I. Introduction: Perfect Liquidity Models
The economics of the financial markets has a primary consideration the determination of asset prices. The natural inclination for economists is to value an asset in one of two ways. If the asset is a direct claim to a stream of payments, such as a stock or a bond, the asset can be priced as the present discounted value of its expected cash flow. Alternatively, if the price of one asset is known (or, in the case of domestic currency, is taken to be numeraire), another asset can be priced by determining its value relative to the first asset. This is the class of pricing structures based on the idea that there should be no profitable riskless arbitrage opportunities. The ideas of covered interest parity, and to a lesser extent, purchasing power parity1, are examples of this sort of pricing models in the foreign exchange markets. No-arbitrage conditions are also useful for pricing domestic assets such as stocks and bonds, and are commonly used for pricing derivative assets. For example, the well-known Black-Scholes model for the pricing of options is based on a no-arbitrage condition, used to price the derivative asset in terms of the properties of the underlying asset and cash.
Either of these two paradigms of asset pricing leads naturally to the derivation of a (unique) market price P for a given asset. It is then generally assumed that an investor can trade an unlimited amount of the asset at that price if it is common knowledge that the investor has no informational advantage. The argument given for this perfectly elastic supply is that the asset has been priced “fairly” relative to other assets at its derived price. P is chosen to equate the value of the cash flows from the asset to its opportunity cost: investing P dollar anywhere else in the economy. Any drop in the market price below P would therefore cause this asset to offer excess returns, and would attract an effectively unlimited demand for the asset as every investor in the economy would sell other assets to acquire the asset offering excess returns. Similarly, an increase in the market price above P would cause an unlimited supply of the asset.2
Whatever its intellectual intuitive appeal, the idea that markets for financial assets are characterized by perfect elasticity of supply and constantly at their “fundamental” values does not appear to be matched by reality. Some examples of this include:
- In October 1987, a sharp drop in stock prices occurred in many developed countries. There was no contemporaneous significant change in the underlying economies, and therefore no significant change in the expected cash flows accruing to stockholders. Indeed, this sharp drop was reversed in most countries in the ensuing months and years.
- Events which bear no informational value can affect international prices. For example, Boudoukh and Whitelaw (1993) have found in Japan that being designated a “benchmark” government bond increases the market price of that particular bond. In the United States, inclusion in the Standard and Poor's 500 index has a temporary effect of increasing the market price of the company's stocks (see among others Harris and Gurel (1986)).
- Institutional traders who must buy and sell large quantities of stock do not do so all at once, but spread their large trades into “programs” which last several days. As Chan and Lakonishok (1995) found, this is because the markets are imperfectly liquid and a large trade would have a substantial unfavorable effect on the market price.
The idea that markets are perfectly liquid at a “fundamental” price remains common in the economic literature, but is now recognized as a modeling convenience. In many applications, this may be an unacceptable simplification. As a result, recent developments in the financial economics literature have explored the effects of market microstructure and noninformational trading. This paper will explore two strands in this literature that explain why prices of financial assets can deviate from their fundamental values: noise traders and herding behavior.
II. Noise Traders
An idea often seen in the modern financial economics literature is that there are some traders in the market who trade for noninformational reasons. This may be because they wish to speculate on the direction of the financial markets (although they have no information of actual value), because they have time-varying liquidity needs, or for other reasons. Collectively, these sorts of agents appearing in economic models are known as noise traders. For simplicity, they are often considered to be inelastic buyers or sellers of a specific amount of the asset, although this need not be the case.
If noise traders are perfectly inelastic buyers or sellers, in order to derive a market price we must have some other agents in the marketplace who are willing to trade the asset, but have some price sensitivity. Implicitly, these agents are providing liquidity to the noise traders. Indeed, it is often considered in the market microstructure literature that certain agents may be in the market explicitly for the purpose of providing liquidity to the noise traders. These agents are called market makers. In fact, this is the way organized markets work in the real world, particularly financial markets with organized exchanges. People who wish to sell a stock, for example, go to their broker, who (generally) conveys that order to the floor of a stock exchange. Often, the stock exchange merely matches that seller with a prospective buyer of stock. However, it is also likely that someone will buy the stock from the seller merely for short-term purposes, planning to sell the stock to the ultimate buyer within the day. On some stock exchanges, designated “specialists” are required by the exchange to perform this role.
The incentive for these liquidity providers is that they expect to earn a profit by conducting the round trip transaction. They are providing liquidity, or “immediacy,” to the public trader at a cost implicit in the transaction prices. One estimate of this cost of immediacy is the “bid-ask spread,” which is the difference between the price a dealer offers to buy an asset (the “bid”) and the price at which a dealer offers to sell an asset (the “ask”). This implicit payment to the dealer for immediacy covers the opportunity cost of capital and labor committed to the market-making venture as well as the risk the dealer bears while being exposed to fluctuations of the market price of her inventory. Since the market maker will generally hold assets for a very short time, the opportunity cost of capital is generally not a large cost consideration. The primary marginal cost of providing liquidity is generally the risk inherent in holding more of the asset temporarily.
In a world characterized by differing costs of immediacy, an investor will, ceteris paribus, prefer to trade in markets with low costs of immediacy, that is, very liquid markets. In fact, it is useful to think of liquidity as a valuable asset in itself. As will become clear, the same fundamental asset will have a higher equilibrium price if it sells in a market with lower expected transactions costs. This is called a liquidity premium.
B. A Simple Model
A seminal model in the noise trader literature is that by Grossman and Miller (1988). An adaptation of this model is instructive, as it offers a relatively simple framework in which to explore the provision of liquidity.
In the Grossman and Miller model, there are public uninformed traders coming to the market whose net demand for the asset is zero. However, the traders do not all arrive at once. Instead, some arrive in the first period with the remainder arriving in the second period. Hence, the net demand in the first period equals the net supply in the second period. In period three, the asset will be liquidated at some price P3. P3 is not known ex ante but information is revealed before each of the first two periods about its value.
There are Mt, identical risk-averse market makers who have a utility function: with a constant coefficient γ of absolute risk aversion. This utility function is employed
because if (as is the case in this model) the distribution of wealth is normal, a person with constant absolute risk aversion will act as if to maximize a linear function of mean and variance of wealth:
These market makers will provide immediacy by taking the other side of the first period trades and unwinding their position in the second period. However, they will do this only if the expected profit is sufficient to compensate them for the risk of holding the position. This risk derives from the uncertainty about the information that will be revealed between the first two periods. Since expected profits are linear in the amount xt of the asset held:
but variance of wealth is quadratic in xt:
equation (2) can be rewritten as:
Taking the first order condition then reveals that the optimal choice of xt, is linear in the expected return:
If there is a noise trader demand of Nt shares, the price must adjust to the point where the noise trader demand is met by the market makers:
Noninformational noise trader demand therefore affects market price. The effect of a given amount of noise demand on market price is greater when there is a high variance of future prices, a high risk aversion amongst the market makers, or when there are few market makers. The number of market makers can also be made endogenous (and is endogenous in the actual Grossman and Miller paper), since the makers will only join the market if the expected utility of market making is sufficient to cover the opportunity cost of being in the market.
The model also exhibits negative autocorrelation of returns: a positive shock to demand, for example, causes a contemporaneous increase in the market price, which is followed by a drop in price as the noise traders reverse course. This extreme reversal of noise trading can be relaxed without changing the qualitative result of negatively autocorrelated returns.
C. Empirical Evidence
There are at least two empirical implications of the above noise trader model that are robust to alternative theoretical specifications. First, isolating events that may be likely to attract noninformational trades provides a natural experiment. Perfect-liquidity theories of pricing predict that these will have no impact on price, while noise trader models predict at least a temporary effect on the market price. Second, models of imperfect liquidity by definition have the property that noise traders will affect the market price. Since these noise traders are generally expected to be transitory in nature, the effects they have on the markets should be temporary in nature. Therefore, although we cannot necessarily identify ex ante which trades are motivated by noninformational considerations, those trades which are so motivated should result in only temporary shifts in market pricing.
Standard efficient market theories predict that the only news that will affect prices is that which contains information that would cause a rational trader to update the expectations about the cash flow stream that would accrue to the holder of the asset. For example, a member of the corporate board of directors selling shares should result in a drop in price due to the possibility that the director is selling because he possesses negative private information. However, the trades of the uniformed public should not affect the market price. News concerning macroeconomic events or events with implications for the security issuer should affect the market price, but events which have no implications for the asset cash flow should not.
The financial markets provide us with events that would be expected to result in an ad hoc shift in the demand for an asset, but which should not be informative with respect to the fundamental value of the asset. Such events provide us with experiments to test the theory that noninformational trades affect prices.
The bond markets of major industrialized countries are quite well developed. However, since most indebted governments have many different bonds outstanding, there can be differences in the liquidities amongst different bonds. In the United States, the most-recently issued Treasury bond is traded more often than any other long-term Treasury bond. Currently this is the bond due in February 2026 with a 6 percent coupon. This bond will be much more liquid (that is, much easier to trade in large quantities without dramatically affecting the market price) than other long term bonds, such as the 6⅞ percent coupon bond maturing in August 2025. The same is true of other sorts of Treasury securities. For example, the most recently issued ten-year Treasury note will be more liquid than any other Treasury security with a similar maturity.
The U.S. equilibrium, where liquidity adheres to the most recently issued Treasury security, is not the unique equilibrium. It may result partially from a slow process of newly issued securities “finding a home” in long-term portfolios, or it may merely reflect the theoretical findings of Pagano (1989) who points out that which markets are liquid can be relatively arbitrary. This is because liquidity (and illiquidity) is self-reinforcing: more liquidity attracts more trading, which creates more liquidity. Although the origins of the liquidity pattern are somewhat ad hoc, the implications of the noise trader models for the market are clear. The liquid assets should be valued more highly by market participants than similar illiquid assets. As predicted, Warga (1992) finds that the liquid securities indeed trade at a higher price than illiquid Treasuries with equivalent properties. Indeed, Redding (May 1996) has shown that this effect is so strong that it frequently results in negative forward interest rates for the horizon leading up to the most recently issued (and therefore longest time to maturity) Treasury bond.
This differential liquidity is an international phenomenon. In Japan, the government periodically designates a “benchmark” government security. This security then becomes the focal point of traders' attention, and therefore become more liquid. Boudoukh and Whitelaw (1993) find that selection as a benchmark security, and even speculation about the selection of a benchmark security, causes a liquidity premium to be priced into a particular bond. As in the U.S. case, this is not a result of a change in expected cash flows: all government bonds in both countries are considered nominally riskless and in any case, the designation of a “benchmark” does not indicate any change in cash flow at any bondholder. The price change is merely the result of a change in demand resulting from the change in liquidity.
Another even that may be expected to attract noninformational traders is membership in the Standard and Poor's 500 Stock Index. The decision to add a company to the index is based purely on publicly available information, and therefore the decision brings no new information about the expected cash flows to stockholders. However, there are classes of investors who prefer stocks in the Standard and Poor's 500. Some mutual funds, for example, avoid the expenses of active management by “indexing,” or holding all the shares in a stock index. The Standard and Poor's 500 is a common choice for these funds. Also, there may be some institutional investors who may face fiduciary constraints that encourage investing in stocks included in major indices.
Again, classical efficient market theory would predict that these consideration would have no effect on price. Any potential effect on price would be immediately eliminated by other investors who would be happy to take any higher price and move on to another investment. Models where liquidity is provided at a cost, however, predict the opposite, that the incoming investors will have to pay a premium to encourage a liquidity provider to accommodate them. Indeed, this turns out to be the case. Harris and Gurel (1986) show that introduction into the Standard and Poor's 500 does have a positive effect on market price.
The Grossman-Miller model has a clear and simple implication for the dynamics of asset prices. An increase in price in the first period signals a drop in price in the second period. In terms of asset returns, the prediction is that the return for the first period (when the noise trading hits) should be negatively correlated with the return for the second period (when the noise trading disappears).
In general, although the effects of noise trading would not be expected to be offset as completely and quickly as in the Grossman-Miller model, the transitory nature of noise trading predicts that returns should be negatively autocorrelated. This prediction does not result from most models of perfect-liquidity asset pricing. Although certain economic fundamentals may be stationary processes with negative autocorrelation, the fact that the assets are claims to an entire stream of payments implies that the total return should approximate a random walk. The predictability in asset returns that results from negative autocorrelations creates arbitrage opportunities that are generally eliminated from perfect-liquidity models.
Evidence generally indicates that the effects of noise traders on price are in fact transitory in nature, especially for noise trading in individual issues. For instance, much of the price effect of introduction into the Standard and Poor's 500 is temporary in nature (although some remains, reflecting an increased liquidity premium). Also, events such as the publication of brokerage recommendations in such high-profile forums as the annual Barron 's roundtable have only temporary positive influences on the market price.
The evidence for the autocorrelation of returns in more aggregate markets is somewhat more mixed. Noise trader models predict that there should be some negative autocorrelation if noise trading (or investment fads) affect aggregate market prices. Summers (1986) points out that tests of long-term investment fads have low power since the prediction of the models is that the noise trader effects will decay slowly, and so that decay will only be a small portion of the observed return variance. However, the evidence still supports the finding that most financial markets exhibit negative long-term autocorrelation, or mean reversion. Fama and French (1988) find this to be the case for U.S. stock prices, and Cutler, Poterba, and Summers (1991) find that this is true for most of the developed countries' stock and bond markets as well.
Short-term autocorrelation, however, in many financial markets, is found to be positive. One explanation of this result is herding behavior, which is explored in section three. This mean-averting behavior is also consistent with noninformational short-term “bandwagon” effect. DeLong, Shleifer, Summers, and Waldmann (1990) offer a theoretical explanation of this bandwagon effect. In their model, there are noninformational traders who always follow the trend, buying when prices have risen and selling when prices have fallen. They reach the somewhat surprising conclusion that these “positive-feedback” traders can earn higher expected returns (although with higher risk, and therefore lower utility) than fully informed rational traders. The existence of these positive-feedback traders causes rational traders to aggressively buy as well, in order to sell to the positive-feedback traders. The resulting combination can create a bandwagon effect consistent with positive short-term autocorrelation.
The Grossman-Miller model presumed that the only traders arriving before the market makers were uninformed noise traders. The case where some investors are informed and some are uninformed is more realistic and has received a great deal of attention in the literature. In this case, the market maker who stands ready to buy and sell at certain prices faces an informational problem if the market maker is uncertain about the final price of the asset (but knows its distribution). Trading with uninformed noise traders is on average profitable to the market maker, but trading against informed traders results in losses to the market maker, since informed traders generally make only profitable trades.
Since the informed and uninformed traders are a priori indistinguishable, it is possible that the bid-ask spread will widen sufficiently in equilibrium for the market maker to make enough money from trading with noise traders to cover the losses from trading with informed traders. It is also possible that there will be a sort of separating device that enables the market makers to distinguish informed from uninformed traders. For example, Easley and O'Hara (1987) offer a model in which there are different bid-ask spreads for large trade sizes than for small trade sizes. People who are informed still generally find it profitable to pay the higher transaction costs in order to establish a larger position. Indeed, the idea that it is not only the bid-ask spread, but also the amount of the asset available at the quoted bid-ask spread, that is important for large traders is brought out by the study of a sample of institutional trades by Chan and Lakonishok (1995).
In any of these noise trader models with informational issues, a signal extraction problem exists. Trades that we perceived to be from informed agents will have permanent effects on the price, since they will cause market makers to revise their estimates of the fundamental value of the asset. Trades perceived to be from uninformed noise traders, however, will have only temporary effects.
III. Herding Models
Another class of models that explains a potential deviation of prices from their fundamental levels includes models of herding behavior and informational cascades. This occurs when people follow the crowd instead of purely using their own information. If this results in their own information not being publicly observed, that information will never be priced into the asset. Banerjee (1992) offers an example of this. Some agents receive a signal as to which asset will be profitable, and some receive no signal at all. However, even the agents who are informed of a signal may be misinformed. Agents sequentially make an investment decision, which can be observed by all. “Herding” behavior results when an informed agent discards his own information and instead makes an investment decision based on the observed decisions of other traders. This results in socially inefficient outcomes since the externality of this herding decision is that the agent's own information is never revealed to others.
The externality value of information is also developed in Caplin and Leahy (1994). In this model, agents generally do not find it worthwhile to act on their information due to transaction costs. However, when one agent acquires “strong” information (indicating the asset is mispriced to a significant degree) she acts. This action is interpreted by other agents for its informational content, who then combined with their own information may have enough motivation to act themselves. Consequently, a large portion of information can be suddenly and endogenously revealed, potentially leading to a market crash.
Froot, Scharfstein, and Stein (1992) also present a model where herding behavior can prevent information from being released. In this case, however, herding behavior prevents information from even being acquired. The model is one where the liquidation value of the asset is a combination of two independent factors. If speculators have long horizons, competitive pressures will cause them to acquire information that few other traders are acquiring, to earn a larger profit when the asset is liquidated. In equilibrium, then, an equal number of speculators pursue information on each factor, and most of the information is revealed. However, if speculators have short horizons, they will be selling the asset to subsequent speculators, rather than realizing the true liquidation value. In this case, it is in their interest to pursue the same information as the speculators who follow. In the resulting equilibrium, one sort of information is pursued while the other is completely ignored, leading to a systematic deviation of price from its true liquidation value.
Romer (1993) also offers a model of informational cascades, but in this case the cascade is not about the expected value of the asset, but about the precision with which that value is known. Fluctuations in market prices that are not associated with contemporaneous news releases are explained as information revealed by the trading process itself. In the model, some investors are uncertain about the quality of other agents information. A noninformational shock to supply therefore enables an investor to learn the slopes of the other investors' demand curves. From this, she can infer the quality of their information. Learning the quality of other traders information enables a trader to better interpret other traders activities, and therefore can lead to a large revision in each trader's estimate of the aggregate information in the market. Noninformational shocks to supply can therefore have large and lasting effects on price, due to the information they indirectly cause to be revealed. In the same paper, Romer also presents a model to explain why market prices can move even when no information appears to have revealed. In this model, information is dispersed across many agents. Unless these agents pay a fixed cost, they will have to wait until an exogenous later period to trade. Therefore, some pieces of information are not incorporated into market prices until a later date.
The idea that markets, especially financial markets, always reflect fully the information about assets, and therefore represent exactly their “fundamental” values, is an intuitively appealing one to economists. However, experience with actual financial markets seems to suggest that there is more to the story. This paper has described the efforts economists have made to incorporate the idea that markets may be affected by trades known to have no informational value and by the incomplete incorporation of available information. The noise trader and herding behavior literature, respectively, have been developed to address these issues. Existing tests of the empirical literature of these ideas have been favorable. They therefore represent a valuable tool to economists thinking about the realities of price behavior in financial markets, including equities, debt instruments, precious metals, and foreign exchange.
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