Informed Trading and Intertemporal Substitution

• Author: YIZHOU XIAO
• Published date: 01 April 2020
• Date: 01 April 2020
• DOI: http://doi.org/10.1111/jofi.12857

THE JOURNAL OF FINANCE •VOL. LXXV, NO. 2 •APRIL 2020

Informed Trading and Intertemporal

Substitution

YIZHOU XIAO∗

ABSTRACT

I examine the possibility of information-based trading in a multiperiod consumption

setting. I develop a necessary and sufficient condition for trade to occur.Intertemporal

substitution introduces a desire to correlate current consumption with future aggre-

gate shocks. When agents have heterogeneous time-inseparable preferences, infor-

mation differentially affects relative preferences for current and future consumption,

making information-based trading mutually acceptable. The no-trade result contin-

ues to hold if there is no aggregate shock, or if agents have either homogeneous or

time-separable preferences.

EACH DAY WE OBSERVE A significant volume of trades in the markets. The no-

trade theorem, however, has established that when the market is complete for

all endowment shocks and agents are rational and share the same prior beliefs,

it is impossible to generate trades for purely informational reasons, even in the

presence of asymmetric information.1Because the no-trade theorem serves as

a key benchmark in financial economics, understanding its scope is important.

In this paper, I extend the original single-period consumption no-trade model

to multiperiod consumption settings and identify intertemporal consumption

smoothing as a mechanism that generates information-based trading.

Dynamic consumption extensions are possibly the most natural way to check

the robustness of results in a single-period consumption model. In the no-trade

literature, however, dynamic consumption extensions are widely believed to be

trivial. Because consumption in different periods can be treated as different

goods in agents’ consumption bundles, common sense suggests that when the

market is complete across all endowment shocks, any multiperiod extension

∗Yizhou Xiao is with the CUHK Business School, Chinese University of Hong Kong. I am

especially grateful to Paul Pfleiderer, Bradyn Breon-Drish, Peter DeMarzo, and TimothyMcQuade

for their invaluable support and advice. I also thank the editor (Philip Bond), the anonymous

associate editor, and two anonymous referees for their valuable suggestions that substantially

improved the paper. For helpful comments and stimulating discussions, I also thank Anat Admati,

Jaroslav Borovicka, Alberto Teguia, Steven Grenadier, Zhiguo He, Peter Koudijs, Ilan Kremer,

Hanno Lustig, Paul Milgrom, Andrzej Skrzypacz, Robert Willson, Liyan Yang, and audiences at

various seminars and conferences. Any errors that remain are mine. I do not have any potential

conflicts of interest to disclose, as identified in The Journal of Finance’s disclosure policy.

1In the no-trade literature, the state of the world can be decomposed into two components.

One component includes events that directly affect agents’ endowments or preferences. The other

component compromises signals that have no direct real effect on endowments but may influence

agents’ beliefs. No-trade theorems work when the market is complete for all endowment shocks.

DOI: 10.1111/jofi.12857

C2019 the American Finance Association

1135

1136 The Journal of Finance R

should be isomorphic to a corresponding single-period case with an appropri-

ately defined consumption bundle. Thus, while researchers have considered

many explanations for trade, such as heterogeneous beliefs, liquidity trading,

and market incompleteness in endowment states, dynamic consumption gen-

erally has not been considered.

In this paper, I show that dynamic consumption extensions are nontrivial for

two reasons. First, in addition to trading for mutual insurance across endow-

ment shocks, agents trade to smooth their consumption over time. Concerns

about intertemporal substitution incentivize agents to correlate their current

consumption with future shocks. Second, a dynamic consumption extension im-

poses natural constraints on feasible allocations through ex-ante trading. The

nature of time suggests that all securities are measurable to information filtra-

tion, and hence no security can pay different amounts of current consumption

based on the realizations of future endowment shocks, even when the market

is complete across all endowment shocks. As a result, agents are not able to

correlate their current consumption with future shocks through ex-ante trad-

ing. Information-based trading, however, maybe mutually acceptable because

it enables agents to adjust their consumption profiles based on additional infor-

mation about future shocks. These adjustments allow agents to achieve some

allocations that are infeasible ex-ante.

I study a simple exchange economy with multiperiod consumption and agents

with Epstein-Zin-type preferences. I characterize a necessary and sufficient

condition for trade to occur in dynamic consumption environments. Indeed,

concerns about intertemporal substitution fail to generate trades under only

three scenarios. In the first case, without future aggregate risk, agents

hold the same position in all future endowment states, and hence, the re-

alization of future states becomes irrelevant. In the second case, all agents

have time-separable utility functions. With time-separable preferences, each

agent’s marginal utility on current consumption is independent of her future

consumption, and her optimal allocation does not vary across future states.

When agents have standard time and state-separable preferences (Milgrom

and Stokey (1982), Tirole (1982)), the no-trade theorem holds in dynamic con-

sumption environments. In the last case, agents have homogeneous preferences

that lead them to smooth consumption in the same way, resulting in no gains

from trade.

Given the Epstein-Zin-type preferences in the baseline model, one may won-

der whether the trades are driven by nonexpected utility preferences. To ad-

dress this concern, in Section III.B, I study a simple example with habit for-

mation preferences. Habit formation preferences are dynamically consistent,

are state-separable, and belong to the family of expected utility (EU) functions.

I show that concerns about intertemporal substitution continue to generate

trade because habit formation preferences are time-inseparable.

This paper contributes to the literature on information-based trading. Be-

ginning with Aumann (1976), a series of no-trade theorems challenged the

commonsense intuition of information-based trading (Kreps (1977), Grossman

and Stiglitz (1980), Milgrom and Stokey (1982), Tirole (1982), Blume, Coury,