The South Sea Bubble: An Additional Cost To Shorting October 2008 Update Andrea Matranga October 28, 2008

Abstract In 1720, the South Sea Company’s stock was at the center of extraordinary price volatility, rising from a value of around £128 per share in January to just below £1000 in July, and then falling back below £200 by December. The episode has been the focus of much research, as one of the first possible bubbles with extensive price series documentation. Researchers skeptical of the existence of bubbles have made a case that the price was actually justified, either because the company had a business model with significant upside probability, or because due to lax contract enforcement the futures transactions should actually be interpreted as options. We analyze the plausible business model argument, and show its merits. However we also note that since there were no significant barriers to entry, in the absence of regulatory interference competition would have eroded the advantage. Since free competition was in this case socially optimal, the company could only turn a profit by convincing political powers to act against the public good, by either upfront payments to the state, or through bribes. The sum of these two costs are likely to exactly offset the excess profits expected, and hence the optimism over the values of the share was unjustified.

keywords: South Sea Company, Short Selling, Bubbles

1

Introduction

The South Sea Company scandal is one of three episodes (the other ones being the Dutch Tulipmania and the Mississipi Company) generally credited as representing the first instance of a financial bubble. Like several economics terms that are taken from daily life (e.g. contagion), speaking of bubbles has the disadvantage that people can’t help bring to the debate their own concept of what constitutes outside of the economic realm. The risk is that most of the debate will center on what a bubble is, rather than whether a given episode constituted in fact a bubble, if a given model has realistic assumption or indeed implies a bubble (at least in the sense that the author of the paper gave to the term). A minimalist definition defines a bubble as an episode of trade in high volumes at prices that are considerably at variance from intrinsic values [1]. Besides the inability to explain the price series in terms of any reasonable valuation technique, there is also broad agreement that bubbles possess a certain element of self-referentiality, which generally translates in the idea that people are buying at a given price only because they think that the price will 1

rise still further, rather than because they think that the security is underpriced in the conventional sense (the expected net present value of revenue stream associated with it is above the current price). The attentive reader will notice the problem with the fairly loose definition above, since firstly, it is very hard to determine what the ”right” price of an asset is; and secondly, economic agents buy assets on the expectation of capital gains all the time, and this behavior doesn’t by itself constitute a bubble. Knowledge of these fundamental ambiguities should inform the reader for the rest of this paper, and help explain the widely discordant views on the phenomenon held by economists.

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Literature Review

2.1

Academic birth of the Bubble: Mackay

The earliest work generally quoted in the bubble literature is Extroardinary Popular Delusions and the Madness of Crowds by Charles MacKay [4], which presented a rather moralistic narrative of several of the episodes which would be studied time and again by later academics. Secondary sources often give the impression that the scotsman’s work is chiefly concerned with financial bubbles, but in reality Mackay devotes only thee chapters out of nineteen to episodes of this kind, with the rest being devoted to the crusades, to relics, to the commotion surrounding the increase in the price of tickets at a London theater, and so on. The chapters that do discuss financial episodes are on the Mississipi Bubble, the South Sea Company, and the Dutch Tulipmania. He appears to be happily oblivious to any notion that markets should always price assets correctly, which perhaps explains some of the disapproval directed his way by proponents of efficient markets. His retroactively unorthodox economics stance aside, it does indeed appear that he may have at least overstated the extent of the Tulipmania, which is not surprising since he was writing more than two hundred years after the event. Considering the non-specialist nature of the publication, we can hardly expect his price data to be good regression fodder. Still, considering that his chief call to fame in life was his successful lyric writing for popular songs, he can be thought of as the music author that caused more debate in economics circles at least until Bono from U2 decided to take a shot at the title.

2.2

Bubbles Don’t Exist

This view, featuring perhaps Peter Garber as its most notable proponent, can be traced to two main underpinnings: a critique of some of the more outlandish claims made by proponents of the existence of bubbles, and a firm faith in the pricing power of markets. Justification for the high reported prices of specific episodes rely chiefly on three methods, often used in combination: 1. The prices reported are higher than those actually prevalent at the time. This criticism is usually leveled at the earlier instances of bubbles (the Mackay Three) and is often plausible, given that the higher a reported price is (be it an actual transacted price, a quote, or merely a rumor) relative to the prevalent ones, the more likely it is to be recorded, and consequently to be available to us. 2. The prices reported can be explained by the contractual structure that was favorable to buyers. 2

This is especially applicable to the Mackay three, since contract enforcement for future contracts was haphazard as well, and in the case of the tulipmania specific legal provisions enacted at a certain point allowed buyers to renege on their obligations by paying a fee, in practice turning the ”prices” into the strike price of an option. 3. The prices reflected the best information at the time, a.k.a the ”20/20 Hindsight” argument. This critique of bubble theory posits that while prices were in retrospect above what would have been optimal with perfect foresight of future events, at the time it could have looked quite possible at the time for the asset to have grown in a way justifying the valuation. This argument can in some sense always be made, for sufficiently relaxed definitions of ”plausible valuation”, though occasionally the thought process involved would put the economic agents of the day on the foolhardy side of optimism. While a complete discussion of the literature on the existence or not of bubble is beyond the scope of this article, it is however useful to note that Mackay’s words had indeed entered the economics literature through the side door, and with only the most cursory of inspections. To Garber goes the merit of having at least weeded out some of the more outlandish constructs and implausible anecdotes, as well as to have stimulated more rigorous research in the field.

2.3

Bubble Theory

One notable strand of research aims at providing a theoretical underpinning under which Bubbles can be explained. A notable example is Blanchard and Watson (1983), which show that under fairly plausible assumptions, bubbles are consistent with investor rationality, and can cause the rapid price increase and falls that are associated with them in the popular press. The authors also propose statistical tests to determine if bubbles are present, which however can only produce circumstantial results if data on both prices and returns isn’t available. The general idea behind rational bubbles is that if an expectation is in place that prices are to increase in the future, the expected capital gain is classified as a cashflow from the asset, which therefore justifies a higher price today. Depending on the specific setup, this can lead to a hard or soft landing after the bubble, may or may not require an infinite supply of agents to be sustainable, and might be dependent on specific restrictions to short-selling to be in place to develop. The main problem with the approach is that while the theory assumes that the agents are rational, it also postulates an expectation of a price increase which while self-sustaining, is introduced ex machina in the beginning. While a few attempts have been made to find an initial cause for the price increase, these models usually rely on very specific assumptions about the utility function and probability distributions that are not robust to alternative formalizations.

2.4

Disincentives To Short-Sale

Much of the skepticism surrounding the existence of bubble ultimately arises from the perception that their existence would imply that markets are unable to correctly price assets, which in one way or another implies that agents are not behaving rationally. However it should be noted that the assumption that agents are ”rational” isn’t generally made in the blind faith that all the participants in the markets always have continuous, locally non satiated, transitive preferences. The assumption is warranted in the aggregate only because it is expected that irrational agents would be weeded out by the efficient market mechanism and that the summing of preferences over several agents will smooth 3

out the discontinuity. In particular, if the market mechanism is not efficient, and is inefficient in a way that fails to weed out the irrational agents, all results that assume a textbook representative agent are not required to hold. In the conventional models, bubbles can’t happen due to the ability of market agents to sell stock they don’t currently own, i.e. their ability to sell short. The idea is that even if a small group of investors became irrationally optimistic about the prospects of a given asset, the rational and informed agents would be willing to supply virtually any amount of the stock to the eager buyers, so long as the price remained over the fundamental valuation. The ability to short-sell is critical because otherwise, a small clique of optimistic agents could sell the stock amongst themselves. The rational agents would never enter this market, since they would correctly surmise the stock to be overpriced and would thus refuse to buy it. The prices could remain above fundamentals for extended periods of time, as all those with a share to sell would be agents which where optimistic about the stock to begin with. If we imagined the stock market as a forum for public debate on what the price of an asset should be, the realistic agents would not be allowed to express their opinion. The possibility to sell borrowed stock, or even to enter into naked shorts, is the only way to ensure agents no longer have to first enter the market for an asset to be able to ”vote”, and are always able to influence the price. Armed with this knowledge, some authors have attempted to search for a mechanism that would prevent short-selling, thus undermining the applicability of efficient market theorems to bubble phenomena. Noise traider risk. DeLong, Shleifer et al. (1990 [5]) show that if a significant amount of trading is based on strategies that are uncorrelated with fundamentals(i.e. is done by ”noise traders”), the needless increase in risk associated with the extra unpredictability in the market may drive the more realistic traders out of the market, thus contributing to a further increase in variability as the ”sophisticated” traders move on to less troublesome pastures. Synchronization risk. Abreu and Brunnermeier(2002 [2]) used another approach, which relies on the sophisticated investors being unwilling to attack the bubble due to difficulties in coordinating the attack on the price with their peers. Since an attack exposes the agent to a loss of the cost of capital and exposed his to the whims of the noise traders, who might make the price move against him, the onset of arbitrage is delayed and prices can meanwhile stray considerably from fundamentals.

2.5

Black Box Analysis

A different way of approaching the problem has been offered by researchers who have tried to determine whether some evidence can be found of the existence of bubbles, regardless of whether they are compatible with the standard academic assumptions of how asset markets should be modeled. An example of this is Temin and Voth (2004 [7], who try to determine what the ”smart money” was betting on during the South Sea scandal by analyzing the books of a banker who did well during the South Sea company. The paper showed that whatever his strategy was, he didn’t seem to be shy about buying South Sea stock. However the assumption that since he made money, he must have been part of the ”smart money” might strike some as rather Protestant (in the Weber sense). Several authors have studied the price series for assets that are somehow related to try to find mismatches: 4

Closed End Mutal Funds in 1929 DeLong and Shleifer (1991 [10]) look at funds which published their stock holdings at regular intervals, and the evidence suggests that the funds were priced well above of the underlying stocks) The South Sea Company Dale et al. analyze the differential between the prices for subscription scrips and the underlying shares, and concludes that the mismatch is incompatible with rational preferences.

3 3.1

A Brief History of The South Sea Company The sovereign debt market

The taxing power granted from the Crown to Parliament, meant that for the first time the British state was a credible borrower. The Houses could now introduce a new import duty, and immediately receive a lump sum net present value of it by issuing bonds against the revenue stream. The problem was that each bond would only be repaid as fast as the actual duties came into the state coffers. Since this flow was uncertain, and depended on the particular tax that backed the bond, the secondary market for sovereign debt issues was illiquid. This in turn meant that government paper was traded at heavy discounts, and hence issuing debt was more expensive than it needed to be. Further detracting from the attractiveness of the market were the lengthy waiting periods necessary to have transfers of bonds entered into the registers.

3.2

The equity market

Contrast this with the market for shares. Since each company generally had only one type of share, the market for each security was much deeper. Also, this market was relatively free of government interference: transferring ownership of a share was a straightforward private agreement between two parties, and the change of ownership needed only be notified for dividend collection purposes. This meant a position in shares could be liquidated quickly and inexpensively if the cash was needed to finance consumption, or some other investment opportunity. Conversely a bond holder might be forced to accept a heavy discount if he wanted to convert his holdings to cash on short notice. Shares were undergoing a transformation at the time. At their inception, shares were essentially accounting devices. The people who used them generally knew all about the underlying venture and the management behind the security. They usually knew, and might even have been related to, some or all of the other investors in the venture, as well as the management of the company. In the years under study however, more and more people started to buy stocks of companies they knew little or nothing about, under the apparent assumption that the prevalent prices had to be about right. They were attracted by the higher returns that shares had over other asset classes, as well as by the ease with which positions could be entered into and then liquidated. Lack of technical proficiency in the business of the underlying was not considered a good reason not to participate in the market, after all if somebody else had recently executed a trade at the same price, the real value could usually be counted on being somewhere in the vicinity of that figure. This was especially true for markets with high volume, which would have given more observations on which to gauge market depth, volatility and so on. What information investors did collect, was either received through gossip, or through the myriad

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newsletters and newspapers that sprung up to quench the thirst of information of the new investors. Since journalism was in its infancy, this information was often less then perfect. However since everybody else read it as well, it was nonetheless essential for market participants to be aware of it.

3.3

The South Sea Company

Given the preference that investors seemed to accord to the liquid shares over the tightly controlled and erratically payed bonds, one understands why it must have seemed a good idea to try to package bonds to make them as similar as possible to holding shares. The method chosen was to have a company with little or no other assets issue shares and buy government bonds with the proceeds from the sale. The interest paid by the bonds would be paid as dividend to the shareholders (the company would be a pass-through vehicle). In practice this was akin to creating a cooperative of creditors to manage all the members assets. The effect would be that of replacing several classes of bonds, with different maturities and underlying feeder-taxes with a single class of stock, representing all these claims on the government. Since stocks could be sold easily and without government intervention, the expectation was that the shares would collectively be worth more than the market value of the bonds they controlled, the difference amounting to a liquidity premium, i.e. what people were willing to pay to control a more liquid asset. In essence, this is a form of regulatory arbitrage.

3.4

Public Offering Structure

The fundamental goal is to keep piling bonds on the asset side of the balance sheet, while loading the liabilities side with equity. This is done under the underlying assumption that bonds are underpriced relative to equity, at least from the point of view of a very large agent who expected low levels of liquidity shocks, and in any case held a position in bonds that was either very well diversified, or privileged in some way due to its size. If this mispricing is true, then the scheme is pareto-efficient in the sense that all the parties can be made better off. The government can issue its debt at a cheaper price (and thus pay a lower effective debt financing cost), the bond holders can sell their debt for more than it was worth to them or receive shares that due to their liquidity are worth more on the market than their old bonds were, and the company can keep a part of the interest payment revenue stream to finance its operation and expansion. There are multiple ways to achieve this asymmetric balance sheet, and the South Seas Company used several of them. The simplest is probably the direct debt/equity swap, where holders of sovereign debt are offered to exchange their bonds for share in the SSC at a fixed rate. If people agree to do this, then as desired their bonds go straight into the asset side and their shares obviously weigh in on the liabilities. Alternatively, the stock could be issued beforehand and sold at its prevailing market price, with the proceeds from the sale then buying bonds. This is of course essentially equivalent, though the timing is not simultaneous as in the previous example. Another method employed was the stock subscription. Investors were invited to pay an advance fee, and to then buy the stock on subscription with a payment schedule over several years, but predetermined in advance. There was some uncertainty over whether the theoretical obligation to pay the subscription fees would actually be enforced (thus making the instrument futures-related),

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or could have been ignored at no penalty (which would have made the subscriptions more similar to options).

3.5

Market Manipulation

On top of the possible confusion arising from the complex placement strategy, the SSC management spent a fortune bribing members of parliament and other figures of influence, buying the own companys stock on the open market to drive up the price, and manipulating the public image of the company. This was partly possible due to the political cover that Tory interests afforded the company, since they saw it as a useful tool in the proxy war against the Whigish Bank of England.

3.6

The Bubble

While the importance of the relative contributions of these different elements is yet to be determined, what is known is that the price of the SSC jumped from roughly 100 to 1000 in the absence of news that could have begun to explain the rise. Far from being the only company to experience a price shift, the SSC price spike was accompanied by similar increases in the share prices of it’s chief competitor, the Bank of England, as well as other companies of the time. In addition several companies took advantage of the loose financing conditions to issue stock for the first time, as all sorts of equities (including some endeavors who’se merits were dubious indeed) flooded the market.

4

Price Lock-In

As we have seen in the literature review subsection on short-selling, the ability of investors to participate in the price-setting mechanism without having to buy into the stock to begin with is crucial for avoiding a self-selection dynamic that leaves the market for assets undergoing pressure from only the overoptimistic participants. In this section we will show that on top of noise trader risk and synchronization risk, putative shortsellers of South Sea Company faced an additional disincentive, whose effect, while present in some sense for most securities, was magnified in the specific case by the specific offering structure used by the company.

4.1

Debt Equity Swaps and the Short Seller’s Pitfall

As seen in the public offering section, the business plan of the SSC relied on exchanging (directly or otherwise) freshly issued stock for government debt, under the expectation that the increase in liquidity would create value. Under normal conditions, theory would predict the total market capitalization of the company to be roughly in line with the total value of the government debt held, plus a premium for the advantage in liquidity offered by the equity instrument. And indeed the evidence shows that the price of the first issue of stock for debt was consistent with this valuation method. However the business model employed by the company called for successive equity issues, which were to be executed at the prevailing market price. Since the price would be higher than par due to

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the liquidity gain, this meant that the second time around the company would be able to buy more government debt for each £100 of equity issued. The new debt acquired would be reevaluated upwards due to the advantages of stocks over bonds. Therefore the new equity holders would also receive a capital gain. The pre-issue holders of equity however would gain as well: on average, each new share issued brought in more bonds than the current debt held/equity ratio of the company. Since the current shareholders are making something extra, it follows that the new shareholders must be making something less. This stands to reason, the debt they’re exchanging for their shares is more than what those that preceded them brought in, so in effect their holdings are being diluted. Like in pyramid schemes, the SSC business model favored getting in early to profit on those that came later. Besides the natural price increase deriving from the liquidity-swap cycle, investors could also gain by timing the issues to exploit temporarily high stock prices (due to variable market sentiment, for instance). Since they were under no obligation to also perform issues during low prices, the higher the variance of the prices, the greater the chance of cashing in on a high peak. If the prices could also be in some way influenced besides being observed, even a short increase in price could create lasting benefits to existing shareholder. To clarify the mechanism by which this is possible, an example is provided in the next subsection.

4.2

A baseline case

1. Lets assume the company is holding a single government bond worth £100, and has a single outstanding share. We would expect the price of this share to be some figure close to £100 plus the liquidity premium, λ. 2. If the company issues another share it will receive £100 × λ for it, and will thus be able to buy more bonds than the first issue brought. The stock price will increase, and the existing shareholders will profit. The new shareholders will also profit (because of the liquidity premium), but not as much as the original shareholders did when they set up the company (the algebra for this and a few numerical examples are dealt with in a later section). 3. If the price were significantly higher than the current value of the bonds held (taking λ into account), we would expect rational agents to be willing to sell the stock short, since the mispricing should eventually be corrected. 4. But if the price were such that it currently couldn’t be justified, but it might be after a few more liquidity/swap cycles, the willingness of agents to bet against the price would depends on their probability estimates for the swaps happening. 5. Now let’s look at how variance in the price further complicates things. Let’s say that the current value of the stock (however it be determined) is £110, but the market prices the stock at £125. A sophisticated investor sees this and decides to sell it short. Before eventually falling, the price first rises to £200 (e.g. through noise trading activity), and the company issues a new share, and swaps it for some publicly held bonds. If the swap were executed at the then prevailing price ratio of £200/£100 = 2, the asset side of the balance sheet would receive two bonds, while the liability side would only add another share to the first one. So now the stock price is £200, the company has £300 worth of bonds, and two shares outstanding. This means that each share now controls £150 worth of bonds: even if the price reverted to the fundamental value, it would never return to the original value of £110.

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6. If agents can anticipate this risk, they will be less enthusiastic in pursuing short selling strategies. The SSC did in fact issue new stock aggressively while the price was high, and as expected, the price never fully fell to its pre-bubble levels. This is all the more remarkable considering the vast misappropriation of funds that was carried out by the management for personal gain or for bribes, market manipulation efforts, etc. The management of the company made no secret of their intention to engage in further debt equity stocks and indeed openly tendered for the bulk of the outstanding government debt. So even if an investor thought the price increases were irrational, fear of the price moving permanently against him would have prevented him from entering the market with a contrarian attitude. This is fairly straighforward arithmetic, but like other theories of rational bubbles, what remains to be explained is the original source for the expectation of higher prices in the future. Unfortunately it is very difficult to formally model a shift in subjective probability estimates in a way that doesn’t in some way or an other assume the result required. Nonetheless, in the next section we will try to provide a few plausible explanations for the change in expectations, and to present what evidence is available to support it.

5

Model

The framework assumes that agents are at least well-behaved enough to price shares according to the formula P = M/N where P is the share’s price, M is the total value of the compnay, and N is the number of share outstanding. Since N is in principle an observable quantity, whatever it is that makes the market outcome differ must reside in how agents determine the quantity M . Government bonds are sold on the open market, and give a payoff of £100 one period in the future. From the realized sale price, we can calculate the implied interest rate i that the market applies to government debt. Since the actual payments were often late, and the debt was difficult to sell on the secondary market, we would expect i to be moderately high (i.e. the government paper would be traded at a large discount). If ρ < i is the true cost of capital we would expect the following equality to hold. i=ρ+β Where β is the penalty associated with the unfavorable financial instrument, and it reflects both the expectation that the payments will be late (so that the same interest rate is applied to a longer period) and the knowledge that it will be difficult to close the position. The market price for a one year bond can thus be written as π = 100 × 1/1 + i = £100/(1 + i) We can model the South Sea Company as an entity that simply raises cash from the capital markets through public offerings of its own equity, and invests the proceeds in bonds. The shares of the company are perfectly liquid, and it expects to receive punctual payments from the government due to its large size and negotiating power. We assume that it raises 100 in equity, and uses it to buy A bonds, where A = £100 ×

1 1 = £100 × = (1 + i) π 100/(1 + i)

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If the company simply held the bonds as they where, collecting the coupons as they naturally came due and paying the proceeds out of the dividends, there would be no net creation or destruction of wealth, and the value of the stock would still be 100. However the new shares are easier to trade on the secondary market, and this eats into the β parameter that depressed bond prices. Indeed, the surplus value makes it possible for the company to offer to charge the government a lower interest, both to gain regulatory approval, and in return for always being paid on schedule, which of course removes the reason behind the rest of the β by taking away uncertainty over the timing of the cashflow and realigning the expected date with the stated one. So the company now holds a claim to a payment of £100 × A = 100 × (1 + i) one period in the future, which however the market will discount at ρ < i. This means that the price of the single unit of stock issued will be P = £100 ×

(1 + i) < £100 (1 + ρ)

Which implies that value was created, and therefore means that for the right conditions of price offered for the bonds and amount issued, the shareholders can make money on their investment, the bondholders can be paid a little bit more than what their bonds are worth, the government can pay a slightly lower interest, and the organizers of the scheme can still keep something for their trouble. The total value created by the scheme for each £100 of stock issued can be expressed as £100 ×

A 1+i A − £100 × = £100 × (1 + ρ) (1 + i) 1+ρ

This is a fairly simple calculation, and well within the limits of financial knowledge of the age. However if the company is set to raise capital on successive issues, with every new issue the junior shareholders will have to pool the bonds they bring into an ever larger existing pile, thus receiving a successively decreasing fraction of the value their equity is creating. On the other hand, by entering they stand to make profit out of the issues done after theirs. The price would appear to possess a self-referential element to it, and to thus be good fodder for a rational bubble setup. In reality however the above framework contains an important mistake. It doesn’t take into account the likely effect that the operation would have on the β parameter, and it doesn’t allow for the possibility of market entry by competitors of the company. If agents are willing to enter the scheme making somebody else richer for now, on the expectation of becoming richer later, they must believe that there will be a steady flow of debt/equity swaps themselves. But if that is assumed, than it would stand to reason that the market for bonds should become itself more liquid. If the price of bond rises as a result, this would cause a further decrease in the profitability of the scheme from the point of view of new investors at the subsequent public offerings. Another important point is that in the absence of regulatory interference, no investor would ever buy a share at a price higher than what the original investors had to pay. If the shares were offered to them at a higher price, groups of investors could pool their assets and found their own companies that operated exactly along the same lines as the SSC, and reap the higher profits the original shareholders did, rather than the lower latecomer benefit of the second and successive offerings. Since each successive wave of investors in the same company is worse off than the one that preceded it, it follows that the incentive to create a SSC clone increases with time. If entrepreneurs are free to

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setup competing services, regardless of where the price of buying the ready made shares stands, new debt-equity swaps will only find takers at the ratio at which the original investors were able to swap. Even if what you were interested in was the possibility of sharing into the successive waves of investors, after the original SSC becomes —say— five iterations old, you should probably be willing to be amongst the founders of a clone, because you would assume that subsequent investors would rather be on the second rung of the new company rather than on the sixth. The result would be the unwillingness, due to better options, of any agent to pay more for a newly issued share of an existing company than π×

C N

Where C is the amount of bonds held by the company. This means that the possibility of the large cash windfalls only makes sense under the assumption that the SSC will hold a monopoly over the transaction. But in as sophisticated a market place as London, the only way to even dream of doing that is if government grants you a monopoly over the business. If nobody else can open an SSC clone, than the whole pyramid scheme can work, without it is doomed to have its margins eroded by new entrants. Even with government support, it is not clear how the business plan could work in the long run, since bond prices would likely rise as the SSC made them more and more liquid by providing a regular outlet. Eventually it would hold such a large fraction of them that it could try to restrict liquidity by refusing to sell them, but at that point backwards induction would tell the possible new investors that the scheme is about to dry up because the available debt for new waves is about to dry up. And surprisingly enough, government support doesn’t come cheap. The company management had to pay the political powers both over and under the table to secure the exclusivity of their concession, as well as offer a lower interest rate than originally planned. It is hard to see how the company could ever have retained enough value over £30 million of government debt to offset the £7.5 million that they had offered the government for the honor of being allowed to buy the debt, and this doesn’t include the large bribes offered all around the palaces of power. So a rational investor should have assumed that if competition was allowed, the rents from entering into the company would dry up, and a prudent one should have reasoned that to win freedom from competition, the price paid to the government for the privilege made it not worth the effort.

5.1

And Yet The Bubble Happened

If the above had been common knowledge at the time, we would have expected everything to go well, as the prices would have remained firmly grounded on fundamentals. But we know that was not the case, and similarly any observer at the time armed with the knowledge above would conclude that his reasoning, while sound, was evidently not universally shared. One of the functions of financial markets according to the theory literature is to disseminate and aggregate information, so that the final prices reflect the best knowledge of the market. Clearly, the prices in any case reflected the belief that the South Seas Company would earn excess returns for its shareholders, but this was unlikely in the long run, since the government and the bondholders had sufficient market power between them to incorporate most if not all of the value created by the transaction. 11

The unsustainability of the arrangement was stated at the time by knowledgeable sources, and presumably at least some investors should have been aware of the situation. So the fact that the prices show a belief in the bubble must constitute an informational failure on the part of the market. As we have seen earlier this might be connected to short sale constraints. And unfortunately, as we have seen, while a rise in price followed by an offer of new equity didn’t necessarily mean that the new entrants would make money, it did mean that anybody who sold short at a lower price was probably in trouble. If sophisticated investors were aware that the SSC had the backing (bribe-induced or otherwise) of important figures of government, and they further knew that the management was quite willing to spend vast amounts in propping up the price of the company’s own stock, they could have no faith in prices not raising significantly in the short run, and might therefore have feared having the fundamental value of the share move above the price they had entered the short position at.

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Conclusions

At this point the hope is that the reader will be convinced that the SSC’s business plan could indeed superficially be styled as a pyramid scheme, in the sense that agents apparently faced payoffs that strongly encourage early entry, and that these payoffs depended on the presence of further generations of investors participating in the same scheme. However, there are several important points that make the plan unworkable even as a pyramid. 1. As markets adjusted to the existence of the company, the β parameter for the liquidity penalty on bond discounting rates would almost inevitably decrease. The narrowing in the valuation gap between bond and equity instruments would reduce the profitability of the scheme. 2. If other companies could offer the same service, competition would erode the redistribution of wealth from new entrants to old shareholders, since the aspiring investors could choose a company that sold it’s stock for less. 3. So to even hope of working as a pyramid scheme, the company must have a government-enforced monopoly. But the government can demand conditions which make all the value from the scheme in excess of cost of capital and time of the organizers accrue to itself. These three factors combined, which don’t rely on any mathematical concept or information that wouldn’t have been known at the time, should have made a rational investor dismiss the possibility of the pyramid scheme taking off. He would have been willing to participate in the first offering, but not in the following ones. The fact that this knowledge was not disseminated by the market mechanism is probably due to the constraints to short-sale discussed in the text. Examination of what appeared to be a textbook example of rational bubble actually showed the proposed cyclic mechanism to not be in practice plausible. The exercise of discovering the gap felt rather like examining one of those proposed perpetual motion machine with magnets and steel balls carried up slopes, where one knows it can’t be right, but it takes a little of while to understand where friction works itself in. It would be interesting if it turned out that any proposed rational bubble always has some flaw of this sort in it. In particular, if a proof of this statement was found, then there could be no such thing as a 12

rational bubble, since the very existence of something that looked like it would imply that it actually wouldn’t work. In the end, it would appear that the British financial authorities of the time would have done better to simply offer to do the swap themselves, offering new standardized securities that would pay a lower interest rate, but would always be paid on time, in exchange for the old patchwork of sparse issues. Alternatively instead of demanding a one off payment in exchange for a monopoly, an arrangement which attracted predictable rent-seeking behavior, could have let several different companies offer competitive terms, which would have made a relatively painless search for the equilibrium price more likely.

References [1] King, Ronald R.; Smith, Vernon L.; Williams, Arlington W. and van Boening, Mark V. ”The Robustness of Bubbles and Crashes in Experimental Stock Markets,” R. H. Day and P. Chen, Nonlinear Dynamics and Evolutionary Economics. Oxford, England: Oxford University Press, 1993 [2] Abreu, Dilip and Brunnermeier, Markus. ”Synchronization Risk and Delayed Arbitrage”. Journal of Financial Economics 66, 2002. [3] Lamont, Owen and Richard Thaler, (2003), Can the Market Add and Subtract? Mispricing in Tech Stock Carve-Outs , Journal of Political Economy. 111(2): 227-268. [4] MacKay, Charles; ”Extraordinary Popular Delusions and the Madness of Crowds”, with a foreword by Andrew Tobias (1841; New York: Harmony Books, 1980). [5] DeLong, Bradford; Shleifer, Andrei; Summers, Lawrence and Waldmann, Robert, 1990, ”Noise Trader Risk in Financial Markets.” Journal of Political Economy 98, pp. 703-38. [6] Garber, Peter; ”Famous First Bubbles” Peter M. Garber, The Journal of Economic Perspectives, Vol. 4, No. 2. (Spring, 1990), pp. 35-54. [7] Temin, Peter and Hans-Joachim Voth. ”Riding the South Sea Bubble”. American Economic Review 94, 2004. [8] Blanchard, Olivier J. and Mark W. Watson. Bubbles, Rational Expectations and Financial Markets.” Crises in the Economic and Financial Structure, Paul Wachtel, editor, pp. 295-316. Lexington, MA: D.C. Heathand Company, (1982). [9] Dale, R.S., Johnson, J.E.V. and L. Tang (May 2005). ”Financial Markets can go mad : Evidence of irrational behaviour during the South Sea Bubble.” The Economic History Review, LVIII, 2, 233-271. [10] Bradford De Long, and Andrei Shleifer, 1991, ”The Stock Market Bubble of 1929: Evidence from Closed-End Mutual Funds.” Journal of Economic History, 51(3), pp. 675-700.

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The South Sea Bubble

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