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This article was downloaded by: [University of Windsor]On: 19 November 2014, At: 06:33Publisher: RoutledgeInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House,37-41 Mortimer Street, London W1T 3JH, UK
Journal of Behavioral FinancePublication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/hbhf20
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
To link to this article: http://dx.doi.org/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
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embe
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Tabl
e3.
The
Des
crip
tive
Stat
isti
csfo
rth
eM
ean
CA
PM
Bet
a,M
ean
BA
PM
Bet
aan
dM
ean
BE
CA
PM
BE
TA
BA
PM
BE
TA
BE
Per
iod
99-0
219
9920
0020
0120
0299
-02
1999
2000
2001
2002
99-0
219
9920
0020
0120
02
Mea
n0.
6627
60.
6224
70.
5838
10.
6692
10.
7564
30.
3311
20.
1777
10.
2580
60.
3428
10.
4739
20.
3316
40.
4447
60.
3257
40.
3264
00.
2825
1St
anda
rdE
rror
0.08
701
0.03
079
0.03
242
0.09
256
0.02
657
0.11
966
0.03
296
0.03
560
0.08
685
0.05
256
0.06
696
0.04
772
0.02
455
0.01
519
0.06
700
Med
ian
0.62
354
0.63
005
0.56
429
0.66
559
0.71
421
0.34
044
0.16
617
0.25
416
0.34
626
0.42
134
0.32
444
0.44
290
0.30
148
0.30
870
0.21
441
ST.D
evia
tion
0.59
013
0.20
882
0.21
986
0.62
777
0.18
022
0.81
157
0.22
356
0.24
143
0.58
907
0.35
647
0.45
417
0.32
368
0.16
648
0.10
304
0.45
441
Kur
tosi
s−0
.865
450.
2624
9−0
.528
23−0
.620
17−0
.296
17−0
.862
602.
1333
70.
8827
6−0
.123
140.
2753
30.
1431
9−0
.373
111.
3239
50.
6313
34.
1886
3Sk
ewne
ss0.
2272
6−0
.244
070.
3213
30.
3085
50.
4661
80.
0345
2−0
.816
56−0
.472
920.
2941
80.
7114
20.
6705
50.
3592
30.
7865
3−0
.311
831.
6169
2O
bs46
4646
4646
4646
4646
4646
4646
4646
T-St
ats
for
Mea
n=
07.
6171
220
.217
3218
.009
267.
2300
828
.467
412.
7672
15.
3911
57.
2495
93.
9469
89.
0170
24.
9525
19.
3194
713
.270
2221
.483
934.
2165
9T-
Stat
sfo
rM
ean
=1
−3.8
7587
−12.
2621
1−1
2.83
876
−3.5
7383
−9.1
6656
−5.5
8984
−24.
9460
6−2
0.84
257
−7.5
6664
−10.
0094
9
216
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nloa
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ity o
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19
Nov
embe
r 20
14
Tabl
e4.
The
Des
crip
tive
stat
isti
csfo
rth
eM
ean
Alp
ha,M
ean
Bet
aan
dM
ean
Mu
AL
PH
AB
ET
AM
U
Per
iod
00-0
220
0020
0120
0200
-02
2000
2001
2002
00-0
220
0020
0120
02
Mea
n0.
2250
50.
2308
50.
2142
80.
2327
40.
0032
10.
0039
90.
0055
30.
0004
70.
2262
40.
2324
80.
2157
60.
2334
1St
anda
rdE
rror
*0.
0110
00.
0098
30.
0024
00.
0076
30.
0034
60.
0027
20.
0026
70.
0025
10.
0115
70.
0115
90.
0041
60.
0083
3M
edia
n0.
2269
60.
1847
90.
2180
00.
2176
50.
0005
50.
0014
00.
0006
20.
0001
00.
2321
80.
1930
10.
2289
20.
2180
2ST
.Dev
iatio
n0.
0746
10.
0667
00.
0162
50.
0517
50.
0234
80.
0184
50.
0180
80.
0170
20.
0784
60.
0786
10.
0282
10.
0565
0O
bs46
4646
4646
4646
4646
4646
46T-
Stat
sfo
rM
ean
=0
20.4
5791
23.4
7307
89.4
1287
30.5
0248
0.92
625
1.46
565
2.07
388
0.18
731
19.5
5772
20.0
5707
51.8
7418
28.0
1774
Not
e:T
heco
mpu
tatio
nof
the
stan
dard
erro
ran
dT-
stat
istic
sw
ere
adju
sted
for
inte
rdep
ende
nce.
217
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nloa
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ity o
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19
Nov
embe
r 20
14
Tabl
e5.
The
Num
ber
ofU
nder
reac
tion
,IP
Ean
dO
verr
eact
ion
for
the
Peri
od20
00-2
002
2000
-200
220
00-2
002
CO
MPA
NIE
SO
(−)
O(+
)U
(+)
U(−
)IP
E(+
)IP
E(−
)E
MH
Info
CO
MPA
NIE
SO
(−)
O(+
)U
(+)
U(−
)IP
E(+
)IP
E(−
)E
MH
Info
AM
PD
IVR
.PR
.TR
UST
06
09
034
106
155
HIL
LS
MO
TO
RW
AY
20
146
808
011
0A
MP
IND
.TR
UST
00
30
10
9296
JUPI
TE
RS
00
880
106
00
194
AR
MS.
JON
ES
OFF
.0
00
00
112
13L
EN
DL
EA
SEC
OR
P.0
019
60
168
01
365
AN
Z28
210
03
745
751
6M
AC
MA
HO
NH
DG
S0
019
084
023
126
AU
SPIN
E0
30
00
015
916
2M
AC
QU
AR
IEO
FF.T
R.
00
177
047
015
239
AU
ST.G
AS
LIG
HT
119
00
00
123
835
8M
AY
NE
NIC
KL
ESS
00
420
215
025
282
BR
AM
BL
ES
IND
.0
255
098
3058
244
3M
IM0
011
80
159
018
295
BR
LH
AR
DY
027
106
4124
288
396
NA
B0
00
015
40
273
427
BH
P0
50
70
045
146
3N
EW
CR
EST
MN
G.
00
820
40
215
301
BU
RSW
OO
D17
00
00
2612
016
3O
ILSE
AR
CH
00
142
089
079
310
CA
PRA
LA
LU
MIN
IUM
00
00
00
100
100
OR
ICA
00
880
460
914
3C
AR
TE
RH
.HA
RV
EY
60
00
03
8695
PMP
CO
MM
.0
036
016
011
316
5C
CI
HO
LD
ING
S0
00
06
255
63Q
BE
INSU
RA
NC
E0
013
00
110
06
246
CB
A0
106
06
00
515
627
RE
IN.A
US.
60
10
5013
272
CO
CA
-CO
LA
AM
AT
IL0
190
60
025
628
1R
IDL
EY
CO
RP.
00
920
410
3917
2C
OL
ES
MY
ER
20
00
02
192
196
RIO
TIN
TO
00
160
048
00
1765
7C
SL0
026
70
278
01
546
SAB
RE
GR
OU
P0
041
015
06
62C
SR0
015
10
149
032
362
3SA
NT
OS
00
206
023
20
2446
2E
NE
RG
YD
EV
.0
067
060
047
174
SEV
EN
NE
TW
OR
K0
084
061
07
152
GA
ZA
LC
OR
P.0
031
058
00
89ST
RA
TE
GIC
P.D
EV
.0
611
945
52
78G
EN
ER
AL
PR.T
ST.
00
00
142
011
325
5T
EL
EV
ISIO
N&
ME
DIA
00
156
061
021
238
GO
OD
MA
NFI
EL
DE
R0
014
40
382
01
527
WE
STE
RN
ME
TAL
S0
059
015
90
2123
9H
AR
VE
YN
OR
MA
N0
073
070
014
157
TAB
LIM
ITE
D0
015
50
285
00
440
218
Dow
nloa
ded
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vers
ity o
f W
inds
or]
at 0
6:33
19
Nov
embe
r 20
14
Tabl
e5.
1.T
henu
mbe
rof
Und
erre
acti
on,I
PE
and
Ove
rrea
ctio
nfo
rth
ePe
riod
2000
2000
2000
CO
MPA
NIE
SO
(−)
O(+
)U
(+)
U(−
)IP
E(+
)IP
E(−
)E
MH
Info
CO
MPA
NIE
SO
(−)
O(+
)U
(+)
U(−
)IP
E(+
)IP
E(−
)E
MH
Info
AM
PD
IVR
.PR
.TR
UST
00
00
00
3737
HIL
LS
MO
TO
RW
AY
00
00
270
027
AM
PIN
D.T
RU
ST0
00
00
017
17JU
PIT
ER
S0
00
033
00
33A
RM
S.JO
NE
SO
FF.
00
00
00
44
LE
ND
LE
ASE
CO
RP.
00
20
980
010
0A
NZ
00
00
00
103
103
MA
CM
AH
ON
HD
GS
00
190
180
340
AU
SPIN
E0
00
00
038
38M
AC
QU
AR
IEO
FF.T
R.
00
200
130
1548
AU
ST.G
AS
LIG
HT
00
00
00
7676
MA
YN
EN
ICK
LE
SS0
021
026
00
47B
RA
MB
LE
SIN
D.
091
02
00
194
MIM
00
630
00
063
BR
LH
AR
DY
025
00
90
7510
9N
AB
00
00
20
8587
BH
P0
00
00
083
83N
EW
CR
EST
MN
G.
00
00
00
4949
BU
RSW
OO
D0
00
00
034
34O
ILSE
AR
CH
00
440
10
449
CA
PRA
LA
LU
MIN
IUM
00
00
00
2121
OR
ICA
00
30
200
932
CA
RT
ER
H.H
AR
VE
Y0
00
00
020
20PM
PC
OM
M.
00
00
30
2730
CC
IH
OL
DIN
GS
00
00
60
511
QB
EIN
SUR
AN
CE
00
470
40
253
CB
A0
00
00
013
213
2R
EIN
.AU
S.0
00
038
00
38C
OC
A-C
OL
AA
MA
TIL
00
00
00
5252
RID
LE
YC
OR
P.0
01
019
00
20C
OL
ES
MY
ER
00
00
00
4141
RIO
TIN
TO
00
180
120
00
138
CSL
00
130
880
010
1SA
BR
EG
RO
UP
00
100
00
010
CSR
00
700
210
4313
4SA
NT
OS
00
220
640
086
EN
ER
GY
DE
V.
00
160
00
016
SEV
EN
NE
TW
OR
K0
00
033
07
40G
AZ
AL
CO
RP.
00
00
170
017
STR
AT
EG
ICP.
DE
V.
06
06
31
218
GE
NE
RA
LPR
.TST
.0
00
00
015
15T
EL
EV
ISIO
N&
ME
DIA
00
370
100
047
GO
OD
MA
NFI
EL
DE
R0
01
099
00
100
WE
STE
RN
ME
TAL
S0
031
020
00
51H
AR
VE
YN
OR
MA
N0
016
013
014
43TA
BL
IMIT
ED
00
260
400
066
219
Dow
nloa
ded
by [
Uni
vers
ity o
f W
inds
or]
at 0
6:33
19
Nov
embe
r 20
14
Tabl
e5.
2.T
heN
umbe
rof
Und
erre
acti
on,I
PE
and
Ove
rrea
ctio
nfo
rth
ePe
riod
2001
2001
2001
CO
MPA
NIE
SO
(−)
O(+
)U
(+)
U(−
)IP
E(+
)IP
E(−
)E
MH
Info
CO
MPA
NIE
SO
(−)
O(+
)U
(+)
U(−
)IP
E(+
)IP
E(−
)E
MH
Info
AM
PD
IVR
.PR
.TR
UST
00
00
00
4747
HIL
LS
MO
TO
RW
AY
20
06
178
033
AM
PIN
D.T
RU
ST0
03
01
039
43JU
PIT
ER
S0
043
04
00
47A
RM
S.JO
NE
SO
FF.
00
00
00
77
LE
ND
LE
ASE
CO
RP.
00
680
690
013
7A
NZ
021
00
31
186
211
MA
CM
AH
ON
HD
GS
00
00
440
044
AU
SPIN
E0
00
00
059
59M
AC
QU
AR
IEO
FF.T
R.
00
560
310
087
AU
ST.G
AS
LIG
HT
180
00
00
102
120
MA
YN
EN
ICK
LE
SS0
019
071
025
115
BR
AM
BL
ES
IND
.0
143
00
300
017
3M
IM0
039
039
018
96B
RL
HA
RD
Y0
210
132
1615
621
7N
AB
00
00
680
8215
0B
HP
01
07
00
191
199
NE
WC
RE
STM
NG
.0
00
04
091
95B
UR
SWO
OD
150
00
00
5368
OIL
SEA
RC
H0
039
04
064
107
CA
PRA
LA
LU
MIN
IUM
00
00
00
4040
OR
ICA
00
270
210
048
CA
RT
ER
H.H
AR
VE
Y0
00
00
029
29PM
PC
OM
M.
00
40
130
6279
CC
IH
OL
DIN
GS
00
00
02
3234
QB
EIN
SUR
AN
CE
00
490
520
410
5C
BA
010
60
60
013
724
9R
EIN
.AU
S.0
00
012
12
15C
OC
A-C
OL
AA
MA
TIL
00
00
00
112
112
RID
LE
YC
OR
P.0
035
01
029
65C
OL
ES
MY
ER
20
00
00
7476
RIO
TIN
TO
00
142
011
70
025
9C
SL0
044
016
30
020
7SA
BR
EG
RO
UP
00
160
40
626
CSR
00
810
128
040
249
SAN
TO
S0
01
015
20
2417
7E
NE
RG
YD
EV
.0
019
012
042
73SE
VE
NN
ET
WO
RK
00
490
00
049
GA
ZA
LC
OR
P.0
012
026
00
38ST
RA
TE
GIC
P.D
EV
.0
04
323
40
34G
EN
ER
AL
PR.T
ST.
00
00
113
024
137
TE
LE
VIS
ION
&M
ED
IA0
076
012
00
88G
OO
DM
AN
FIE
LD
ER
00
420
154
00
196
WE
STE
RN
ME
TAL
S0
012
084
01
97H
AR
VE
YN
OR
MA
N0
038
043
00
81TA
BL
IMIT
ED
00
150
165
00
180
220
Dow
nloa
ded
by [
Uni
vers
ity o
f W
inds
or]
at 0
6:33
19
Nov
embe
r 20
14
Tabl
e5.
3.T
heN
umbe
rof
Und
erre
acti
on,I
PE
and
Ove
rrea
ctio
nfo
rth
ePe
riod
2002
2002
2002
CO
MPA
NIE
SO
(−)
O(+
)U
(+)
U(−
)IP
E(+
)IP
E(−
)E
MH
Info
CO
MPA
NIE
SO
(−)
O(+
)U
(+)
U(−
)IP
E(+
)IP
E(−
)E
MH
Info
AM
PD
IVR
.PR
.TR
UST
06
09
034
2271
HIL
LS
MO
TO
RW
AY
00
140
360
050
AM
PIN
D.T
RU
ST0
00
00
036
36JU
PIT
ER
S0
045
069
00
114
AR
MS.
JON
ES
OFF
.0
00
00
11
2L
EN
DL
EA
SEC
OR
P.0
012
60
10
112
8A
NZ
280
00
06
168
202
MA
CM
AH
ON
HD
GS
00
00
220
2042
AU
SPIN
E0
30
00
062
65M
AC
QU
AR
IEO
FF.T
R.
00
101
03
00
104
AU
ST.G
AS
LIG
HT
101
00
00
160
162
MA
YN
EN
ICK
LE
SS0
02
011
80
012
0B
RA
MB
LE
SIN
D.
021
096
058
117
6M
IM0
016
012
00
013
6B
RL
HA
RD
Y0
00
50
857
70N
AB
00
00
840
106
190
BH
P0
40
00
017
718
1N
EW
CR
EST
MN
G.
00
820
00
7515
7B
UR
SWO
OD
20
00
026
3361
OIL
SEA
RC
H0
059
084
011
154
CA
PRA
LA
LU
MIN
IUM
00
00
00
3939
OR
ICA
00
580
50
063
CA
RT
ER
H.H
AR
VE
Y6
00
00
337
46PM
PC
OM
M.
00
320
00
2456
CC
IH
OL
DIN
GS
00
00
00
1818
QB
EIN
SUR
AN
CE
00
340
540
088
CB
A0
00
00
024
624
6R
EIN
.AU
S.6
01
00
120
19C
OC
A-C
OL
AA
MA
TIL
019
06
00
9211
7R
IDL
EY
CO
RP.
00
560
210
1087
CO
LE
SM
YE
R0
00
00
277
79R
IOT
INT
O0
00
024
30
1726
0C
SL0
021
00
270
123
8SA
BR
EG
RO
UP
00
150
110
026
CSR
00
00
00
240
240
SAN
TO
S0
018
30
160
019
9E
NE
RG
YD
EV
.0
032
048
05
85SE
VE
NN
ET
WO
RK
00
350
280
063
GA
ZA
LC
OR
P.0
019
015
00
34ST
RA
TE
GIC
P.D
EV
.0
07
019
00
26G
EN
ER
AL
PR.T
ST.
00
00
290
7410
3T
EL
EV
ISIO
N&
ME
DIA
00
430
390
2110
3G
OO
DM
AN
FIE
LD
ER
00
101
012
90
123
1W
EST
ER
NM
ETA
LS
00
160
550
2091
HA
RV
EY
NO
RM
AN
00
190
140
033
TAB
LIM
ITE
D0
011
40
800
019
4
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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
34.2
5%30
.634
*17
4436
.35%
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
.95%
54.5
02*
3020
62.9
4%83
.104
*32
5365
.00%
88.9
84*
EM
H45
4437
.02%
73.4
73*
1014
41.0
5%36
.424
*17
7837
.06%
45.9
77*
1752
35.0
0%44
.503
*In
form
atio
nD
ays
1227
310
0.00
%24
7010
0.00
%47
9810
0.00
%50
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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