ABSTRACT
 
Developing equity markets xutfer from thinness of
trading problems that is the low frequency with
which securities are traded on the markets. Thin
trading poses the non-synch onous trading problem A
nor synchronous trading problem arises when market
index at time t is based on stocks with!ith closing
prices at time that does not synchronise with the
measurement time of market at t Any estimate of
returns and systematic risk of individual stocks or
portfolios based on index with thinly traded stocks
will he incorrectly measured and the use of biased
beta estimates will!ill seriously affect the
usefulness of studies on securities markets This
paper addresses the problems of non-synchronous
trading and estimation of betas adjusted or thin
trading of security prices on KLSE over the period
1975 to 1989 The findings show that beta measure of
individual securities using OLS is biased by thin
trading However the Dimson-Fowler-Rorke (DFR) beta
estimated individual securities using 2 lead/lag
spec if specification tends to mitigate the effect
of thin trading bias on portf olio basis the OLS
beta is smaller in value than the OLS and DFR beta
for individual securities implying that securities
ities research esearc in thinly traded markets using
portfolio approach might not necessarily require e
adjustment for thin trading bias
 
INTRODUCTION
 
Developing equity markets suffer from different
degrees of thinness of trading, that is the low
relative frequency with which securities are traded
on the markets.  The Kuala Lumpur Stock Exchange
(KLSE) is no exception. Securities Markets research
based on thinly traded stocks can pose some
problems.  Research on thin trading suggests that
the normality assumption in returns generating
models is not met in returns data generated by
thinly traded stocks.
 
Thin trading poses the non-synchronous trading
problem. A non-synchronous trading problem arises
when the market index at time t is based on stocks
with closing prices at time t l or t 2 or anytime
that does not synchronise with measurement time of
market at t. Any estimate of returns and Systematic
risk of individual stocks or portfolios based on an
index wit thinly traded securities will be
incorrectly measured In general thinly traded stocks
will have underesti mated beta and returns, whereas
actively traded stock will have overestimated beta
and returns. Beta coef ficient measures the
volatility of the stocks returns vis-a vis the
market returns. Beta may be defined a the slope of
the regression of the stocks returns on the market's
returns.  The use of biased beta estimate will
seriously affect the usefulness of studies on
securities markets.
 
The issue of non-trading bias has been discussed in
the financial literature [(Scholes and William
(1977), Dimson (1979), Sinclair (1981), Dimson an
Marsh (1983), Fowler and Rorke (1983), Cohen
Hawawini, Maier, Schwartz and Whitcomb (1983 Ariff
(1987) and Ariff and Justin Lim (1989)] an several
solutions to correct the bias have been suggested.
For example, Ariff (1987) and Ariff and Justin Lim
(1989) has suggested that given a reasonably large
data set, the Dimson's method with FowlerRorke's
corrections is feasible for estimating unbiased
betas in thinly traded markets.
 
Dimson (1979) suggested that the effect on non
trading bias can be corrected by specifying a market
model with lags and leads in a time-series and
aggregating the resulting beta coefficients to
obtain the appropriate value of unbiased beta
estimate. For example, the b for stock j at time t =
0, is estimated as follows:
 
* bø = b-t = bø + b+'
 
J , J
 
The number of lags and leads required in Dimson ' s
model is determined by the convergence of the
aggregated betas to the expected value of one.
Fowler and Rorke (1983) explained that the beta
coefficients in the Dimson's procedure should be
corrected by weighting the betas with serial
correlations in the market returns to provide
consistent and unbiased estimators.  Dimson's market
model (Equation A) specified in time series
illustrates that beta measure is given by the
aggregated amount of the beta values.
 
(A) Rjt = at + Bjt L (Rmt L) + ... Bit g (Rmt g) +
B,t (Rmt) + Bit+l (Rmt+L) + + Bit+n (Rmt+n)
 
 
Fowler and Rorke (1983) suggest corrections to
individual beta coefficients using weights (W) in
the Equation A above, as follows:
 
(B.) BDFR = Wt Bt + wt. l Bt L + wt. 2 Bt 2 +
 
+ Wt+L Bt+L + Wt+2 Bt+2 +
 
The subscriptj has been intentionally let out from
equation B to simplify the formula. BDFR is the
corrected systematic risk measure from the
DimsonFowler-Rorke (DFR) model. The BDFR is unbiased
and consistent relative to BOLS (BOLS is the
systematic risk measure using Ordinary Least Square
method).
 
This paper intends to address the problem of non
synchronous trading and the estimation of betas ad
justed for thin trading of security prices on KLSE
over the period 1975-1989. Dimson (1979, 1983),
Sinclair (1981), Ariff (1987) and Ariff and Justin
Lim (1989) have provided evidence that thinness in
trading produces biased estimates of the
beta-metric.
 
The presence of this bias will be confirmed if the
aggregate value of beta for all returns exceed
unity. The issue of biased betas is specifically
addressed by comparing the values of betas estimated
by Ordinary Least Squares (OLS) and by the
Dimson-FowlerRorke (DFR) approach on 244 listed
firms.
 
In a thinly traded market, the average OLS beta for
all securities is expected to be greater than DFR
beta.  The value of DFR beta should approach unity.
It is also expected that the value of OLS beta for
thinly traded securities is lower than for actively
traded securities.  This paper also intends to
compare the average OLS beta for portfolios with the
average OLS beta for individual stocks. If the
average OLS beta for portfolios is smaller in value
than the average OLS beta for individual securities
and the former approaches unity, it will imply that
research on security prices in thinly traded markets
using the portfolio approach need not necessarily
adjust the beta for thin trading bias.
 
DATA AND METHODOLOGY
 
The data for this study is drawn from monthly price
relatives of 244 stocks traded on KLSE over the
period 1975 to l989. The price relatives are
adjusted for capitalisation changes and dividends.
 
In estimating the DFR beta, a 2 leads and 2 lags
model is arbitrarily chosen as prescription on
priors is difficult to state. For example, the BDF,{
for stock j on day 0 is estimated as follows:
 
(C) *Bjø= W2 (Bj 2) + W1 (Bj t) + Bjø
 
+ W1 (Bj+t) + W2 (Bj+2)
 
(D) Rit = at + Bj 2(Rmt 2) + bj ' (Rmt 1)
 
+ Bj ø(Rmt) + Bj+'(Rmt+L) + B+2(Rmt+2) + lit
 
(E) Rmt = rO + r 2 (Rmt 2) + r t (Rmt L) + Ut
 
 
Equation E gives the weights (W) for correcting the
beta coefficients as follows ows:
 
(F) W1= 1 +2P,+p2 I +2pl +2P2 (G) 1 + rt + r2 1 + 2
rt + 2r2
 
Superscripts - I and + I in equation C refers to the
first period lag/lead specification and superscripts
-2 and +2 refers to the second period lag/lead
specification. r is the serial correlation
coefficient and r, refers to the first order serial
correlation between Rm, and Rm, l and r, refers to
the second order serial correlation between Rm, and
Rm, 2.
 
To ascertain the difference in value of average OLS
portfolio beta and average OLS beta for individual
stocks, all individual stocks were sorted to form
portfolios with the lowest frequency of trading
(this having most biased estimation error) to the
highest frequency of trading. Ten portfolios were
formed and the aggregate OLS beta for each portfolio
and the average beta for all portfolios are
computed.
 
RESULTS
 
The results from the average aggregate OLS and DFR
beta for the period 1975 to 1989 are shown in
Appendix I and the findings are summarised in Table I 
below.
 
The OLS market beta measures the extent of non
synchronous bias in the market. The deviation from
expected beta of unity for the market is 17.9
percent over the whole test period. Thus it is
obvious that the market model measure has too
serious an estimation bias for the beta metric to be
useful in research.
 
The DFR beta with 2 lead/lag tends to regress
towards unity but is not equal to one (I.l()). This
confirms the findings of earlier studies on other
developing markets [Arit'f (1987) and Ariff and
Justin Lim (1989) on the Stock Exchange of Singapore
(SES)I that the use of methods that correct for thin
trading bias drives the market beta asymptotically
towards the true value of unity. It is possible that
an increase in lagging/leading (for example 3
leads/lags) periods using DFR approach might result
in a better adjustment for thin trading bias.
 
The results for the aggregate value of portfolio
betas are summarised in Table 2. The results show
that the value of OLS betas for thinly traded
portfolios are lower than betas of frequently traded
portfolios.
 
However, the OLS estimate of the market's beta from
a portfolio approach (beta=0.97)is inconsistent with
OLS estimate of market's beta of all individual
securities (beta = 1.17). in fact, the OLS estimate
of the market's beta from portfolios approach unity
and is smaller in value than the DFR estimate of
market's beta of all individual securities (beta =
1.10). This suggests that research on securities in
a thinly traded market using portfolio approach need
not necessarily adjust systematic risk measure for
the thin trading bias.
 
CONCLUSION
 
Systematic risk measure of individual securities on
KLSE are biased by the thin trading bias. However
the DFR beta estimate for individual securities
using two lead/lag specification tends to regress
towards unity, thus mitigating the effect of thin
trading bias on the systematic risk measure.  The
OLS estimate of market's beta from the portfolios
approach tends to regress towards unity and is
smaller in value than OLS and DFR average beta for
individual securities, implying that securities
research using the portfolios approach in a thinly
traded market might not necessarily require
adjustment for thin trading bias in the systematic
risk measure.
 
 
REFERENCES
 
Ariff, M. (1987). "The Effects of Thinness of
Trading on Market Parameter in Singapore Equity
Market", Singapore Management Review, 9(2): pp.
40-46
 
Ariff, M., and Lim, K. M. (1989). " Methods
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Ariff, M., and Johnson, L. W. (1990). securities
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Cohen, K. J., Hawawini, G. A., Mailer, S. F.,
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Dimson, E., and Marsh, P. (1984). "An Analysis of
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Fowler, D. J. and Rorke, C. H. (1983). "The Risk
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Scholes, M., and Williams, J. (1977). "Estimating
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