Olmo Insider Trading

7/28/2019 Olmo Insider Trading

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Detecting the presence of insider trading via structural break tests

Jose Olmoa,b, Keith Pilbeamb,*, William Pouliotb

aCentro Universitario de la Defensa. Academia General Militar. Ctra. Huesca s/n. 50090

Zaragoza. SpainbCity University, Northampton Square, London EC1V 0HB, UK

This version: 14th March 2011

ABSTRACT

The occurrence of abnormal returns before the unscheduled announcement of price sensitive

information is a potential indicator of insider trading. We identify insider trading with a

structural change in the intercept of an extended capital asset pricing model. To detect such a

change we introduce a consistent timing structural break test (CTSB) based upon a U-statistic

type process. Unlike the traditional CUSUM test, the CTSB test provides a consistent

estimator of the timing of a break in the intercept that occurs across the whole evaluation

period. We apply our test to a rich data set covering 370 price sensitive announcements

relating to FTSE 350 companies. Our test is able to detect potential insider trading far more

reliably than the standard CUSUM test. We also show that the majority of suspected insidertrading takes place in the 25 days prior to the release of market sensitive information.

JEL classification: C14; G11; G12; G14; G28; G38

Keywords: CUSUM tests; ECAPM; Insider trading; Structural change; U-statistics.

*Corresponding author. Tel.: +44 207040 0258; fax: +44 207040 8580

E-mail addresses: [email protected] (J. Olmo), [email protected] (K.S.Pilbeam),

[email protected] (W. Pouliot)

We are extremely grateful to participants at the European Economics and Finance Society

annual conference held at Athens in June 2010 for invaluable comments. In particular, we are

also heavily indebted to an anonymous referee for very helpful advice on an earlier version of

the paper.


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1. Introduction

The detection of insider trading is generally considered to be essential to maintaining the

integrity of the financial system and consequently its detection is given a high priority by the

Securities Exchange Commission (SEC) in the US and the Financial Services Authority

(FSA) in the UK. Recent research of Grgoire and Huang (2009) has analyzed some of the

consequences that insider trading and inside information have on the cost of issuing new equity. In particular, their model indicates that such information can cause the market todemand a higher premium over the risk-freerate of interest on newly issued equity1. As suchfinancial regulators haveincentive to detect such trading and where appropriate prosecute thisform of market abuse.

There are several alternative approaches in the literature to detect insider trading. From a

statistical point of view, Dubow and Monteiro (2006) develop a measure of market

cleanliness based on detecting abnormal stock returns prior to the release of an announcement

of price sensitive information. The authors implement an extended capital asset pricing model

to capture the dynamics of risky returns and use a definition of abnormal returns as the

residuals of the corresponding time series regression. To detect insider trading, they use

bootstrap techniques to approximate the finite sample distribution of the sequence of

abnormal returns before an unscheduled announcement and compare this distribution against

the magnitude of four-day and two-day cumulative returns taken four days before and one

day after the announcement to see if these observations are in the tails of the bootstrap

1In a similar veinVo (2008) has shown thatwhen information of this nature is not disclosedto financialmarkets in a timely fashion the price of equity is positivelycorrelated with thisinformation.


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distribution. This method is further refined by Monteiro et al (2007) to allow for serial

correlation and conditional heteroscedasticity in the data.

Other methods are employed by regulators, for example, the Korea Exchange employs a

market stock price monitoring model combined with a period stock price monitoring model

to detect abnormal transactions. The market stock price model develops two linear

regressions: one for stockprice and the other for trading volume. Both models are used to

detect when prices/volumes deviate from some normal trading range. The period stock price

monitoring model detects variations in cumulative average returns and consists of three

models: a stock price base model, a trading volume base model and a concentration ratio base

model. A more sophisticated model of insider trading is developed by Park and Lee (2010)

who use their model to characterize the time series of stock price returns. To identify insider

transactions using a time series, they assume that information exposed from insider trading at

time t can be determined by a particular mixed strategy AR(1) process which they use to

establish that the return series must follow an ARMA(1,1) process. They develop three

criteria for detecting insider trading and conduct two validation tests.

In this paper, we argue that a natural methodology to detect possible insider trading is to look

at unexpected changes in the idiosyncratic component of capital asset pricing models. In

particular, we claim that the occurrence of insider trading leading to abnormal price

movements will be potentially reflected in sudden shifts in the mean of asset pricing

equilibrium models. Thus, we identify insider trading with a structural change in the intercept

of an extended asset pricing model that, as for the previous authors, includes lags of the

idiosyncratic return and of returns on the market portfolio. However, in contrast to the work

of Dubow and Monteiro (2006) and Monteiro et al (2007) we take a novel view on the


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statistical detection of insider trading. Using their theoretical extended capital asset pricing

model (ECAPM) for pricing the risk premium on a risky asset, we develop a powerful new

statistical test called the consistent timing structural break test (CTSB) which is designed to

detect insider trading prior to the announcement of price sensitive information and,

importantly, we are able to place an approximate timing on the insider trading.

The main advantage of our proposed test is that it can detect possible insider trading in the

run up to the release of price sensitive information compared to the traditional CUSUM test

which proves to be poor at picking up potential insider trading in the lead up to a price

sensitive announcement. Also, compared to the bootstrap technique previously discussed, our

method is more straightforward and less data-dependent since the asymptotic theory of the

test is well known, implying that critical values can be tabulated. As such, by means of

simple critical values it can alert regulators of potential cases of insider trading. The

application of our method to a rich data set covering 370 price sensitive announcements

relating to FTSE 350 companies shows that there is evidence of abnormal returns and

potential insider trading for 92 companies comprising the index. As a by product, we also

show that the majority of suspected insider trading takes place in the 25 days prior to the

release of market sensitive information.

The paper is structured as follows. In Section 2 we discuss how to identify the occurrence of

abnormal returns using an asset pricing model in equilibrium. In Section 3 we develop our

novel test statistic for a structural break in the intercept and relate it to potential insider

trading detection for an extended capital asset pricing model (ECAPM). Section 4 shows via

a Monte Carlo simulation that the statistical power of our CTSB test statistic is significantly

greater than that of the traditional CUSUM test. Section 5 compares the performance of our


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test at picking up potential insider trading cases against a CUSUM test using a confidential

data set relating to the release of 370 price sensitive announcements on FTSE 350 companies

supplied by the FSA. Finally, Section 6 concludes.

2. Detecting insider trading via abnormal returns in equilibrium pricing models

Insider trading can be detected directly by looking at unusual trading volumes in the equities

or derivative markets or alternatively by looking for unusual share price movements prior to a

price sensitive announcement or a combination of the two. In their study, Dubow and

Monteiro (2006) use the pricing approach and examine two kinds of announcements, trading

statements by company issuers and public takeover announcements by companies to which

takeover code applies. The methodology developed by Dubow and Monteiro (2006) and

Monteiro et al (2007) for detecting informed price movements and insider trading defines

abnormal stock returns as:

1[ ] (1)it it t it it AR R E R

whereARitis the abnormal returns,Ritrefers to returns on stocki at time tand 1[ ]t itE R is the

expected return at time t conditional on information up to time t-1. The expected return can

be modelled using time series or cross-section methods. We follow the literature on asset

pricing in equilibrium and describe the dynamics of the expected return via an Extended

Capital Asset Pricing Model (ECAPM) similar in spirit to the above authors model but based

on excess returns given by equation (2):

* * * *

1 1 2 1 3 1[ ] (2)t it mt mt it E R R R R


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where *it

R denotes returns in excess of the risk-free asset ,tR mtR refers to the market return at

time t, and 1 , 2 and 3 are the slope parameters corresponding to the different risk factors.

The use of lagged variables in the model acts as a filter for the presence of serial dependence

in the data.

We argue that a natural methodology to detect possible insider trading is to look for a

positive/negative shift in the mean of the abnormal return sequence caused by a change in the

intercept of the above ECAPM. Theoretically, under a normal functioning of the market and

the standard assumptions on market efficiency the risk premium on a risky asset can be

modelled by the standard CAPM. We assume an extended version of it given by equation (2).

Thus, if there is a positive (negative) price sensitive information that is only revealed to a

reduced group of market participants the price of the stock is bound to increase (decrease) by

a smaller amount than it would be in the case that the information was publicly available.

Figure 1 illustrates the difference for a positive price shock.

Figure 1 The effects of insider trading

Price

QuantityD1

D2D3

Q1

S1

P1P2P3


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Note that unless the company raises more equity its supply curve is fixed at S1. On the other

hand, the demand curve is downward sloping. The D1 curve is the demand curve of

uninformed investors. The equilibrium price determined by P1 corresponds to no insider

trading and defines the return on that asset. In equilibrium the return on the asset can be

expressed by equation (2). If there is a small group of informed traders that decide to trade on

the asset then the new demand curve shifts to the right to D2 implying a new equilibrium

price P2 which is higher than P1 but smaller than the equilibrium price P3 that would prevail if

the inside information were fully publicly available corresponding to demand curve D3. The

return implied by the difference between P2 and the initial price P1, denotedRins, is the sum of

the return produced by trade from uninformed investors, denoted Runi plus an extra

quantitydue to private information and given by the difference between P2 and P1. In

equilibrium, the risk premium on the asset required by uninformed investors is only affected

by the correlation with the market portfolio. Mathematically,

* * * * * *

, , 1 , 1 1 2 1 1 3 1 , 1[ ] [ ] [ ] [ ] (3)ins t uni t t uni t t mt t mt t uni t R R and E R E R E R E R

This result implies that the observed risk premium on the asset affected by insider trading is

* * * * *

1 , 1 , 1 1 2 1 1 3 1 , 1[ ] [ ] [ ] [ ] [ ] (4)

t ins t t uni t t mt t mt t uni t E R E R E R E R E R

in contrast to the no insider trading case, where the risk premium is

* * * * *

1 , 1 , 1 1 2 1 1 3 1 , 1[ ] [ ] [ ] [ ] [ ]. (5)t ins t t uni t t mt t mt t uni t E R E R E R E R E R

The existence of potential insider trading or abnormal price movements can therefore be

detected by unexpected changes in the asset pricing formula in equilibrium. A similar

technique is widely used in the mutual fund industry to uncover assets and portfolios

outperforming the market. The difference in our case is that we aim to detect changes in the

value of the intercept and occurrence of excess returns prior to the announcement of price


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sensitive information. The following section introduces a statistical method to detect

structural breaks in the intercept of linear regression models, and hence of the statistical

version of the ECAPM model given by equation (2).

3. Econometric analysis

The econometric representation of the ECAPM model discussed above is:

* * * *

1 2 1 3 1 , with (6)it mt mt it it it it it R R R R a a

where, following Monteiro et al (2007), the process

2

it is modelled as a GARCH(1,1)

process:

2 2 2

0 1 1 2 1 (7)it it it a

with 0 1 2( , , ) the vector of weighting parameters satisfying certain regularity

conditions. The expected value of the error term it is zero, 1[ ] 0,t itE and the variance is

one, 21[ ] 1.t itE The model makes allowance, however, for a time varying conditional

variance since 2 21[ ] .

t it it E a The estimated abnormal returns are obtained from equation (1).

For the purposes of this paper, we rule out the presence of breaks in , the parameters of the

conditional volatility process, and assume that the process is genuinely changing over time,

depends on past information and can be modelled with the GARCH structure set out in

equation (7). In this framework, we will identify a structural break in the intercept of equation

(6) that occurs before an unscheduled announcement with potential insider trading. In the

presence of these events one would expect to observe an increase in the risk premium of the

risky asset that is not explained by the systematic beta component and is therefore reflected


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by a change in the intercept of model given by equation (2). Consequently, it is important to

construct a test for structural breaks that is able to detect changes only affecting the intercept.

Chow (1960) was one of the first to develop tests for structural breaks in linear regression

models. In particular, he constructed two test statistics capable of detecting a one-time change

in regression parameters at a known time. Work by Brown et al (1975) and Dufour (1988)

extended Chow's test to accommodate multiple changes in regression parameters that may

occur at unknown times. Influential works in the change point detection literature claim,

however, that CUSUM methods are unable to detect changes in the intercept of regression

models, see for example, Maddala (1999) and McCabe and Harrison (1980) who show the

CUSUM tests of Brown et al(1975) have asymptotically low power against instability in the

intercept but not against instability of the entire coefficient vector. An alternative

methodology based on standard econometric testing methods such as likelihood ratio tests

and the asymptotically equivalent alternatives given by Wald and Lagrange multiplier tests is

developed by Andrews (1993) and Andrews and Ploberger (1994). Some of their methods are

optimal in the sense of maximizing power to reject the null hypothesis of no change in the

model parameters. Unfortunately, the optimality only applies to a compact region of the

parameter space and hence these methods are not adequate for detecting changes outside of

this region. Insider trading, on the other hand, is an exercise that usually concerns detection

of anomalies right before the end of the evaluation period.

To overcome the limitations of these methods, and in particular of the CUSUM test, we

propose a novel method to detect insider trading via structural break tests for the intercept of

linear regression models. Our test is based on the use of a U-statistic type process that is

sensitive to detecting changes in the intercept that occur at any time in the evaluation period


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and which after applying a suitable supremum functional provides a consistent estimator of

the timing of the change. Further, this new test can accommodate the presence of weight

functions that can be tuned to have more power against specific alternatives, as for example

in early/late detection. We begin by illustrating the U-statistic type process considered by

Gombay et al(1996). These authors consider the following setting:

Let {Y1, Y2, ... , YT} forT2; 3;...., be a sequence of independent and identically distributed

observations. The interest is in testing for the presence of at most one change in variance at a

distinct but unknown time in the process

*

, 1 * (8)

, *

t

t

t

t tY

t t T

where is the mean of the process, and * are positive constants and the errors t are

independent and identically distributed, with 2[ ] 0, [ ] 1t t

E E , 4[ ] ,t

E and*t is the

timing of the change in the intercept. Assuming that * then the no change in variance

null hypothesis can be formulated as:

H0: *t T

versus the at-most-one change in variance alternative:

HA : 1 * .t T

To test the null hypothesis Gombay et al (1996) use the change in mean framework to

develop a statistic suited to testing for at most one change in the variance. Their process,

reproduced below, compares two estimators of the variance before and after the change:


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[ ](1) 1/ 2 2 2

1 1

1 1( ) (1 ) ( ) ( ) 0 1 (9)

T T

T t t

t t T

M T Y YT T T

where (1)T

M is a U-statistic type process, is the fraction of the sample where the change in

the variance of the process {Yt} occurs and [.] denotes the integer part. One estimator is

fashioned from the first T observations and then compared to the estimator constructed

from the last ( 1)T T observations. After some simple algebra, the above process can be

re-expressed as:

[ ](1) 1/2 2 2

1 1

( ) ( ) ( ) 0 1 (10)T T

T t t

t t

M T Y Y

Gombay et al(1996) substitute the sample mean_

TY of the series tY for , the population

mean, to arrive at:

[ ] _ _(1)

1/2 2 2

1 1( ) ( ) ( ) 0 1 (11)

T T

T Tt T tt tM T Y Y Y Y

This methodology can be extended to a mean process, (Xt), that depends on a vector of

explanatory variables Xt. Let Ytbe

*

* *

( ) , 1 (12)

( ) ,

t t

t

t t

X t tY

X t t T

Further, Gombay et al (1996) explore the use of weight functions to improve the statistical

power of related tests to detect changes in the parameters produced at specific subsamples of

the evaluation period. In particular, they study the following family of weight functions to the

process captured in equation (10):

( , ) {( (1 )) , 0 1/ 2} (13)q


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where q is a weight function, a tuning parameter and is in the interval [0,1].

Olmo and Pouliot (2008, 2011) propose refinements of this method and of the process in

equation (10) to detect structural breaks in risk models, and in the intercept of linear

regression models that are robust to changes in the slope parameters. In this setting, the linear

regression model of interest is the ECAPM discussed in equation (2), that under the

alternative hypothesis of a change in the intercept becomes a piecewise linear regression

model:

(1) '

(2) '

, 1 * (14)

, *

t t t

t

t t t

X t tY

X t t T

where*

Y =R ,t it* * *

t 1 1X (R R R ) 'mt mt it , t defined as in (7),(1) (2) and the error term

satisfies conditions detailed after equation (7).

The null and alternative hypotheses are:

OH : *t T

versus the at-most-one change in intercept alternative

AH : 1 *t T

The task here is to construct a test to detect such deviations and which is robust to the

presence of conditional heteroscedasticity in the data. The U-statistic type process proposed

by Olmo and Pouliot (2008) is:

[ ]

(2 ) 1/ 2 ' '

1 1

( ) ( ) (15)T T

T t T t T

t t

M T Y X Y X

Using this process a test statistic for H0 and a consistent estimator of *t under the alternative

hypothesis can be fashioned. In this context, we are concerned with how large this process


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can be for 0


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Theorems 1 and 2 of Antoch et al(1995) detail the consistency and the limiting distribution

of the above estimator using the weight function q(t/T ,). The critical values of the CTSB

test are obtained from the supremum of the weighted Brownian bridge process introduced

above. Gombay et al (1996) detail the limiting distribution for = 0.5, the asymptotic

distribution has an extreme value distribution from which critical values can be generated by

most standard statistical packages; for values between 0 and 0.5 see Olmo and Pouliot

(2008, 2011).

The test statistic set out in equation (16) can be made robust to changes in the slope

parameter by calculating the statistic using the available data and then estimating *t as in

equation (18). This *t would then be used to estimate two separate slope parameters, one

estimate that is obtained using the estimated version of (15) for t = 1,...., *t and then

estimating (15) again but using data corresponding to t = *t +1,......, T. During this

estimation only one intercept parameter is estimated which can be done with careful use of

slope dummy variables. Using Ferger (2001), it can be shown that the test statistic (16) is

robust to the presence of conditional heteroscedasticity in the data.

4. A simulation of CTSB and CUSUM tests for a one time change in the intercept

In what follows, we explore the statistical properties, size and power of our CTSB test and

the CUSUM test. The section aims to shed some light on the failure of CUSUM type tests to

detect changes in intercept and hence to provide support to the choice of structural break test

methods based on U-statistics and described above. We discuss first the CUSUM method of

Brown et al(1975). This method is based on recursive residuals, standardized appropriately.

In particular, the cumulative sum of recursive residuals is given by:


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( )

2

1(19)

rr

t

t K

W w

where ( )rW is the sum of the first rrecursive residuals2 tw , and is the OLS estimate of the

standard deviation. The test statistic is:

1

( )

1 max

11 21

(20)

k r T

rW

T KCUSUM test

r KT K

The null hypothesis of parameter constancy is rejected whenever this test statistic exceeds

some critical value obtained from the distribution of0 1

sup | ( ) |B

, where ( )B is a

Brownian bridge. Tabulated values of this distribution can be obtained from Orasch and

Pouliot (2004) (cf. Table I). Here, K, refers to the number of parameters in the linear

regression model under estimation. The estimator of the timing of the break *t is detailed by

the following formula:

1

( ) ( )

1 1* min : max1 1

1 2 1 21 1

(21)k r T

r rW W

T K T K CUSUM t r

r K r K

T K T K

The comparison of the standard CUSUM against the test given by equation (17) is done via a

Monte-Carlo simulation for the following model:

2For more information on recursive residuals we refer the reader to Brown et al(1975).


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(1) ', 1 * (22)

(2) ', *

X t tt tYt

X t t Tt t

where is constant and the error termssatisfy the conditions given after equation (7).

For the Monte Carlo exercise considered here, the number of slope parameters Kwas set to 1

in equation (21). As a result of this restriction, the linear regression model considered for this

exercise consisted of an intercept and one slope parameter . Both the

parameters and (1) were set to 1 while (2 ) was set to values 1.25, 1.5, 1.75, 2. Table 1

details the simulated nominal coverage probability of both the CTSB and CUSUM test of

Brown et al (1975) under the null hypothesis of no change in the intercept. As the

significance level was set at the usual 5% level the simulated nominal coverage should

approximate this value. From the table, we observe that both the CTSB and CUSUM

statistics perform well in terms of nominal coverage.

Table 1Nominal coverage

T=75 T=100 T=125

CTSB 0.087 0.079 0.067

CUSUM 0.050 0.029 0.040

The second part of our Monte Carlo experiment consists of comparing the simulated power of

the two tests to detect a one-time change in the intercept for different percentage changes.

This comparison allows a realistic assessment of the ability of the CTSB statistic to detect a

one-time change in the intercept and in particular its ability to pick up the timing of the

change in the intercept. Table 2 tabulates the empirical power for the model set out in


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equation (22) using the same changes in intercept and sample sizes discussed above. The

change in the intercept varies from 25% to 100% in the simulation, while the fraction of the

sample before the break occurs has been set at 5% (early detection), 50% (middle detection)

and 90% (late detection). When it comes to early detection, the CTSB performs better than

the CUSUM particularly as the magnitude of the break becomes larger. When it comes to

middle detection, the CTSB is generally speaking much better than the CUSUM test. Further,

the estimate of * , where** / ,t T based on the CUSUM statistic ranged from a minimum

of 0.5 (25% change in intercept and T = 75) to a maximum of 0.923 (100% change in

intercept and T= 125). This emphasises the inconsistency of the CUSUM estimator for the

change fraction, , which should be near 0.5 for a one-time change in intercept that occurs in

the middle of the sample. We see that the CTSB estimator of * had smaller variability and

was much closer to 0.5, especially for moderate to larger sample sizes; the estimator was

0.491 when T=125 and there was a 100% change in intercept. For a change late in the

sample, the CTSB has higher empirical power than the CUSUM test across sample sizes and

models explored under the alternative hypothesis. In particular, for a 100% change in

intercept and T= 125 the power of the CTSB statistic is 0.574 and that of the CUSUM test is

0.077. Also, the estimator of * based on the CTSB statistic estimates the break fraction to

be 0.766 which is much closer to the true value of (0.9) than the CUSUM that estimated

the break fraction to be 0.476. The latter result is consistent with the lack of power of the

CUSUM method.

Overall, this small simulation experiment clearly shows the outperformance of the CTSB

method to detect structural breaks in the intercept of linear regression models compared to the

standard CUSUM technique. The following section illustrates these results with a financial

application to detect insider trading from return data on companies trading on FTSE 350.


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5. Empirical application to FTSE 350 companies return series

We now use our CTSB estimator to detect potential insider trading activity. Our confidential

data set consists of 370 price sensitive announcements relating to FTSE 350 companies

supplied by the Financial Services Authority with 251 return observations per company per

announcement and standardization of the announcement on the 250th day3. We only have

information concerning the timing of the announcement but not on the nature of this

announcement or the name of the company under study. The number of announcements (370)

implies that for some companies there is more than one announcement.

Table 3 shows equation (6) parameter estimates for five of the 370 series in the available

sample. The results show that the ECAPM model performs well at explaining the return

series. The residuals of the different series are well behaved. Unreported results show that the

coefficients corresponding to the conditional volatility process in equation (7) are not

statistically significant. The results for the rest of series under study are similar to those

reported in Table 3.

3We are very grateful to the FSA for supplying us with this dataset. The dataset covers 370price sensitive announcements on FTSE 350 companies relating to the period 2000 to 2006.

In order to maintain complete confidentiality, the series does not name any of the companies,

the nature of the price sensitive announcement which could be due to a reporting of profits, a

takeover bid, a profit warning or some other price sensitive announcement.


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Table 2 Empirical power, timing estimates and intercept changes

Early detection * 0.05

| (2 ) 1.25 | (2 ) 1.5 | (2 ) 1.75

Statistic T=75 T=100 T=125 T=75 T=100 T=125 T=75 T=100 T=125 CTSB 0.091 0.081 0.059 0.09 0.086 0.105 0.093 0.123 0.175

CTSB *

0.407 0.407 0.404 0.410 0.392 0.377 0.384 0.362 0.314

CUSUM 0.050 0.080 0.088 0.103 0.163 0.196 0.251 0.305 0.427

CUSUM *

0.446 0.464 0.444 0.486 0.481 0.480 0.499 0.513 0.514

Middle detection * 0.5

CTSB 0.098 0.095 0.149 0.273 0.432 0.504 0.644 0.800 0.920

CTSB *

0.406 0.405 0.416 0.423 0.452 0.461 0.468 0.479 0.484

CUSUM 0.047 0.061 0.078 0.136 0.205 0.254 0.366 0.459 0.626

CUSUM *

0.502 0.523 0.570 0.673 0.717 0.761 0.809 0.847 0.886

Late detection * 0.9

CTSB 0.089 0.064 0.084 0.096 0.105 0.110 0.146 0.203 0.281

CTSB *

0.382 0.403 0.415 0.427 0.473 0.530 0.526 0.594 0.642

CUSUM 0.042 0.044 0.043 0.052 0.044 0.043 0.039 0.054 0.051

CUSUM *

0.224 0.224 0.179 0.227 0.242 0.186 0.252 0.324 0.238

Note.Numbers in rows CTSB and CUSUM show the empirical power of the test, while numbers in rows CU

estimated timing of the structural break.


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Table 3 Typical parameter estimates from the ECAPM model

* * * *

1 2 1 3 1it mt mt it it R R R R

Series 1 2 3

1 -0.002

(0.001)

0.490

(0.129)

0.139

(0.066)

-0.290

(0.131)

2 0.006

(0.001)

0.258

(0.104)

0.205

(0.060)

-0.070

(0.106)

3 -0.002

(0.001)

0.399

(0.177)

0.018

(0.063)

0.013

(0.178)

4 -0.001

(0.001)

0.454

(0.139)

0.266

(0.062)

0.140

(0.142)5 0.000

(0.001)

0.660

(0.108)

0.021

(0.063)

-0.032

(0.116)

Note. Standard errors are in parenthesis.

After fitting the regression model given by equation (6) we compute for each series the test

statistic given by equation (17) with the parameter set at 0.5, and the CUSUM test of Brown

et al(1975) for the full dataset N=250. The latter test detects 35 series where there is at least

one break in the abnormal return sequence. However, 18 of these appeared early in the

sample period in the region of 0 to 0.2 and there were no detections after 80% of the sample

size showing that the test is unable to pick up structural breaks when insider trading is most

likely to be prevalent in the run up to a price sensitive announcement. By contrast, using the

CTSB test for=0.5 we obtain 92 breaks in the data with 38 of these breaks occurring after

0.9 indicating potential insider trading in the 25 day run up to the price sensitive trading

announcement.

We argue that given the decisive timing of the break, these are cases that merit further

investigation for insider trading practices. To gain further insight on the timing of these late


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rejections and see their statistical reliability we have also computed 95% confidence intervals

using the bootstrap method described in Antoch et al (1995). The results suggest that from

these 38 potential cases there are 4 cases in which the confidence interval indicates that the

rejection is right before the announcement. For the remaining 34 cases the uncertainty in the

abnormal returns makes the precise timing of the rejection inconclusive4. Table 4 summarizes

these results for the 4 significant cases.

Figure 2 The CUSUM versus CTSB for detecting insider trading, N=250

4Bootstrap confidence intervals cannot be computed for the CUSUM of Brown et alsincethe method does not satisfy the assumptions in Antoch et al(1995). This represents another

advantage of using statistical tests based on equation (15).


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Table 4 Bootstrap exercise for N=250, M=10,000 replications

Series 9 17 32 61

Timing of

rejection

248 248 245 248

95% bootstrapc.i.

[240,248] [239,248] [241,246] [234,248]

This table reports four cases where the CTSB test was able to time the structural break with a

high degree of confidence. In other cases, there was greater uncertainty in the timing of the

structural break confidence intervals. The upper limit of the interval is 248, indicating that

with a 95% confidence interval the occurrence of the abnormal return is before the

announcement.

To analyze the effect of the tuning parameter, we repeated the exercise for different test

statistics, we report in particular=0 (unweighted test statistic), that we compare against

=0.5 which empirically proves to be optimal for detecting the breaks in the data. Figure 3

reports these results and illustrates the findings by Worsley (1983) that discusses the lack of

power of unweighted CUSUM type test statistics to detect breaks near the tails in linear

regression models. The weight function defined by =0.5 seems to be empirically much better

suited in this insider detection framework.


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Figure 3 The empirical effects of different values of the tuning parameter, N=250

Some of these timings, especially those corresponding to early detection of potential insider

trading, can be due to considering the entire trading year for our analysis5. To check the

robustness of our results for smaller sample sizes we have repeated our method for different

sample sizes corresponding to six and three months before the announcement. The exercise is

more challenging due to the lower number of observations in the sample. Nevertheless, as

shown in our results reported in Figures 4 and 5 for sample sizes 125 (6 months of the trading

year) and 63 (3 months of the trading year) the CTSB method is still able to detect structural

breaks for relatively small sample sizes.

5Since time of the announcement can be any day during the trading year, the early detectionsin the 250 day trading year are unlikely to be January effect observations. This is further

confirmed in our 6 month and 3 month tests, where we have removed the first 125 and 187

observations and still find significant cases of early detection.


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The results of these two experiments confirm our previous findings on the existence for some

companies of potential insider trading right before the occurrence of relevant announcements.

For the CTSB test, both sample sizes of 125 and 63 observations yield results similar to those

reported for the sample size of 250. We observe a slight overall decrease in the number of

abnormal returns as the sample size decreases. Interestingly, for the change in the sample size

from 250 to 125 this decrease occurs in late detection while for sample sizes 125 to 63 the fall

is in early detection. The decrease in detection of potential insider trading cases can be due to

a fall in statistical power of the test as the sample size decreases or a true decay due to there

being less actual breaks when the data set is decreased. Concerning the CUSUM test, for a

sample size of 125, the test still shows some power for early detection but continues to fail at

late detection. For the sample size of 63, the CUSUM test became infeasible due to the lack

of meaningful observations necessary to invert the relevant matrix to compute the recursive

residuals.

Figure 4 The CUSUM versus CTSB for detecting insider trading, N=125


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Figure 5 The CTSB for detecting insider trading, N=63

For completeness, we also carried out a further bootstrap exercise for those companies later

in the sample to obtain confidence intervals for the timing of the structural break. We were

able to get reasonable confidence intervals for four companies for the timing of the rejection

which are reported in Table 5. Interestingly, for sample sizes 125 and 63, three of the four

companies with less uncertainty in the timing of the rejection are the same as in the 250

sample size case. The confidence intervals were robust to the choice of the sample size in the

sense that they report very similar results, however they widened with the smaller sample

sizes. The intervals suggest that the timing of the detection is fairly close to the

announcement.


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Table 5 Bootstrap exercise for N=125 and N=63. M=10,000 replications.

N=125

Series 9 17 32 237

Timing of

rejection

248 247 246 249

95% bootstrap

c.i.

[239,250] [238,249] [234,249] [239, 250]

N=63

Series 9 17 32 237

Timing of

rejection

248 246 245 249

95% bootstrap

c.i.

[230,249] [231,248] [231,248] [237,249]

6. Conclusions

The occurrence of abnormal returns before unscheduled announcements is usually identified

with insider trading. Of course, not all price movements before the release of price sensitive

market announcements are solely due to the effect of insiders attempting to make a profit

from inside information, there are other factors, such as, market manipulation, large position

taking prior to an announcement and liquidity in the particular share that can cause the

structural break in the data. By giving a fairly precise timing of the structural break our CTSB

test can alert regulators to potential cases worth investigating. Also, because the statistical

method relies on price movements, the effects of unusual derivative trading by insiders can

also be examined as these ultimately impact upon the price of shares more than on trading


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volume6. Finally, the GARCH structure that we have adopted enables us to distinguish cases

of potential insider trading even in periods of changing market volatility.

We have shown that the presence of potential insider trading can be detected by running

structural break tests for the intercept of an extended capital asset pricing model. Our

procedure which requires a change in the intercept of the regression model yields a number of

possible abnormal price movements meriting investigation for insider trading. More

importantly, our test statistic enables us to check for potential insider trading over an

extended trading range rather than be limited to say an evaluation of trading volumes in the

five days run up to an announcement. Our test statistic based upon a U-statistic type process

has a considerable advantage over the CUSUM test since it has more power to detect changes

that occur over the entire evaluation period. Furthermore, the CTSB has far more statistical

power and accuracy in detecting the timing of a structural break than the CUSUM test.

Another advantage of using the CTSB test is that it proves to be quite robust and effective

with smaller sample sizes.

Further research could include the detection of timing for more than one break in the

intercept during the evaluation period and also combining breaks in the price data with

information from trading volumes as well as information from changes in the volatility

process.

6 Insider traders may well use derivatives markets such as call and put options so as tomaximise the leverage on their trades. Such derivatives activity will affect the price of the

underlying shares. It is for this reason that looking at volumes of trades on a share is an

unreliable guide to insider trading activity and why regulators increasing look at abnormal

price movements.


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