A BIAS‐CORRECTING PROCEDURE FOR BETA ESTIMATION IN THE PRESENCE OF THIN TRADING

• Date: 01 March 1989
• Author: Vijay M. Jog,David J. Fowler,C. Harvey Rorke
• Published date: 01 March 1989
• DOI: http://doi.org/10.1111/j.1475-6803.1989.tb00098.x

The Journal of Financial Research • Vol. XII,

No.1.

Spring 1989

ABIAS-CORRECTING PROCEDURE FOR BETA ESTIMATION IN

THE

PRESENCE OF THIN TRADING

David J. Fowler

York University, Ontario, Canada

C. Harvey Rorke

Deceased

Vijay M. Jog

Carleton University, Ontario, Canada

Abstract

In this paper, an alternative technique is developed for obtainingconsistent estimates of

beta in the presence of thin trading. The new estimator is tested on simulated data and the

results are compared with those obtained from the Dimson [4] Scholes and Williams [9] tech-

niques. The new estimator is found to have approximately the same bias as the others, but it

has a considerably lower variance.

I. Introduction

That beta estimates are biased in markets characterized by thin trading is well

documented [1, 2, 4, 7, 8, 9]. Techniques designed to reduce this bias are based on

econometric techniques utilizing observed returns and are essentially limited-informa-

tion estimators. The trade-offs among the different techniques are between (1) the

bias and efficiency of the estimators; and (2) the computational complexities and in-

formation requirements of the econometric procedures.

Two of the techniques (Dimson [4], Scholes

and

Williams [9]) involve the aggre-

gation of leading and lagged beta estimates calculated from measured returns to ar-

rive at consistent beta estimates. Another, by Cohen, Hawawini, Maier, Schwartz,

and Whitcomb (CHMSW) [1], is based on an analytical model

that

describes the

structure of returns in terms of market "frictions" and relies on a series of regressions

using observed returns to obtain asymptotic estimates of beta. Afurther technique,

suggested by Marsh [8], involves observing the index on exactly the same day as the

trades occur for the thinly traded security, thus synchronizing the index to the trading

events of the security before the beta is calculated using standard OLS procedures.

The procedure developed in this paperfor achieving a consistent betaestimate is also a

statistical approach,

but

security-specific information (in the form of a frequency dis-

tribution of trades within the differencing period) is required to implement

it.'

This paperwas funded jointly by the Social Sciences and Research Council and the Financial Research

Foundation, both of Canada. The authors are indebted to Professor M. Brennan for comments on another

paper

that

inspired this work.

IAll the methods described except CHMSW implicitly or explicitly assume

that

observed prices are

equilibrium prices. This may not be true with thinly traded securities. The violation of this assumption,

however, is probably not very significant. In thinly traded securities, observed prices are usually "out-of-

23