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Information-Adjusted Noise Model: Evidence ofInefficiency on the Australian Stock MarketVikash Ramiah a & Sinclair Davidson ba Senior Lecturer, School of Economics, Finance, and Marketing , RMIT University ,239 Bourke Street, Melbourne, Victoria, 3000, Australia Phone: 61-3-9925-5828 Fax:61-3-9925-5828b Professor of Institutional Economics, School of Economics, Finance, and Marketing , RMITUniversity , 239 Bourke Street, Building 108, Melbourne, Victoria, 3000, Australia Phone:61-3-9925-5869 Fax: 61-3-9925-5869Published online: 05 Dec 2007.

To cite this article: Vikash Ramiah & Sinclair Davidson (2007) Information-Adjusted Noise Model: Evidence of Inefficiency onthe Australian Stock Market, Journal of Behavioral Finance, 8:4, 209-224, DOI: 10.1080/15427560701698926

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The Journal of Behavioral Finance Copyright C© 2007 by2007, Vol. 8, No. 4, 209–224 The Institute of Behavioral Finance

Information-Adjusted Noise Model: Evidence of Inefficiencyon the Australian Stock Market

Vikash Ramiah and Sinclair Davidson

We describe the interaction between noise traders and information traders. We do notassume that information traders are error-free. Instead information traders make mis-takes leading to under-reaction and over-reaction. Information traders may even addto pricing errors in the market. These interactions are captured in our information-adjusted noise model. We test our model using data from the Australian Stock Ex-change. This market has a continuous information disclosure regime that allows us todetermine when information is released to the market. We present evidence consistentwith the notion that the market is often informationlly inefficient.

keywords: Information traders, Noise Traders, Informational efficiency

In this paper we describe the interaction betweeninformation traders and noise traders. Unlike much ofthe behavioral finance literature, we do not assume thatinformation traders necessarily return markets to fun-damental values. Information traders trade on the basisof information but may well make errors in interpret-ing that information. Noise traders trade in the absenceof information. Information traders may well correctthe pricing errors introduced by noise traders—thisis just one of the outcomes we describe. On the otherhand, information traders may undercorrect or overcor-rect noise errors. This gives rise to either underreac-tion, or overreaction. Furthermore, information tradersmay make similar errors to noise traders and add topricing errors on the market and not reduce those er-rors. The interaction between information traders andnoise traders is not likely to be one of informationtraders mechanistically correcting pricing errors; ourInformation-Adjusted Noise Model (IANM) capturesthose subtlies.

The Australian Stock Exchange provides an idealtesting ground for our model. The ASX has a con-tinuous disclosure regime where firms are required toimmediately disclose any price relevant information tothe market. Our model requires us to “predict” when in-formation traders are likely to be active on the market.We make the assumption that noise traders are con-tinually active in the market, but information traders

Vikash Ramiah Senior Lecturer, School of Economics, Finance,and Marketing, RMIT University, 239 Bourke Street, Melbourne,Victoria, 3000, Australia. Tel: 61-3-9925-5828; Fax: 61-2-9925-5986; Email: vikash.ramiah@rmit.edu.au

Sinclair Davidson Professor of Institutional Economics,School of Economics, Finance, and Marketing, RMIT Univer-sity, 239 Bourke Street, Building 108, Melbourne, Victoria, 3000,Australia. Tel: 61-3-9925-5869; Fax: 61-3-9925-5986; Email:sinclair.davidson@rmit.edu.au

only trade when information comes to the market. Byobserving firms making information disclosure we candetermine when information traders are likely to betrading. We present evidence that the ASX is often in-formationally inefficient. Over our sample period wefind the efficient markets hypothesis (EMH) is violatedon 62.98% of days. The most common violation oc-curs where information traders add to pricing errors.The second most common violation of information ef-ficiency is underreaction.

In the second section we describe our model, thethird section contains our empirical estimates and thefourth section outlines our conclusions.

Information-Adjusted Noise Model

This section sets out the intuition of the information-adjusted noise model and an empirical analogue of themodel. It will also provide a brief differentiation be-tween the efficient market hypothesis in Modern Fi-nance Theory and the efficient market hypothesis inBehavioral Finance theory.

We define information traders as individuals whoform expectations on the basis of information and tradeon those expectations. We do not assume that informa-tion traders are omniscient or that they always formthe correct expectations. Our definition of informationtrader is broader than Shefrin and Statman’s [1994]definition. They define an information trader as some-one whose subjective beliefs coincide with objectiveprobabilities. To our minds this is an ex post defini-tion of information traders and is likely to occur bychance. Our definition is that traders base their ex-pectations on information but do not always interpretthat information correctly. In other words, informationtraders can make mistakes. Noise traders do not employinformation to form their expectations and may trade

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RAMIAH AND DAVIDSON

for any number of reasons. Information traders onlytrade in a particular stock when value relevant infor-mation has been released to the market. Noise traders,however, can and will trade in any stock on any day.Imagine that on any given day, t, information may bereleased to the market or not. On those days when nonew information comes to market, noise traders willtrade amongst themselves. On days that information isreleased to the market an information event (IE) oc-curs, and both noise traders and information traderstrade. On days that information is not released to themarket, only noise traders trade—information tradersdo not enter the market.

The Modern Finance Theory EMH states that thereshould be no behavioral errors on the market. In otherwords, the expected value of any behavioral error giventhe information set, should be zero, E(BEt|�t) = 0.The expected change in the behavioral error, givena change in the information set, is a random fore-cast error, E(�BEt|��t ) = ε. In terms of Behav-ioral Finance, a market is behaviorally efficient whenE(BEt|�t) �= 0, but

∑∞i=1 BEit = 0.1 The IANM mod-

els the random forecast error as follows:

� BEit = α + β IEit + εit (1)

Where �BEit = is the change in the behavioral errorfor stock i on day t. IE = an information event, i.e., thearrival of news. We treat this variable as a dummy =1on days information is released to the market, and = 0when no information is released to the market. We donot differentiate between “good” or “bad” news. α =the mean change in the behavioral error attributable tonoise traders. β = the proportion of the mean changein behavioral error attributable to information traders.We assume β �= 0.

The IANM has the advantage over other noise tradertype models by being able to isolate the impact ofnoise traders and information traders. In particular, avariable mu (µ = α + β) reflects the mean changes inbehavioral error caused by noise traders and informa-tion traders. If the Modern Finance Theory EMH istrue, then α + β = µ = 0 and �BEit = ε. If we re-lax the assumption the Modern Finance Theory EMHis true, then α + β = µ �= 0. We exploit this relation-ship in order to differentiate between different types ofpotential market inefficiencies. In an efficient marketinformation traders would quickly correct noise traderspricing errors. This contrarian investment strategy im-plies α = −β.

Noise Trader Risk on Non-information Days

On non-information release days, IEit = 0, theIANM will take the following form:

� BEit = α + εit (1.2)

If alpha is zero, then market efficiency does not change.To the extent alpha is not zero the market becomes be-haviorally inefficient. We define a positive alpha asPure Noise. In this situation, noise traders are increas-ing stock market inefficiency and distorting prices. Thisargument is consistent with the large literature2 sup-porting the notion that traders may drive prices awayfrom fundamental values. A negative alpha could beinterpreted as a “Friedman effect.” Noise traders inthis situation are trading “as if” they were informationtraders. By reducing the BE, noise traders are tradingin the “correct” direction and “returning” the marketto fundamental values.

Noise Trader Risk on Information Days

On the days that information is released, IEit = 1,the model will take the form of Equation (1). A sig-nificant beta indicates that noise traders and informa-tion traders have differential impacts on the market.Beta shows the impact of information traders on thechange in behavioral errors and it will show whetherinformation traders increase or decrease the changesin behavioral errors. The interaction of noise tradersand information traders will determine the change inBE on any particular day. Finance theory indicates thatinformation traders should follow contrarian strategiesto noise traders. To the extent that this does in factoccur α + β = 0.

Inefficient Markets

UnderreactionEdwards [1968] uses the concept of conservatism

to explain underreaction. Conservatism means that hu-man beings slowly adjust their beliefs with respectto new information. Cutler et al. [1989], Andreassen[1987], Jegadeesh and Titman [1993], Rouwenhorst[1998], Chan [1996] and many others3 demonstratethat underreaction occurs. Our model explains under-reaction as follows: The market does not clear all er-rors. Information comes to the market and informationtraders realize that the market is trading at noisy lev-els, and trade to reduce these errors. The informationtraders trade in the “correct” direction, but fail to elimi-nate the errors. This underreaction can be differentiatedinto two components, positive underreaction U (+) andnegative underreaction U (−).

The first type of underreaction is positive under-reaction, i.e., U (+), and it will occur when alpha ispositive and mu is positive as well. There is an erroralpha caused by noise traders, and information traderstrade to reduce this error. They fail, however, to elimi-nate the error, and α + β = µ > 0.

When alpha is negative (i.e., α < 0, a Friedmaneffect) information traders will reduce this error by apositive beta amount. To the extent that information

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INFORMATION-ADJUSTED NOISE MODEL

traders fail to eliminate the error a negative mu willremain.

The conditions that are required for U (+) to prevailon the market can be written as µ, α > 0 and β < 0.The conditions for U (−) can be written as µ, α < 0and β > 0.

OverreactionFrank [1935], Griffin and Tversky [1992], De Long,

Shleifer, Summers and Waldmann (DSSW) [1990] andOdean [1998] wrote about the consequences of over-confidence and show that overconfident traders overre-act. In our model, overreaction will occur when infor-mation traders adopt a Contrarian Investment Strategyand while trading in the “correct” direction, overesti-mate the magnitude of the errors. Information traderswill move prices away from fundamental values. Thisoverreaction can be differentiated into two compo-nents, positive overreaction O (+) and negative over-reaction O (−).

Negative overreaction occurs when noise traders areincreasing noise levels (α > 0) and while informationtraders following a CIS overestimate the magnitude ofthe errors. Initially the errors are at alpha level andare decreased by beta (which is a greater amount thanthe initial noise) leading to a negative mu (α + β =µ > 0). Positive overreaction is the converse situationwhere the alpha was negative and information tradersovercompensate leading to a positive mu (α + β =µ > 0).

The conditions for negative overreaction can bewritten as α > 0, µ < 0 and β < 0. On the other hand,positive overreaction will prevail if α < 0, µ > 0 andβ > 0.

Information Pricing Error (IPE)A serious type of market error occurs when infor-

mation traders fail to adopt a CIS and so increase thenoise level in the market. Under these conditions bothalpha and beta will have the same sign. We refer tothis type of error as Information Pricing Error (IPE).Similarly to overreaction and underreaction there canbe two types of Information Pricing Error, which willdepend on the sign of alpha. IPE will occur when infor-mation traders copy noise traders’ trading technique.They behave as noise traders and add to the existingerrors.

Positive IPE, IPE (+), occurs when both alpha andbeta are positive. As alpha and beta are of the samesign, information traders have failed to adopt a CIS.Consequently, the noise level in the market is increased(α + β > 0). Negative Information Pricing Error, IPE(−), occurs where alpha is negative and informationtraders fail to adopt a CIS (α + β < 0).

For IPE (+) to occur, α and β > 0 and for IPE (−)α and β < 0.

Table 1. Summary of Market Effects

Effects α β µ

Underreaction U(+) > 0 < 0 > 0U(−) < 0 > 0 < 0

IPE IPE (+) > 0 > 0IPE (−) < 0 < 0

Overreaction O (+) < 0 > 0 > 0O (−) > 0 < 0 < 0

Summary

Studying the component parts of Equation (1) itis possible, on information days, to identify variousmarket effects. For the market to be behaviorally ef-ficient mu should not be statistically significantly dif-ferent from zero. On those days that it is significantlydifferent from zero it is possible to identify variouseffects, namely, underreaction, overreaction and IPE.This framework develops a new method of testingwhether the market is behaviorally efficient. It is nowfeasible to check the hypothesis just by testing if muis statistically different from zero. If mu is not statisti-cally different from zero, it will be possible to concludethat the market is free from errors and thus the marketis efficient. In the event that mu is different from zero,this will give rise to either one of the following effects,underreaction [U (+) or U (−)] or overreaction [O (+)or O (−)] or Information Pricing Error [IPE (+) or IPE(−)]. Table 1 summarizes all the different conditionsthat are required for any of the above effects to hold.

Data and Empirical Results

The major challenge in testing the IANM is in deriv-ing the behavioral error, and the subsequent changesin behavioral error. In this section, we make use ofthe CAPM and differing market indices to derive ameasure of that error. We then collect data on informa-tion releases and relate those information events to thechanges in our measure of behavioral error.

Misspecified CAPM

As the CAPM does not allow for noise traders, it willgenerate biased estimates. In other words, according toShefrin and Statman [1994], the CAPM beta will have anoise trader risk component and an efficient beta (i.e.,the behavioral beta). Equation (2) shows the excessreturn CAPM.

r̃it − r̃f t = φi + βci [r̃mt − r̃f t ] + ε̃it (2)

where r̃it is the asset i’s return at time tr̃f t is the risk free return at time t

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RAMIAH AND DAVIDSON

r̃mt is the return on the market at time tε̃it is the error termφi is the intercept of the regression equation

(E(φi) = 0)βc

i is the CAPM beta

The CAPM beta (βci ) is misspecified and Equa-

tion (2) can be rewritten to include noise trader risk(NTR). Equation (3) decomposes the CAPM beta intotwo components namely the efficient beta (βB

i ) and theBehavioral Error (BEi). For the purposes of our discus-sion, we refer to Equation (3) as the Behavioral AssetPricing Model (BAPM).

r̃it − r̃f t = φi + (βB

i + BEi

)[r̃mt − r̃f t ] + ε̃it (3)

where r̃it , r̃f t , r̃mt , ε̃it , and φi are defined as per Equa-tion (2)

BEi is the Behavioral Error, and is expected tobe highly correlated with noise trader risk.

βBi is the efficient beta, i.e. free from noise

trader risk(βB

i + BEi) is the CAPM beta βCi

The Behavioral Error can be defined as the differ-ence between the CAPM beta and the BAPM beta.Equation (4) shows the relationship between the effi-cient beta and the CAPM beta.

BEi = βCi − βB

i (4)

Equation (4) implies the BAPM beta is lower than theCAPM beta by the amount of the behavioral error,which is consistent with Shefrin and Statman [1994].

The CAPM beta can be easily estimated using OLSand Equation (2). The behavioral beta, however, is noteasily estimated. Shefrin and Statman [1994] providesome guidance in this regard. They argue that a BAPMshould use a different proxy for the “true” market port-folio. Hence the BAPM is similar to the traditionalCAPM (Equation (2)), with the exception that a dif-ferent market portfolio proxy is used. This behavioralproxy should capture the noise traders’ investment uni-verse and be composed of stocks they prefer. Anotherway of looking at this is to say that the BAPM isa model based on “sentiment.” Lee, Jiang and Indro[2002] show that excess returns are contemporane-ously positively correlated with shifts in sentiment.Brown [1999] investigates a direct measure of investorsentiment using data from the American Association ofIndividual Investors Sentiment Survey. Unfortunatelysuch data are not available in Australia.

Data

The data used in the tests were taken from DataS-tream. All listed firms were initially considered forinclusion in the study. Firms that were delisted, sus-pended, “died” or where no dividend data could bedownloaded were removed from the sample. The dailydata cover the period June 22, 1998 to December 31,2002. There were 90 firms that passed the above test;of the 90 firms studied, 46 were selected for furtheranalysis. Data collection and data entry are very longand costly processes, and as a result only a subset(46 firms) of the 90 companies was investigated. Pastannouncements4 on each of these individual stockswere downloaded from the Australian Stock Exchange(ASX) on a daily basis for the period 1999-2002. Inaddition the Dow Jones Interactive database and LexisNexis database were used to investigate the dates theseitems were reported in the media. In essence the testshere can be considered as semi-strong tests of the EMH.Noise Trader Risk was calculated for the periods of2000-2002, 2000, 2001 and 2002.

The exclusion of the remaining firms may have re-sulted in survivorship bias and could probably con-stitute a downward bias in the beta estimates. This,however, would impact on both the CAPM and BAPMestimates equally and the quality of the results wouldnot be affected.

Construction of the Behavioral Index

An index that is often employed in the media to de-note sentiment is the “Mums and Dads” Index (MDI)developed by Commonwealth Securities (CommSec).We employ this sentiment index as our proxy for thebehavioral index. The MDI contains just 10 stocks5

that are either household names (and some blue-chipcompanies) or have been subject of demutualizationor privatizations. The component stocks are: AMP,Commonwealth Bank, Coles Myer, IAG (ex NRMA),Qantas, Suncorp Metway, TAB, Tabcorp, Telstra andWoolworths. The index got its name as it provided en-try point to the share market for many small investors.CommSec constructed this index in 1999 to track theperformance of shares held by retail investors.

In order to replicate the MDI, data for the con-stituent stocks was downloaded from DataStream. Thedaily market prices (and number of shares) for the 10firms were downloaded for the period June 22, 1998 toDecember 31, 2002 with the former as the base period.From June 22, 1998 to August 7, 2000, the index con-sisted of only nine stocks, as IAG was not listed duringthat period. All 10 stocks were included for the periodAugust 8, 2000 to December 31, 2002. The inclusionand exclusion of stocks in indices is a problem allindices face and MDI is no different from this perspec-tive. Chow tests were conducted to determine whether

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INFORMATION-ADJUSTED NOISE MODEL

FIGURE 1Graph of the AOI and MDI

the inclusion of IAG constitutes a “break point” in thedata. The result shows that IAG does not constitute abreak point and thus permits the inclusion (exclusion)of IAG.

The MDI was then calculated as per Equation (5).

Indext =

10∑i=1

(S∗

i Pit

)10∑i=1

(S∗

i0Pi0) ∗ Io (5)

where

Si is the number of shares outstanding in stock i

Si0 is the number of shares outstanding at time t = 0Pi0 is the price of stock iat time t = 0I0 is an arbitrary multiplier and is equal to 25006

i is for the 10 companies used in the MDI

To be consistent with the AOI price index, no ad-justments were made for dividend distribution, stocksplits and right issues in the construction of the MDI.

Figure 1 shows graphs of the All Ordinaries price in-dex and the MDI. It is difficult to (graphically) discerndifferences in the two indices. The correlation betweenAOI returns and MDI returns is 0.53.

Table 2 shows the descriptive statistics for the re-turns on the two different indices. Returns are calcu-lated as the log relatives, rit = ln(It /It−1). In additionto calculating summary statistics for the entire period1998–2002, annual subperiod summary statistics arealso calculated. The difference between the means of

the returns, for all the different periods, was tested.Finn and Koivurinne [2000] argue that if it is possibleto outperform an index over an extended period, thenthat benchmark index must be necessarily ex ante inef-ficient. Further, they provide evidence of inefficiencyin the AOI. The results here, however, do not appearto indicate that the AOI is inefficient compared to theMDI as the behavioral index return is not statisticallyhigher7 than the AOI price index return (see Table 2).F-statistics indicate that the variances of the returns onthe indices are statistically significantly different (ex-cept in 2002). In order to be confident that this result isnot simply an artefact of index construction the MDIreturns were standardized, i.e., the daily return of thebehavioral index was multiplied by mean of the returnon AOI and divided by the mean return of the MDI.

The lower variance in the AOI is likely to beattributed to the diversification benefits, i.e., as thenumber stocks increases variance decreases. Anotherpossible explanation is the irrational behavior of unin-formed investors increases volatility. These character-istics, identical mean and higher variance, indicate thatthe behavioral beta will be lower than CAPM betas.

Behavioral Error Computation

Daves, Ehrhardt and Kunkel [2000] showed thatdaily return interval results in the smallest standarderror of the beta, i.e., the greatest precision of thebeta estimate. Their study also points out that thechoice of the estimation period for daily return intervalis a dilemma. Levich [1998] recommends a 260-day

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RAMIAH AND DAVIDSON

Table 2. Descriptive Statistics of the Return on the AOI and Return on the MDI for the Period 1998-2002

1998-2002 1998 1999 2000 2001 2002

Mums And Dads Index

Mean 0.000345 0.003665 0.000288 −0.000021 −0.000202 −0.000443Median 0.000000 0.003141 0.000014 −0.000061 0.000000 −0.000619Standard Deviation 0.012622 0.020517 0.012537 0.013137 0.010728 0.007084Variance 0.000159 0.000421 0.000157 0.000173 0.000115 0.000050Obs 1181 138 261 260 261 261

All Ordinaries Index (Price)

Mean 0.000126 0.000368 0.000544 0.000056 0.000241 −0.000466Median 0.000030 0.000000 0.000792 0.000208 0.000126 −0.000183Standard Deviation 0.008211 0.010524 0.007826 0.008753 0.007905 0.006856Variance 0.000067 0.000111 0.000061 0.000077 0.000062 0.000047Obs 1181 138 261 260 261 261

Testing if Return on the MDI Differs From Return on the AOI

t-Test Statistic* −0.498588 −1.679747 0.279632 0.079245 0.537022 −0.035363p-Value 0.618116 0.094146 0.779871 0.936868 0.591482 0.971804

Testing if Variance of the MDI Differs From Variance of the AOI

F-Test Statistic 2.363003 0.263124 0.389623 0.443938 0.542938 0.936600p-Value 0.000000 0.000000 0.000000 0.000000 0.000001 0.597838

Note: As returns on MDI and AOI are not independent over the period, the standard errors for the difference between the twomeans were calculated with the covariance terms.

estimation period based on the Basel Committee betacalculation. Allowing for time-varying betas, we henceuse a 260 rolling day window period to estimate dailybetas. Each daily beta was calculated using the past260-day data and rolled forward one day at a time.This method is used to calculate the daily betas for theentire year, and then the beta for the year calculated asan average of the daily betas. The same technique wasused to estimate both BAPM and CAPM betas. Thistechnique generates highly correlated and dependentbetas, which will bias any statistical testing. Conse-quently the betas need to be corrected for dependence.

Mitchell [2002] calculates an algebraic formula forthe variance of the mean of a set of windowed estimates(for a single company). Let n equal to the number ofestimates, and L be the length of the window. If Vc isthe sample variance of the windowed estimates, andassuming that the covariance between the estimates ofbeta is directly proportional to the number of sharedobservations, then the variance of the mean of theseestimates is

Var = 3L(L + 1)Vc

2n2+ (n − L)Vc

n2(6)

when n = L, the actual variance will be reduced to:Var ≈ 1.5Vc

Furthermore as the CAPM betas and the BAPMbetas are not independent and the CAPM betas and

BAPM betas use the same dependent variables, thestandard error will be computed in the following way:

W is a matrix that represents the weights of each ofthe companies, and as there are N companies, and theyare all of equal weights, W

W =[

1

N. . . . . . . . .

1

N

]� =

σ 21 . . . σ1,N

σ1,2 σ 22

. .

. .

σ1,N . . . σ 2N

� is the variance-covariance matrix of a variable acrossthe N different firms. This is a matrix that has thevariances of the variable (either BAPM betas, CAPMbetas or Behavioral Errors) on each asset down themain diagonal and the covariance’s between the firmsin the off diagonal positions. The variance of the meanis computed by finding the product of W.�.W−1.

We initially provide a visual analysis of our results.We ranked the CAPM betas (for the 1999–2002 period)from smallest to largest and plotted the correspondingbehavioral beta in Figure 2. In terms of the discussionwe expect the behavioral beta to differ from the CAPMbeta. As can be seen from Figure 2, the CAPM betais usually larger than the BAPM beta, which is con-sistent with Shefrin and Statman [1994]. Furthermoreit appears that the difference between the two models

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INFORMATION-ADJUSTED NOISE MODEL

FIGURE 2Average BAPM Beta and Average CAPM Beta of 46 Firms for the Period 1999-2002

is smaller for lower risk companies and increases withthe level of risk.

Testing if the behavioral beta values are significantlydifferent from the CAPM beta values is equivalent totesting whether the BEs are significantly different fromzero. Table 3 shows that the BEs are not zero in allthe different periods and proving that the BAPM betadiffers from the CAPM beta. The positive mean valuesof the BE shown in Table 3 indicate that the BAPMbetas are lower than the CAPM betas. The average ofthe 46 mean CAPM and mean BAPM were tested tosee if they were equal to the market beta of one. Bothmodels showed that the averages were below one andthe 46 firms were equally weighted.

The empirical evidence shows that the null hypoth-esis of CAPM betas and BAPM betas being are equalis rejected on a number of occasions. There is a diver-gence between the two betas suggesting the presenceof noise traders. More precisely, the BAPM betas tendto be lower than the CAPM betas and Shefrin and Stat-man [1994] would suggest that the BAPM betas aremore appropriate. The existence of BE also impliesthat sentiment does affect the Australian market.

Evidence of Irrationality

Table 4 shows the mean alpha, mean beta and meanmu across the different firms. Standard errors wereadjusted for independence in the computation of thet-statistic. The results show that alpha is positive andsignificantly different from zero in all the different pe-riods, implying that noise traders were active in themarket. Furthermore, MU, the measure of noise traderrisk, is positive and significant. On the other hand, in-

formation traders (captured by beta) appear to havebeen active in 2001 only, i.e., this was the only periodwhere they were eliminating the errors. A significantmu can represent either an overreaction or underreac-tion, or IPE. The firms that displayed inefficiency afterinformation traders’ involvement are now investigatedon a day-to-day basis and are categorised as eitheroverreaction or underreaction or IPE.

Alpha, beta, mu and the respective t-statistics werecomputed on a day-to-day basis. Then the sets of condi-tions summarized in section 2.4.4 were applied to theseestimates. These conditions will classify each firm bytheir respective effects. Table 5, Table 5.1, Table 5.2and Table 5.3 report the results for the different peri-ods. Table 5 shows the results of the possible effects,i.e., underreaction (positive or negative), IPE (positiveor negative) and overreaction (positive or negative) forthe period 2000-2002; while the remaining tables, Ta-ble 5.1, Table 5.2 and Table 5.3 report the result for2000, 2001 and 2002, respectively. Table 6 provides asummary of the results.

Over the entire 2000-2002 period, there were 12,273information days for the 46 companies investigated.This study analyses every single day and checks if themarket is efficient, or whether there is some underre-action, IPE or overreaction. Those different effects arethen broken down into two parts, namely positive ornegative. Table 6 reports the number of O (+), O (−),IPE (+), IPE (−), U (+), U (−) and EMH that havebeen occurring on the information days. The table alsoshows the results in the different subperiods.

Overall, the efficient market hypothesis is supportedby the data just under 40 percent of the time. Of 12,273information days, 4,544 days are consistent with the

215

Dow

nloa

ded

by [

Uni

vers

ity o

f W

inds

or]

at 0

6:33

19

Nov

embe

r 20

14

Tabl

e3.

The

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crip

tive

Stat

isti

csfo

rth

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ean

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PM

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a,M

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PM

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iod

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216

Dow

nloa

ded

by [

Uni

vers

ity o

f W

inds

or]

at 0

6:33

19

Nov

embe

r 20

14

Tabl

e4.

The

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217

Dow

nloa

ded

by [

Uni

vers

ity o

f W

inds

or]

at 0

6:33

19

Nov

embe

r 20

14

Tabl

e5.

The

Num

ber

ofU

nder

reac

tion

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verr

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the

Peri

od20

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218

Dow

nloa

ded

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at 0

6:33

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Nov

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14

Tabl

e5.

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Tabl

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Tabl

e6.

Num

ber

ofO

verr

eact

ions

,IP

Ean

dU

nder

reac

tion

sA

cros

sth

e46

Fir

ms

onth

eIn

form

atio

nD

ays

2000

-200

220

0020

0120

02

Num

ber

Per

cent

age

Z-T

est†

Num

ber

Per

cent

age

Z-T

est†

Num

ber

Per

cent

age

Z-T

est†

Num

ber

Per

cent

age

Z-T

est†

Ove

rrea

ctio

n62

85.

12%

0.58

812

24.

94%

−0.1

3931

06.

46%

4.11

7*19

63.

92%

−3.9

53O

(+)

448

3.65

%−7

.973

122

4.94

%−0

.139

273

5.69

%2.

063*

531.

06%

−27.

239

O(−

)18

01.

47%

−32.

562

00.

00%

N/A

370.

77%

−33.

486

143

2.86

%−9

.100

Und

erre

actio

n29

9024

.36%

49.9

70*

488

19.7

6%18

.420

*96

620

.13%

26.1

41*

1536

30.6

9%39

.406

*U

(+)

2843

23.1

6%47

.699

*48

019

.43%

18.1

28*

943

19.6

5%25

.543

*14

2028

.37%

36.6

78*

U(−

)14

71.

20%

−38.

721

80.

32%

−40.

902

230.

48%

−45.

336

116

2.32

%−1

2.61

2

Info

rmat

ion

Pric

ing

Err

or41

1133

.50%

66.8

87*

846

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4436

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45.1

44*

1521

30.3

9%39

.053

*IP

E(+

)39

2732

.00%

64.1

17*

845

34.2

1%30

.601

*17

1235

.68%

44.3

63*

1370

27.3

7%35

.499

*IP

E(−

)18

41.

50%

−31.

914

10.

04%

−122

.525

320.

67%

−36.

875

151

3.02

%−8

.202

Tota

lIne

ffici

entD

ays

7729

62.9

8%13

3.01

2*14

5658

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54.5

02*

3020

62.9

4%83

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*32

5365

.00%

88.9

84*

EM

H45

4437

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73.4

73*

1014

41.0

5%36

.424

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7837

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77*

1752

35.0

0%44

.503

*In

form

atio

nD

ays

1227

310

0.00

%24

7010

0.00

%47

9810

0.00

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0510

0.00

%

Not

e:Si

gnifi

cant

at1%

Lev

elof

Con

fiden

ce.

†Te

stin

gif

the

prop

ortio

nis

grea

ter

than

5%(Z

-Sta

tistic

s).

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INFORMATION-ADJUSTED NOISE MODEL

EMH being ‘true’ over the period 2000-2002. Noisetraders appear to be present in the market 60% of thetime. That 60% can be split into 5% overreaction, 25%underreaction and around 35% of IPE.

Any effect that is around 5% could be argued tobe simply a TYPE I error, and consequently a test ofproportion was carried out to see if the proportion isstatistically greater than 5% (TYPE I error). Table 6shows that the Z-statistics for all the different effectsand across the different periods. The Z-statistics rejectthe hypothesis that our results are due to a TYPE Ierror.

Conclusion

The purpose of this paper was to develop amodel that captures and explains risk generated bynoise traders. The theoretical model (IANM) pro-posed demonstrates that the aim of this study has beenachieved. Furthermore the methodology provides a testof market efficiency.

The results contradict the traditional finance schoolof thought in various areas but are consistent with thebehavioral theories. There is confirmation that noisetraders were present in the Australian market in someperiods. Their influence on the market took differentforms, namely overreaction, underreaction and the IPE.On the other hand, the study of beta confirms the ex-istence of some information trading on the basis ofnoise.

Another conclusion that can be drawn out of thisstudy is that the Australian traders tend to underreactrather than overreact, implying that the market dis-plays slow adjustments to new information rather thanoverconfidence.

Acknowledgements

We thank Pravna Appadoo and Marie-Anne Camfor their research assistance. Previous versions of thispaper have been presented at seminars at RMIT Univer-sity and Politecnico Di Milano. Conference presenta-tions include the Australian Conference of Economists,the Australasian Finance and Banking Conference, theGlobal Finance Conference and the AIBF Banking andFinance Conference. We thank participants for theircomments

Notes

1. This view is based on Shefrin and Statman’s [1994] definitionof a market being behaviorally efficient if and only if behavioralerrors average to zero and are uncorrelated to wealth.

2. Keynes [1936], Lewellen, Schlarbaum and Lease [1974],Shiller [1979], [1981], [1984], Arrow [1985], Black [1986],

Poterba and Summers [1988], Fama and French [1988], DSSW[1990), Shefrin and Statman (1994), Brown [1999] and manyothers.

3. Bernard [1992], Abarbanell, Bernard and Victor [1992], andMendenhall and Richard [1991].

4. These announcements include Activities Report; Results ofAGM; Annual reports; Employee Share Options; Progress Re-ports; Asset Acquisitions; Dividend Rate; Changes in Man-agement; Changes in Substantial Shareholding; and any otherannouncements that might potentially move stock prices.

5. It initially started with 12 stocks but only 10 remained ac-tive. The two other stocks (Colonial and Telstra 2) have beenabsorbed into other components.

6. The arbitrary value of 2500 was chosen for scaling purposes inorder for the MDI to be of the same scale as the AOI.

7. Except for 1998.

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