Does the Probability of Informed Trading Model Fit Empirical Data?

Published date01 February 2017
Date01 February 2017
The Financial Review 52 (2017) 5–35
Does the Probability of Informed Trading
Model Fit Empirical Data?
Quan Gan
The University of Sydney
Wang Chun Wei
Macquarie Investment Management, Macquarie GroupLimited
David Johnstone
The University of Sydney
The probability of informed trading (PIN) is used widely as a measure of information
asymmetry. Relatively little work has appeared on how well PIN models fit empirical trade
data. We revealstructural limitations in PIN models by examining their marginal distributions
and dependence structures represented by copulas. We develop a distribution-free test of the
goodness-of-fit of PIN models. Our results indicate that estimated PIN models have generally
poor fit to actual trade data. These results suggest that researchers should be cautious when
PIN estimates are plugged into empirical models as explanatory variables.
Keywords: PIN, dependence structure, copula, mixture model, Rosenblatt’s transformation,
goodness-of-fit test
JEL Classifications: C52, G14
Corresponding author: Discipline of Finance, The Universityof Sydney, Sydney 2006, Australia; Phone:
+61 2 91140831; Fax: +61 2 93516461; E-mail:
We are grateful to AndrewPatton, Stephen Satchell, Takeshi Yamada, Wai-Man(Raymond) Liu, the Edi-
tor Richard Warr,and one anonymousreferee for their valuable suggestions. The paper was presented at
the 8th Nordic Econometric Meeting, 2015 Asian Finance Association Annual Conference, 8th Interna-
tional Conference on Computational and Financial Econometrics, and research seminars at the Australian
National University.We thank the participants for their helpful comments and suggestions.
C2017 The Eastern Finance Association 5
6Q. Gan et al./The Financial Review 52 (2017) 5–35
1. Introduction
The probability of informed trading (PIN) is used widely to measure informa-
tion asymmetry in trading activity. PIN was originally developed by Easley, Kiefer,
O’Hara and Paperman (1996) and modified by Easley,Hvidkjaer and O’Hara (2002)
(hereafter EHO-PIN). Estimates of PIN are obtained by fitting a structural model
of buyer-initiated trades (buys) and seller-initiated trades (sells). Trade data do not
explicitly reveal informed or uninformed trading. Instead, the PIN is inferred statis-
tically from the characteristics of the observed trades.
Empirical studies commonly take PIN estimates as explanatory variables in
regressions and other models.1However, these studies rarely present the underlying
PIN parameter estimates or offer any indication of the quality of model fit. Instead
PIN is effectively taken as a black box. Given that such reliance on PIN is common,
we set out to examine PIN models in terms of both their structural properties and
their ability to fit empirical data.
Some recent studies cast doubt on the robustness of PIN as an informed trading
proxy. Moharam and Rajgopal (2009) show that while PIN does predict future re-
turns in EHO’s sample, it is not robust to alternativespecifications and periods. They
find no direct relationship between PIN and the implied cost of capital, contrary to
propositions in the previous literature, and conclude that it is questionable whether
PIN truly reflects information asymmetry. Aktas, de Bodt, Declerck and Van Op-
pens (2007) study PIN around merger and acquisition announcements and find that
PIN estimates do not seem to accord with the evidence of information leakage and
informed trading during the pre-event periods. They argue that PIN fails to capture
informed trading because it considers only market orders, while informed traders
may often use limit or hidden orders.
The veracity of PIN is bound to depend on how well the PIN model captures the
behavior patterns (arrival and trade direction) of the different trader subpopulations.
A valid model should exhibit good empirical fit with the characteristics of actual
Although PIN is adopted widely in the literature, few studies consider the
aspects of its empirical fit. Duarte and Young (2009) show that EHO-PIN dictates
a negative correlation between buys and sells, and yet most stocks on the NYSE
exhibit positive correlation. To correct for this inconsistency, Duarte and Young
(2009) propose a modified PIN model (hereafter DY-PIN) in which they introduce
a positive liquidity shock that simultaneously impacts buy and sell order flows. An
important characteristic of DY-PIN is that it produces positively correlated numbers
1These studies include, but are not limited to, the following: analyst coverage (Easley, O’Hara and
Paperman, 1998), stock splits (Easley, O’Hara and Saar,2001), initial public offering underpricing (Ellul
andPagano, 2006), firm credit ratings (Odders-White and Ready, 2006), put-call ratios (Pan and Poteshman,
2006), seasonality effects (Kang, 2010) and cross-sectional returns (Easley,Hvidkjaer and O’Hara, 2002).

To continue reading

Request your trial

VLEX uses login cookies to provide you with a better browsing experience. If you click on 'Accept' or continue browsing this site we consider that you accept our cookie policy. ACCEPT