Studying asset bubbles in the lab

An asset or price bubble is a situation where the price of an asset far exceeds the asset’s fundamental value. For instance, consider a house. The price of the house should reflect the value of the land on which the house stands as well as the total cost of the building itself. While there is certainly scope for differences in valuation and, therefore, some deviation in the price of the house from its underlying value, these deviations should not be huge, and, in any event, should not persist for long periods of time. A similar argument is true of shares in a company.

The current price of the share should reflect the risk adjusted discounted value of expected future dividends to be paid on it.5 So, the current price should subsume all the relevant information and this price should not change unless something fundamental changes about the company, people’s expectations or the market conditions. This, in turn, implies that prices should track the fundamental value closely and that it should be difficult to "beat the market” by buying and selling such shares. If all traders are perfectly rational and equally well informed about the market conditions, then they should all price the share in a similar way. This idea that prices of financial assets such as shares should track the fundamental value is the essence of the efficient markets hypothesis, as proposed by Eugene Fama of the University of Chicago in the 1970s.

But, as we know now, not everyone is rational, or at least not rational to the same extent. They are also not equally well informed and, more importantly, we know that people are subject to a wide range of biases. All of these suggest that, while the efficient markets hypothesis may be an elegant theory, in practice this may not quite hold. But there are problems in trying to understand bubble formation in markets with naturally occurring data on prices and quantities. For one thing, it is not always obvious when a bubble is forming due to speculative frenzy as opposed to shifts in underlying demand and supply conditions. It is also not always easy to separate the price dynamics from other potential confounds.

Vernon Smith, fresh from his success in demonstrating the rationality of traders and the ability of the decentralized ascending bid—descending ask double auction mechanism to corroborate the Walrasian tatonnement conjecture, now decided to turn his attention to the efficient markets hypothesis. Smith s question was: are bubbles feasible and realistic or are they merely artefacts of particular historical or social circumstances? If we took an asset whose fundamental value is known and common knowledge, should we expect to see speculative bubbles arise as a routine matter? Or are price bubbles anomalies that occur infrequently?

Smith s ex ante conjecture was that, just as he found in the case of double auctions that decentralized trading between rational, self-interested buyers and sellers will lead to efficient outcomes, the same would be true in related markets where people trade financial assets. What he found was that these markets (or the buyers and sellers in these markets) behaved dramatically differently. There are large and persistent asset bubbles with prices hovering far above any feasible fundamental value for long periods.

For this work, Smith teamed up with a colleague at Arizona, Gerry Suchanek, and one of Smith’s long-time collaborators, Arlington Williams (of Indiana), whom we met in Chapter 14. Smith and his colleagues have done voluminous work in this area, which has become the standard paradigm for studying and understanding the formation of asset bubbles in markets. I am going to provide a broad overview of their design and use that as the benchmark for the rest of this chapter.

Suppose you own a financial asset in the form of shares in a company. If you hold on to these shares, then you can earn dividends from the company. To keep things simple, I will use the term “share” to indicate one unit of this financial asset. Further, suppose that these shares last for a finite amount of time after which point they become valueless.6 Let us say that, because company earnings are not certain, the dividend payments are uncertain too. But you know for sure that, for each share you hold, there is a one-quarter chance that this dividend payment will take one of four values: $0, $0.08, $0.28, and $0.60. This implies that in any period, the expected dividend is (l/4)*(0 + 0.08 + 0.28 + 0.60) = $0.24. So, in any given period, on average, you would expect to earn $0.24 in dividend payment for each share held.

Smith et al. then set up a large number of experiments, where each experiment acts as a market. Typically, each market consists of somewhere between nine and 12 traders. These traders are going to interact for 15 periods. At the start of the experiment, each trader receives some cash money and some shares. The cash held earns interest but it can also be used to buy shares. Now, remember that each share earns you an expected dividend of $0.24 per period. This means that if you hold on to one share for the entire 15 periods, then your expected earnings from that share is ($0.24)*(15) = $3-60. For the sake of simplicity, we are not going to discount future pay-offs since it does not make any difference to the underlying intuition of this exercise. Typically, Smith et al. set up their markets such that in a market with nine (12) traders, there are three (four) traders of each of the following three types: one group with three shares and $2.25 in cash; a second group with two shares and $5.85 in cash and a third group with one share and $9-45 in cash. Notice that the effective endowment of each group is the same: $13-05. For example, given an expected value of $3-60 per share, the first group received $10.80 in shares and $2.25 in cash; the second $7.20 in shares plus $5.85 in cash and so on. A trader’s total earnings from the entire session is given by cash endowments to start with, plus any interest earned, plus any dividends received, plus any profit from selling shares, minus any payments made for buying shares.

Trading of shares is done using a continuous double-auction mechanism. Buyers of shares can submit bids to buy, sellers can submit asking prices (asks) to sell. In any period, each bid (ask) must be higher (lower) than the previous bid (ask). Bids that are lower than the current highest bid or asks that are higher than the current lowest ask are put in a rank queue behind the current low bid or high ask. Buyers and sellers are also able to accept standing asks or bids, respectively, if they wish to buy or sell at that price. Each period lasts somewhere between 3 to 5 minutes during which time buyers and sellers can submit bids and asks, respectively, or accept standing asks or bids. They are, of course, free to not do anything and simply hang on to their cash endowment, which earns interest, and their share endowment, which earns dividends.

Three points are worth noting at the outset. First, as opposed to real-life markets, where there are many things happening at the same time and the degree of uncertainty is high and level of common knowledge low, the variables within the experiment are controlled tightly. Not only that, all the experimental parameters are common knowledge. Participants know what the expected dividends and interest rates are; they know how many periods they will interact for; they know exactly who has how much cash and/or shares. This is vastly different from real markets, where not all participants are aware of relevant opportunity costs. For example, if Grace opens a day-trading account and decides to buy some shares of Air New Zealand, she may or may not know accurately the value of other variables that might impact her choice. Would she be better off investing in gold? Or via buying NZ/US dollars or euros? The advantage to the stylized markets set up by Smith et al. is that it allows us to identify specific mechanisms at work behind the formation of bubbles. If bubbles arise in the fairly sanitized confines of the lab where all information is common knowledge, then we can plausibly expect that they are more likely to arise in situations where there are many more potential confounds.

Second, given this experimental control over the parameters and common knowledge of those parameters among participants, the fundamental value of a share should also be commonly understood. Given that each share becomes valueless at the end of the 15th period and yields an expected dividend payment of $3-60 per share, it would seem unlikely that the price at which these shares are bought and sold should deviate significantly from the underlying fundamental value. So, at the beginning of the session, the expected value of a share is $3-60, which is the sum of the expected dividends over time. With ten periods left, the expected value of the share is $2.40; with two periods left, the share is worth only $0.48 and so on.

Finally, note that the earnings of the traders include the possibility of capital gains. For instance, if a trader hangs on to a share, then his/her expected earnings for the share would be $3-60, but if he/she could sell this share to another trader for $5.60, then he/she can make a profit (or capital gain) of $2.00. If this second trader then manages to sell that share for $8.00, then he/she, in turn, makes a capital gain of $2.40. Why another trader should be willing to buy at $5.60 (or $8.00) is a question that we will discuss later and at length.

Figure 15.3 shows what happens in a typical such session. As noted, there is voluminous work done by Smith et al. and many successors. The finding is ubiquitous with some exceptions that I will discuss below. All of these markets reliably demonstrate a bubble and crash pattern just like the US housing market or the South Sea Company shares. In this figure, I have taken data from one of my own replications, which contained a larger number of traders than in the Smith markets but, nevertheless, does a good job of illustrating the typical price pattern of shares in such a market. This is a busy graph; so, let me explain. The solid black horizontal bars going down like a step from the left to the right is the fundamental value of a share. At the beginning of Period 1, this value is equal to $3-60, which is depicted as 360 in the diagram. At the beginning of Period 2, the fundamental value is ($0.24*14) = $3-36 and so on. The vertical grey dashed lines indicate the periods. The lighter shaded dots indicate the transactions that took place in each of the 15 periods. The dark dashed line tracks the average transaction price over time. It is worth noting that we will often focus on the average market price over an entire trading period but the average price may sometimes mask the price dispersions from the average within a period.

Figure 15.3 Results from an asset market experiment

As noted, this figure does a comprehensive job of presenting the main findings of Smith et al. First, prices usually tend to start low, often below the fundamental value. Smith et al. argued that, by and large, participants tend to be risk averse in the beginning such that trading starts at prices below the fundamental value. In this particular market, average price started marginally above the fundamental value of $3-60 in Period 1, where there is a large volume of transactions with a number of shares changing hands. From then onward, the average transaction price ticks upward, partly fuelled by participant expectations that prices will continue to rise, until it reaches an average value of approx. $7.40 in Period 6. It is noteworthy that this is more than twice the share’s initial expected value of $3.60. It is also the case that in Period 6, with nine periods left, the expected remaining dividend stream from this share is only $2.l6. So, if Grace buys that share at $7.40, she can expect to receive at most $2.16 from holding on to the asset, a loss of $5.24, unless, of course, she manages to find another buyer who is willing to pay an even higher price for the share. In this particular case though, Grace will most likely find that she was the one with the most inflated expectation of future price increases. She ends up buying the share at the peak of the bubble, with prices crashing toward the fundamental value after that. Smith et al. also find that not only does this bubble and crash pattern arise repeatedly in their markets towards the end of the session, there is also a reduction in the volume of transactions, with many fewer shares changing hands.

These results raised questions about the validity of the efficient markets hypothesis. It became clear that even in the very controlled atmosphere of the lab with common knowledge of outcomes and opportunity costs, bubbles and crashes happen reliably. Smith et al., however, note that the fact that prices do crash and return to the fundamental value provides some affirmation of efficient markets: that such bubbles will probably not be infinitely lived either and prices will eventually come back down to earth. However, it is also clear that there may be extended periods where prices are dissociated from underlying fundamental values. The same double-auction mechanism that provides strong support for individual rationality and ensures smooth convergence to equilibrium in markets for goods does not provide similar vindication for rationality in financial markets, where there is no distinction between buyers and sellers and the potential for speculative gains loom large.

Smith et al. concluded by saying that a common dividend and common knowledge thereof is insufficient to induce common expectations. They interpreted this as uncertainty among the participants about the actions of other buyers. These authors posit a lack of common knowledge regarding the rationality of other traders in generating this bubble phenomenon. Obviously, while the experimenter can control all other aspects of the experiment, he/ she has less control over the home-grown beliefs of participants or their inherent preferences. However, whether the bubble-and-crash pattern can be attributed entirely to irrationality or not is a topic I will return to shortly.

 
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