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Asset bubble theory

Interesting discussion of hedge funds and housing by Tom Abate at the San Francisco Chronicle. After what's come to be the usual discussion of bubble, Abate takes the extra step of delineating asset bubble theory:
-- The low worldwide interest rates of the past few years could have encouraged speculation in certain categories of assets similar to the stock market bubble of the late 1990s.
-- Such easy money has flowed especially into housing, as buyers took advantage of low rates, and into hedge funds, lightly regulated investment pools for institutions and the rich.
-- If housing prices or hedge funds went bust, consumers could retrench and major financial institutions could be endangered, damaging the global economy.
-- The possibility of bubblelike conditions means that the Federal Reserve and other central banks can't raise interest rates too fast as they battle inflation for fear of triggering such a crash.
(Nicely done!)
In Northern Virginia, a part of the Washington DC metro area, the number of active listings was 2,983 in April 2005, which increased by 241% to 10,038 in April 2006 (MRIS).

As Jim A wrote in a comments section of the The Housing Bubble Blog:
It’s all about the inventory, stupid. Back when there was no inventory to speak of, say the ‘03-’04 timeframe people in the market to buy a house would have the repeated experience of having houses that they looked at go under contract before they could decide to buy or not. Low inventories create a “buy now or it’s gone” frenzied atmosphere.
But prices have risen far above the cost of construction, so that builders have put huge inventories of new homes (especially condos)on the market. With these large inventories, buyers don’t have to jump immediately just because a nice house is for sale. They can take their time, if one house sells, there are plenty of others on the market to choose from. They’re no longer pressured to meet the sellers price immediately or lose the chance at the house. They can offer less and see how desparate the seller is. This is why the idea that we have reached a new plateau of prices where forever in the future people will pay a higher percentage of their income on housing is so absurd.
The dramatically increasing supply of housing units in bubble markets across the country has and will continue to change the housing market. Meanwhile, demand is also declining albeit at a much slower rate then the increase in inventory. The dramatic increase in supply coupled with the moderate decrease in demand is causing price declines in most bubble markets.

Speculative Bubble

What does it Mean? A temporary market condition created through excessive buying, and an unfounded run-up in prices occurs.
Investopedia Says... Speculative bubbles are generally a result of the "bandwagon effect." Investors, seeing an upward trend in prices, quickly enter long positions in an attempt to participate in the stocks' profitability. Typically, these bubbles are followed by even faster sell-offs once the prices begin to decline.
An economic bubble (sometimes referred to as a "market bubble", a "financial bubble", or a "speculative mania") refers to a market condition in which the prices of commodities or asset classes increase to absurd or unsustainable levels (that no longer reflect utility of usage and purchasing power). It occurs when speculation in the underlying asset causes the price to increase, thus encouraging even more speculation. The bubble is usually followed by a sudden drop in prices, known as a crash or a bubble burst. Both the boom and the bust phases of the bubble are examples of a positive feedback mechanism, in contrast to the negative feedback mechanism that determines the equilibrium price under normal market circumstances. Prices in an economic bubble can fluctuate chaotically, and become impossible to predict from supply and demand alone.
The cause of bubbles is often disputed although some experts believe that the cause of bubbles can be explained by the "greater fool's theory." The greater fool's theory explains the behavior of a perennially optimistic market participant (the fool) who buys an overvalued asset in anticipation of selling it to another rapacious speculator (the greater fool) at a much higher price. The bubbles continue as long as the fool can find another (greater) fool to pay up for the overvalued asset. The bubbles will end only when the greater fool becomes the greatest fool who pays the top price for the overvalued asset and can no longer find another buyer to pay for it at a higher price.
Other experts argue that the cause of bubbles is excessive monetary liquidity in the financial system. Excessive monetary liquidity (a.k.a. easy credit) potentially occurs while central banks are implementing expansionary monetary policy (ie. lowering of interest rates and flushing the financial system with money supply). When interest rates are going down, investors tend to avoid putting their capital into savings accounts. Instead, investors tend to leverage their capital by borrowing from banks and invest the leveraged capital in financial assets such as equities and real estate. Simply put, economic bubbles often occur when too much money is chasing too few assets, causing both good assets and bad assets to appreciate excessively beyond their fundamentals to an unsustainable level. The bubbles will burst only when the central bank reverses its monetary accommodation policy and soaks up the liquidity in the financial system. The removal of monetary accommodation policy is commonly known as a contractionary monetary policy. When the central bank raises interest rates, investors tend to become risk averse and thus avoid leveraged capital because the costs of borrowing may become too expensive.
Still others say that economic bubbles are mainly driven by the greed and irrational exuberance of overly bullish investors. They argue that investors tend to extrapolate past extraordinary returns on investment of certain assets into the future, causing them to overbid those risky assets in order to capture those abnormal rates of return. Overbidding on certain assets will at some point result in inadequate rates of return for investors, only then the asset price deflation will begin. When investors feel that they are no longer well compensated for holding those risky assets, they will start to demand higher rates of return on their investments. This in return may reflect as shortage of skilled labour causing a vicious circle since young skilled workers tend to go abroad for better financial oppurtunities due to a halt in the industry. The economic downtime however stagnates once a dedicated pool of workers is allocated but this obviously comes at the cost of high service rates.
Australia from the last three years has been facing such a problem. Although it is a stable economy, young skilled labour follows a trend to come down to the United Kingdom and other European countries on work visas. This creates a demand and supply gap chain which is then fullfilled by allowing immigration into the country on suitable basis. The issue is readily addressed as a 'Floating Economic Bubble' which strains the economy for that particular time but eventually phases out. During the period, the Australian Government takes appropriate measures to avoid the outsourcing of any business and therefore implements strict control over labour shortage both in the skilled and highly skilled feilds.
Since this phenomenon creates a high assumed charge over exact prices and rates, a 'Constant Economic Bubble' may emerge as happened in 2004 when National Australia Bank lost A$360 million resulting from foreign currency trades undertaken by 4 option traders.
Due to this phenomenon, some regard bubbles as related to inflation and thus believe that the causes of inflation are also the causes of bubbles.
Others take the view that there is a "fundamental value" to an asset, and that bubbles represent a rise over that fundamental value, which must eventually return to that fundamental value.
There are chaotic theories of bubbles which assert that bubbles come from particular "critical" states in the market based on the communication of economic actors.
Finally, others regard bubbles as necessary consequences of irrationally valuing assets solely based upon their returns in the recent past without resorting to a rigorous analysis based on their underlying "fundamentals".

Fictitious capital

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Fictitious capital is a concept used by Karl Marx in his critique of political economy. It is introduced in the third volume of Das Kapital, a manuscript which Marx never edited for publication.
Fictitious capital could be defined as a capitalisation on property ownership. That ownership itself was very real and legally enforced, and so were the profits made from it, but the capital involved was fictitious in the sense that it was not backed by any real physical asset value or earning power.
Marx saw the origin of fictitious capital in the development of the credit system and the joint-stock system.
Governments and banks could create additional money or credit, which generated purchasing power unrelated to the value of real production or real consumption, or to the real value of physical assets owned.
They could also issue debt securities of various kinds which could be traded in, regardless of whether these were backed by assets or deposits, and which became objects of speculation.
Companies could likewise issue share certificates that were speculated in. Again, this caused fluctuations in asset values unrelated to what a business and its production were really worth.

[edit] Effects

The general effect was that:
  • the market value of physical and financial assets could, backed by credit, be driven up and artificially inflated by some margin, purely as a result of supply and demand factors which could themselves be manipulated for profit. That margin of value could, however, just as suddenly disappear, if large amounts of capital were withdrawn.
  • profit could be made purely from trading in a variety of financial claims existing only on paper.
  • profit could be made by using only borrowed capital to engage in (speculative) trade, not backed up by any tangible asset.
In addition, changes in underlying technology of a competitor, such as a labor saving advance, can render market value of paper claims to an asset "fictitious." Many features of modern global capitalism reflect the impact of such changes. Thus, a business firm may attempt to prop up the market value of its stock by increasing the rate of exploitation of its work force in order to keep up with the innovating firm. Other firms may attempt to use legal sanctions in the form of, for example, intellectual property law to prevent competitors, or potential competitors, from developing labor saving advances.

[edit] Illustration

Marx cites the case of a Mr Chapman who testified before the British Bank Acts Committee in 1857:
"though in 1857 he was himself still a magnate on the money market, [Chapman] complained bitterly that there were several large money capitalists in London who were strong enough to bring the entire money market into disorder at a given moment and in this way fleece the smaller money dealers most shamelessly. There were supposed to be several great sharks of this kind who could significantly intensify a difficult situation by selling one or two million pounds worth of Consols and in this way taking an equivalent sum of banknotes (and thereby available loan capital) out of the market. The collaboration of three big banks in such a maneouvre would suffice to turn a pressure into a panic." (Das Kapital Vol. 3, Penguin edition, p. 674).
Marx added that:
"The biggest capital power in London is of course the Bank of England, but its position as a semi-state institution makes it impossible for it to assert its domination in so brutal a fashion. None the less, it too is sufficiently capable of looking after itself... Inasmuch as the Bank issues notes that are not backed by the metal reserve in its vaults, it creates tokens of value that are not only means of circulation, but also forms additional - even if fictitious - capital for it, to the nominal value of these fiduciary notes. And this extra capital yields it an extra profit." (ibid., p. 674-675, emphasis added).

Tulip mania

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Pamphlet from the Dutch tulipomania, printed in 1637
Pamphlet from the Dutch tulipomania, printed in 1637
Anonymous 17th-century watercolor of the Semper Augustus, the most famous bulb, which sold for a record price.
Anonymous 17th-century watercolor of the Semper Augustus, the most famous bulb, which sold for a record price.
The term tulip mania (alternatively tulipomania) is used metaphorically to refer to any large economic bubble. The term originally came from the period in the history of the Netherlands during which demand for tulip bulbs reached such a peak that enormous prices were charged for a single bulb. It took place in the first part of the 17th century, especially in 1636-37.
The event is remembered in part because of its extended discussion in the book Extraordinary Popular Delusions and the Madness of Crowds, written by popular British journalist Charles Mackay in 1843, more than two centuries after the event. Mackay omitted mentioning that during 1636-37, the Netherlands suffered from an epidemic of bubonic plague, and severe setbacks in the Thirty Years War. [1]. Modern scholars (e.g. Garber) consider the event much less extraordinary than did Mackay. Indeed, the belief in the existence of a Dutch tulip mania may itself be an extraordinary popular delusion.

[edit] History

The tulip, introduced to Europe in the middle of the 16th century from Ottoman Turkey, experienced a strong growth in popularity in the United Provinces (now the Netherlands), boosted by competition between members of the upper classes for possession of the rarest tulips. Competition escalated until prices reached very high levels.
Tulip cultivation in the United Provinces is thought to have started in 1593, when Charles de L'Ecluse first bred tulips able to tolerate the harsher conditions of the Low Countries from bulbs sent to him from Turkey by Ogier de Busbecq. The flower rapidly became a coveted luxury item and a status symbol. Special breeds were given exotic names or named after Dutch naval admirals. The most spectacular and highly sought-after tulips had vivid colors, lines, and flames on the petals as a result of being infected with a tulip-specific virus known as the Tulip Breaking potyvirus.

[edit] Popular view

In 1623, a single bulb of a famous tulip variety could cost as much as a thousand Dutch florins (the average yearly income at the time was 150 florins). Tulips were also exchanged for land, valuable livestock, and houses. Allegedly, a good trader could earn sixty thousand florins a month.
By 1635, a sale of 40 bulbs for 100,000 florins was recorded. By way of comparison, a ton of butter cost around 100 florins and "eight fat swine" 240 florins. A record was the sale of the most famous bulb, the Semper Augustus, for 6,000 florins in Haarlem.
By 1636, tulips were traded on the stock exchanges of numerous Dutch towns and cities. This encouraged trading in tulips by all members of society, with many people selling or trading their other possessions in order to speculate in the tulip market. Some speculators made large profits as a result.
Some traders sold tulip bulbs that had only just been planted or those they intended to plant (in effect, tulip futures contracts). This phenomenon was dubbed windhandel, or "wind trade", and took place mostly in the taverns of small towns using an arcane slate system to indicate bid prices. A state edict from 1610 (well before the alleged bubble) made that trade illegal by refusing to enforce the contracts, but the legislation failed to curtail the activity.
In February 1637 tulip traders could no longer get inflated prices for their bulbs, and they began to sell. The bubble burst. People began to suspect that the demand for tulips could not last, and as this spread a panic developed. Some were left holding contracts to purchase tulips at prices now ten times greater than those on the open market, while others found themselves in possession of bulbs now worth a fraction of the price they had paid. Allegedly, thousands of Dutch, including businessmen and dignitaries, were financially ruined.
Attempts were made to resolve the situation to the satisfaction of all parties, but these were unsuccessful. Ultimately, individuals were stuck with the bulbs they held at the end of the crash—no court would enforce payment of a contract, since judges regarded the debts as contracted through gambling, and thus not enforceable in law.
Lesser versions of the tulipomania also occurred in other parts of Europe, although matters never reached the state they had in the Netherlands. In England in 1800, it was common to pay fifteen guineas for a single tulip bulb. This sum would have kept a labourer and his family in food, clothes and lodging for six months.

[edit] Competing views

Mike Dash, author of the modern popular history "Tulipomania," states
The history of the tulip mania itself, however, remains remarkably obscure, and even now it has never been the subject of an exhaustive scholarly inquiry.
....My general feeling, after reviewing the available material, is that even after sounding the necessary notes of caution about the reliabilty of the popular accounts, historians and particularly economists remain guilty of exaggerating the real importance and extent of the tulip mania. (p.222, footnote)
A 2002 paper by UCLA's Earl A. Thompson and Jonathan Treussard, "The Tulipmania: Fact or Artifact?", provides an alternate explanation for Dutch tulip mania: that it was not caused by irrational speculation, but rather by a Dutch parliamentry decree (originally sponsored by Dutch investors made skittish by the Thirty Years' War then in progress) that made the purchase of tulip-bulb "futures contracts" a nearly risk-free proposition:
...both the famous popular discussion of Mackay and the famous academic discussion of Posthumus, 1929, point out a highly peculiar part of this episode. In particular, they tell us that, on February 24, 1637, the self-regulating guild of Dutch florists, in a decision that was later ratified by the Dutch Parliament, announced that all futures contracts written after November 30, 1636 and before the re-opening of the cash market in the early Spring, were to be to [sic] interpreted as option contracts. They did this by simply relieving the futures buyers of the obligation to buy the future tulips, forcing them merely to compensate the sellers with a small fixed percentage of the contract price.
Given data about the specific payoffs present in the futures and option contracts, the authors determine that tulip bulb prices in fact hewed closely to what a rational economic model would dictate: "tulip contract prices before, during, and after the 'tulipmania' appear to provide a remarkable illustration of market efficiency."
At last, however, wiser heads began to see that this folly could not last for ever. Rich people no longer bought the flowers for their gardens, but to sell them again at profit. It was realised that somebody must lose badly in the end. As this concern spread, prices fell, never to rise again.
Confidence was now destroyed. Dealers were gripped by universal panic and began defaulting on contracts. For example:
  • Dealer A had agreed to purchase ten Sempers Augustines from dealer B.
  • The agreed price was at four thousand florins each.
  • The delivery time was six weeks after the signing of the contract.
  • B was ready with the flowers at the appointed time.
  • But the price had fallen from four thousand florins to just three or four hundred florins,
  • Dealer A refused either to pay the difference or receive the tulips.
Defaulters were announced day after day in all the towns of Holland.
Hundreds of people who had begun to believe poverty would be banished from the land, suddenly found they were owners of bulbs worth only a small fraction of what they had paid for them.
The cries of distress resounded everywhere, and each man accused his neighbour. The few who had enriched themselves by selling their bulbs when the market was at its height hid their wealth or invested it in the English or other markets. Many who, for a brief season, had emerged from the humbler walks of life, were cast back into their original obscurity. Noble families were ruined and large merchants were reduced almost to the level of beggars.
Tulip-holders held public meetings hoping to find the best way forward. Deputies were sent to the government in Amsterdam, seeking a solution. At first, the government refused to interfere. It advised the tulip-holders to agree a plan among themselves.
Several meetings were held for this purpose, all of which were stormy.
After a lot of bickering and ill-will, it was agreed, in Amsterdam, that all contracts made in the height of the mania, or prior to the month of November 1636, would be null and void. For contracts made after that date, buyers would be freed from their contracts on payment of ten percent of the contract value to the seller.
Unfortunately, this decision gave no satisfaction. The sellers, who had tulips they had arranged to sell at high prices were naturally discontented. Those who had made contracts to buy were also unhappy at even having to pay ten percent of the contract price because tulips that had been worth six thousand florins, were now worth five hundred florins. Actions for breach of contract were threatened in all the courts of the country; but the courts refused to act on what they regarded as gambling transactions.
The matter was finally referred to the Provincial Council at the Hague. The council deliberated for three months before announcing that they could offer no final decision until they had more information. They advised that, in the mean time, every seller should, in the presence of witnesses, offer the tulips to the purchaser for previously agreed contract price. If the buyer refused to take them, they might be put up for sale by public auction, and the original buyer held responsible for the difference between the actual and the stipulated price. This was exactly the same as the failed plan recommended by the deputies. There was no court in Holland that would enforce payment.
The question was raised in Amsterdam, but the judges unanimously refused to interfere, on the ground that debts contracted in gambling were not debts in law.
To find a remedy was beyond the power of the government. And so the matter ended.
Those who were unlucky enough to be left holding worthless tulip were left to bear their ruin as philosophically as they could. Those who had made profits were allowed to keep them. Dutch commerce had suffered a severe shock, from which it took years to recover. The Dutch mania spread to some extent to England. In the year 1636 tulips were publicly sold on the London Stock Exchange, where brokers worked hard to push prices up to the levels seen in Amsterdam. In Paris brokers also strove to create tulipmania. In both cities, however, brokers enjoyed only partial success.
The mania ultimately brought the flowers into great favour, and amongst a certain class of people tulips have ever since been prized more highly than any other flowers.

Business Review

January/February 1996
Lee E. Ohanian
The fundamental value of an asset is usually defined as the present value of the expected payoff from that asset.
Market fundamentals, combined with the efficient markets theory, provide a simple tool for interpreting fluctuations in security prices. According to the efficient markets theory, security prices fluctuate only as investors respond to new information concerning changes in market fundamentals (the discounted sum of future cash flows).
A bubble is defined as any deviation of an asset's price from its fundamental value.
We can think of an asset's price as consisting of two components: one associated with market fundamentals and the other representing the bubble. The bubble theory suggests that securities may go through periods of under- and overvaluation relative to fair-market values. One reason for this may be investor overreaction.
Bubbles may also reflect investors' reactions to factors unrelated to fundamental economic and business conditions. Hypothetically, individual investors may rush into the stock market because they believe everyone else is making money in the market. In this case, they prefer to buy stocks immediately rather than miss an excellent buying opportunity. As a result, the anticipation of rising prices becomes a self-fulfilling prophecy, and market participants enjoy profits that may not necessarily reflect favorable business prospects.
If enough investors behave this way, prices rise and expectations become self-fulfilling.
Certain types of bubbles can be difficult to explain in a sensible way. They are similar to Ponzi schemes and chain letters in that participants will benefit from the game as long as others can be found who are eager to play the game. Of course, Ponzi schemes crash as soon as individuals believe it will be difficult to find others willing to participate. Similarly, some types of bubbles imply that dramatic declines in security prices are the result of investors finally realizing that rising prices may never be justified on economic grounds. At that point, investors try to sell their assets and prices drop: the bubble bursts.
While certain types of bubbles seem to be inconsistent with rational behavior, there is a class of bubbles called rational bubbles. A rational bubble reflects a self-fulfilling belief among rational investors that an asset's price depends on variables unrelated to market fundamentals. In this context, a rational investor is an individual who efficiently uses relevant information for assessing the value of a security. Within the bubbles framework, the fact that investors are rational means that while bubbles can exist, obvious profit opportunities cannot exist. This simply means that if an easy profit opportunity were available, a rational investor would exploit it and quickly eliminate the opportunity. In other words, for simple types of bubbles, the expected rate of return on a security must be the same whether or not the price includes a bubble.
This means that one key feature of a rational bubble is that the evolution of the bubble over time is restricted to rule out easy profit opportunities. For example, a situation in which all investors expect a security to double in price between today and tomorrow, but fall back to its original value the following day would not constitute a rational bubble. In this case, everyone would rationally want to sell the security tomorrow, so that the price would fall before the following day. Alternatively, an asset could be overpriced 20 percent relative to its fundamental value and, thus, could exhibit a rational bubble, as long as both the fundamental value and the bubble component are expected to grow at the same rate. For example, suppose that market fundamentals for a security were expected to grow at 5 percent per year forever. The price of this security would have a rational bubble if the bubble component also grew at 5 percent per year. In this case, the rate of return on the security with the bubble component would be identical to the rate of return on the security without a bubble.
Bubble interpretations have been popular with professional investors and the financial press for many years. In his introduction to Charles Mackay's Memoirs of Extraordinary Popular Delusions and the Madness of Crowds, the noted investor Bernard Baruch wrote, "All economic movements, by their very nature, are motivated by crowd psychology...Men think in herds; it will be seen that they go mad in herds, while they only recover their senses slowly, and one by one."
A number of historical episodes of extreme price movements have been interpreted as bubbles.
Perhaps the most famous episode occurred in 17th century Holland with an unlikely asset: diseased tulip bulbs. Tulipmania, as it is often called, began quietly when a nonfatal virus, known as a mosaic, attacked tulip bulbs. The effect of the virus was to produce a variegated flower of brilliant stripes and colors. The virus affected only a relatively small number of bulbs, and these bulbs became highly prized by collectors.
Interestingly, speculation apparently spread to common bulbs unaffected by the mosaic virus. In the first week of February 1637, prices peaked, and common bulb prices rose 20-fold in one month. Then, prices fell dramatically. While historical data from this period are sketchy at best, Peter Garber of Brown University has estimated that common bulb prices lost about 95 percent of their peak values just three months after the crash. A century later, the bulbs were virtually worthless. The strikingly colored Semper Augustus bulb, which traded for about $60,000 (in current dollars) in February 1637, commanded just 50 cents in 1739.
The martingale model predicts that portfolios chosen at random should perform, on average, about the same as those chosen by portfolio managers. In many of these experiments, random picks do just as well as many of Wall Street's leading traders.
Moreover, critics of the bubble theory point out that technical analysis, which is the practice of trying to identify systematic patterns in security price movements, should be useful in choosing securities if bubbles are present.
In general, these approaches have not significantly outperformed randomly chosen strategies or buy-and-hold strategies.
The tulipmania and the South Sea bubbles are striking examples of how prices may diverge from fundamental values. Many economists think it unlikely that similar episodes could occur today. If there are bubble or nonfundamental components in asset prices, chances are they will be much less dramatic and harder to distinguish from market fundamentals.
Robert Shiller of Yale University developed and implemented one popular test that has been used to evaluate whether prices are consistent with market fundamentals. Shiller constructed an economic model of the fundamental price of an asset. The test compares the volatility of the observed security price with the volatility of the fundamental price. These tests are typically called variance bounds tests, since the basic idea is to determine whether the observed variability of market price is consistent with the observed variability of market fundamentals.
A constructed series represents the sum of discounted dividends from stocks listed in the Standard & Poor's 500 graphed against the price of the S&P 500 since 1871 (Figure 1). Clearly, stock prices are many times more volatile than the present value of discounted dividends. Given the relatively stable history of dividends over the last century, market fundamentals, constructed this way, clearly cannot account for the extreme volatility of asset prices.
One interpretation of these data is that stock prices are too volatile relative to observed changes in cash flows and that some factor unrelated to business conditions is responsible for the bulk of asset price fluctuations.
However, there are some important caveats associated with interpreting these tests.
First, there is no unique way to determine how investors discount future cash flows.
The typical procedure carried out in these tests (and in Figure 1) is to assume that the discount factor (interest rate) is constant, which may not be true.
Second, we cannot observe people's expectations of future dividends directly, so we must infer them.
It is common to simply assume that today's stock price is exactly equal to the future discounted sum of dividends.
But this practice leads to difficulties in evaluating whether market fundamentals are consistent with price data.
Instead, Robert Flood, Robert Hodrick, and Paul Kaplan, in a 1986 paper, suggested that apparent violations of variance bounds tests reflect errors in the model. That is, the test depends on the underlying economic model being correct. Of course, this is a very strong assumption, and test results may simply reflect misspecification of the economic model. While there may be bubble components to asset prices, this type of test will not likely resolve the debate.
An alternative approach for testing whether variations in security prices are consistent with variations in market fundamentals is to determine whether the trend rate of growth in the asset price is similar to that in market fundamentals.
Specifically, if market fundamentals are growing at a slower rate than the price of the corresponding asset, we may reasonably conclude that prices include a particular type of bubble component.
This procedure can be used to detect the presence of bubbles that grow continuously over time. In 1985, James Hamilton and Charles Whiteman, and in 1988, Behzad Diba and Herschel Grossman, conducted tests along these lines. To determine whether market prices grow at a faster rate than market fundamentals, we must evaluate the trends in the data.
First, we test the data on annual stock prices and annual dividends to see if there are trends.
If both series have trends, the series are "differenced." For example, to calculate the differenced data for market prices, subtract the price of the asset last year from its price this year.
The differenced data for market prices and dividends are then tested for trends. If both of these differenced series have trends, the series are differenced again, and the trend tests are repeated. This process of successively differencing the data continues until the transformed data do not have trends.
If market prices must be differenced more times than market fundamentals, we may reasonably conclude that a bubble is present in market prices.
This analysis for dividends and stock price data, which appears in Figure 2, offers evidence that both prices and dividends have trends, but when differenced once, both do not. This implies that prices over this period have not grown consistently faster than dividends and provides evidence against the notion that stock prices have included a growing bubble component.
Moreover, there don't appear to be any differences in the trend behavior of market fundamentals and prices for either bonds or foreign exchange.
The extreme volatility of security prices has been a source of considerable interest since financial assets have traded in organized markets. It is important to distinguish between market fundamentals and bubbles when analyzing the volatility of any security. If there are dramatic changes in fundamental economic factors, we would expect to see highly volatile security prices. If the volatility of security prices is considerably greater than the volatility of underlying business conditions, or if asset prices tend to grow much faster than the asset's associated cash flows, price movements may reflect a bubble component.
Unfortunately, these tests often rely on assumptions that make interpretation of results very difficult. Test results that show differences between security prices and market fundamentals may be due to bubble components, but they may also reflect errors in the model for market fundamentals.
Since market fundamentals are generically unobservable, it will always be difficult, if not impossible, to analyze data on asset prices and determine whether price movements can be entirely reconciled with movements in market fundamentals.

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