Nonfundamental Speculation Revisited

• Author: LIYAN YANG,HAOXIANG ZHU
• Date: 01 December 2017
• Published date: 01 December 2017
• DOI: http://doi.org/10.1111/jofi.12548

THE JOURNAL OF FINANCE •VOL. LXXII, NO. 6 •DECEMBER 2017

Nonfundamental Speculation Revisited

LIYAN YANG and HAOXIANG ZHU∗

ABSTRACT

We show that a linear pure strategy equilibrium may not exist in the model of

Madrigal (1996), contrary to the claim of the original paper. This is because Madri-

gal’s characterization of a pure strategy equilibrium omits a second-order condition. If

the nonfundamental speculator’s information about noise trading is sufficiently pre-

cise, a linear pure strategy equilibrium fails to exist. In parameter regions where a

pure strategy equilibrium does exist, we identify a few calculation errors in Madrigal

(1996) that result in misleading implications.

MADRIGAL (1996)PRESENTS AND SOLVES A MODEL IN WHICH a “nonfundamental

speculator” observes superior order flow information that allows him to partly

infer the insider’s fundamental information. This type of behavior remains

highly relevant today.For example, many investors and regulators suspect that

high-frequency traders and other proprietary trading firms obtain valuable

information about investors’ order flows and profit from it.

However, the equilibrium solution by Madrigal is only partially correct. This

note reports and corrects the errors in his original paper, using his original no-

tation. Contrary to the claim of the original paper, a pure strategy equilibrium

may fail to exist in Madrigal’s model. Moreover, a few calculation errors in

Madrigal (1996) result in misleading implications for some market outcomes,

such as market liquidity and price discovery in the early period. Section Iof this

note reproduces Madrigal’s (1996) model and states the correct characterization

of a linear pure strategy equilibrium. Section II.A proves the nonexistence of a

pure strategy equilibrium if the speculator’s information is sufficiently precise.

Section II.B corrects the calculation errors when a pure strategy equilibrium

exists and discusses the implications for market outcomes.

I. The Setup of Madrigal (1996) and Characterization of a Pure

Strategy Equilibrium

Madrigal (1996) considers a two-period Kyle (1985) model with one risky

asset. The risky asset has a liquidation value given by a random variable

∗Yang is with the Rotman School of Management, University of Toronto and Guanghua School

of Management, Peking University. Zhu is with the MIT Sloan School of Management and NBER.

We thank the Editor (Bruno Biais), the Associate Editor, and two anonymous referees for helpful

comments. Yangthanks the Bank of Canada and Social Sciences and Humanities Research Council

of Canada (SSHRC) for financial support. The views expressed herein are not necessarily those of

the Bank of Canada and are the authors’ alone. The authors have read the Journal of Finance’s

disclosure policy and have no actual or perceived conflicts of interest to disclose.

DOI: 10.1111/jofi.12548

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