I don’t understand why the fundamental value is declining!

A common refrain from students is: why is the fundamental value declining? When someone owns a house, the value of the house typically does not decline; it may well increase over time and the horizon is longer lasting than the 15 periods in the lab. As I noted earlier, these bubbles and crashes are not an artefact of the finite lives of the assets. These patterns arise even when the fundamental value is flat. Charles Holt of Virginia, along with long-time collaborator Jacob Goeree and others, has done extensive work looking at situations where the fundamental value is constant, often referred to as a ‘‘flat’’ fundamental value. Given that we cannot really run infinitely long experiments, the flat fundamental value paradigm is a good approximation of an asset (such as a house) that is long-lasting and does not lose value over time.

Like Smith, participants in the Holt et al. studies also start out with cash, that earns interest, and shares, with the exception that these shares will be redeemed at a fixed value at the end of the session. In Figure 15.4, I show what happens in such markets. In doing this, I am presenting data from a study by David Dickinson (of Appalachian State) along with Ananish Chaudhuri and Ryan Greenaway-McGrevy (both at Auckland). (The results reported in Holt’s studies are similar.) I will discuss this study in greater detail in Case Study 15.2. The basic set-up is the same as that in the Holt studies. Groups of 7—13 subjects (median group size = 11 subjects) participated in the online asset market experiment. Here, all participants have the same endowment of cash and 6 shares. Each share has a constant fundamental value of $7 in all rounds of all treatments. Cash held at the end of each round received 10% interest. In each round, each share earns a dividend of either $0.40 or $1.00 (so, the expected dividend is $0.70 per round) and shares are redeemed for $7.00 at the end of the final period of the treatment.7

Dickinson et al. collect data from many markets and I have presented data for only three of those. I have chosen these because they help establish my point but they are not all that different from many other markets in that study or in studies done by other researchers, for that matter. As in Smith, participants interact for 15 periods. More in keeping with Smith’s arguments, in all three markets, initial prices start at less than the fundamental value. But then the prices take off. In Market 1, prices rise steadily to $45 until Period

Figure 15.4 Results from asset markets with flat fundamental value. Re-created on the basis of data in Dickinson et al. (2019)

9 before declining relatively smoothly down to the fundamental value of $7 by the last round. In Market 2, however, the bubble never crashes! Prices increase slowly but inexorably till, even in Period 15, the average price is more than $40, for shares that are worth only $7. Market 3 demonstrates a huge bubble and a precipitous crash. Prices reach $80 in round 13. Then, no shares change hands in Period 14, in line with Smith s observation that trading volume reduces dramatically towards the end. Finally, in Period 15, the market crashes to the fundamental value.

Holt’s findings show that the bubble-and-crash pattern arises even where the financial asset is long (or infinitely) lived and has a flat fundamental value rather than a declining value. This also shows that one does not need to have traders with different endowments of cash and shares for bubbles to arise. In Holt’s work and Dickinson et al.s, all participants have the exact same endowment of cash and shares, yet both observe significant bubbles. We know a few other things. The bubble phenomenon tends to be more pronounced in Smith- type markets with declining fundamental value as opposed to Holt-type markets with flat fundamental value. Further, even in markets with flat fundamental value, the magnitude and duration of bubbles tend to be larger with more liquidity. For the markets in Figure 15.4, if we doubled the dividend payments from $0.40 and $1.00 to $0.80 and $2.00, such that the expected dividend is now $1.40, and also doubled the interest rate from 10% to 20%, such that the fundamental value remains unchanged at $7 ($1.40/$0.20), the bubbles will be larger (in the sense of greater dispersion of prices from fundamental value) and longer lasting. So, in terms of Figure 15.4, one way to think about this is that if you took the participants from Market 2 but doubled the expected dividend and interest rates, then the bubble-and- crash pattern will be similar to Market 3-

This is not an artefact of having students take part. In their work, Smith et al. brought in business people including people familiar with stock trading from the local community. Those markets generated similar bubbles as well, a finding replicated by others subsequently. What about introducing some confederates of the experimenters who are well versed with the issue and understand the underlying problems, such as graduate students in Economics? This does not make a difference. Neither does communication among the traders. Arlington Williams ran very large markets with more than 300 students, who could take part over a number of days, during which the students are talking to one another and the instructor is also often discussing the phenomenon in class. This, too, does not minimize bubbles.8

What about various forms of short-selling? Since this is not a course in behavioural finance, I am going to refrain from going too much into the details of such financial manoeuvres. But, briefly, we can define short-selling in two ways. First, suppose you are in Period 9 of Market 2 of Figure 15.4. The share price has gone up to $45. You understand that a crash is coming. You strike a future deal (enter into a contract to be conducted in the future) with another trader that at the end of Period 15, you will sell a certain number of shares to him/her at $30 per share. You do this even though you actually do not possess any shares currently. The other trader may be willing to accept this offer, given that it appears that you are offering to sell shares that are currently trading at $45 per share at a discount of $15 per share. But, in Round 14, prices have fallen to $12 per share. You buy up those shares at $12 per share and then sell it to the other trader for $30 per share according to the terms of your deal, thereby earning a profit of $18 per share. Of course, if the price does not crash and ends up above $30, then you will make a loss since you will have to buy those shares at a higher price and then re-sell them at $30 to fulfil the terms of your contract.9

A second option is that, in Period 9, you borrow money against shares from a stockbroker. Currently, the shares are selling for $45 per share. You borrow $4,500, which is the equivalent of 100 shares at $45 per share. However, here, the deal is that you will have to repay the broker 100 shares rather than $4,500. You wait until Period 15, when the share price drops to $8. You buy 100 shares at $800, return them to the broker and make a profit of $3,700. But once again, if, for some reason, the price does not drop and remains above $45, then you are looking at making heavy losses. For example, if you followed this strategy in Market 2, you may be in trouble. Suppose you are in Period 10 of Market 2 with prices at $25 per share. You expect them to drop to $10 per share by Period 15. You borrow $2,500 from the broker as the current price of 100 shares, expecting that the price will drop to $10. If and when it does, you can buy 100 shares for $1,000, return them to the broker and make a profit of $1,500. But, when Period 15 arrives, the share price is at $45. This means that in order to return 100 shares to the broker, you now need to pay $4,500 against your earlier borrowing of $2,500. Now, you are looking at a loss of $20 per share.111

Why is this relevant? Because, if there are a lot of people who are doing this, then the traders or brokers whom they are striking deals with should begin to get the impression that someone or more than one out there thinks that the prices are going to crash. After all, the only way you can make money is if the market crashes. But this should signal an impending crash to others and they should, in turn, shy away from buying and/or selling at very high prices. If and when that happens, prices should converge to fundamental value more rapidly. The evidence here is mixed. Some of the early studies in the area, including that done by Smith, suggested that short-selling does not have an impact on bubbles. But some subsequent studies have suggested that short-selling may indeed lead to smaller bubbles. It is also the case that the greater the short-selling capacity (or the more the number of traders who anticipate a market crash and engage in short-selling), the more the price tracks the fundamental value, but even large amounts of short-selling does not get rid of bubbles completely or quickly. The only thing that reliably seems to get rid of the bubbles is experience with these markets. The more experience traders have, the less the tendency to bid up prices and the fewer the bubbles, with market prices tracking fundamental values with greater experience.11

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