenomena can be understood under the umbrella of the so-called “Feedback Model”. As Robert Schiller summarizes:

When speculative prices go up, creating successes for some investors, this may attract public attention, promote word-of-mouth enthusiasm, and heighten expectations for further price increases. The talk attracts attention to “new era” theories and “popular models” that justify the price increases. This process in turn increases investor demand and thus generates another round of price increases. If the feedback is not interrupted, it may produce after many rounds a speculative “bubble”, in which high expectations for further price increases support very high current prices. The high prices are ultimately not sustainable, since they are high only because of expectations of further price increases, and so the bubble eventually bursts, and prices come falling down.

WRAP UP

Take for instance, a simple model of the price of an asset. Say P = V + e, where P is the observed price and V captures the underlying value, the “truth” (as you can see, this is a generous model). On the other hand, e is some kind of error, possibly due to problems in measurement. Given all assets in the world, we would expect e to be usually small, if our pricing system is reasonable. Sometimes, however, it might be non-negligible – there are so many assets on Earth that in at least some of them we must be making noticeable mistakes. But if a pricing mistake happens, anyone that profits from it might be subject to self-attribution bias, and think they invested correctly. Their story might spread, and the growth in price, that was a simple random error, might be taken as a sign of quality of the asset. For rational “bubble riders”, even the certainty of correction (fall in prices) in the future is not enough to hold back from short term gains. And as seen in the laboratory p-beauty contest, people wait more to sell than in the Nash-equilibrium, given the belief of unsustainable growth – evidence that a market environment is not enough to make bubbles go away immediately.

Besides the obvious implications of widespread financial collapse after a big enough bubble, the reason why economists are so interested in them is that they are not very easy to reconcile with market efficiency. They make us think about humans and their peculiarities, instead of the bland, if quite useful, homo economicus. In case we want to design regulations and markets that allocate resources more efficiently, however, we better pay attention to them, before the next burst takes us by surprise.

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References

• From Efficient Markets Theory to Behavioral Finance, by Robert J. Shiller.

• Behavioral Economics, by Edward Cartwright.

• Bubbles throughout history: https://fortunly.com/infographics/historical-financial-bubbles-infographic/#gref