Trading under uncertainty about other market participants

• Published date: 01 May 2023
• Author: Dimitris Papadimitriou
• Date: 01 May 2023
• DOI: http://doi.org/10.1111/fire.12333

DOI: 10.1111/fire.12333

ORIGINAL ARTICLE

Trading under uncertainty about other market

participants

Dimitris Papadimitriou

King’s Business School, King’s College, London,

UK

Correspondence

Dimitris Papadimitriou,King’s Business School,

King’s College, LondonWC2B 4BG, UK.

Email: d.papadimitriou@kcl.ac.uk

Fundinginformation

AlexanderS. Onassis Public Benefit

Foundation

Abstract

I present an asymmetric information model of financial mar-

ketsin which there is uncertainty and learning not only about

fundamentals but also about the proportion of informed-

to-noise traders in the market. Extreme news leads to an

increase in both types of uncertainty, while it decreases

price informativeness. Uncertainty about the market com-

position constitutes a type of liquidity risk and is associated

with high expectedreturns. The resulting price–volume rela-

tionship is U-shaped and positively sloped. In a dynamic

extension of the model I show that this mechanism gener-

ates momentum as well as history-dependent volatility and

price informativeness.

KEYWORDS

asymmetric information, market composition, noise trading, price

informativeness, volume

1INTRODUCTION

Throughout the history of financial markets, there have been numerous occasions where investors were puzzled by

an extreme price movement (EPM). Black Monday,the flash crash of 2010, or the more recent flash rally episode of

2014 in the US Treasurymarket are a few such examples. A common theme in many of these instances was investors’

uncertainty about the cause and the informational content of these large price movements.

Most papers in the finance literature try to explain such phenomena using models that assume that traders know

the degree of rationality of other investors inthe market. More recently,models with additional dimensions of uncer-

tainty havebeen explored, yielding many new and interesting insights. However, eventhese models fail to fully capture

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and

reproduction in anymedium, providedthe original work is properly cited.

© 2023 The Authors. The Financial Review published by WileyPeriodicals LLC on behalf of Eastern Finance Association.

Financial Review. 2023;58:343–367. wileyonlinelibrary.com/journal/fire 343

344 PAPADIMITRIOU

the ways that investors use prices to learn about their marketenvironment and hence miss one important part of the

trading activity.In this paper, I instead take the perspective of sophisticated investors (“hedge funds”) who are uncer-

tain about the proportion of informed—compared to noise—traders in the market, and I study a mechanism through

which they can use equilibrium quantities to learn about the composition of the market.

I, thus, contribute to the growing literature on nonlinear equilibria in a number of ways. First,I establish that uncer-

tainty about market composition—a term I will use interchangeably with “uncertainty about the proportion of informed

traders”—increases when there is an extrememarket outcome (e.g., a crash). Second, I show that the variation in mar-

ket composition constitutes a type of risk, unrelated to fundamentals, for which investors demand higher expected

returns. Third, I find that during a crash traders rely less on cash flow news to update their expectationsabout future

payoffs. Fourth, using a simple dynamic model, I show that this mechanism can be responsible for momentum and

history-dependent volatility and informativeness of prices. Finally,the model generates a price–volume relationship

that fits well with the relevant stylized facts established in the empirical literature.

The model consists of three types of agents: hedge funds, informed investors, and noise traders. Hedge funds act

as rational uninformed investors who are using the information in prices to make their portfolio choices. Informed

traders can be thought of as insiders who hold information about payoffs and trade based on it. Noise traders are

the irrational investors in the market, who tradeeither on the basis of erroneous information or based on sentiment

shocks. Funds areuncertain about whether they are trading against both types of traders, thus making their inference

problem much more challenging. The intuition behind the learning process is simple: when the size of the price signal

is high, the probability that the rest of the traders are of the same type is also high, and thus under some general

conditions, uncertainty regarding the number of informed traders increases.

My first result is that market crashes (and booms) make hedge funds more uncertain about both the market

composition and the fundamentals. This is because such extreme outcomes are actually very informative about the

belief dispersion of investors in the market; in the limit, they can only occur when all investors behave in the same

way—in other words, when investors are either all informed or all noise. However, these two cases lead to very

different interpretations of the price movement; in the first case, its informativeness is the highest possible, while

in the latter, it should be completely ignored. Thus, assuming there is no further way to distinguish between the

two cases (symmetry assumption), fund managers become less confident about how to interpret the price and their

uncertainty about fundamentals increases. Therefore, I find that during a crash, the risk premium part of the price

increases.

The main intuition of the above mechanism can be explained using an illustrativeexample. Assume that there are

only two investors in the market, who are either of type A or type B, and who receive (normally distributed) payoff

signals sAor sB, depending on their type. Now consider a third person who observes a mixture 

sof their signals (i.e, 

sis

the average signal). If both types are A,thensimply 

s=sA;ifbothareBthen 

s=sB. If one is Aand the other is B,then



s=1

2sA+1

2sB.IfsAand sBhave the same distribution, then var[1

2sA+1

2sB]<var[sA]=var[sB]. Therefore, observing a

very large 

s(in absolute value), should make the observer believethat either both investors are of type A, or they are

both of type B. Now if signals sAand sBcarry very different informational content (e.g., Abeing informed and Bnoise),

then the observer who sees a large 

swould subsequently become more uncertain about its informational value and

would demand a higher risk premium to participate in the market.

Another important result is that expected returns are increasing in the uncertainty about the marketcomposition.

Forexample, a market with fewer sources of information is naturally perceived to have a lower degree of belief disper-

sion and is associated with a higher variation in the ratio of informed-to-noise traders. As described above, managers

who try to interpret the information contained in prices are less confident about their interpretation. This constitutes

atype of risk, which they anticipate, and hence, when the market is dominated by hedge funds, this uncertainty is trans-

lated into a higher expected return on the asset. One way to interpret such type of risk is to identify it as the variable

component of liquidity risk, which has been found to predict higher returns (Sadka, 2006).

Furthermore, I analyze the effect of this uncertainty on the sensitivity of price to signal. I show there is an asym-

metry in the sensitivity of prices to positive and negative shocks, which gets amplified as the uncertainty about the