Microstructure and Asset Pricing

By

David EasleyDepartment of Economics

Cornell University

And

Maureen O’HaraJohnson Graduate School of Management

Cornell University

Prepared for the Handbook of Financial EconomicsEdited by G. Constantinides, M. Harris, and R. Stulz

Elsevier Science

August 2002

We would like to thank Joel Hasbrouck, Ravi Jagannathan, Rene Stulz, and Ivo Welch for helpful comments.

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Microstructure and Asset Pricing

1. Introduction

Market microstructure analyzes the behavior and formation of prices in asset

markets. Fundamental to this approach is the belief that features of the particular trading

mechanisms used in markets are important in influencing the behavior of asset prices.

The asset pricing literature also considers the behavior and formation of asset prices.

This literature focuses on linking asset price dynamics to underlying economic

fundamentals. While these two literatures share a common focus, they also share a

common flaw: neither literature explicitly recognizes the importance and role of the

factors so crucial to the other approach. Thus, microstructure provides extensive

characterizations of short-term price behavior, but fails to consider how these

microstructure factors may influence asset returns. The asset pricing literature

extensively studies asset returns, but it rarely looks to see if these returns are related to

underlying asset specifics such as private information or trading practices. Given the

central importance of asset pricing in finance, a junction of these two very important

literatures would seem beneficial.

In this article, we seek to foster this process by surveying the work linking

microstructure factors to asset price dynamics. In the short run, these asset price

dynamics involve issues such as the auto-correlation and cross-correlation structure of

stocks, and our survey will examine the literature relating these correlation structures to

microstructure factors such as non-synchronous trading and dealer behavior. In the

longer run, issues such as liquidity and the relation of private information to asset price

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dynamics dominate the research agenda. Here our work will survey the theoretical work

linking microstructure factors to long run returns, and in particular consider why stock

prices might be expected to reflect premia related to liquidity or informational

asymmetries. We also survey the extensive empirical literature testing these

relationships.

We note at the outset that while our focus in this survey is broad, it is not

exhaustive. Market microstructure factors can exert great influence over the level of

transactions costs, the way rents are split between dealers and investors (or between

different classes of investors), and the interactions between markets. All of these

undoubtedly affect asset returns but, while important, they will remain largely outside of

the scope of our inquiry. Similarly, a wide range of factors including behavioral biases

may influence asset prices, and these factors, in turn, may be affected by microstructure

variables.1 These issues, too, will generally be left to the side. Our exclusion of these

factors reflects the inevitable difficulty of trying to tie together large and diffuse

literatures, requiring us to focus our efforts on only a limited number of issues. There

are, however, a number of excellent survey articles and other sources on market

microstructure issues (see Stoll [2001]; Madhavan [2000]; Bias, Glosten, and Spatt

[2000]; Lyons [2001]; Hasbrouck [1996]; O’Hara [1995]) to which we refer the

interested reader.

What we hope to accomplish in this survey is to show that asset pricing dynamics

may be better understood by recognizing the role played by microstructure factors. We

also hope to influence the direction of microstructure research towards greater analysis of

1 For example, the market structure may greatly influence the volatility of asset prices. If investors react to volatility in predictably biased ways, then the microstructure may be an important determinant of these effects.

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the linkages of microstructure and fundamental economic variables. To do so, we will try

to highlight what is known and not known about the effect of microstructure variables on

short-run and long-run asset price behavior. The paper’s final section will then

summarize what issues remain contentious, and provide some guidance for future

research in this area.

2. Equilibrium Asset Pricing

A useful starting point for our analysis is the standard explanation for asset price

behavior (see, for example, Cochrane (2001)). The basic result is that the price of an

asset at date t is the expectation at t of the return on the asset at t+1 times a stochastic

discount factor. In the consumption-based capital asset pricing approach (in which

rational individuals choose asset holdings to maximize their expected utility of

consumption over time) this stochastic discount factor is the discounted ratio of marginal

utility of consumption at t+1 to marginal utility of consumption at t.

From this basic pricing equation follows the two principles that much of the

literature examines. First, idiosyncratic risk should not be priced. The price of an asset

is its expected payoff discounted by the risk free rate plus the covariance of its payoff

with the stochastic discount factor. If this covariance is zero there is no adjustment in

price for the risk in the asset’s payoff; or more generally, if the payoff on the asset is

correlated with the market only the correlation is priced and any idiosyncratic risk is not

priced.

Second, viewing the return on an asset as its dividend plus its future price, it

follows from the basic equation that asset prices net of dividends follow martingales.

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The distribution used in computing the expectation is the original distribution of payoffs

transformed by the stochastic discount factor. This is simply the risk neutral probability

measure. In the case in which individuals are risk neutral, or there is no aggregate risk,

and discounting is ignored, or included in a drift term, this reduces to the random walk

hypothesis for prices. This has the important implication that asset prices are not

predictable in the sense that simple trading strategies based on past price behavior cannot

be profitable. From this standard asset pricing point of view, regardless of how asset

prices are actually attained in the economy, an asset’s risk and return can be analyzed

from the underlying decision problems confronting agents in the economy.

This simple story, or a variant of it, has proved a useful construct for countless

economic analyses of asset prices. Unfortunately, the elegance of this story may be

deceptive. Asset price dynamics are much more complex than this characterization

allows. Individuals can face substantial transaction costs in buying and selling securities,

and these costs can influence their demand for and supply of securities.2 Price

adjustments may be complicated by market maker’s inventory positions, by price

discreteness, or even by exchange price continuity rules. The informativeness of asset

prices is complicated by the existence of private information that transforms securities

trading from a simple transaction into a strategic game between traders. This

transformation also imparts importance to other market data such as volume, trade size,

and the timing of trade, as each of these variables can be informative of future security

price movements. These difficulties raise the specter that equilibrium in asset prices is

2 These costs may even influence the type of securities we see being issued. Specifically, some securities may have such high trading costs that we never observe them in actual markets.

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best viewed not as an outcome, but as a process in which the asset price cannot be viewed

independently of the mechanism by which it is attained.

How, then, to reconcile this picture of asset pricing dynamics with the idealized

one given above? One answer is to argue that these complications are second-order

effects; that the idealized version of asset price dynamics is “close enough”, particularly

if asset prices are looked at over long time intervals. Moreover, since microstructure

research focuses on the trade-by-trade determination of prices, any microstructure effects

must either be very short-lived or diversifiable across securities in any case.

Yet, numerous researchers have found that asset price movements exhibit predictable

patterns both in the short-run and in the long run. These patterns raise the potential for

profitable arbitrage, and at the very least imply a disequilibrium in the market

inconsistent with the Olympian perspective given above. This predictability suggests that

insights derived from microstructure analyses of the trading process may improve our

understanding of asset pricing dynamics, even in long run. Of particular importance here

are market features such as dealer behavior, trading patterns, and the nature of intra-day

and inter-day price adjustment to information. In the next section, we consider how such

microstructure variables may relate to some puzzles in short-term asset pricing.

3. Asset pricing in the short-run

Consider the following empirical findings:

1. Weekly and monthly portfolio returns are positively autocorrelated (Conrad and

Kaul [1988]; Conrad, Kaul, and Nimalendran [1991]; Lo and MacKinley [1988];

Mech [1990])

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2. Short horizon returns on individual securities are negatively autocorrelated (Fama

[1965]; French and Roll [1986]; Lo and Mackinley [1990]; Conrad, Kaul, and

Nimelandran [1991])

3. Stock returns on large firms lead stock returns on small firms (Lo and MacKinley

[1990]; Boudoukh, Richardson, and Whitelaw [1994])

4. High volume security returns lead low volume security returns even on a monthly

basis (Gervais, Kaniel, and Mingelgrin [1999]; Chorida and Swaminnathan

[2000])

5. Return reversals follow high volume days for large firms, but return continuations

follow high volume days for smaller firms (Llorente, Michaely, Saar, Wang

[2001]; Antoniewicz [1993]; Stickel and Verrecchia [1994]).

Each of these findings suggests that short-term stock price movements are

predictable. Not surprisingly, each of these findings has also unleashed a torrent of

research designed to uncover what is responsible for such behavior (see for example,

Boudoukh, Richardson, and Whitelaw [1994]). The usual suspects investigated include

measurement error, irrational or biased trading behavior, and microstructure effects.

While not denying the potential importance of the first two causes, the fact that many of

these analyses are based on transactions prices lends support to the notion that

microstructure effects are involved. Rather than focus on the specific asset-pricing

anomalies, let us instead consider more generally how specific microstructure factors

affect price behavior

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A. The mechanics of pricing behavior

Suppose we consider a simple depiction of asset prices.3 Let the observable asset

price pt be given by

, (1)

where vt is the underlying “efficient” price and the st are random variables representing

frictions potentially due to microstructure effects. At this point, we leave the origins of

these frictions unspecified, but we assume that whatever their cause they have mean zero

and are uncorrelated with vt. A standard example of the st is to link these frictions

explicitly to trades, or st = (s/2)xt where xt is a trade indicator taking the value +1 if the

trade at time t is a buy and –1 if the trade at time t is a sell, buys and sells are equally

likely and s is bid-ask spread.

In an efficient market, prices follow a martingale, which simply means that vt can

be thought of as a conditional expectation given market information of the random value

of the asset, V, (i.e. where It is the market’s information). The true efficient

price vt is not, of course, observable, a point made with admirable clarity by Hasbrouck

(2000), so the actual estimation of this efficient price is a non-trivial problem. In general,

we will only be able to make inferences about this true value by looking at transactions

prices, bid and ask quotes, or possibly other market data.

A traditional approach in finance is to argue that if we look at prices with long

periodicity then we would expect that price movements are driven by changes in this

underlying efficient price. Given reasonable stationarity assumptions, these price

changes would be expected to follow a random walk, so that the microstructure related

3 Hasbrouck [1996] provides an excellent and more detailed description of these statistical models.

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price movements captured by st would be unimportant. Looking over shorter intervals,

however, the change in prices can have predictable patterns unrelated to changes in the

underlying efficient price. As Hasbrouck [1996] notes “At the level of transactions

prices, …, the random walk conjecture is a straw man, a hypothesis that is very easy to

reject in most markets even in small data samples. In microstructure, the question is not

“whether” transactions prices diverge from a random walk, but rather “how much?” and

“why?”

To see this, let us look more closely at price changes:

Rt= t + st – st-1 = t +(s/2)(xt – xt-1) (2)

where t = E[V| It] – E[V| It-1], or the change in conditional expectations. In the absence

of new information, t should be zero. The change in the market frictions term, however,

need not be zero, and in particular, may introduce particular patterns into security prices.

Suppose we assume that this market friction is a given bid/ask spread which arises

due to exogenous factors such as order processing costs. Then s/2 is half the effective

spread and the vt term in the pricing equation can be proxied by the spread midpoint. Roll

[1984] was the first to point out that market frictions such as the bid/ask spread could

lead to divergences in price behavior from the simple random walk story. In particular,

Roll demonstrated that in the statistical framework given above Cov (Rt, Rt-1) = -s2/4. The

intuition for this is that in the absence of any new information, observed trade prices

move between the bid and the ask price. If the price is already at the bid, for example,

the following trade at the bid results in a zero price change, while a trade at the ask

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results in a mean reverting process. Thus, observable price movements become

negatively serially correlated.4

The market friction term may include more complex effects. For example,

suppose that dealers try to manage their inventories by adjusting prices.5 If a dealer has a

preferred inventory position Q*, then the pricing equation can be modified as

pt = vt - b(Qt – Q*) +(s/2)xt (3)

Now, the observed spreads will include both the order processing component and an

inventory related factor. Because the dealer is setting prices to induce movement toward

his optimum, dealer quotes (and thus prices ) and inventory will be mean reverting.

Moreover, the mid-price of the observed spread need not be a good proxy for the

underlying efficient price.

An extensive literature has tested for these inventory effects in prices (see for

example, Hasbrouck [1988], Madhavan and Smidt [1993], Madhavan and Sofianos

[1998], Manaster and Mann [1992], Lyons [1998] ). In general, results from equity

markets have found positive but rather small effects, while results from other markets

such as futures or foreign exchange find stronger effects. Another large literature (see

Glosten and Harris [1988], Stoll [1989], George, Kaul, Nimalendarn [1991]) decomposes

spreads into components due to inventory, order processing, and information (an issue we

will address shortly). From our perspective here, these results suggest that over a short

time horizon, prices can exhibit patterns unrelated to changes in the underlying efficient

price, patterns that provide at least the potential for price predictability.4 Roll argued that “an interesting feature of this spread-induced serial covariance is that it is independent of the time interval chosen for collecting successive prices” Thus, whether we are looking at trade by trade movements or across days, this negative serial correlation will be present. See also Harris [1990] for statistical analysis of the Roll measure.5 For the dealer’s inventory control to be effective trades must be price sensitive. See Hasbrouck [1996] for more detail.

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An important feature of these particular frictions is that they are linked to trading.

For example, trades bouncing between the bid and ask quotes result in the observed trade

price process exhibiting negative serial correlation, even though the underlying true price

process remains a random walk. However, an important feature of actual markets is that

trades do not occur with regular periodicity, but instead depend upon order arrivals. Even

the most active stocks exhibit intra-day patterns in these order arrivals, so that trades do

not occur regularly throughout the day. This has the important implication that trade

prices provide only a censored sample of the underlying true price (see Lo and

MacKinley [1990]; Easley and O'Hara [1992]).

An immediate implication of this censoring is that comparing trade prices across

stocks can result in spurious inferences. In particular, suppose that we have two stocks

with identical underlying true price processes. Now, let an innovation occur to this true

price. If orders do not arrive simultaneously for both stocks, then trades will occur at

different times for the two stocks. Looking at the most recent trade price in the two

stocks will reveal different prices, even though the underlying true price of the assets is in

fact the same. This non-synchronous trading introduces lags into observed price

adjustment, and thus cross-sectional differences in the auto-correlation patterns in returns.

Numerous authors (see for example, Lo and Mackinley [1990]; Mech [1993]; Kadlec

and Patterson [1999]) have shown that nonsychronous trading plays an important role in

explaining the observed pattern of large firm weekly returns leading small firm weekly

returns. Indeed, Boudoukh, Richardson and Whitelaw [1994] argue a “large fraction” of

the observed effect may be explained by this factor, while Kadlec and Patterson [1999]

estimate it to be more on the order of 25%. An important feature of these analyses is that

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the order arrival process, while dependent on firm type, is not assumed linked to the

underling true process per se. If new information causes trading, however, then non-

trading may be correlated with the underlying true price process, suggesting a greater

complexity to the observed patterns in asset price dynamics. To understand this linkage,

we need to look more closely at the role of information in price adjustment.

B. The adjustment of prices to information

To this point, we have considered models in which the underlying value of the asset

and the trade process were independent. Trades mattered only because they caused

transaction prices to move between bid and ask prices that bracket the underlying value.

However, much of the microstructure literature considers a more complex story, see Kyle

(1985), Glosten and Milgrom (1985), Easley and O’Hara (1987) or O’Hara (1995) for an

overview. In this story, some traders, the informed, know more about the underlying

value of the asset than do other traders, the uninformed, or the market maker. The market

maker cannot distinguish between informed traders and uninformed traders who are

trading for non-informational reasons such as liquidity shocks. He loses to the informed

traders, so to have zero expected profits he must make profits from the uninformed

traders. He does this by setting a bid-ask spread. The actual spread may, of course,

include compensation for the fixed cost of doing business and an inventory component,

as well as this asymmetric information component. We focus first on this asymmetric

information component.

In this setting, buy and sell orders convey information so they affect the expected

value of the asset. Let be the prior expected value of the asset, where It is

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the public information prior to the trade at time t. The trade indicator is again if

the trade at t is a buy and –1 if the trade at t is a sell. The ask price, the price a trader has

to pay for a unit of the asset, is and the bid price, the price a trader

will receive if he sells a unit of the asset, is . This pricing strategy

induces a spread, st = , but only if the order type affects the expected value of the

asset. This occurs in markets in which some orders come from informed traders. When

an order to buy arrives at the market, the expected value of the asset rises because this

order is a signal of good news about the value of the asset. Similarly, the arrival of an

order to sell is bad news, the expected value of the asset falls and the transaction price is

lower.

The observable price of the asset at time t, pt, is thus

(4)

Here again trade causes prices to bounce between a bid price and an ask price. In the

previous section (ignoring active inventory control for now), this bounce was purely

transitory; there was no effect of a trade at time t on the price at time t+1. Now there is

also a permanent component. An order to buy at time t causes a transaction at the time t

ask price, , and it changes the expected value of the asset to . Bid and ask prices at

time t+1 bracket this new expected value of the asset.

Orders at time t+1 also cause prices to adjust, and this adjustment process can be

complex. In particular, if prices have not adjusted to true values, then informed traders

can be expected to continue trading all on the same side of the market, buying when there

is good news and selling when there is bad. In a simple world where information events

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are known to have occurred, this repeated trading is incorporated by the market maker

into his price-setting decision, and prices exhibit Markov behavior. If there is uncertainty

about information, however, then the sequence of trades may also be informative.

Sequence effects can also arise from the actions of uninformed traders who may opt to

reduce the price effects of large trades by splitting orders (see Bernhardt and Hugheson

(1999). Numerous authors (see Hasbrouck [1996] for review) have shown that trades are

positively auto-correlated, a result consistent with this non-Markovian pattern.

Returning to equation (4), it is also possible to add back into this model fixed

components of the spread and inventory control components. Glosten (1987) analyzes a

model with both asymmetric information and fixed components. He shows that the

asymmetric information component has different implications for prices than do fixed

components, in particular the true price of the asset and the random spread effect are

correlated. Of particular importance is the part of the bid-ask spread that is due to

asymmetric information versus order processing costs or inventory control. Glosten and

Harris (1988) show that a permanent adverse selection effect is important for a sample of

250 NYSE stocks. Stoll (1989) analyzes NASDAQ stocks and concludes that 43% of the

spread is due to adverse selection, 10% is due to inventory cost and 47% is due to order

processing costs. Huang and Stoll (1997) use a more general model on 19 actively traded

NYSE stocks to conclude that 10% of the spread is due to adverse selection, 29% is due

to inventory cost and 62% is due to order processing costs. The variation in results

suggest that the matter is not yet settled, but it is clear that all three factors are important,

and that they have differing implications for statistical biases in asset returns.

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Huang and Stoll [1994] reinforce these results by examining whether

microstructure effects can explain quote revision or transaction price revision. In

particular, these authors demonstrate that the movement of both quotes and prices can be

predicted by factors linked to both inventory theories and information-based theories.6

Consequently, at least over very short intervals, microstructure variables appear to predict

subsequent stock price movements.

Microstructure spread effects may also explain the behavior of stock prices over

somewhat longer time intervals. In particular, an enduring puzzle in asset pricing is the

role of taxes in affecting valuation. Numerous researchers (most notably, Elton and

Gruber (1984)) argued that the ex-dividend behavior of stock prices was evidence that the

market values capital gains more than cash dividends. Miller and Scholes (1982) pointed

out, however, that transactions costs are not negligible when compared with the usual

magnitude of cash dividends. Boyd and Jagannathan (1994) demonstrated that the

implicit bid-ask spread can explain the price pattern observed on ex-dividend days, thus

undermining the argument for tax effects. Frank and Jagannathan (1998) provide further

evidence for microstructure effects by showing that trading costs can explain the ex-

dividend behavior of stock prices in Hong Kong (a country without capital gains taxes).

A natural conclusion from this work is that microstructure effects may be large enough to

explain a variety of short-run asset price movements.

6 Huang and Stoll [1994] note, however, that this need not imply the existence of arbitrage profits as the transactions costs of implementing trades may preclude such profits.

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C. Statistical and Structural Models of Microstructure Data

In the previous two sections we considered simple reduced-form models of

microstructure data that were designed to allow estimation of parametric effects of

microstructure features on asset prices. An alternative approach is to forego structure and

employ a purely statistical time series model of high frequency microstructure data. This

data consists of trade characteristics such as price and quantity as well as the time of the

trade, or the elapsed time since the last trade. Much of the literature in this area attempts

to use time series models to forecast prices, price changes or volatility and to infer the

information content of particular variables.7

We first consider time series models in which time is taken to be trade-time rather

than clock-time. Here, the data is treated as if observations of trades and price changes

occurred at equally spaced intervals in real time. The statistical models in the previous

section are examples of this approach. In their reduced-form, these models are bivariate

vector autoregressions with structure imposed by the underlying economic model.

Hasbrouck (1991) takes this approach to estimate the information content of trades,

which in this setting is given by the persistent price impact of the unexpected component

of trades. Numerous authors have used this permanent and temporary price effects

approach to estimate various asset price regularities such as the informativeness of small

trades (see Hasbrouck [1991]) or the impact of block trades (see Saar [2001]).

An alternative approach is to consider trades in real time and ask if there is

information content in the time between trades. Two papers here are particularly

relevant. Diamond and Verrecchia (DV) [1987] develop a model in which short sale

constraints impart information content to the time between trades. In their model, traders

7 For a review of some of the issues in modeling high frequency data see Goodhart and O’Hara [1998].

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learning bad news may be unable to short the stock, so longer times between trades may

signal bad news. Easley and O’Hara (EOH) (1992) show that if the existence of new

information is uncertain, then the time between trades carries information. Their idea is

that when there has been an information event, orders arrive from both uninformed and

informed traders, resulting in more trades per time interval. So when trades occur fast

they have more information content, and produce greater price impacts than when trades

occur slowly. This implies that the volume of trade now signals information. We discuss

the literature on volume later in this section. A direct implication of both the DV and

EOH models is that time itself may be predictive of future price movements.

This functional role for time is investigated empirically by Engle and Russell (ER)

[1998] and by Hasbrouck [1999]. Engle and Russell develop a new approach to

modeling irregularly spaced data called the autoregressive conditional duration model.

The ACD model focuses on the inter-temporal correlations of the time interval between

events. In this setting, the events can be trades, or quote updates, or even depth changes.

The ACD model “treats the arrival times of the data as a point process with an intensity

defined conditional on past activity”. The ACD model essentially estimates how long it

will be until prices or quotes change given this past activity.

With its focus on price changes, the ACD model is related to models of volatility.

Indeed, Engle [2000] finds that, as suggested by the asymmetric information model,

longer time between trades and longer expected times between trades are associated with

lower price volatility. Engle and Russell [1997] apply this technique to foreign exchange

data and they find that changes in the bid-ask spread are predictive of future price

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changes. These future price changes are defined over a short horizon, but these analyses

show how patterns in trade and quote data can result in predictable price variation.

Treating volatility in this way allows for the explicit inclusion of microstructure

features such as intra-day seasonalities. While the asset-pricing literature is replete with

models of volatility (for an excellent survey see Bollerslev, Chou and Kroner [1992]),

typically these models require a high degree of stationarity in the data. Thus, analyses

using ARCH-type models (i.e. GARCH, P-GARCH, E-GARCH, etc.) typically remove

seasonalities or other microstructure factors from the data. Hasbrouck [1999] makes the

important point that such real-time stationarity is refuted by the clustering of trades, price

and quote changes that characterize microstructure data. Thus, he notes “a fast market is

not merely a normal market that is speeded up, but one in which the relationships

between component events differ.” This characterization is consistent with the Easley

O’Hara [1992] argument that the information structure differs between fast and slow

markets.

Investigating the linkage of microstructure variables to price volatility may also

provide insights into more basic questions regarding the evolution of prices. In an

intriguing paper, French and Roll [1986] showed that return volatility is significantly

higher when measured during the trading day than it is during non-trading hours. They

attribute this result to noise generated by the trading process. But how exactly is this

occurring? Is it the case that trading creates volatility, in effect inducing traders to

transact simply because the market is open? Or, if trading in fact reveals information,

then might not prices be volatile because of learning?

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These issues are important in microstructure because, at least over short horizons,

most microstructure time-series are non-linear. Thus, while French and Roll noted the

distinction between market-open volatility and market-closed volatility, other authors

have shown distinct volatility patterns during the day. In particular, numerous authors

have shown that price volatility overall tends to be U-shaped, while the volatility of ask

price changes actually declines over the day (see Madhavan, Richardson, and Roomans

[1997]).

From our earlier discussion, it seems natural to attribute these volatility patterns to

factors relating to information flows and to factors related to market frictions.8

Hasbrouck [1993] uses a VAR approach to decompose volatility into these components,

while Madhavan, Richardson, and Roomans (MRR) [1997] develop a structural model to

do so. This latter approach uses a simple model in which the intra-day variance arises

from four components: price discreteness, asymmetric information, trading costs, and an

interaction term. Estimating the model using intra-day NYSE data reveals a number of

interesting findings. In particular, MRR find that the public information component of

volatility declines by one-third over the day, consistent with the revelation of information

through trading. Conversely, the market frictions component of volatility increases over

the day, accounting for 65% of the price variance by the close of trading. Of these

market frictions, the bid-ask spread plays an important role, explaining more than a third

of total volatility by the close of trading.

8 Stoll and Whaley [1990] present evidence that the structural procedure for opening stocks on the New York Stock Exchange appears to affect price volatility.

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D. Volume and Price Movements

Because the time between trades is inversely related to the number of transactions, the

findings discussed above imply that there may be information content in the number of

trades and in volume. A widely-cited aphorism is that “it takes volume to move prices”,

or simply that volume and volatility are positively correlated. Such an empirical finding

has been demonstrated by numerous authors, see for example Galant, Rossi and Tauchen

(1992), or Campbell, Grossman and Wang (1993). Whether this volatility linkage is due

to the volume of trades or to the number of transactions is contentious. Jones, Kaul and

Lipson (1994) argue that it is the number of trades that matters; they present empirical

evidence that there is no additional information in volume beyond that conveyed in the

number of trades. Other researchers (particularly research on liquidity which we address

in the next section) argue the opposite.

It is well known that volume is also serially correlated. There is a recent theoretical

literature showing how the serial correlation in volume and the correlation between

volume and volatility can arise in a competitive market. He and Wang (1995) show that

even when information is uncorrelated over time volume will be serially correlated in a

partially revealing rational expectations equilibrium, and that volume and volatility will

be contemporaneously correlated. This model relies on private information affecting

trade in both the current period and possibly in future periods as traders learn from

current and past prices.9

9 In effect, traders here can profit from using technical trading rules based on prices. Such technical trading strategies have also been analyzed by Brown and Jennings [1989] and Grundy and McNichols [1989].

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Blume, Easley and O’Hara (1994) provide a model in which volume and volatility are

positively correlated and in which volume has predictive content for future price changes.

In this model, volume itself is informative because it provides data on the quality or

precision of information in past price movements. Thus, traders watching volume can

learn information regarding the future movement of prices. BEO argue that this

informative effect of volume is likely to be particularly important for small, less widely

held firms, a result confirmed empirically by Conrad, Hameed, and Niden [1994] in their

analysis of the relation of volume and weekly returns.

Campbell, Grossman and Wang [1993] develop a model in which volume can help

distinguish between price changes due to public information and those that reflect

changes in expected return. In their model, variation in the aggregate demands of

liquidity traders can generate high volume, as can days in which there is new information.

Their model predicts “price changes accompanied by high volume tend to be reversed

while this is less true of price changes on days with low volume”. Empirical evidence in

Llorente, Michaely, Saar, and Wang [2001] using daily data on volume and first-order

autocorrelations for individual stocks listed on the NYSE and AMEX confirms these

results.

That volume may be predictive of short-run movements in prices is consistent with

microstructure effects arising from the adjustment of prices to public and private

information. What is more difficult to understand is the apparent role of volume in

predicting longer-term price movements. In particular, a number of researchers have

found that conditioning on past volume is useful in predicting asset returns for months in

advance. Gervais, Kaniel, and Mingelgrin [1999] find that stocks experiencing unusually

21

high trading volume over a period of one day to a week tend to appreciate over the next

month and continue to generate significant returns for horizons as long as 20 weeks.

Brennan, Chordia, and Subrahmanyam [1998], looking at normal as opposed to abnormal

volume, find that that high volume stocks tends to be accompanied by lower expected

returns, a result they attribute to liquidity effects. We consider these liquidity issues more

fully in the next section.

What are more puzzling still are results of Lee and Swaminathan [2000]. These

authors find that price momentum is stronger among high volume stocks, and that past

trading volume predicts the magnitude and timing of price momentum reversals.

Jegadeesh and Titman [1993] demonstrated that portfolios of “winner” stocks tend to

experience higher returns and “loser” stocks experience lower returns over the next

three-year period. These momentum effects are puzzling because they suggest the

market somehow “under-reacts” to good and bad news. Lee and Swaminathan confirm

these effects, but they also show that over years 3 to 5 the return pattern reverses, with

winners now under-performing, and conversely. Of particular importance is their finding

that high volume winners and losers experience faster momentum reversals. Thus,

volume predicts both the level and turning points of returns.

Momentum effects pose serious challenges to virtually all asset-pricing theories.

Various explanations have been proposed, but momentum appears robust to obvious

causes such as measurement errors and transactions costs (see, for example, Grundy and

Martin [2000]; Conrad and Kaul [1998]; Jegadeesh and Titman [2001]). Could

microstructure effects provide part of the solution? Possibly, but the link is not obvious.

It is hard to envision how dealer inventory management or price discreteness, or bid-ask

22

spread changes or intra-day volatility patterns could produce such long-run effects. And

more puzzling still is seeing how these factors could explain the non-linearity in

momentum effects.

The linkage of volume and momentum suggests that the answer might lie in the

complex role played by information. Microstructure analyses highlight the important role

of private information in affecting price behavior. Indeed, Hvidkjaer [2000] finds that

buy-sell imbalances in momentum portfolios are consistent with traders acting on the

basis of such information. What is needed is an understanding of why microstructure

could influence asset returns in the long run, and it is this issue we address in the next

section.

4. Asset Pricing in the Long-run

The previous section examined the effects of microstructure variables on short-run

asset pricing dynamics. While the specific influences discussed differ from one another,

a feature common to these variables is their relation to the mechanics of trading and the

subsequent adjustment of prices to equilibrium levels. Thus, the negative serial

correlation found in transactions prices induced by bid/ask bounce or by market maker

inventory behavior can be viewed as an artifact of the market clearing process. Similarly,

the informative role of volume or the time between trades arises because of the price

discovery role of markets. Over short horizons, it should not be surprising that the

mechanics of trading can affect prices in predictable ways.

What may be more perplexing is why microstructure variables should have any

effect on long-term asset returns. There are two issues to consider here. First, and

23

foremost, is the economic origin of such effects. Certainly, apart from short time

intervals, the problems of non-synchronous trading or bid/ask bounce will not influence

asset returns. And the excessive volume on any given day will quickly dissipate once

prices have adjusted to new equilibrium levels. But other, more fundamental factors can

arise in the long-term that affect the risk and return faced by traders. In particular,

liquidity and the underlying information risk of the asset may influence the utility of

investors, an issue we address further shortly.

But even if these effects exist, there is a second problem, namely the ability to find

them empirically. There is an overarching problem of econometric power when looking

for microstructure effects in long-run data.10 One immediate difficulty is that expected

returns may be small relative to return variation (in effect, a low signal-to-noise ratio). A

second difficulty is multi-collinearity, both with respect to economic factors and with the

components of trading cost. Thus, microstructure effects may be correlated with other

economic features such as firm size. Similarly, high variance firms may have more

asymmetric information, so that higher returns attributed to volatility may actually reflect

compensation due to more complex informational risks. These econometric concerns

dictate both caution in interpreting extant findings, and support for the need to develop

better, more sensitive econometric techniques. Abstracting from these empirical

difficulties, we now turn to the basic question of how, or why, microstructure variables

could affect long run asset returns.

10 We thank Joel Hasbrouck for bringing this point to our attention.

24

A. Liquidity

Virtually all would agree that the liquidity of an asset is an important feature; exactly

what this liquidity is would elicit more debate. In its simplest form, liquidity relates to

trading costs, with more liquid markets having lower costs. Indeed, this view of liquidity

is put forth by Amihud and Mendleson [1986] who note "illiquidity can be measured by

the cost of immediate execution". Abstracting from the definitional battles of what is

meant by cost (or immediate, for that matter), this view of liquidity leads to the simple

axiom that liquidity is a desirable property for an asset; that other things equal, traders

would prefer assets in which execution costs are lower.

Whether liquidity is valued enough to affect asset returns is more controversial. Over

a short period of time, higher levels of transactions costs must lower the return available

to investors, and ceterus paribus, lower the price they are willing to pay for the asset.

But given a long enough time horizon, are such effects large enough to actually affect

returns?

The traditional view in asset pricing is no. For example, Constantinides [1986]

shows theoretically that transactions costs can only have a second-order effect on the

liquidity premium implied by the equilibrium asset returns in an inter-temporal portfolio

selection model. A similar conclusion is reached by Aiyagari and Gertler [1991], Heaton

and Lucas [1996], Vayanos [1998], and Vayanos and Vila [1999]. In effect, these authors

all argue that the transactions costs are just too small relative to the equilibrium risk

premium to make any real difference. Huang [2001] agrees that in general this is true,

but that it need not be the case if traders are constrained from borrowing against their

25

future income stream.11 Holmstrom and Tirole [1998] develop a model in which firms

demand liquidity to meet future cash flow needs. In this model, assets’ expected returns

are affected by the covariance of their returns with market liquidity.

The counter-argument is put forth by Amihud and Mendlesohn (AM) [1986; 1988],

who argue that liquidity can more generally affect required returns. In the AM model,

traders seek to maximize the present value of expected cash flows. The model allows

traders to diversify and to have different time horizons. Traders buy and sell assets as

part of their portfolio problem and they face execution costs in doing so. AM proxy

illiquidity by the bid/ask spread, and so higher spreads result in lower overall returns for

traders. AM show that a clientele develops in the market for assets with different

liquidity. In particular, only traders with long horizons will hold illiquid assets, and they

will demand compensation for doing so. Thus, their model predicts that in equilibrium an

asset's return will be an increasing and concave function of its bid/ask spread.

The simplicity of the AM argument is quite appealing. In this setting, illiquidity

functions as a type of exogenous tax, and while some traders avoid it altogether by

eschewing such assets in their portfolio, others bear the tax but demand compensation in

the form of higher returns. Because bid/ask spreads measure this liquidity, the question

becomes are spreads linked in an economically meaningful way to returns?

There is an extensive body of empirical research investigating this question.12 AM

[1986; 1988] find a significant positive effect of bid-ask spreads on stock returns, and

their results are supported by Eleswarapu [1997] and by Chalmers and Kadlec [1998]

11 Huang [2001] looks at how liquidity shocks affect traders in a continuous time setting. His model uses uncertain holding periods and liquidity shocks to show how borrowing constraints may result in substantial return premia for less liquid securities. 12 We limit our discussion here to studies involving the equity markets, but this linkage of liquidity and asset returns has been investigated in other settings as well. See for example, Amihud and Mendelson [1991] and Kamara [1994].

26

who link amortized spreads to returns. However, Chen, Grundy and Stambaugh [1990],

Chen and Kan [1996] and Eleswarapu and Reinganum [1993] conclude the opposite, as

does recent research by Easley, Hvidkaer, and O'Hara [2001] who find no direct link

between spreads and returns for the period 1983-1998.13 Indeed, Chen and Kan argue

that the positive findings of AM and others are due to mis-specification of risk; that "

when returns are not "properly" adjusted for risk, variables that are functions of the most

recently observed price of a stock, such as size, dividend yield, and the relative bid-ask

spread, are often found to possess explanatory power on the cross-sectional difference in

the risk-adjusted return". Their argument captures Berk's [1995] observation that any

price-related variable will be related to returns under improper risk-adjustment.14

But are spreads necessarily the correct measure of liquidity? Certainly, as a proxy for

trading costs, spreads are only a part of the story; factors such as trading commissions,

the overall volume in the market, the price impact of trades or even the trading

mechanism itself also are important (see Keim and Madhavan [1995] for empirical

analysis of the trading costs facing institutional traders). Indeed, the recent dramatic

declines in spreads due to structural changes in tick sizes and regulatory changes

highlight the limitations of this measure. A natural direction for research, therefore, is to

investigate how returns are affected by alternative measures of liquidity.

13 ER find that the association between bid/ask spreads and stock returns is mainly confined to the month of January, a result hard to reconcile with the underlying AM arguments. EHO find that spreads are insignificant when added to a Fama-French (1992) regression. However, they do find that spreads may have an effect when added to a return regression that also includes the standard deviation of returns, volume, and the volatility of turnover. This spread effect appears to arise because of the high correlation between spreads and standard deviations.14 Essentially, the argument here is that spreads are derived from prices, and as Miller and Scholes [1982] pointed out prices may be correlated with a security's beta, so any finding of a link between spreads and returns could simply be a measurement error of beta.

27

Datar, Naik, and Radcliffe [1998] propose share turnover (i.e. the number of shares

traded over the number of shares outstanding) as such a proxy for liquidity, arguing that

liquidity should be correlated with trading frequency. They find that stock returns are a

decreasing function of turnover rates. Brennan, Chordia and Subrahmanyam [1998]

demonstrate a similar negative relation between average returns and dollar volume.

Anushman, Chordia, and Subrahmanyam (ACS) [2000] also find negative relationships

between returns and measures of turnover and dollar trading volume. More puzzling is

their finding that returns are negatively related to the volatility of these measures. ACS

argue that traders prefer volatility as it enhances their ability to implement trading

strategies, but this explanation is contentious given the negative impact on utility usually

associated with volatility.

That volume-related measures appear related to returns is intriguing, but is this effect

due to liquidity? In the previous section we saw that volume plays a complex role in

markets, in part because of its relationship with information on the stock's underlying true

value. Indeed, Lee and Swaminathan [1998] argue that turnover may be a less than

perfect proxy for liquidity because the relation between turnover and expected returns

depends on how stocks have performed in the past. As we discussed in the last section,

these authors argue that volume may be most useful in understanding the mysteries of

momentum.

There are, of course, other measures of liquidity to consider. A variety of authors

propose variants on the price impact of trading. In particular, markets in which trades

move prices a great deal are considered less liquid than those with smaller price effects.

Breen, Hodrick, and Korajczyk [2000] calculate liquidity as the relation between price

28

changes and net turnover (defined over 5 and 30 minute periods, respectively). They find

these price impacts exhibit substantial cross-sectional variation, while remaining

remarkably stable when measured over their four-year sample period.

Amihud, Mendleson, and Lauterbach (AML) [1997] use the liquidity ratio, defined as

the daily volume divided by the absolute value of the daily return, to capture this liquidity

effect (see also Cooper, Groth, and Avera [1985] and Berkman and Eleswarapu [1998]

for studies using the liquidity ratio). AML use a natural market experiment, the transition

of trading on the Tel Aviv Stock Exchange from a call auction mechanism to more

continuous trading, to investigate how trading mechanisms affect stock prices. This

clever study shows that the transition between trading mechanisms resulted in both

substantial liquidity gains and significant price increases for the transferred shares.

Whether the enhanced liquidity caused the price increase, however, is not something this

study can determine, in part, because the liquidity ratio itself is defined by daily returns.

Muscarella and Pinowar [2001] show similar effects accompanying the movement of

stocks from call market trading to continuous trading on the Paris Bourse. They find that

stocks moving to continuous trading experience a price gain of more than 5 percent.

Such stocks also exhibit increases in volume and, not surprisingly, in the liquidity ratio.

Interestingly, this study also documents that inactive stocks moving from continuous

trading to call trading did not fare well; prices generally fell, volume remained relatively

stable, and there was a (weakly) significant decline in the liquidity ratio. These results

suggest that call market trading did not enhance liquidity for inactive stocks as has been

conjectured by numerous authors.

29

Brennan and Subrahmanyam (BS) [1996] propose linking illiquidity to the price

impact of trades as captured by the Kyle . The variable is essentially the slope

coefficient in a regression relating the price change to trade-by-trade signed order flow.

In the Kyle [1985] model, the arises because of strategic trading by an informed

investor, and so in that context it is a measure of adverse selection. BS argue that adverse

selection is "a primary cause of illiquidity", and they use the Kyle measure to provide a

proxy for this trading cost. This is also one of the first studies to use transactions data to

measure the nature of illiquidity.

BS conclude "there is a significant return premium associated with the fixed and

variable costs of transacting". They find that the relation between the premium and the

variable cost of transacting is concave, but that it is convex when measured with respect

to the fixed costs of transacting. This latter result is inconsistent with the clientele

argument of Amihud and Mendleson, but it may, as the authors note, reflect more the

difficulty of measuring this cost variable using transactions data.

Amihud [2000] also investigates the idea that illiquidity is the relationship between

the price change and the associated order flow. In this analysis, illiquidity is defined by

the average ratio of the daily absolute return to the (dollar) trading volume on that day. In

effect, this measure gives the percentage daily price change per dollar of daily volume,

and conceptually it is the inverse of the liquidity ratio defined earlier15. The paper finds a

positive cross-sectional link between asset returns and this illiquidity measure. A puzzle

with this and other measures based on daily volume-normalized price movements,

however, is that the theoretical link to investors' trading problems is not straightforward.

Moreover, the earlier findings that volume alone is linked to returns raise difficulties in

15 In some sense, this measure is like a Kyle but defined over total daily price change and volume.

30

knowing exactly how to interpret these composite variables. Of course, given the

difficulty of even defining liquidity, such problems should not be unexpected.

A more controversial argument in this research is that expected market illiquidity

affects expected stock returns. The notion here is that liquidity can be time-varying for

the market as a whole, and investors demand compensation for bearing this market-

related risk. Amihud calculates expected market liquidity by averaging the illiquidity

measure defined above over all firms in the market, and then assuming that investors

expect this market variable to follow an autoregressive process. The analysis

hypothesizes that a rise in expected market illiquidity induces both an income and a

substitution effect. For all stocks, there is a general fall in stock prices to compensate for

the reduced liquidity. However, traders also substitute from less liquid to more liquid

stocks, resulting in an increase in some stock prices.

Pastor and Stambaugh [2001] take this argument one step further by arguing that

liquidity per se is a priced factor in asset returns. These authors use a variant of a

volume-linked price change as their liquidity measure. Their individual liquidity measure

is a complicated one, entailing “the average effect that a given volume on day d has on

the return for day d+1, when the volume is given the same sign as the return on day d”.

This measure is similar to that of Amihud [2000], but its use of today’s volume and

tomorrow’s return makes this essentially the same variable investigated by Llorente,

Michaely, Saar, and Wang [2001]. Pastor and Stambaugh then calculate each stock’s

sensitivity, or “liquidity beta”, by constructing a market liquidity measure, given by the

equally weighted average of the liquidity measures of individual stocks on the NYSE and

31

Amex for the years 1962-1999. Their empirical findings suggest that such liquidity betas

are highly significant factor in explaining asset returns.16

Why would liquidity have a common factor or act as one in asset returns? Chordia,

Roll, and Subrahmanyam (CRS) [2000], Hasbrouck and Seppi (HS) [2001], and

Huberman and Halka (HH) [2001] address this issue. CRS argue that commonality in

liquidity could arise for reasons related to common variation in dealer inventories. If

trading volume induces co-movements in dealers’ inventories, then this in turn could

cause co-movements in liquidity measures such as spreads and depths. Asymmetric

information, one of the usual suspects in microstructure studies, is less likely to be the

source "because few traders possess privileged information about broad market

movements". CRS calculate the time series averages of market spreads, and they provide

evidence of weak commonality in several liquidity variables. Huberman and Halka

[2001] provide similar empirical results, and they conjecture that a systematic component

of liquidity arises “because of the presence and effect of noise traders.” They note,

however, that their empirical results do not provide hard evidence of this explanation.17

Hasbrouck and Seppi [2001], however, question the importance of any commonality

in liquidity. These authors use a principal components analysis to show that common

factors exist in the order flows of the 30 stocks in the Dow-Jones Industrial Average.

Using canonical correlation analysis, they document that the common factor in returns is

highly correlated with the common factor in order flows. Their results on liquidity,

however, are quite different in that variations in liquidity are found to be largely

idiosyncratic. This suggests that variations in liquidity at the aggregate level could be 16 Liquidity betas are calculated using volume signed by future returns to predict returns. As with all priced-linked measures, the issue of mis-specification of risk raised by Berk [1995] must be considered.17 Sias, Starks, and Tinic [2001] investigate whether such noise trader risk is priced. They find no evidence using closed-end fund data that it is.

32

diversified away. They conclude "any liquidity-linked differences in expected return are

most likely due to predictable changes in the level of liquidity, rather than to variability in

liquidity, per se.”

Whether liquidity affects asset returns remains contentious. What does appear robust

is that asset returns behave in ways not predicted by traditional asset pricing theories.

While these divergences may be due to liquidity, there is an alternative microstructure-

based explanation to which we now turn.

B. Information

In standard consumption-based asset pricing models, asset prices are such that the

representative individual, or a collection of individuals with homogenous beliefs, chooses

to hold the existing supply of assets. As the individuals’ beliefs about the value of the

assets change over time, asset prices change, and this movement, along with dividends,

generates returns. This basic model leads to an elegant asset pricing theory in which the

price of each asset is primarily dependent on the covariance of its returns with the returns

on the entire collection of assets, or the “market”. Individuals need not hold idiosyncratic

risk, and so in equilibrium they will not be compensated for holding this risk. Only

market risk is priced.

Much of the market microstructure literature, on the other hand, focuses on

differences in information between individuals, and on how the flows of differential

information generate trade, spreads and price changes. Typically in this literature one

asset is priced at a time.18 There is no mention of market versus idiosyncratic risk;

18 Exceptions to this are work influence of information on basket securities, and the work on stock index futures, see Subrahmanyam [1991].

33

everything seems to be idiosyncratic risk as it is asset-specific. For this reason, it is

natural to suspect that the issues microstructure examines cannot affect long-run asset

prices.

Verifying this conjecture requires integrating these two paradigms of asset prices and

their evolution. At one level this is simple. If everything else is held constant

(endowments and preferences), then in the consumption-based asset pricing approach,

prices evolve because beliefs change. Beliefs change because the information available

to individuals about the fundamental value of the assets changes. So, in a very important

sense, these paradigms are alike: both theories analyze the pricing of assets in response

to information flows.

But pushing the information story a little further reveals differences. If individuals

begin with a common prior on asset values and they receive common information (such

as observations of past prices and realized asset payoffs), then nothing changes in the

standard asset pricing theory: there is no role for information-based effects on returns. If

individuals receive differential information, and the economy is in a revealing-rational

expectations equilibrium, then individuals still have common equilibrium beliefs and,

again, nothing changes. But, more realistically, if the equilibrium in the asset market is

not fully revealing, then individuals receiving differential information will have differing

beliefs in equilibrium. Assets may still be priced according to some “market expectation”

as in Lintner (1969), but no individual’s belief will be characterized by this market

expectation. Individuals will have different perceptions of market and idiosyncratic risk,

and they will hold differing portfolios. Now, it is not just fundamental values that matter

34

for asset prices; the distribution of information also matters, just as it does in the market

microstructure literature.

The literature on partially revealing rational expectations, beginning with

Grossman and Stiglitz (1980), shows how differential information affects asset prices.

Admati’s (1985) paper generalized this analysis to multiple assets, and she showed how

individuals face differing risk-return tradeoffs when differential information is not fully

revealed in equilibrium. Wang (1993) showed in a two-asset, multi-period model that

private information causes uninformed traders to demand compensation for the adverse

selection problem they face, but that this effect is mitigated by the reduction in risk

caused by partial revelation of information. Brennan and Cao (1997) use a similar idea to

explain how superior information about home country assets can help explain

international equity flows. Jones and Slezak (1999) use a multi-asset, multi-period

partially revealing rational expectations to show that standard risk-return predictions are

altered in predictable ways. Easley and O’Hara (2001) construct a multi-asset partially

revealing rational expectations equilibrium in which the distribution of information

affects the required rate of return on assets. This analysis shows that if information about

an asset is private, rather than public, then uninformed investors demand a higher rate of

return on the asset to compensate then for the risk of trading with better informed traders.

The market microstructure literature demonstrates that the existence of

differential information has a significant impact on the fine details of short run asset

prices. The literature above shows that theoretically it could also have an impact on long

run asset prices. But does it? A natural approach to answer this question is to measure

35

the extent of differential information asset-by-asset and ask whether this measure of

differential information is priced.

Since information, particularly private information, is not directly observable its

presence can only be inferred from market data—trades and prices. Fortunately, the

microstructure literature provides ways to do this. Both the Kyle λ, from Kyle (1985),

and the probability of information-based trade (PIN), from Easley, Kiefer and O’Hara

(1997b), are measures of the importance of private information in a microstructure

setting. Kyle’s λ measures the responsiveness of prices to signed order flow. It can be

estimated by regressing price changes on signed order flow. PIN measures the fraction of

orders that arise from informed traders. It can be estimated from data on trades. There is

a substantial literature estimating each of these measures and showing that they provide

insights into microstructure phenomena. See Glosten and Harris (1988), Hasbrouck

(1991), Foster and Viswanathan (1993), Brennan and Subrahmanyam (1996), and

Amihud (2000) on the Kyle λ; and, Easley, Kiefer and O’Hara (1996, 1997a, 1997b),

Easley, Kiefer, O’Hara and Paperman (1996) and Easley, Hvidkjaer and O’Hara (2001)

on the probability of information-based trade.

Brennan and Subrahmanyam (1996) and Amihud (2000) argue that stocks with high

λ’s are less attractive to uninformed investors, and they find support for this argument in

transactions data and daily data, respectively. Easley, Hvidkjaer and O’Hara (2001b) use

a structural microstructure model to estimate the probability of information-based trade in

each NYSE common stock yearly for the period 1983 to 1998. They show this

information variable is priced by including it in a Fama-French (1992) asset pricing

regression. Stocks with higher probabilities of information-based trade are shown to

36

require higher rates of return. A difference of 10 percentage points in the probability of

information-based trade between two stocks leads to a difference in their expected returns

of 2.5% per year. These results provide evidence that asymmetric information affects

long- run asset pricing.

There is another role that information may play in long-run asset pricing that does

not fit into the asymmetric information approach discussed above. Merton (1987)

proposes an asset pricing model in which agents are unaware of the existence of some

assets. In Merton’s model, all agents who know of an asset agree on its return

distribution, but information is incomplete in that not all agents know about every asset.

Merton shows that assets with incomplete information have a smaller investor base, and.

with limited demand, these assets command a lower price. In the standard microstructure

approach, all investors know about every asset but information is asymmetric: some

investors know more than others about returns. Both approaches lead to cross-sectional

differences in asset prices due to information, or to the lack of information.

A related literature considers the role of participation constraints on traders (see,

for example, Basak and Cuoco [1998] and Shapiro [2001]). Here the story is that some

traders are prohibited for exogenous reasons from holding certain assets. These

prohibitions may be from lack of knowledge as in Merton, or they could reflect market

imperfections such as suitability requirements or institutional portfolio restrictions that

limit the securities available for investment. Such prohibitions result in the same

structure analyzed in Merton, although potentially for a different reason. This research

also shows that cross-sectional differences can arise in asset returns. Whether these

constraints are actually binding in the market, or even if they are, whether they can be

37

viewed as part of the market microstructure, is debatable.19 But research in this general

area does suggest that the simple story exposited in traditional asset pricing may be too

rudimentary; that features of trade and trading do matter for asset price behavior.

5. Linking Microstructure and Asset Pricing: Puzzles for Researchers

Our contention in this paper is that features of the trading process provide important

insights into short-term and long-term asset price behavior. We have reviewed a wide

range of literature investigating these asset-pricing effects, but the vastness of the area

dictates that many other papers not mentioned here are relevant to this general question.

What has emerged from this survey is cogent and compelling evidence that

microstructure factors affect asset-pricing behavior. But also apparent from our review

are the many puzzles and challenges that impair our understanding. In this final section,

we outline those issues we think most important for future research.

At the top of the list is the role of volume. As we have seen in this survey, volume

appears to play an important role both in the short-run and in the long-run. Numerous

empirical papers find that statistical significance almost magically appears when volume

(or a member of its extended family such as turnover) is added to a regression. But

theory provides few reasons for this significance, and the range of stories advanced to

explain this phenomenon is impressive, but ultimately unconvincing.

Why should volume matter? We believe it is because volume, as with other market

statistics, proxies for features related to price discovery in markets. Thus, the accounting

literature (see, for example, Kim and Verrecchia [1991]) has linked volume to dispersion

19 A related issue is the impact of short-sale restrictions and other market constraints on investing such as margin requirements. These features introduce heterogeneity into the investor pool, and so may also affect cross-sectional asset pricing.

38

of beliefs regarding public information. Blume, Easley, and O’Hara [1994] have

suggested the link is to the quality of private information. Research on dividend

recapture, or portfolio insurance, or “triple witching” days, have pointed to particular

trading strategies as responsible for episodic high volume. We suspect that all of these

theories may be correct, as well as others yet discovered.

A challenge for theoretical researchers is that volume is extremely difficult to work

with mathematically. Unlike prices, which can, at least with some transformations, be

viewed as approximately normally distributed, the distribution of volume is non-normal

and often complex. In the theoretical microstructure literature, traders (and market

makers) learn from watching market data, and it is this learning process that leads to

market efficiency. Yet our models of learning from volume are few, and our consonant

inability to understand volume may follow as a result.

Increased empirical focus on volume may lead to greater insights into its correlation

with other variables, and this in turn may aid our understanding of its role theoretically.

We may also need to think more deeply about the process of price formation, and

recognize that our existing results are based on models that are mathematically tractable,

but not necessarily economically valid.20

The role of information in long run asset pricing is a second puzzle for

researchers. More theoretical work integrating the microstructure and asset pricing

approaches is needed. So far there is no complete analysis in which: asset prices are

determined in a microstructure setting, without the fiction of a Walrasian auctioneer;

traders are fully optimizing, with rational expectations but differential information and

20 Thus, models of behavioral finance in which prices reflect alternative learning structures may yield insights into market statistics such as volume, and into the behavior or short-and long-run asset prices.

39

unrestricted risk preferences; and, prices are fully endogenous, the fiction of an

exogenous value process common in the microstructure literature is dropped. Indeed, one

way to characterize the shortcomings of both fields is to recognize that microstructure

analyzes the transition to a “true” value process, while asset pricing assumes this

transition has occurred (flawlessly) and then investigates what causes the value process to

arise. As we noted earlier in the paper, this dichotomy is unlikely to capture the complex

process of price discovery.

Addressing these shortcomings may require rethinking basic concepts such as risk

and efficiency. In asset pricing, risk relates only to aggregate uncertainty. The

combination of diversification with the presumed efficiency of the price discovery

process negates any importance to asset-specific risk. Is this view too optimistic? In

microstructure models, prices are always efficient with respect to public information, but

this is relatively meaningless; it is the evolution of prices to incorporate private

information that is important. Why then should the same not be true for the market as a

whole? Does it make sense to assume that the overall market is priced “correctly” when

it is so difficult for each individual asset to achieve this state?

One response to this criticism is simply that if markets are not efficient then

profitable trading opportunities will arise. Thus, asset-pricing models have been

supported largely by empirical findings against such profit opportunities. Yet, recent

empirical research is more troubling. Beta seems, at best, mis-priced, the explanatory

power of traditional asset pricing approaches (at least as captured by R2) is now

vanishingly small, and the persistence of momentum all suggest that this base of

empirical support has eroded. Moreover, the limits to arbitrage literature (see Shleifer

40

and Vishy [1997]) argues that heterogeneity may more accurately characterize markets,

undermining further the story that assets can be viewed interchangeably.

Researchers have responded with the search for new and improved factors in asset

pricing, but the theoretical justification for such variables is often lacking. In our view,

the problem is more basic: if asset prices are not always “efficient”, then traders may

face a wide variety of risks in portfolio selection. And foremost among these may be

risks arising from asymmetric information, which can inhibit the ability of simple

diversification strategies to remove asset-specific risks.

More empirical work is needed to determine how robust are the recent findings

that measures of differential information are priced. Microstructure models provide

measures of private information, but these measures are admittedly crude. Both the Kyle

and the PIN measure developed by Easley et al require an exogenous specification of

the periodicity of information events (conveniently chosen to be a day).21 The measure

involves both prices and aggregated quantities, leading to interpretation difficulties due to

a wide range of factors. The PIN measure uses imbalances of buy and sell orders to infer

the population parameters of informed and uninformed traders as well as the probabilities

of new information and its direction. We would be the first to agree that it is surely too

simple a measure to capture all the dimensions of information; that more complex market

statistics might prove more accurate and have greater predictive ability. In our own

research, we are investigating whether integrating ACD-based approaches with our

sequential trade structural model might lead to better specifications of information-based

trading (see Easley, Engle, O’Hara, and Wu [2000]). We are also investigating the cross-

21 Hasbrouck [1999] argues that such a one-day specification is not supported by analyses of actual market data.

41

sectional determinants of PIN, with a view to understanding its correlation with

accounting-based measures.

Another approach that may prove fruitful in understanding how traders view risk

in markets is experimental economics. Research by Boessarts and Plott [1999] for

example, shows that the CAPM does not hold when traders face limited numbers of

illiquid assets. Experimental research by Bloomfield, O’Hara, and Saar [2002] shows

how informed and uninformed traders contribute to the production of liquidity in an

electronic market. Because experimental analyses can “hold constant” other factors, such

research may also suggest ways to deal with the econometric power problem in empirical

long term asset pricing studies noted earlier.

A third puzzle for researchers is the role and importance of liquidity in asset

pricing. Here, the challenges are legion, as even defining liquidity entails controversy.

Nonetheless, liquidity issues seem to be important in a wide range of markets, and for

assets ranging from equities to bonds to derivatives and real estate. Is liquidity best

viewed as a type of tax borne by investors, or is it something more complex, and

potentially more important? Is liquidity time-varying, suggesting that traders need be

concerned with more than the first moment of liquidity? Is liquidity a priced factor,

or are “liquidity” shocks really serving as a proxy for more fundamental disturbances in

the economy?

These questions suggest revisiting the fundamental issue of whether liquidity

effects, per se, are simply too small relative to aggregate shocks to be important in asset

pricing. The argument advanced by Huang [2001] that liquidity matters when investors

cannot borrow seems intriguing, but it seems more likely to provide insights into the

42

liquidity of different classes of assets, rather than the cross-sectional differences within

an asset class. Moreover, the liquidity spillovers between markets that prompt the

infamous “flights to quality” suggest that liquidity issues may be important in a portfolio

context (see Chordia, Sarkar, and Subrahmanyam [2002]). Increased empirical research

on liquidity seems particularly promising in shedding light on these issues.

43

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