Information Diversity and Complementarities in Trading and Information Acquisition

• DOI: http://doi.org/10.1111/jofi.12226
• Published date: 01 August 2015
• Date: 01 August 2015

THE JOURNAL OF FINANCE •VOL. LXX, NO. 4 •AUGUST 2015

Information Diversity and Complementarities

in Trading and Information Acquisition

ITAY GOLDSTEIN and LIYAN YANG∗

ABSTRACT

We analyze a model in which different traders are informed of different fundamentals

that affect the security value. We identify a source for strategic complementarities

in trading and information acquisition: aggressive trading on information about one

fundamental reduces uncertainty in trading on information about the other funda-

mental, encouraging more trading and information acquisition on that fundamental.

This tends to amplify the effect of exogenous changes in the underlying information

environment. Due to complementarities, greater diversity of information in the econ-

omy improves price informativeness. We discuss the relation between our model and

recent financial phenomena and derive testable empirical implications.

SECURITY PRICES REFLECT INFORMATION available to traders about future pay-

offs. Uncertainty about these payoffs typically involves multiple dimensions.

Obvious examples include multinational firms, for which there is uncertainty

originating from the different countries where the firm operates, and conglom-

erates, for which there is uncertainty about the different industries the firm

operates in. More generally, even focused firms are exposed to multiple dimen-

sions of uncertainty: cash flows depend on the demand for firms’ products and

the technology they develop, on firms’ idiosyncratic developments and the way

they are affected by the macroeconomy or the industry, and on the success of

firms’ operations in traditional lines of business and in new speculative lines of

∗Itay Goldstein is with Wharton School, University of Pennsylvania and Liyan Yang is with

Joseph L. Rotman School of Management, University of Toronto. This paper was previously cir-

culated under the title “Information diversity and market efficiency spirals.” We thank the Editor

(Bruno Biais) and three anonymous referees for constructive comments that have significantly

improved the paper. We also thank Efstathios Avdis, Bradyn Breon-Drish, Henry Cao, Pierre

Chaigneau, Alex Edmans, Vincent Glode, Richard Kihlstrom, P´

eter Kondor, Albert “Pete” Kyle,

Doron Levit, Igor Makarov, Konstantin Milbradt, Tarun Ramadorai, Bart Taub, Dimitri Vayanos,

Xinli Wang, Kathy Yuan, and audiences at the Georgia Tech Finance Seminar, the HEC Montreal

Finance Seminar, the Maryland Smith School Finance Seminar,the Princeton University Finance

Seminar,the Purdue Finance Seminar, the Rutgers Finance Seminar, the Virginia McIntire School

Finance Seminar, the Wharton Finance Seminar,the 2012 Adam Smith Asset Pricing Conference

(Oxford, the United Kingdom), the 2012 EFA Annual Meeting (Copenhagen, Denmark), the 2012

SED Annual Meeting (Limassol, Cyprus), the 2012 Tel Aviv Finance Conference (Tel Aviv, Israel),

the 2013 NFA Annual Meeting (Quebec City, Canada), and the 2013 WFA Annual Meeting (Tahoe,

the United States) for comments and suggestions. Yangthanks the Social Sciences and Humanities

Research Council of Canada for financial support.

DOI: 10.1111/jofi.12226

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1724 The Journal of Finance R

business. In the modern world, information is so complex that traders tend to

have a comparative advantage or specialize in different types of information.

The price of the security is then based on the trading activities of the different

types of informed traders, reflecting the overall expected value of the security

given the information in the market.

A key question in understanding the workings of financial markets is what

is the nature of interaction between the different types of informed traders.

Suppose that people informed about one dimension of uncertainty trade more

aggressively on their information or that there is more information produced

on this dimension of uncertainty. Does this encourage people with expertise on

other dimensions to trade more aggressively on their information and produce

more information, or does it deter them from doing so? If the former holds, then

there is strategic complementarity between the different groups in trading on

their information and producing information. If the latter holds, then there is

strategic substitutability between these differentially informed groups. There

is long-standing interest in the literature in understanding mechanisms for

strategic complementarity versus substitutability in financial markets, since

complementarities are generally thought to amplify shocks, whereas substi-

tutabilities are thought to attenuate them.

In this paper, we address these questions using a model in the spirit of

the seminal work of Grossman and Stiglitz (1980). In particular, we extend

their setting to include two dimensions of uncertainty about the payoff from

the traded security, say, the technology of the firm and the demand for its

products. We first consider an economy in which traders are endowed with

different types of information; for example, some traders are informed about the

technology and others are informed about the demand for the firm’s products.

As in Grossman and Stiglitz (1980), traders are risk averse, and trade in a

market with uninformed traders and noisy supply. We then extend the model

to endogenize the decision to produce information. Finally, we allow traders to

become informed about the two dimensions simultaneously.

Consider the trading stage and suppose that the size of the group of

technology-informed traders increases. Will this cause traders informed about

product demand to trade more or less aggressively on their information? The

presence of more technology-informed traders implies that more of their in-

formation will get into the price. When they trade, demand-informed traders

condition on the price of the security (as is typically the case in the Grossman-

Stiglitz framework), and hence the information in the price affects their trading

decision. The additional information about technology has two opposite effects

on how demand-informed traders trade on their own information. First, the

increased technology information in the price reduces the uncertainty that

demand-informed traders have to face concerning technology issues when they

trade, which causes demand-informed traders to trade more aggressively on

what they know without being exposed to risks they do not understand. This

is the “uncertainty reduction effect,” which favors strategic complementarities

in trading on different types of information. Second, the additional informa-

tion about technology in the price also makes demand-informed traders use

Complementarities in Trading and Information Acquisition 1725

the price more to infer the level of the fundamental of technology. This will

make demand-informed traders trade less aggressively on their own informa-

tion. More specifically,suppose demand-informed traders have a positive signal

about the demand for the firm’s product, which causes them to take a large

long position. But, holding the price constant, when the price contains more

information about technology, a strong demand fundamental implies a weak

technology fundamental, and thus demand-informed traders will scale down

their positions, trading less aggressively on their information. We call this ef-

fect the “inference augmentation effect,” and we note that it favors strategic

substitutability in trading. Overall, when the uncertainty reduction effect dom-

inates the inference augmentation effect, trading on one type of information is

a complement to trading on the other type of information.

It is important to note that strategic complementarities do not arise naturally

in most models of financial markets.1In particular, the uncertainty reduction

effect that we identify here as a source of strategic complementarities is muted

in traditional models in the literature that have one dimension of uncertainty

(these models go back to Grossman and Stiglitz (1980) and Hellwig (1980)).

Indeed, it appears that such an effect is consistent with many financial phe-

nomena in recent years. For example, as uncertainty about the macroeconomy

and government policy was growing, commentators argued that traders were

pulling out of the market in an attempt to limit their exposure to risks not

within their range of expertise. Traders, who traditionally trade on informa-

tion concerning traditional aspects of the activities of financial institutions and

other firms, appear to have become concerned about other dimensions that

might be driving these institutions’ cash flows, such as their exposure to both

more exotic assets and counterparty risks (as in the motivation for the recent

paper by Caballero and Simsek (2013)). Since these traders do not know much

about such dimensions, the uncertainty involved with trading the securities

of these institutions induced traders to pull out of the market, not even trad-

ing on the information they had. We therefore find that, once it becomes more

difficult to obtain information on one dimension of uncertainty from the price,

traders reduce their trading on information they may have involving other di-

mensions of uncertainty. This is the complementarity that might lead changes

in the underlying informational environment to have large effects.

The result of trading complementarities has important implications for mar-

ket outcomes in our model. For example, in equilibrium, trading on the two

types of information is complementary to each other when the trading inten-

sity on one dimension of uncertainty is relatively close to the intensity on the

other dimension of uncertainty. As a result, we find that the diversity of infor-

mation in the economy improves the overall amount of information revealed

by prices. That is, fixing the total mass of informed traders, an economy with a

diverse information structure—that is, with a greater balance between the two

1There is a growing literature on sources for complementarities in financial markets. In Section

V, we discuss a few papers that are closely related to ours in that they consider different types of

information/fundamentals.