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Efficient market hypothesis: an experimental study with uncertainty and asymmetric information

Mondher Bouattour et Isabelle Martinez

Résumé

The efficient market hypothesis has been the subject of a wide debate over the past decades. This paper investigates the market efficiency by using laboratory experiments. We ran three experimental treatments with two distinguishing dimensions: uncertainty and asymmetric information. Results show that both uncertainty and information asymmetry affect the level of market efficiency with information asymmetry having a pronounced impact. Market efficiency is reduced when the fundamental value of stocks is volatile. In addition, we find that participants under-react to information and that this under-reaction is not corrected during trading periods and prices remain stable.

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Texte intégral

The authors gratefully acknowledge the comments of the two anonymous reviewers and the co-editor, Jean-François Gajewski.

1. Introduction

  • 1 Other definitions of market efficiency have been formulated. For example, Jensen (1978) argues that (...)

1In efficient markets, competition between investors is so aggressive that prices instantly adjust to new information. At all times, a financial instrument trades at a price determined by its return and its risk. Fama (1965) stresses that in an efficient market the actual trading price of a stock will be a good estimation of its fundamental value. The concept of efficiency is based on the arguments put forward by Samuelson (1965), who states that the price of a financial asset fluctuates in a random way: future information is unpredictable and the changing price of each financial asset follows a random pattern. According to Fama (1970), a financial market is efficient if prices always fully reflect available information. If an asset’s price fully expresses all events occurring up to date t, then only new information can change it1. Three forms of efficiency have been defined by distinguishing between different categories of information (Fama, 1970, 1991). The semi-strong informational efficiency hypothesis suggests that current prices fully incorporate all publicly available information. This information comprises not just the history of past prices, but also companies’ financial publications and studies conducted by financial analysts. This hypothesis can be empirically tested by studying the reaction of prices to announcements made by companies: the price of a stock should react immediately and appropriately to any relevant disclosure of information. Empirical studies use the event study methodology (see in particular Brown and Warner, 1985). However, they do not really lead to any homogenous conclusions regarding the semi-strong efficiency (see for example Bernard and Thomas, 1989; Ikenberry and Ramnath, 2002; Spyrou et al., 2007; Truong, 2011; Hsu et al., 2013; Huynh and Smith, 2017).

2By taking into account the mixed results on previous literature, we investigate the semi‑strong form of market efficiency by means of laboratory experiments. The purpose here is to test whether uncertainty and information asymmetry impact market efficiency. To alleviate the difficulties linked to event studies (particularly the wide variability of results depending on the method used to calculate expected and/or abnormal returns, the choice and length of calculation period used, etc.), the experimental method seems useful because it can control the information held by the subjects and observe their behavior. The protocol used in this paper represents actual trading platforms and includes three experimental treatments which differ according to the information level held by the subjects. In the first two treatments (noted T1 and T2), the information is symmetrical between the subjects. The difference between T1 and T2 is the level of uncertainty: T2 is characterized by uncertainty about future dividends whereas in T1, dividends are known by the subjects. In the third treatment (noted T3), there is information asymmetry between the subjects. In all three treatments, trading in stocks is fluid since the stocks are liquid and trade without transaction costs. Experiment participants are continuously informed of the fundamental value of the traded stock: this is a crucial piece of information which allows us to compare the prices established on the market and the fundamental value without making any auxiliary hypotheses. We find that trading is not efficient but also that both uncertainty and information asymmetry affect the level of market efficiency. Stock prices show greater deviation from fundamental value when information is asymmetric which in consistent with the existent literature. Ultimately, participants under-react to information announcements. This under-reaction, which is more pronounced in markets with information asymmetry between subjects, is not corrected, and prices remain stable to the end of the trading periods. Furthermore, the results show that the difference between price and fundamental value is particularly strong when the latter varies significantly. Thus, the more volatile the fundamental value, the more the informational efficiency is reduced.

3This paper contributes to the literature. While most experimental studies focus on prices formation in the presence of symmetric and asymmetric information (see for example Kirchler, 2009; Kelly and Ljungqvist, 2012), it is the first time, to the best of our knowledge, that the semi-strong efficiency hypothesis under uncertainty is tested thought an experimental study. We investigate the difference of the information dissemination between markets with uncertainty and asymmetric information structure. This implementation of uncertainty and asymmetric information seems very realistic: on real financial markets, the fundamental information is distributed along a continuum across investors. In addition, this paper provides useful insights for financial market participants such as individual or institutional investors. Real financial markets are characterized by uncertainty and information asymmetry between investors. The gap between stock prices and their fundamental values is especially wide when information asymmetry is high. This difference can be exploited by investors to build arbitrage strategies that enable securities prices to adjust more quickly to the fundamental value. Managers are also encouraged to reduce the information asymmetry which in turn implies better information efficiency.

4The remainder of this paper is structured as follows. Section 2 presents the literature review. Section 3 outlines the experimental design. Section 4 reports the results and Section 5 concludes the research.

2. Literature review

5The semi-strong informational efficiency hypothesis has traditionally been tested using the event study methodology. This involves measuring abnormal return as the difference between the observed return of a stock and its theoretical return (also referred to as expected or normal return). According to the semi-strong efficiency hypothesis, prices adjust rapidly to any new information and abnormal or excess returns should be observed as soon as the information is made public (with no time lag). Most studies covering short event windows (a few days around the announcement date) illustrate instant price adjustment to public information (Anderson et al., 2001; Dasilas and Leventis, 2011). A large part of literature has used this methodology to investigate whether dividend contains information. For example, Aharony and Swary (1980) find a small but significant dividend announcement effect (average excess return of about 1% over the 2-days announcement period). Asquith and Mullins (1983) find large and significant positive excess returns on the announcement day of dividend initiations but no reaction thereafter. By studying the abnormal returns following dividend initiations and omissions, Michaely et al. (1995) show that short reactions to omissions are greater than for initiations (-7% versus +3.4% over a 3-days window). In the French market, investors react favorably to dividend increase announcements: share prices increase by an average of 2.95% by the close of the fifth day after the announcement (Bouattour, 2007).

  • 2 Studies in financial behavior show that investors are subject to cognitive biases that influence th (...)

6Other studies using a longer event window show that the reaction to new information continues during the months following the announcement (Bernard and Thomas, 1989; Ikenberry and Ramnath, 2002; Truong, 2011). Ball and Brown (1968) were the first to highlight abnormal returns throughout the 60 days following earnings announcements, proving the persistence of the announcement effect. Bernard and Thomas (1989) rank shares according to the degree of surprise in earnings announcements. They show that, over the six months that follow the announcement dates, a portfolio with good news records an average return higher than that of a portfolio with bad news. These results illustrate that information is underestimated at the time of the announcement, then gradually integrated into prices. According to Bernard and Thomas (1989), the tendency in stock prices following the event is consistent with an under-reaction to information, which is gradually corrected after the event. Truong (2011) analyzes abnormal returns over event windows running from two days to as many as 60, 120 or 250 days after the earnings announcements. The results show the existence of a trend following announcements. Over a one-year period, the strategy of holding stocks that have announced improved earnings and selling stocks that showed a decline in earnings generates a gain in the order of 9%. The calculation of abnormal returns over event windows of two and three years shows that cumulative abnormal returns remain constant. This result shows that the duration of the post-earnings announcements drift is 12 months. Michaely et al. (1995) also highlight a post-announcement drift: in the 12 months after the dividend announcement, there are positive excess returns for firms initiating dividends (7,5%) and negative excess returns for firms omitting dividends (-11%). Abnormal returns have been demonstrated for other events such as initial public offerings (Ritter 1991; Loughran and Ritter 1995; Zheng, 2007), share repurchases (Ikenberry et al., 1995; Cheng et al., 2015) and stock splits (Ikenberry and Ramnath, 2002; Boehme and Danielsen, 2007). While Ball and Brown (1968), Bernard and Thomas (1989), Ikenberry and Ramnath (2002), Truong (2011) and Huynh and Smith (2017) show the existence of an under-reaction to information, other authors (for example Mai, 1995; Clements et al., 2009; Alwathainani, 2012; Tai, 2014; Kudryavtsev, 2018) highlight an excessive price reaction to information. This initial over-reaction is followed by a correction process which reflects the adjustment of stock prices to the stock’s fundamental value.2

  • 3 In his article published in 1998, Fama suggests, “Market efficiency must be tested jointly with a m (...)

7However according to Fama (1991, 1998), the joint hypothesis problem3 can skew results and efficiency is not directly testable since the use of a price-formation model is necessary. For some cases, several studies prove inefficiencies without resorting to price-formation model. This is the case of twin shares, corporate spinoffs and dual share classes (for a review of these anomalies, see Rosenthal and Young, 1990; Lamont and Thaler, 2003; Maymin, 2011). These inefficiencies are due mainly to the limits to arbitrage (Shleifer and Vishny, 1997) which is explained by fundamental risk, noise trading risk, transaction costs and short selling constraints. However, these analyses do not make it possible to study the market efficiency as a whole, but only particular cases.

  • 4 For a summary of the experimental method, see in particular Plott (1991), Davis and Holt (1993), Ca (...)

8The experimental method can overcome these difficulties4. Laboratory (or lab) experiments involve creating a controlled “sterile” environment and isolating the effect of certain variables on the phenomenon. In contrast, in a natural experiment, the researcher “simply observes naturally occurring, controlled comparisons of one or more treatments with a baseline” (Harrison and List, 2004, p. 1041). Lab experiment employs a standard or non-standard subject pool (convenience sample) while in a natural experiment, the subjects naturally undertake tasks and are not informed on their participation. Experiments in laboratory are also more controlled than in nature: the experimenter can control the number of participants, the conditions of environment (for example uncertainty and asymmetric information regarding the market structure), and the information held by participants. Moreover, they allow to measure variables that are difficult to quantify (for example the fundamental value of the stock for Kirchler, 2009). According to Levitt and List (2007), a critical assumption underlying the interpretation of data from lab experiments is the generalization of results, i.e. their extrapolation beyond the laboratory. However, even if this question is crucial because humans are the subjects, environments constructed in the lab are conforming to real-world and “those aspects of economic behavior under study are perfectly general” (Harrison and List, 2004, p. 1009). Finally, Harrison and List (2004, p. 1009) note that lab experiments permit “sharper and more convincing inference”.

9With these main advantages, lab experiments are used to test the informational efficiency hypothesis. For example, Theissen (2000) studies informational efficiency in three different market structures: an auction call market, a continuous market, and a dealer market. He shows that prices reflect the available information on continuous and auction call markets. This finding is consistent with Friedman (1993) who finds that informational efficiency in dealer markets is weaker than in continuous markets. Docherty and Easton (2012) test the market efficiency hypothesis and observe that prices underreact to good and bad news and that they display significant short term momentum. Other experiments have been developed by taking into consideration a constant or a variable fundamental value. Smith et al. (1988) employ a model in which the fundamental value is decreasing over time. They observe the development of a bubble, characterized by a phase of growth in prices and followed by a crash at the end of the experiment. Their study shows that speculation prevents prices from revealing the fundamental value of the traded asset. Lei et al. (2001) modify the standard framework of Smith et al. (1988) by forbidding speculation. They demonstrate that speculative bubbles are due to the presence of irrational behavior, in line with the “active participation hypothesis”, since experimenters often encourage subjects to actively participate, and this represents a potential source of errors. In order to reduce speculative bubbles, Smith et al. (2000) show the importance of a single dividend payment. Lei and Vesely (2009) consider that the market experience in subjects is not necessary to eliminate bubbles in the type of market studied by Smith et al. (1988), and introduce a pre-market phase designed to draw the subjects’ attention to the structure of the dividends they can collect: this suffices to ensure the efficiency of the market.

10In the case of a constant fundamental value, Noussair et al. (2001) observe that bubbles diminish in markets. Hommes et al. (2005) present a different model, again with a constant fundamental value, but in which the subjects submit risky-asset price forecasts for the subsequent period. They find that prices fluctuate slightly around, or slowly converge towards, fundamental value. For Kirchler (2009), the study of investor behavior under growing, and above all fluctuating fundamental value, is essential since it reflects the reality of the financial markets. He focuses on price movements in response to fluctuating fundamental values following a stochastic process, and observes an under-reaction by participants to changes in the fundamental value. This under-reaction is more pronounced when there is information asymmetry between subjects.

11Surprisingly, while uncertainty appears an important factor to explain investors’ behavior, in our knowledge, none experimental study uses uncertainty to test the semi-strong efficiency hypothesis. In his survey aiming to better understand investor psychology, Hirshleifer (2001) indicates that high uncertainty increases the tendency for psychological biases that affect investors’ behavior. The uncertainty increases the overconfidence of investors (Daniel et al., 1998, 2001; Zhang, 2006). According to Daniel et al. (1998, 2001), the return predictability should be stronger in firms with greater uncertainty because investors tend to be more overconfident when firms’ businesses are hard to value. This argument implies that greater uncertainty is related to relatively higher (lower) stock returns following good (bad) news. Finally, Jiang et al. (2005), Zhang (2006) and Francis et al. (2007) document that the higher information uncertainty, the greater the under-reaction.

12The present paper tests the hypothesis of semi-strong efficiency in financial markets by using laboratory experiments in which the variable fundamental value is clearly known by the subjects. The reaction to this information is directly studied by observing whether and how stock prices adjust to the fundamental value. While most experimental studies focus on prices formation in the presence of symmetric and asymmetric information, we enrich literature by taking in consideration not only the asymmetry of information between the subjects but also the level of uncertainty about future dividends.

3. Experimental design

3.1. Treatments

13We consider three treatments that differ according to the nature of the information provided to the subjects: this enables us to study the semi-strong informational efficiency hypothesis in three different controlled environments. In the first two treatments (T1 and T2), all subjects receive the same information but the level of uncertainty about future dividends differs between T1 and T2. The third treatment (T3) is characterized by information asymmetry between the subjects. Each treatment includes six experimental sessions, each one composed of 24 periods of 100 seconds. This periodicity is used by Kirchler and Huber (2009), Kirchler (2009) and Hanke et al. (2010). At the beginning of each session in all three treatments, each subject is endowed with 50 shares and 1000 experimental units (EU) in cash. The subjects were briefed using written instructions at the beginning of each session. Four trial periods followed to allow them to familiarize themselves with the trading screen.

  • 5 In experiments conducted at the University of Innsbruck (Austria), Kirchler and Huber (2007) select (...)

14Interaction between the subjects is based on the dividends disclosed at the beginning of each period. The wealth of each subject is a function of the number of stock and cash holdings. Wealth is also a function of market price, and evolves with each transaction. It always changes, even if the subject took no action in the last transaction. At the beginning of each period, the dividend is updated. When a subject sells some of their shares, their cash holding increases in real time, receiving an interest at the end of each period at a risk-free rate of 3%. The risk-adjusted interest rate is set at 10% and remains constant until the end of the experiment5. It is used to calculate the present value of the shares by discounting the future dividends known to the subjects. We inform the subjects of the risk-adjusted interest rate (re). The starting wealth is the same for all participants, and all shares are assumed to have been bought at the same price at the beginning of the experiment. This price is equal to the present value for the first period of the game. This value reflects the quality of an efficient market and therefore our starting point corresponds to an efficient market: if we assume that all subjects buy their shares at time t= 0 seconds and that the market is efficient at this time, all participants will have bought the share at the market price, which is assumed to be equal to its present value.

3.1.1. Treatment T1: disclosure of four dividends

15The subjects trade shares on the basis of changes in future dividends. At the beginning of each period, each subject knows the dividend for the current period and coming dividends for the next three periods (Kirchler and Huber, 2009). Subjects are therefore presumed to be well-informed and know the precise values of future dividends (Kirchler and Huber, 2007). For each experimental session, the number of subjects varies between 10 and 14.

16For the six experimental sessions of treatment T1, six series of dividends are generated. They have a bullish then bearish nature (or vice versa) in order to place the subjects in gain and loss situations. Other series are presented to the subjects in graphic form before the beginning of each experiment, in order to show them the randomness of dividends. The dividend process is a “random walk”, determined as follows:

Image 10000000000002B5000000C6C6B484EACBB42CE8.jpg

17Dt is the dividend for period t.εt is a normally-distributed random variable with an expected value of zero and a variance of 0.16. The dividend for the first period is equal to 2 EU per share held.

18The present value (PV) of the stock is calculated by applying the dividend discount model and assuming that the last dividend is perpetual and constant (see for example Huber et al., 2008; Kirchler and Huber, 2009). To calculate the present value for period t, we discount the dividends for period t and those for periods t+1, t+2 and t+3 at the rate of 10%.

Image 10000000000002AC00000070B08290C0DF44F8B2.jpg

19PVt and Dt represent respectively the present value and the dividend for the current period t. re is the risk-adjusted interest rate equal to 10%.

3.1.2. Treatment T2: disclosure of a single dividend

20This second treatment is characterized by uncertainty about future dividends. In this treatment, the subjects are informed of the dividend for the current period and the present value of the share. The only difference between T1 and T2 is the number of dividends disclosed to the subjects. In T1, the subjects are informed of the dividends of the current period and those of the next three periods. However, in T2, the subjects are only informed of the dividend of the current period. This implies that the subjects in T1 have more visibility on the future dividends and negotiate the share based on dividends of the current period and also those of the next three periods. However, the subjects of the T2 treatment are in situation of uncertainty about future dividends and trade on the basis of the current dividend only.

21As before, 10 to 14 subjects participate in each T2 experimental session. To enable comparison with the first treatment, we used the same present value series as calculated in T1. We therefore calculated the series of dividends Dt by multiplying the series PVt by 0.1. However, in this case the dividend for the first period is no longer 2 EU. We inform the subjects that the dividend for the first period is around 2 EU and will change randomly. The present value is calculated as follows (re is the risk-adjusted interest rate equal to 10%):

Image 10000000000002B80000005773FF49A49753E89D.jpg

PVt= present value; Dt= dividend; re= risk-adjusted interest rate; t= current period.

3.1.3. Treatment T3: information asymmetry between the participants

  • 6 For this third treatment, we are more restrictive on the number of subjects in each session. In ens (...)

22This third treatment is characterized by information asymmetry between the subjects. At the beginning of each experimental session, participants are randomly allocated to one of the four information levels (I1 to I4) and this allocation remains unchanged throughout the entire session. 12 subjects participate in each experimental session, three for each information level6. The best-informed subjects, belonging to information level I4, know the dividend for the current period and the next three periods. Subjects in information level I3 know the dividend for the current period and the next two periods, etc. The least-informed subjects (information level I1) know only the dividend for the current period (see Figure 1).

Figure 1. Overview of traders’ knowledge about future dividends in T3

Image 100000000000021B000000B03057124267160794.jpg

23The conditional present value (PV) is a function of the dividends known by the subjects. It is calculated using the dividend discount model, in which the last dividend is presumed to be perpetual and constant:

Image 10000000000002B00000005722C188AD127AC41D.jpg

  • 7 We assume that the risk-adjusted interest rate remains unchanged for the 3 treatments and for the 4 (...)

24PVj,t and Dt represent respectively the conditional present value of the information level j (from 1 to 4) and the dividend for the current period t. re is the risk-adjusted interest rate7 of 10%. To calculate the conditional present value for period t, we discount the dividends known to each subject at the rate of 10%.

25For this third treatment, the value of the shares for all subjects at the beginning of the session is equal to the conditional present value for the best-informed subjects (information level I4). We explain to the subjects that they all bought the share at the same price, without however informing them that this price represents the conditional present value for the best informed subjects. The starting wealth is thus the same for all subjects, regardless of their information level.

3.2. Market architecture

26The market in which the subjects operate can be considered as a simplified but representative of most real stock exchanges. This is an electronic market which provides direct confrontation between buying and selling offers. The trading mechanism is implemented as a continuous double auction with an open order book. The subjects can place their orders at any time during a given period. Each participant can trade shares with other participants by submitting limit orders (specifying price and quantity) or accepting orders at market price (specifying only the quantity to trade). Like Brandouy and Barneto (1999) and Kirchler (2009), we do not include a pre-opening market phase. The order book is empty at the start of each trading period. All bids and asks are recorded in the order book. A bid (or ask) is only valid if the proposed price is higher (or lower) than the best offer on the market. The offers are then publicly communicated to all the participants. The best offer can be accepted by another participant at any time. The partial execution of limit orders is available. In such cases, an exchange is concluded at the price offered for the desired quantity. Trading takes place without transaction costs. In order to guarantee liquidity, the prices offered are restricted to a maximum of one digit after the decimal point. Finally, stocks and cash holdings are carried over from one period to the next. The participants receive information in real time about dividends, the (conditional) present value, their wealth, their shares and cash holdings, and a chronological list of transaction prices.

3.3. Experimental implementation

27Most experimental studies are conducted with students as subjects (Kirchler, 2009; Hanke et al., 2010) because they have plenty of time and are motivated by relatively modest monetary gains, leading to a low cost for the experimenter. Porter and Smith (2003) have shown that the behavior of students in experimental stock markets is very similar to that of real-life professional investors. We conducted our 18 experimental sessions (3 treatments x 6 sessions) in a computer laboratory with a total of 213 students. All of the students were taking courses in finance. Each student participated in only one experimental session and, when asked, confirmed whether they had understood the instructions. Each session lasted about 90 minutes. While each experimental session is composed of 24 periods, the instructions given to subjects state that the game involves 20 to 30 periods, and that the end of the game is random with equal probability for each period. The aim is to prevent strategic behavior by participants at the end of the experiment (Kirchler and Huber, 2009; Hanke et al., 2010). The experiments were programmed and performed using z-Tree software (Fischbacher, 2007).

28In order to engage the students and motivate them to make good decisions, a voucher-based tournament incentive structure is used. The value of the voucher awarded is between 0 and 30 euros, depending on each subject’s trading performance compared to the other subjects. In T3, incentives for trading are benchmarked by the performance of the other participants in the same information level. The vouchers are awarded at the end of each experimental session. Each subject’s gains at the end of the session are calculated in Experimental Units and are equal to the sum of the gains achieved over all 24 periods of the session. For a given period, the gain is equal to the variation in the wealth as measured at the end of the period.

29To sum up, Table 1 summarizes the experimental differences between the three treatments.

Table 1. Differences between the three treatments

Description

T1

T2

T3

Number of experimental session

6

6

6

Number of subjects per experimental session

10-14

10-14

12

Number of information levels per experimental session

1

1

4

(3 subjects in each information level)

Information

Dt, Dt+1, Dt+2 and Dt+3 + Present Value (PV)

Dt + Present Value (PV)

Known dividends + conditional present value (PV)

Pay-out at the end of the experiment

[0; € 30]

Subjects were paid according to their trading performance relative to all other participants.

[0; € 30]

Subjects were paid according to their trading performance relative to all other participants.

[0; € 30]

Subjects were paid according to their trading performance relative to other participants at the same information level.

4. Results

4.1. Descriptive statistics

30In the two treatments T1 and T2, the fundamental value (FV) is equal to the present value of the stock. In treatment T3, the FV is equal to the conditional present value for the best-informed subjects, i.e. those who know the dividends for the current period and the next three periods. This makes it possible to compare the prices established on the market with the fundamental value of the share. For each experimental session, we calculated two measures of efficiency proposed by Theissen (2000) for the opening price (O), the average transaction price weighted by the transaction volumes for each period (P) and the closing price (C). The first measurement, MAE, represents the mean absolute error between the transaction price j and the fundamental value.

Image 10000000000002BA00000060AAD862EE50B2575E.jpg

31where Pt,j is the transaction price; FVt is the fundamental value; t is the trading period ranging from 1 to 24 for each experimental session. j indicates whether the transaction price considered is the opening price (O), the volume weighted average transaction price (P) or the closing price (C).

32The second measurement, MRE, is the mean relative error. The absolute deviation between the price and the fundamental value is divided by the share value, and then an average for all the periods of each session is calculated. This measurement makes comparisons possible between experiments with different fundamental values.

Image 10000000000002AA0000006488A5549F321FC4EB.jpg

  • 8 Similarly, Hanke et al. (2010) and Kirchler et al. (2011) test market efficiency by using the absol (...)

33If the market is efficient throughout all trading periods of each experimental session, then the opening prices, average transaction prices and closing prices should adjust to the fundamental value. These two measurements are built on an absolute value since we test the semi-strong informational efficiency hypothesis8. They should therefore tend towards 0.

34Table 2 presents MAE and MRE for each experimental session and their average for each of the three treatments.

Table 2. Measurements of informational efficiency - descriptive statistics

Image 10000000000001DD000001C319EF749CBB801A9F.jpg

35The mean of the MAE for average transaction prices is 1.70, 1.64, and 3.68 EU respectively for the three treatments. The measurement MRE, which expresses the price deviation as a percentage of fundamental value, is better suited to comparison between experimental sessions when the movement of fundamental values differs. For deviation calculated on the basis of average transaction prices, this measurement comes to 9.56%, 8.72% and 19.38% respectively for the three treatments. This shows that informational efficiency is reduced to a greater extent where there is information asymmetry.

  • 9 In the study by Theissen (2000), an improvement in prices between opening and closing is found in t (...)

36For treatment T1, in five sessions out of six, closing price-based measurements are lower than opening prices, reflecting the convergence of prices towards the fundamental value9. The only exception is session T1-M4. In this session, the opening price MRE measurement is 12.39% and increases to 14.67% by the end of the trading periods, proving that the opening prices are closer than the closing prices to the fundamental values. The improvement in informational efficiency during trading periods seems weak for the first treatment. Observing the mean MRE measurement over the six experimental sessions, we note that it fell by 1.02% (9.83% – 8.81%) between the beginning and end of the trading periods. For the sixth T1 session, the MRE measurement was 20.16% and 15.90% respectively for the opening and closing prices, which demonstrates an improvement of 4.26% in informational efficiency. The MAE measurement for average transaction prices shows that the absolute deviation between price and fundamental value is 1.70 EU on average. This measurement takes its highest value in the M6 market (2.67 EU). Over the six experimental sessions of the first treatment, the improvement in informational efficiency during the trading periods was an average 0.20 EU (|1.60 – 1.80|).

37For treatment T2, informational efficiency appears to deteriorate and the closing prices deviate to a greater extent from the fundamental value than in T1. The mean MRE measurements for the six sessions of this second treatment show that informational efficiency declined by 1.39% (9.46% – 8.07%) between the beginning and end of the trading periods. The MAE measurement for average transaction prices (P) shows that the absolute deviation is equal to 1.64 EU, and the decline in informational efficiency between the beginning and the end of the periods is an average 0.25 EU (1.79 – 1.54). However, the MRE measurement shows that in the two sessions M1 and M6, the closing prices, compared to the opening prices, adjusted slightly to the fundamental value. In the four other sessions, the opening prices reflect increased informational efficiency. This result suggests that, depending on the information received at the beginning of each period, subjects react strongly (impulsive behavior) by selling or buying stocks, but then revise their beliefs and subsequently their initial trading strategy, which increases the deviation between price and fundamental value at the period-end. In this second treatment, the subjects only receive information related to the current period. Following an increase in the dividend for the current period, they buy stocks at prices close to the fundamental value, but the uncertainty related to future periods encourages them to revise the trading prices offered. Likewise, when the dividend for the current period falls, they sell some of the shares in their possession in order to collect interest on their cash holdings, but adjust the trading prices at the end of the period.

38For treatment T3, the MAE measurement for average transaction prices shows that the absolute deviation between price and fundamental value is an average 3.68 EU. This measurement reaches its highest value for the M6 market (4.99 EU). Over the six T3 experimental sessions, the improvement in informational efficiency during the trading periods is an average 0.23 EU (|3.61 – 3.84|), which seems consistent with the improvement in informational efficiency under T1 (0.20 EU). Observing the mean MRE measurement for the six experimental sessions, we note a decline of 0.75% between the beginning and end of the trading periods (19.89% – 19.14%). This measurement is 19.38% for average transaction prices (P), and is significant compared to T1 (9.56%) and T2 (8.72%). Thus, in the presence of information asymmetry, the deviation between price and fundamental value is relatively high, and the heterogeneity of information between subjects leads to weaker informational efficiency.

39In the three treatments, we note that for average transaction prices, the highest MRE value corresponds to the M6 market. It is 19.40% for T1 (for which the average MRE is 9.56%), 13.35% for T2 (average MRE 8.72%) and 35.37% for T3 (average MRE 19.38%). The M6 market thus reflects weak informational efficiency compared to the other markets. Conversely, the lowest MRE measurement relates to the M3 market, in all 3 treatments. It is 4.32% in T1, 5.53% in T2 and 11.67% in T3. These three experimental sessions thus reflect the best informational efficiency. Despite the separate nature of the experimental sessions (the information on dividends and subjects are not the same in the three treatments), the T1-M3, T2-M3 and T3-M3 markets have the lowest MRE measurement, while the T1-M6, T2-M6 and T3-M6 markets show the highest MRE measurement. A possible explanation for this similarity may relate to the fact that for a given session, the series of fundamental values is kept constant across the 3 treatments. To verify this, the relationship between MRE (P) and the standard deviation of the relative variation in fundamental value (σ(DFV)) of each experimental market is studied. The variable DFV is calculated as follows:

Image 10000000000002AE00000058DDCE789B6F9D2A21.jpg

40FVt being the fundamental value and t being the trading period, running from 2 to 24.

41Figure 2 illustrates the MRE (P) measurement for each of the 18 experimental markets according to the standard deviation of the relative variation in fundamental value.

Image 1000000000000221000001F3AC2C7DF757A6E039.jpg

42We observe that the adjustment in prices (MRE) is a function of the relative variation in the fundamental value. The higher the variation in fundamental value, the less prices adjust efficiently to fundamental value. The M3 markets for each of the three treatments show the weakest MRE and (σ(DFV)) values, while the M6 markets for each treatment have the strongest measurements. The other experimental sessions have intermediate values. This implies that the higher the relative variation in fundamental value, the more prices deviate from the fundamental value of the share. The positive MRE -(σ(DFV)) relationship can be interpreted in two ways. The first interpretation is that when the variation in fundamental value is significant, participants react excessively (over-reaction) to the information contained in the dividend announcements. The second interpretation is compatible with the hypothesis of under-reaction to information: when there is a large variation in fundamental value, the subjects do not submit sufficient purchase and sale orders to allow prices to reach the fundamental value.

4.2. Informational efficiency and trading periods

43In order to see whether stock prices align with fundamental value during trading periods, we performed a test on paired series, involving comparison of MRE(O) and MRE(C) for the 144 observations (24 periods x 6 sessions) in each treatment. The MRE measurement is used since it expresses the price deviation as a percentage of fundamental value, and is therefore more relevant in the case of pooled data. If there is price improvement during trading periods, then the differences between MRE(O) and MRE(C) should be positive and significant. In this case, prices adjust to fundamental value during trading periods. Since the results of skewness, kurtosis and global normality tests indicate that the two series MRE(O) and MRE(C) for each of the three treatments are not normally distributed, a non-parametric Wilcoxon test is performed.

Table 3. Comparison of the adjustment of opening and closing prices to fundamental value

Mean

Median

Wilcoxon Z

Probability P

MRE(O) – MRE(C)

T1

0.0102

0.0061

-1.410

0.159

T2

-0.0139

-0.0012

-1.376

0.169

T3

0.0075

0.0052

-1.532

0.125

Ti: Treatment (i from 1 to 3); O: opening price; C: closing price; MRE(O): mean relative error between opening price and fundamental value; MRE(C): mean relative error between closing price and fundamental value; Wilcoxon Z is the statistic indicating whether the matched-pairs MRE(O) and MRE(C) are different, and P is the associated probability.

  • 10 Theissen (2000) shows that correction of price errors is non-significant in the fixing market (nega (...)

44The results show a difference between the three treatments. For T1 and T3, the change in price errors is positive, which implies that the closing prices are closer than opening prices to the fundamental value. This convergence of prices towards the fundamental value is measured as a mean 1.02% and 0.75% respectively for T1 and T3. However, the Wilcoxon median test shows that the improvement in informational efficiency is non-significant (P= 0.159 and 0.125 > 0.05). For T2, the MRE measurement is lower for opening prices than closing prices: the opening prices are therefore closer than the closing prices to the fundamental value. The difference is a mean -1.39%, but non-significant according to the Wilcoxon test. Thus, no statistically significant difference is observed between the MRE(O) and MRE(C) pairs. This result is consistent with Theissen (2000) who shows a non-significant price error reduction in experimental double-auction markets10.

4.3. Price stability during trading periods

45We investigate the equality of opening prices (O), average transaction prices (P) and closing prices (C). For the three treatments, a test on paired series is performed using the three following couples: (O – P), (C – P) and (O – C). Each series consists of 144 observations. Studying the distribution of the series allows us to conclude that they follow a normal pattern. A Student test on paired series is applied in this case.

Image 10000000000002980000017B03D40B2308A3D477.jpg

46For all treatments, the mean difference in each pair of observations is close to 0 for the three pairs of series. The bilateral probability of the Student test is higher than 5% for all combinations. The mean difference between the pairs of observations is therefore null, and there is no significant difference between the three prices studied. The results of this test, combined with those of the non-parametric test performed on the MRE(O) and MRE(C) series, show that prices remain stable until the end of the trading period. No conclusion can be drawn from these results as to the nature of the participants’ reaction to information: they may under- or over-react to the disclosure of dividends but prices remain stable during the trading periods. This stability of prices can be explained by the mimetic behavior of the subjects. When a new dividend is disclosed at the beginning of each period, the subjects submit buying and selling orders in the open order book. The supply and demand of the share implies an opening price. The subjects have access to all the information on the trading screen, and more specifically to orders and transaction prices. Although each subject has his own strategy of negotiation, they tend to follow the other participants. This mimetic behavior leads to price stability during the trading period.

4.4. Adjustment of prices to the fundamental value

47So far, we have shown that the prices established in experimental markets do not reflect all the available information, and that a deviation persists between market price and fundamental value. Figure 3 provides an illustration of the relationship between the average prices (P) and fundamental values (FV) within the 18 experimental markets. We use the average transaction price (P) since prices remain stable during trading periods. Each graph represents markets characterized by a change in FV and average prices corresponding to treatments T1, T2 and T3.

Figure 3. Comparison of fundamental values (FV) and average market prices for the three treatments over the trading periods

Image 100000000000012E0000028D628B0221061E40BC.jpg

Image 100000000000014100000288A4FED6F3761B9953.jpg

48We can clearly see that prices do not adjust to the fundamental value. The degree of mispricing increases when the variation in fundamental value is important. This is visible in all markets and especially in the M6 markets, which are characterized by high volatility in the fundamental value (see Figure 2). Mispricing between prices and fundamental values remained even during the final periods of the experimental sessions. This confirms that the learning effect was low and did not have an impact on the subjects’ trading strategies. Additionally, stocks were undervalued in bullish markets and overvalued in bearish markets, which suggests under-reaction in all experimental markets. This under-reaction is more pronounced in T3 (more pronounced undervaluation in bullish markets and more pronounced overvaluation in bearish markets). These undervaluation and overvaluation respectively in bullish and bearish markets are similar to those obtained by Kirchler (2009).

49To determine the degree of the reaction to the information disclosed, we use the model defined by Theissen (2000) and estimate the following regression for each session of the three treatments:

Image 10000000000002A700000055E8FE9B5BB925C742.jpg

50(P)= average transaction price; FV= fundamental value, t= current period (t-1= previous period).

  • 11 Time series regressions are privileged here since they enable us to compare different sessions of e (...)

51According to Theissen (2000) and Kirchler (2009), if the market is efficient, then the value of β should not be different to 1. Conversely, if the subjects under-react (over-react) to information, we would expect a β coefficient lower (higher) than 1. The γ coefficient should be negative since previous price errors should be corrected during the current period. This implies that undervaluation in bullish markets and overvaluation in bearish markets during the previous period t-1 will be corrected during the current period t. The results of time series regressions11 are presented in Table 5.

Table 5. Adjustment of prices to information

Image 1000000000000171000002865E5452A50876A4D0.jpg

52Results show a similarity between T1 and T2, which are characterized by information symmetry between the participants. The β coefficients are significantly different from zero at the 1% level, and lower than one in 11 of the 12 experimental sessions. This confirms the existence of an under-reaction to information in these two treatments. The subjects react weakly to a variation in fundamental value. This weak adjustment of prices is consistent with Weber and Welfens (2009) and Kirchler (2009), which highlight an under-reaction to information. In session T2-M3, the variation in fundamental value is accompanied by a change in prices of 0.867. This is the only session for which H0: β=1 is accepted, implying that the market is efficient for this session. This result is explained by the low volatility in fundamental value: as discussed earlier in the descriptive analysis, this session presents the lowest (σ(DFV)) value. Furthermore, the subjects in this session only have information for the current period, and this is reflected in a more significant adjustment of prices to fundamental value.

  • 12 Another explanation of this result is as follow: The dividend series are generated as a random walk (...)

53Analysis of the results shows that under-reaction is more significant in the first treatment (β coefficient is 0.583 in T1 and 0.707 in T2). This result is not in line with the behavioral finance literature which stipulates a greater under-reaction for a high level of uncertainty (Jiang et al., 2006; Francis et al., 2007). This is explained by the fact that the subjects in T2, which is characterized by uncertainty, not having any information related to future periods, react more strongly to the arrival of new information (greater surprise effect). Indeed, during a given period, T2 subjects have no information on the dividend for the next period, and their reaction is reflected more in the prices. In contrast, in T1, the dividend for the current period has already been known since the three previous periods. Each pair of sessions belonging to the treatments contains the same change in fundamental value. This proves that in the first treatment, the subjects trade shares on the basis of the fundamental value and the dividend for the current period, but do not ignore the information they hold on future dividends12. The sign for the γ coefficient is negative, as expected. In the 12 experimental sessions in T1 and T2, 7 coefficients (4 in T1 and 3 in T2) are significant at the 5% level. This proves that previous evaluation errors are corrected during the current period.

54Treatment T3 presents results that differ from the first two treatments. The β coefficients are positive but non-significant. All these coefficients are close to 0 and are lower than 1 at the 1% level in all 6 experimental sessions. This shows that the under-reaction is more pronounced in T3 characterized by information asymmetry between the subjects. This result is confirmed by the average β coefficient, which stands at 0.100 and is strictly lower than 0.583 for T1 and 0.707 for T2. All the γ coefficients for the 6 experimental sessions are significant. This proves that the under-reaction (highly pronounced in T3) of the previous periods is corrected during the current period.

5. Conclusion 

55We investigate the semi-strong informational efficiency hypothesis by using experimental method. This method has the advantage of controlling the information held by subjects, and enables us subsequently to compare the resulting prices with the fundamental value. Following Huber et al. (2008) and Kirchler (2010), we use an experimental protocol with three treatments that are differentiated according to the nature of the information disclosed to the subjects. Consistent with Theissen (2000), we find that informational efficiency does not improve during trading periods. The deviation between price and fundamental value is high when the variation in the fundamental value is large. Informational efficiency is therefore weak when the fundamental value is volatile. The findings also show that prices remain stable during trading periods. The regression results and tests performed before (MRE(O) - MRE(C) and price stability tests) show that when information is first released, evaluation errors (under-reaction) occur on the experimental markets that remain uncorrected until the end of the trading periods. In treatment T2, which is characterized by uncertainty about future dividends, subjects show impulsive behavior and react strongly to new information. This indicates that information is incorporated more into prices in comparison to treatment T1. It also appears that the subjects under‑react to information in all three treatments. The absence of any trend after the information announcement shows that prices do not converge towards the fundamental value of the share and the under-reaction is not corrected during the trading periods. This effect is more pronounced when the participants do not hold the same information on future dividends. In treatment T3 with information asymmetry, the information dissemination process is therefore much slower, and price adjustment to fundamental value is weak. This finding is consistent with Kirchler (2009), who demonstrates that under-reaction to information is more pronounced in the context of asymmetric information.

56Results may interest several stock market actors. In the treatment with asymmetric information (T3), the deviation between stock prices and the fundamental value is more significant than in treatments with symmetric information (T1 and T2). This suggests that managers should disclose all relevant information about company to minimize the information asymmetry between investors, which ensures healthier informational efficiency. Additionally, the implication of high volatility in dividends (and, therefore, in fundamental value) is an under-reaction to information (from investors). Thus, managers should maintain a clear strategy of dividend distribution. If a gap between prices and fundamental values persists, it will be exploited by investors by building arbitrage strategies that ensure securities prices adjust to the fundamental value, which will contribute to better informational efficiency.

57To complete our analysis, it would be useful to study the reasons for under-reaction to information. An initial line of research involves focusing on so-called ‘rational’ explanations related to flaws in financial markets, particularly the illiquidity of stocks and the impact of transaction costs on asset prices. A second research approach considers the limited rationality of investors, with the existence of cognitive biases. Anchoring bias and self-attribution bias could supply an explanation for under-reaction to information. The disposition effect, defined as the tendency for investors to sell winning stocks too soon and hold losing stocks too long, is another possible source of under‑reaction to information. It would thus be useful to explore the relationship between the disposition effect and under-reaction to information further, in particular through an experimental method.

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Notes

1 Other definitions of market efficiency have been formulated. For example, Jensen (1978) argues that a market is efficient when no investor can make substantial gains by speculating on the basis of information that is available on this market. The stock price incorporates all relevant information so that an investor cannot, by buying or selling this stock, make any profit greater than the transaction costs. While this definition includes transaction costs, Malkiel (1992) proposes another definition closely related to Jensen’s (1978): a market is efficient if it fully and correctly reflects all information related to stocks. In such a market, prices would thus be unaffected if all information was revealed to all market participants.

2 Studies in financial behavior show that investors are subject to cognitive biases that influence their decisions and consequently the formation of prices on financial markets (Barberis et al., 1998; Daniel et al., 1998; Grinblatt and Han, 2005).

3 In his article published in 1998, Fama suggests, “Market efficiency must be tested jointly with a model for expected (normal) returns, and all models show problems describing average returns” (p. 285).

4 For a summary of the experimental method, see in particular Plott (1991), Davis and Holt (1993), Cadsby and Maynes (1998) and Nuzzo and Morone (2017).

5 In experiments conducted at the University of Innsbruck (Austria), Kirchler and Huber (2007) selected a risk-free interest rate and a risk‑adjusted interest rate of 2% and 8.5% respectively.

6 For this third treatment, we are more restrictive on the number of subjects in each session. In ensure that no information level has any more impact on the trading, we have set 3 subjects for each information level, which implies necessarily 12 subjects for each experimental session. This is not the case for T1 and T2. In these two treatments, there is only one information level and the number of subjects has no impact on the trading prices. Note that the number of subjects of all the experimental sessions of the three treatments will not be included in the analysis that follows.

7 We assume that the risk-adjusted interest rate remains unchanged for the 3 treatments and for the 4 information levels of the T3 treatment (Kirchler and Huber, 2007, 2009). We inform the subjects of the risk-adjusted interest rate since we do not study here their risk preferences, but the adjustment of prices to the arrival of new information.

8 Similarly, Hanke et al. (2010) and Kirchler et al. (2011) test market efficiency by using the absolute deviation between the average price within a trading period and the fundamental value.

9 In the study by Theissen (2000), an improvement in prices between opening and closing is found in three of six experimental double-auction markets.

10 Theissen (2000) shows that correction of price errors is non-significant in the fixing market (negative value) and double-auction market (positive value). In contrast, this correction is significant in the dealer market.

11 Time series regressions are privileged here since they enable us to compare different sessions of each treatment. Panel data regressions were also conducted. They led to similar results for the three treatments. These results are not presented for reasons of brevity, but are available from the authors upon request.

12 Another explanation of this result is as follow: The dividend series are generated as a random walk. This implies that some dividend increases are followed by dividend decreases. This information is known in T1 and the subjects trade on the basis of this information (increase of the dividend for the current period and decrease of the dividend thereafter). However, T2 subjects are only informed of the dividend of the current period. This implies that a dividend increase in T2 will be more visible in prices. The reasoning is the same for dividend decreases followed by dividend increases.

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Mondher Bouattour et Isabelle Martinez, « Efficient market hypothesis: an experimental study with uncertainty and asymmetric information  »Finance Contrôle Stratégie [En ligne], 22-4 | 2019, mis en ligne le 09 décembre 2019, consulté le 17 mai 2022. URL : http://journals.openedition.org/fcs/3821 ; DOI : https://doi.org/10.4000/fcs.3821

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Mondher Bouattour

CERIIM & LGCO - University of Toulouse 3 Paul Sabatier
bouattourm@excelia-group.com

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Isabelle Martinez

TSM Research - UMR 5303 CNRS University of Toulouse 1 Capitole
University of Toulouse 3 Paul Sabatier
isabelle.martinez@tsm-education.fr

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