Curse of mediocrity - On the value of asymmetric

Curse of mediocrity - On the value of asymmetric

fundamental information in experimental asset

markets∗

Michael Kirchler†

May 21, 2007

∗Without discussions with and assistance of Emanuel Bohler, Michael Hanke, FlorianHauser, Jurgen Huber, and Sonja Huber this paper would not have made it to this ver-sion. We also thank participants of COMPLEXITY 2006 and WEHIA 2006 for very helpfulcomments on earlier versions of this paper. Financial support by the University of Innsbruckis gratefully acknowledged.

†Corresponding author. Innsbruck University School of Management, Departmentof Banking and Finance, Universitatsstrasse 15, 6020 Innsbruck, Austria. e-mail:[email protected]

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Abstract

We analyze data from experimental asset markets with asymmetric

fundamental information to assess the relationship between information

level and return. We find that uninformed human and artificial ran-

dom traders reach the market return and outperform average informed

investors. Insiders outperform the market and all other traders due to

their timing advantages. They buy (sell) before prices rise (fall), whereas

average informed buy (sell) before prices fall (rise). Uninformed traders

are protected by their lack of information and thus are not exploited sys-

tematically. The advantages (disadvantages) in timing can be explained

by the use of fundamental information.

JEL classification: C91, C92, G14

Keywords: information economics, experimental economics, market ef-

ficiency, value of information

1 Introduction and related literature

In his PhD-thesis Louis Bachelier (1900) discovered that stock prices on the Paris

stock exchange follow a random pattern which implies that the knowledge of

past price series does not allow speculators to predict future price movements.

However, for more than 30 years this pioneering work was not recognized in

the academic world. With the contribution of Cowles and Jones (1937) the

hypothesis of stock price changes following a random-walk was presented again

and found increasing acceptance among scientists. Only after Osborne’s paper

in 1959 on Brownian motions to describe price changes on stock markets, the

’random-walk hypothesis’ was broadly accepted in the field.1

1A good overview of the implications of the random-walk hypothesis can be found in Fama(1995).

2

Fama (1970) extended this concept to formulate the ’efficient market hy-

pothesis’ (EMH). Subsequently he defined three levels of market efficiency. If

stock markets are weak-form efficient, prices contain all historical information

at any time t. This concept has strong similarities to the random-walk hy-

pothesis since it renders all trading strategies that concentrate on past price

patterns are useless. According to Fama (1991), controversy about market ef-

ficiency centers mainly around this area. The empirical evidence on whether

there is statistically significant autocorrelation in past returns is mixed. Some

researchers find statistically significant autocorrelation, but the more important

question is whether these patterns are economically significant after transaction

costs, which is rarely the case.2 Semi-strong form efficiency states that stock

market prices contain all publicly available information at any time. Here, a

large body of event study literature exists that concentrates on the adjustment

speed of prices after the arrival of new information. Fama (1991) states that

prices adjust very quickly to changes in dividend payments, mergers or tender

offers. In the strong form of the EMH all information is included in prices at

any time t. If this holds each trader can expect the same return. However, as

Grossman (1976) shows, this hypothesis cannot hold. His so-called ’information

paradox’ states that if additional information would not yield higher returns,

nobody would have any incentive to acquire information. But if nobody (or

hardly anybody) processes information, prices will no longer be informationally

efficient. Also Fama (1991) acknowledges that the strong form of the EMH is

surely false, but may serve as a good benchmark. Consequently, the major ques-

tion is the degree of ineffciency (efficiency) and what groups (if any) of investors

can outperform the market consistently.

According to Lakonishok and Lee (2001), Lin and Howe (1990), Seyhun

(1986), and Stotz (2006) insiders gain above-average returns, whereby stronger

results can be found for purchases than for sales. After including transaction

costs the evidence is mixed. For example, Lin and Howe (1990) report insignif-

2Fama (1991) provides a good survey on tests of weak-form efficiency.

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icant results after transaction costs, whereas Stotz (2006) still finds significant

evidence on insiders’ outperformance.

Another strand of literature on private information deals with the perfor-

mance of ’professionals’ on financial markets. Here, the evidence regarding

mutual fund managers speaks a clear language. Cowles (1933, 1944), Gruber

(1996), Jensen (1968), Malkiel (1995, 2003a,b, 2005) find that about 60 to 80% of

mutual funds underperform the relevant benchmark index. According to many

authors this underperformance is due to transaction costs. After excluding these

costs from the analysis returns roughly equal the market return. In some studies

the authors do not account for the survivorship bias with the consequence that

funds that are taken from the market during the examination period due to

inferior performance are not included in the sample. After correcting for these

shortcomings, the average return of the mutual funds sample will be lower and

could fall below the market return, although transaction costs are not included.

Several attempts in investigating the relationship of information level and

return with more than two information levels have already been performed by

Huber et al. (2005, 2007) in their laboratory experiments. The authors find no

difference in return between weak, average and well-informed investors. Accord-

ing to them only insiders can outperform most of the other information levels

significantly. In similar models, Huber (2007) finds that insiders can outperform

all other information levels significantly, but also that average informed traders

are beaten by the worst informed significantly.

Our goal in this paper is to further investigate the relationship between infor-

mation level and return. We use a new experimental market model which con-

sists of five information levels, ranging from fundamentally uninformed traders

to insiders. In Treatment 1 the uninformed traders are human, whereas in

Treatment 2 computerized random traders play this role. We decide to use

panel regressions which allow us avoiding potential biases resulting from OLS-

regressions. Our results indicate that insiders manage to outperform the market

and all other traders. Average informed underperform the market and are even

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beaten by uninformed traders who earn the market return. The reason for these

patterns are timing advantages of insiders, as they buy (sell) before prices rise

(fall). In contrary, average informed traders buy (sell) after prices have risen

and buy (sell) before prices fall (rise). Uninformed human and random artificial

traders are protected by their lack of fundamental information and thus cannot

be exploited systematically. Thus, they earn the market return. Interestingly,

the timing advantages (disadvantages) of the various information levels can be

explained by the use of fundamental information. Insiders mainly trade accord-

ing to their fundamentals with the consequence of a relatively quick adjustment

of prices. At the time average informed receive this piece of information it is

already incorporated into prices. For them ignoring their fundamental informa-

tion would be useful.

The rest of the paper is structured as follows: In Section 2, we present

our model and experimental design. Section 3 focuses on the formulation of

hypotheses based on the findings from earlier studies. In section 4 we present

the method for investigating the formulated hypotheses. Section 5 reports the

experimental results, relates the main findings to the existing literature and

offers explanations on the negative value of additional fundamental information.

Finally, Section 6 concludes the paper by relating the main findings to the

existing literature and by discussing the practical implications of the results.

2 Model and experimental implementation

In each experimental market 10 traders interact in a continuous double auction

for 24 periods. They trade stocks of a virtual company for virtual money (Taler).

The stock does not pay dividends and no interest is paid for cash holdings.

2.1 Information system

The fundamental value (intrinsic value) of the stock is a random walk process

generated by a geometric Brownian motion:

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Vk = Vk−1 · eα, (1)

where Vk denotes the intrinsic value of period k and α is a normally dis-

tributed random variable with a mean of 0.5% and a standard deviation of

7.2%.3

To implement asymmetric information, we start with the idea of Hellwig

(1982) that better informed traders get relevant information earlier than oth-

ers. We extend this concept to four information levels, Ij (I1 to I4), with the

expression (4 − j) specifying how many periods later than the best informed

(I4) the fundamental value becomes available to a specific information level.

So, only traders with information level I4 know the fundamental value of the

current period k. Fundamental information provided to I4 in period k becomes

available to I3 in period k + 1, to I2 in period k + 2, etc. At the start of each

period traders are provided with new information. At this time information

level I(j − 1) receive the information Ij had one period earlier, while the best

informed receive new information that nobody knew before. Subsequently, the

expression CVj denotes the conditional value of information level j.

Insert Figure 1 about here

Figure 1 visualizes the information structure of one representative market.

Beginning with the insiders, I4, the CV -function of information level j is shifted

(4− j) periods to the right. Basically, all traders receive the same information,

but at different times. Furthermore, we add uninformed traders as a fifth infor-

mation level (I0). They never get any information about the fundamentals of

the stock. Each information level is populated by two traders.

Figure 2 shows the eight value process realisations which are identical in both

treatments. Four are generated randomly and for each realisation one mirrored

version at the dotted line – the expected value of Vk in period k – is calculated.3In this model one period equals one month in reality. With these parameters the intrinsic

value increases by 6.2% p.a. and the annual standard deviaton reaches 25%.

6


The idea behind this information structure is that relevant fundamental in-

formation is first known by insiders (managers of the company) and then trickles

down over time to the broad public (I1), which has an informational disadvan-

tage to the best informed of 3 periods. In reality they receive this information

as soon as it is published in newspapers or circulated via TV. Moreover, unin-

formed traders I0 don’t even collect this relatively old information. They only

know about the name of the company, but they don’t have any information on

the ’hard facts’ of the asset.

2.2 Market architecture

Participants trade in a continuous double auction market with open order book.

Similar to most stock markets all orders are executed according to price and

then time priority. Market orders have priority over limit orders and are always

executed instantaneously. Holdings of cash and stocks are carried over from one

period to the next. Traders can submit as many bids and asks as they want,

provided they have enough money to buy or enough stocks to sell. Any order

size and the partial execution of limit orders are possible. Short selling is not

allowed.

The trading screen provides participants with current information on their

stock and money holdings, and their current wealth, Wi,t (see screenshots in

the Appendix):

Wi,t = (Si,t · Pt) + Ci,t, (2)

where St denotes the number of stocks of trader i at tick t, Ct the corresponding

cash holdings and Pt equals the market price at tick t.

In the center of the screen traders can submit limit orders (specifying price

and quantity) or settle transactions immediately through market orders (spec-

ifying only the quantity they want to trade). All transaction prices with the

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corresponding time are shown in a realtime chart on the left side of the screen.

Traders also get a list of all their sales and purchases. After each period a his-

tory screen provides traders with information on their stock and cash holdings,

wealth, value, the closing price of the market, their trading volume and the total

trading volume of the market for each period.4

2.3 Experimental implementation

At the beginning of each session traders are briefed with written instructions,

which take about 25 minutes to go through. Afterwards we run four trial pe-

riods to allow participants to become familiar with the trading screen and the

different order types. Then we conduct the main experiment which lasts about

45 minutes. Trading in each market ends after 24 periods of 100 seconds each.

To avoid end-of-experiment effects we tell traders that the market is randomly

terminated between periods 20 and 30 with equal probability.

At the start of the main experiment participants are randomly assigned to

one of the information levels and then they remain at this level for the whole

session. In all experimental markets each trader is initially endowed with 40

stocks and 1600 in cash. The information structure is also public knowledge,

i.e., traders know how many information levels exist, how many traders are

endowed with each information level, and they know their own information

level.

At the end of the session all stocks are bought back at the fundamental value

VK (information of the insider, I4) of the last period K. Thus, the final wealth

of each trader in Taler, FWK , equals

FWK = (SK · VK) + CK , (3)

where SK denotes the stock holdings of the final period K and CK equals

the cash holdings at the end of the experiment. The final wealth is converted4For further details see a screenshot in the Appendix.

8

into EUR at the exchange rate of 1EUR equalling 175 Taler.

We conducted 16 markets in November and December 2006 at the University

of Innsbruck with a total of 144 business students and 16 computerized random

traders. Most participants already took part in other experiments in economics,

but none of them participated in more than one of the markets in this exper-

imental series. Each session lasted about 80 to 90 minutes, and the average

earnings were around 19 EUR. The market is programmed and conducted with

z-Tree 3.0.6 (Fischbacher (1999)).

2.4 Treatments

We conduct two treatments differing only in the definition of fundamentally un-

informed traders, I0. In treatment T1 human traders act as uninformed. They

don’t get any information on fundamentals throughout the whole experiment,

but receive the same information on prices and on orders as the other traders.

In T2 the role of the uninformed is covered by computerized random traders.

They do not process any kind of information at any time, instead they randomly

place bids and asks (only limit orders) according to the following rule:

At first, the waiting time between limit orders at time step t, Wtt, is defined,

Wtt = Cwt + 10 · εt, (4)

where Cwt is a constant and εt is an uniformly distributed random term

between 0 and 1.

Then a coin flip decides whether the following limit order will be a bid or

an ask. The bid/ask is calculated as

Bidt = Pt ± εt,

Askt = Pt ± εt. (5)

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Here Pt denotes the current market price at time (tick) t and εt is a standard

normally distributed error term.

Finally, the corresponding quantity Q of the limit order,

Qt = Cq + 4 · εt, (6)

is calculated, where Cq is a constant and εt stands for an uniformly dis-

tributed random term between 0 and 1.

Table 1 gives a brief overview over the parameter set of the two random

agents in each market. ’Agent 1’ is designed as active trader with shorter waiting

times between his orders, Wt, and with a higher market impact in each order.

’Agent 2’ is programmed relatively passively with longer waiting times and less

market impact. Trading behavior of active and passive human traders of earlier

experiments serve as a benchmark for this parameter set.

Insert Table 1 about here

3 Hypotheses

With respect to the strong form of the EMH, no investor can expect above-

average returns (Fama (1970)). Besides the ’information paradox’ of Grossman

(1976), tests on the value of insider information show that the EMH’s strong

form does not hold. Many of these studies indicate that insiders outperform the

market significantly.5 Regarding the performance of well, average and worst in-

formed investors few studies exist. Cowles (1933, 1944), Gruber (1996), Jensen

(1968), Malkiel (1995, 2003a,b, 2005) report that about 60 to 80% of mutual

funds underperform the relevant benchmark index. On average, fund managers

may gather neither insider information nor will they be completely uninformed

about companies fundamentals. However, it is almost impossible to classify the

information level of the different funds managers exactly. To avoid this short-5For further details see Lakonishok and Lee (2001), Lin and Howe (1990), Seyhun (1986)

and Stotz (2006).

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coming, Huber et al. (2005, 2007) and Huber (2007) implement experimental

asset markets with discrete information levels. Huber (2007) reports that av-

erage informed investors underperform the worst informed significantly. In his

study the worst informed still receive some fundamental information, whereas

in our model the worst informed do not get any information on fundamentals.

Based on these references we formulate the following alternative hypotheses:

H1: Insiders (I4) outperform the market, average informed (I1 and I2)

underperform the market and the worst informed (I0) earn the market return.

Clearly, the corresponding null hypotheses states no difference in returns

across the various information levels. If statistically significant differences can

be observed, the question of the origin of this pattern emerges. As the quality

of information is defined as an inverse function of the arrival time, we hypoth-

esize that successful traders have timing advantages compared to unsuccessful

investors. This means that outperformers can predict future price changes,

whereas underperformers are mislead by their information because it may al-

ready be incorporated into prices.

H2: Successful traders buy (sell) before prices rise (fall) and sell (buy) after

prices have risen (fallen). Unsuccessful traders are being exploited as they buy

(sell) before prices fall (rise) and sell (buy) after prices have fallen (risen).

The null hypotheses for H2 indicates no difference in timing across the dif-

ferent information levels. Finally, it would be interesting to see whether this

timing advantages of successful versus unsuccessful traders is driven by the use

of fundamental information. We want to observe what changes in stock hold-

ings (simply coded by ’positive’ or ’negative’) may be induced by the use of

fundamental information of the different information levels.

H3: The timing advantages (disadvantages) of successful (unsuccessful) traders

are induced by the use of fundamental information.

The null hypotheses of H3 indicates no relationship between timing advan-

tages and fundamental information of the different information levels. We run a

similar analysis compared to H2 with theoretical stock holdings and equilibrium

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prices under the assumption of all investors trading on the basis of their funda-

mental information. If very similar coefficients to the empirically observed data

emerge, we have to accept H3. Thus, we can make statements about which

information levels should ignore their fundamental information to escape the

pattern of exploitation due to disadvantages in timing.

4 Method

4.1 Method for the examination of H1

To test H1, we run panel regressions. Each cross-section represents one single

trader with 24 observations over time. This leads to a sample of 1,920 data

points for each treatment and 3,840 data points on aggregate. As dependent

variable we calculate the over-, underperformance relative to the market return,

R′i,k,m, according to equation (7),

R′i,k,m = Ri,k,m −Rk,m, (7)

where Ri,k,m denotes the return of trader i in period k of market m and Rk,m

stands for the market return of period k. Ri,k,m is calculated as the log-change

in wealth from one period to the next,

Ri,k,m = ln(Wi,k,m)− ln(Wi,k−1,m), (8)

where Wi,k,m denotes wealth. The benchmarking on the market average

in equation (7) is a crucial step to eliminate idiosyncratic characteristics of

individual markets. The interesting point to look at is the ability of different

information levels to outperform others, irrespective of upward or downward

movements of the market as a whole. Finally, the regression equation with the

dependent variable R′i,k,m reads as follows:

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R′i,k,m = α + β1I0k,m + β2I1k,m + β3I2k,m + β4I3k,m + β5I4k,m +L∑

l=1

δARl(R′i,k−l,m) + εk,m. (9)

Depending on the information level under investigation we use dummy vari-

ables for the four remaining information levels as independent variables. For

instance, if we focus on I0 we drop dummy I0k,m from equation (9) and ex-

tract the over- underperformance to the market return of I0 from intercept α.

With this approach we analyze each information level’s over- underperformance

to the market and the performance in relation to each of the four remaining

information levels. To account for autocorrelation present in the time series,

we include AR terms. We also account for potential heteroscedasticity in the

residuals within periods by using the White-statistics to compute robust covari-

ances (White, 1980). Based on the findings of Huber (2007) we test H1 for

single-sided alternatives.


To test for hypothesis H2 on timing advantages (disadvantages) of successful

(unsuccessful) traders we compare the changes in stock holdings of each infor-

mation level j in period k of market m,

∆Sj,k,m = Sj,k,m − Sj,k−1,m, (10)

for the changes in the average market price for each period,

∆Pk,m = Pk,m − Pk−1,m, (11)

and try to find whether successful traders are able to predict future price

movements systematically. Therefore we run panel regressions with the changes

in stock holdings, ∆Sj,k,m, as dependent variable,

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∆Sj,k,m = α + β1∆PLAG + β2∆P0 + β3∆PLEAD

+L∑

l=1

δARl(Sj,k−l,m) + εj,k,m. (12)

Each cross-section represents one single market with 24 observations over

time. This leads to a sample of 192 data points for each treatment and 384

data points on aggregate. As independent variables we use lagging and lead-

ing changes in the average market price for each period, ∆Pk,m. The ex-

pression ∆PLAG of coefficient β1 stands for the sum of lag(1) to lag(3) –∑3

n=1 β1∆Pk,m(n) – of changes in mean prices.6 Here, a positive coefficient

β1 indicates that increasing (decreasing) market prices in one to three periods

would lead to increasing (decreasing) stock holdings now. Coefficient β2 with

expression ∆P0 – β2∆Pk,m(0) – indicates the changes in mean price with lag(0)

and β3 with expression ∆PLEAD represents the sum of lag(–1) to lag(–3) of

changes in mean prices –∑−1

p=−3 β3∆Pk,m(p). With β3 we find whether traders’

actions lag behind the changes in average market price. Additionally, we include

AR-terms and account for heteroskedasticity and autocorrelation within cross-

sections by using the period SUR (PCSE) method (Beck and Katz (1995)). The

data are presented for double-sided tests.


As stated above, hypothesis H3 questions whether ”the timing advantages (dis-

advantages) of successful (unsuccessful) traders are induced by the use of fun-

damental information.”

If we assume that all information levels base their trading actions on the6To achieve greater clarity we aggregate these three lags to one variable. If each lag

is included separately, very similar results can be found. One could criticize that a jointhypotheses test like the F -test with the null hypothesis that all coefficients included arezero (Wooldridge (2006)) would be more suitable. This test does not say anything about thedirection of the single coefficients. So, one could see significant results although the coefficientsshow different signs. In this case the aggregation of three coefficients to one is much better,because statements on the direction of the factors can be made.

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fundamental information provided to them, those with the highest estimate of

CV will buy, while those with the lowest CV will sell. As a consequence, prices

will be between the highest and the lowest fundamental CV . Specifically, the

two with the highest CV will buy from the two with the lowest CV . Random

or uninformed traders will be buyer or seller randomly. Thus, the equilibrium

price, PEk,m, in each period will be the median CV , which is the point where

supply and demand curves intersect. Figure 3 gives a short example with CV ′s

of 34.5, 38.7, 41.1 and 42.7. Supply and demand curves cross at the equilibrium

price of 39.9.7 Those traders with a higher estimate buy whereas the traders

with an estimate of 34.5 and 38.7 sell.


The expected changes in stock holdings, ∆SFUNDj,k,m, increase if the CVj,k

of information level j is above the equilibrium price PEk,m – in the following re-

gression we use the code ’+1’ for an expected increase of ∆SFUNDj,k,m. In this

case traders of information level j will buy given their fundamental information

because they think the stock is undervalued. ∆SFUNDj,k,m equals ’–1’ if the

CVj,k of information level j is below the equilibrium price PEk,m. In this case

traders of information level j will sell as they expect the stock to be overvalued.

Following this convention we obtain an increasing (’+1’) or a decreasing (’–1’)

expected change in stock holdings for each information level in each period of

each market. Traders with information level I0 are not included in this analysis

as they receive no fundamental information.8

Using a panel regression methodology we use ∆SFUNDj,k,m as dependent

variable. The leading or lagging changes in equilibrium price, PEk,m, represent

the independent variables,7More precisely, the supply and demand curves intersect within a range of 38.7 and 41.1.

For the sake of simplicity we assume that the price will always be the average of the secondand third largest bid, thus the median.

8Due to the random character of the trades of the uninformed their actions will level outand are thus excluded from our analysis.

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∆SFUNDj,k,m = α + β1∆PELAG + β2∆PE0 + β3∆PELEAD

+L∑

l=1

δARl(∆SFUNDj,k−l,m) + εj,k,m. (13)

Each cross-section represents one single market with 24 observations over

time.9 With the variable ∆PELAG we sum up lag(1) to lag(3) –∑3

n=1 β1∆PEk,m(n) – of changes in equilibrium prices. A positive coefficient of

β1 indicates that in periods prior to an increase in prices the CV of information

level j is above the equilibrium price under fundamental strategy. Following

fundamental strategy the trader would buy the stock now before prices increase.

In this case fundamental information predicts future price movements correctly.

Coefficient β2 with expression ∆PE0 – β2∆PEk,m(0) – indicates the changes in

equlibrium price with lag(0). Besides several AR-terms and the residuals, εj,k,m,

the variable ∆PELEAD –∑−1

p=−3 β3∆PEk,m(p) – serves as further independent

variable. Here a positive coefficient is a sign of fundamental information which is

already incorporated into prices. At the time the trader receives his fundamental

’buy’ (’sell’) signals, the market has already moved due to the actions of better

informed traders. The data are presented for double-sided tests.

5 Results

5.1 On the value of fundamental information – Examina-

tion of H1

Figure 4 gives a visual impression of the relationship of traders overperformance

and information about fundamentals.

Insert Figure 4 about here9To achieve comparability we compute the model with the same CV ′s as in the experi-

mental markets.

16

On aggregate, traders without any information earn roughly the market re-

turn and reach the same performance as the second best informed I3. Especially

the results of the computerized random traders (I0) in T2 are interesting as they

reach higher returns than traders I1 and I2 using a simple random strategy. In

both treatments the best informed traders I4 outperform the market and gain

the highest returns at the expense of the average informed I1 and I2.


Table 2 presents the results of the regression model for the whole data set.10

On aggregate insiders outperform the market and all other traders significantly.

After 24 periods their outperformance to the market return yields 4.1 percentage

points. Interestingly, the underperformance to the market return of the average

informed (I1 and I2) is statistically significant and reaches 1.9 and 2.2 percent-

age points for the total duration of the experiment. Maybe the most remarkable

finding is that the superior performance of uninformed human and computer-

ized random traders in comparison to I1 and I2 is statistically significant with

values of 2.2 and 2.5 percentage points.


Looking separately at T1 and T2 the results are very similar (Tables 3 and

4). The best-informed significantly outperform the market and all other traders

at the 1% or 5% level and I1 and I2 are beaten by I0. More surprisingly,

zero-intelligence traders of information level I0 in T2 gain higher returns than

traders with I1 to I3, whereby they outperform I1 and I2 significantly.11

Insert Table 4 about here10Note, that with this regression method different results compared to Figure 4 emerge due

to the inclusion of AR-terms.11To check whether trading volume differs across information levels we regress the per period

trading volume against the dummies of information levels I1 to I4 (panel least squares). Theintercept shows a per period trading volume of 9.4 for I0. The coefficients of the variousinformation levels are not significantly different from zero. Thus, the calibration of the randomtraders is successful because they exhibit the same trading volume as humans.

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This leads to the stunning conclusion that trading without any fundamental

information or trading randomly is more advantageous than trading on the ba-

sis of average fundamental information. Only insider information can guarantee

significantly above-average returns which is in line with literature on insider

trading by Lakonishok and Lee (2001), Lin and Howe (1990), Seyhun (1986)

and Stotz (2006). Studies on the performance of mutual funds by Cowles (1933,

1944), Gruber (1996), Jensen (1968), Malkiel (1995, 2003a,b, 2005) show that

they equal or slightly underperform the market average, after checking for sur-

vivorship bias and before transaction costs. This pattern can also be observed

for I2 and I3. They, too, have average or good information but are not able

to beat the market. All in all, we reject the null hypothesis of no difference in

returns and accept the above-stated H1. We also have to reject the strong form

of the EMH, which implies no difference in return between groups of investors.

5.2 Explanations for the negative value of fundamental

information

5.2.1 Predictions of future price movements in the experimental

data – Examination of H2

We see from the top panel of Table 5 that traders with insider information I4

show a highly significant positive coefficient of ∆PLAG. These traders increase

(decrease) their stock holdings by 0.74 before prices go up (down) by 100 basis

points within the next 3 periods. Additionally, coefficient β3, the measure for

the lagged changes in stock holdings conditional on changes in average market

prices is highly significantly negative. Insiders decrease (increase) their stock

holdings by 0.45 after prices went up (down) by 100 basis points within the last

3 periods. This pattern of timing advantages of insiders is also mentioned by

authors of empirical studies on insider trading like Lakonishok and Lee (2001)

and Stotz (2006), who report that insiders buy after stock prices have fallen and

sell after stock prices have risen.

18


Traders with average information levels I1 and I2 on the other hand face

disadvantages in timing. Their coefficient β1 of ∆PLAG is significantly nega-

tive which indicates that they sell on average 0.27 and 0.35 stocks before prices

fall (rise) by 100 basis points within the next 3 periods. Additionally, they buy

(sell) on average 0.24 and 0.36 stocks after prices have risen (fallen) by 100 basis

points within the last 3 periods (see variable ∆PLEAD). Uninformed traders,

irrespective whether human or artificial, exhibit no significant coefficients of

∆PLAG, ∆P0 and ∆PLEAD. They are independent and do not make system-

atic errors in estimating future price changes. Very similar patterns are found

in each of the treatments separately as the middle and lower panels of Table 5

show.

Therefore, we reject the null hypothesis of H2 implying no timing advantages

of different information levels. Instead we accept that successful investors (I4)

predict future price changes correctly, as they buy at the time when prices are

low and they sell at higher prices. The unsuccessful traders with information

levels I1 and I2 predict future prices systematically wrong and thus buy high

and sell low. Uninformed traders I0 do not make systematic mistakes in timing.

5.2.2 Theoretical predictions of future price movements according

to traders fundamental information – Examination of H3

Table 6 gives an overview of the results of H3 to analyze whether the empir-

ically observed timing advantages (disadvantages) are induced by the use of

fundamental information.


Especially for the best performer I4 and the worst performer I2 very sim-

ilar signs of the coefficients compared to the empirically observed data can be

found. ∆PELAG for I4 is positive and significant at the 1% level which means

19

that insiders would buy (sell) before equilibrium prices PEk,m rise (fall). Con-

sequently, insiders are able to predict future price changes. The coefficient of

∆PELAG for the average-informed I2 shows a highly significantly negative sign

which implies that they are mislead by their fundamental information. Fol-

lowing their fundamentals they would mainly sell (buy) before prices increase

(decrease). Similar to the experimental data observed in H2, the coefficient β3

of ∆PELEAD of I4 is highly significantly negative, whereas for I2 a signifi-

cant positive value can be found, showing an expected increase (decrease) in

stock holdings after prices have increased (decreased) for the latter. This result

on β3 provides evidence that I2 base their trading on fundamental informa-

tion which is already incorporated into prices. At the time they receive their

fundamental information it becomes misleading, because insiders have already

moved the market. Due to the fact that very similar coefficients compared to

the empirically observed data in H2 emerge, we reject the null hypothesis of H3.

Therefore, we accept the alternative hypothesis stating that ”timing advantages

(disadvantages) of successful (unsuccessful) traders are induced by the use of

fundamental information.”

Qualitatively speaking, insiders mainly use their fundamental information

which is a very good indicator for future price development. Through their

actions prices quickly adjust in the relevant direction. At the time when the

average informed trade, their fundamental information is already incorporated

into prices which leads to the pattern that they buy (sell) after prices have risen

(fallen) and they buy (sell) before prices go down (up). To escape this pattern of

exploitation by the insiders it would be useful for the average informed to ignore

their fundamental information, trade randomly and thus become unpredictable

and unexploitable. That is the reason why the human uninformed I0 in T1 and

the computerized random traders in T2 reach the market return. As they have

no access to the information structure they are independent and thus cannot be

exploited systematically.

20

Due to the fact that the empirically observed patterns of changes in stock

holdings of H2 and the theoretical predictions of H3 coincide, we can infer in-

directly that traders mainly use their fundamental information. Therefore we

check for each transaction whether the traders use their fundamental informa-

tion. If the conditional value, CVj,k, of the trader with information level j is

higher than the resulting market price of his transaction, Pt, he should buy

the undervalued stock. If the CVj,k is below the resulting price, he should sell

the overvalued stock. Following this convention we obtain for each information

level in each period the number of transactions that can be subsumed under

fundamental strategy and divide this by the total number of trades of this in-

formation level in each period. This leads to the percentage of fundamental

strategy, %FSj,k,m, of information level j in period k of market m.

Again, we use the panel regression methodology with %FSj,k,m as dependent

variable. For information levels I2 to I4 dummy variables serve as independent

variables, which yields the following regression model:

%FSj,k,m = α + β1I2k,m + β2I3k,m + β3I4k,m

+L∑

l=1

δARl(%FSj,k−l,m) + εj,k,m. (14)

Several AR-terms complete the model and the period SUR (PCSE) method

accounts for heteroskedasticity and autocorrelation within cross-sections (Beck

and Katz (1995)). As we conject that traders have more confidence in their fun-

damental information with increasing information level, the data are presented

for single-sided tests.12


Table 7 indicates that in aggregate traders with information level I1 use their

fundamental strategy strictly in 53.2% of all trades (see intercept α). Ratios of12Note that the above definition is very strict. If we assume a trader who basically follows

his fundamental strategy but sometimes has the opportunity to buy cheaper than he soldbefore and vice versa within the same period, his ratio would decrease.

21

I2, I3, and I4 are significantly higher with values of 59.5%, 59.1%, and 68.9%,

respectively.

6 Conclusion

In this paper we show that knowing nothing about a company’s fundamen-

tals can yield higher returns than having average information whereas Insiders

outperform the market and all other traders. Insiders face timing advantages

because they buy (sell) before prices rise (fall) and they sell (buy) after prices

have risen (fallen). They mainly trade according to their fundamental informa-

tion with the consequence of a relatively quick adjustment of prices. At the time

when the average-informed receive this piece of information it is already incor-

porated into prices. This leads to the observed pattern that average informed

buy (sell) after prices have risen (fallen) and that they buy (sell) before prices

fall (rise). For them it would be a dominant strategy to become unpredictable

and thus unexploitable. In the experimental markets they should ignore their

fundamental information or trade randomly under the assumption of all other

things being equal. On real asset markets they could reach the market aver-

age with a simple buy-and-hold strategy in passive investment products, such

as broadly diversified Index funds or Index-ETF’s (Exchange Traded Funds).

Uninformed human and random artificial traders are protected by their lack of

information. They have no access to fundamental information and thus cannot

be exploited systematically. Sometimes they buy cheap and sell at higher prices,

sometimes the opposite is the case. On average, they earn the market return.

22

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25

Figures and Tables

0 500 1000 1500 200020

25

30

35

40

45

50

55

60

65

70

Time in sec.

Val

ue, V

; Con

ditio

nal v

alue

, CV

I1I2I3I4

Figure 1: Conditional values, CV , of the different information levels as a function of time in

market 7. The intrinsic value of the asset equals the CV of information level I4. Beginning

with the insiders, I4, the CV -function of information level j is shifted (4 − j) periods to

the right. So, all traders obtain the same information, but the worse informed, the later the

information is received.

26

0 5 10 15 2020

25

30

35

40

45

50

55

60

65

70

Period

Val

ue

M1M2M3M4EV

0 5 10 15 2020

25

30

35

40

45

50

55

60

65

70

Period

Val

ue

M5M6M7M8EV

Figure 2: Intrinsic value, Vk, as a function of period for the eight markets of each treatment.

One can see that each value process is mirrored at the dotted line. So, the average intrinsic

value at any period represents the expected value (dotted line) derived by the parameters of

the geometric Brownian Motion process.

27

Parameter Agent 1 Agent 2

Cwt 5 10Range of Wt 5-15 10-20Cq 3 1Range of Q 3-7 1-5

Table 1: Parameters for the computerized random traders, I0, in treatment T2. Agent 1

simulates an active trader, while Agent 2 is a relatively passive one. Cwt is a constant for

calculating the waiting time between limit orders, ’Range of Wt’ indicates the span of waiting

times, Cq is a constant for the calculation of the trading quantity and the ’Range of Q’ defines

the span of possible trading quantities of the limit orders.

28

0 1 2 3 430

35

40

45

Volume

Bid

s, A

sks,

Equ

libriu

m p

rice

demandsupply

Figure 3: Supply and demand curves under the assumption that all traders use their fun-

damental information with CV ′s of 34.5, 38.7, 41.1 and 42.7. Both functions intersect at the

equilibrium price of 39.9 which is the median of all CV ′s. Those traders with a higher estimate

buy whereas the traders with an estimate of 34.5 and 38.7 sell. For simplicity, traders with

information level I0 are left out from this analysis as they receive no fundamental information.

One can assume, that due to their random character their actions will level out.

29

0 1 2 3 4−0.3

−0.2

−0.1

0

0.1

0.2

0.3

Information level

Ove

r−, U

nder

perf

orm

ance

per

per

iod

in %

: Ri,k′

⋅100

T1T2Aggregate

Figure 4: Per period over- and underperformance to the market return, R′i,k · 100, as a

function of information level. In T1 traders with the average information level I2 perform

worst, whereas uninformed traders, I0, are above the market return and are only beaten by

the insiders, I4. In T2 the computerized random traders, I0, slightly underperform the market

but outperform the better informed I1 and I2. On aggregate the uninformed I0 and the good

informed I3 equal the market return. The insiders I4 clearly gain above average returns on

the expenses of the average informed I1 and I2.

30

Dependent VariableOver-, Underperformance per period, R′i,k

Factor I0 I1 I2 I3 I4

α 0.014 -0.077** -0.089** -0.019 0.172***(0.035) (0.043) (0.039) (0.046) (0.059)

I0 - 0.091** 0.103** 0.032 -0.158**- (0.056) (0.053) (0.057) (0.069)

I1 -0.091** - 0.012 -0.058 -0.249***(0.055) - (0.058) (0.063) (0.073)

I2 -0.103** -0.013 - -0.071 -0.261***(0.053) (0.058) - (0.060) (0.071)

I3 -0.032 0.058 0.071 - -0.191***(0.057) (0.063) (0.060) - (0.074)

I4 0.158** 0.249*** 0.261*** 0.191*** -(0.069) (0.073) (0.071) (0.074) -

*, ** and *** represent the 10%, 5% and the 1% significance levels.

Table 2: Aggregate data for both treatments. Explanatory variables for the dependent

variable over-, underperformance to the market return, R′i,k, for each of the five information

levels. The factors, I0 to I4 are binary dummy variables. The coefficient values are given

in percentage points and the standard errors are mentioned in parentheses. The p-values are

calculated for single-sided tests with respect to the results in Huber (2007). In total, 4 AR-

terms are included, sample size n equals 3,200 with data from 160 cross-sections and R2 is 0.09.

On aggregate I4 significantly outperform the market with 0.17 percentage points per period,

while I1 and I2 are significantly below the market average. The uninformed humans in T1

and the computerized random traders in T2 as a group (I0) are second best and significantly

outperform I1 and I2.

31



α 0.010 -0.004 -0.089** -0.048 0.131**(0.059) (0.060) (0.051) (0.072) (0.066)

I0 - 0.013 0.098* 0.057 -0.121*- (0.084) (0.078) (0.093) (0.089)

I1 -0.013 - 0.085 0.044 -0.135*(0.084) - (0.079) (0.094) (0.089)

I2 -0.098* -0.085 - -0.041 -0.220***(0.078) (0.079) - (0.088) (0.084)

I3 -0.057 -0.044 0.041 - -0.178**(0.093) (0.094) (0.088) - (0.098)

I4 0.121* 0.135* 0.220*** 0.178** -(0.089) (0.089) (0.084) (0.098) -


Table 3: Treatment 1: Explanatory variables for the dependent variable over-, underper-

formance to the market return, R′i,k, for each of the five information levels. The factors, I0

to I4 are binary dummy variables. The coefficient values are given in percentage points and

the standard errors are mentioned in parentheses. The p-values are calculated for single-sided

tests with respect to the results in Huber (2007). In total, 2 AR-terms are included, sample

size n equals 1,760 with data from 80 cross-sections and R2 is 0.122. I4 significantly outper-

form the market, while I2 significantly underperform the market with -0.09 percentage points

per period. Uninformed I0 are second best with 0.10 percentage points per period above the

market return.

32



α 0.001 -0.159*** -0.085* -0.003 0.246***(0.036) (0.044) (0.061) (0.063) (0.093)

I0 - 0.160*** 0.086* 0.004 -0.245***- (0.057) (0.068) (0.073) (0.101)

I1 -0.160*** - -0.074 -0.156** -0.404***(0.057) - (0.073) (0.077) (0.103)

I2 -0.086* 0.074 - -0.082 -0.331***(0.068) (0.073) - (0.086) (0.111)

I3 -0.004 0.155** 0.082 - -0.249**(0.073) (0.077) (0.086) - (0.111)

I4 0.245*** 0.404*** 0.331*** 0.249** -(0.101) (0.103) (0.111) (0.111) -


Table 4: Treatment 2: Explanatory variables for the dependent variable over-, underper-

formance to the market return, R′i,k, for each of the five information levels. The factors, I0

to I4 are binary dummy variables. The coefficient values are given in percentage points and

the standard errors are mentioned in parentheses. The p-values are calculated for single-sided

tests with respect to the results in Huber (2007). In total, 4 AR-terms are included, sample

size n equals 1,600 with data from 80 cross-sections and R2 is 0.067. I4 significantly outper-

form the market with 0.25 percentage points per period, while I1 are significantly below the

market average. The uninformed and computerized random traders, I0, are second best and

equal the market return.

33

Dependent Variablechanges stock holdings, T1 & T2


α 0.09 -0.36 -0.22 0.59** -0.01(0.26) (0.29) (0.27) (0.23) (0.27)

∆PLAG -0.20 -0.27** -0.35** -0.06 0.74***(0.15) (0.13) (0.16) (0.14) (0.15)

∆P0 -0.10 -0.40 0.10 0.71** -0.18(0.31) (0.26) (0.32) (0.32) (0.40)

∆PLEAD 0.09 0.24** 0.36** -0.16 -0.45***(0.15) (0.12) (0.16) (0.12) (0.16)

#AR-terms 3 3 2 3 3R2 0.08 0.09 0.24 0.10 0.36n 224 224 240 224 224

T1Factor I0 I1 I2 I3 I4

α -0.11 -0.05 -0.63** -0.55 0.06(0.43) (0.46) (0.27) (0.42) (0.43)

∆PLAG -0.10 -0.36** -0.29* -0.33* 0.86***(0.30) (0.17) (0.16) (0.20) (0.23)

∆P0 -0.14 -0.34 0.34 0.61 0.22(0.47) (0.32) (0.24) (0.45) (0.56)

∆PLEAD 0.05 0.07 0.46*** -0.13 -0.53**(0.24) (0.14) (0.14) (0.21) (0.27)

#AR-terms 3 3 3 3 3R2 0.13 0.14 0.34 0.12 0.34n 112 112 112 112 112

T2Factor I0 I1 I2 I3 I4

α -0.20 -0.56* -0.14 0.78*** -0.13(0.24) (0.31) (0.43) (0.28) (0.30)

∆PLAG -0.24* -0.25 -0.25 -0.06 0.89***(0.14) (0.15) (0.28) (0.16) (0.20)

∆P0 0.27 -0.23 -0.22 0.61 -1.06*(0.25) (0.31) (0.66) (0.45) (0.60)

∆PLEAD 0.14 0.14 0.24 -0.10 -0.28(0.16) (0.14) (0.30) (0.17) (0.25)

#AR-terms 0 0 2 0 2R2 0.03 0.02 0.15 0.02 0.32n 136 136 120 136 120


Table 5: Panel regression of the changes in stock holdings, ∆Sj,k,m, as dependent variable

and leading and lagging changes in average market price, ∆Pk,m, as independent variables.

∆PLAG represents the sum of lag(1) to lag(3) of changes in mean prices. With the coefficients

of ∆P0 traders predict price movements of the current period. ∆PLEAD indicates how stock

holdings change after prices have changed. The data is presented for double-sided tests with

standard errors in parentheses. On aggregate (top panel), the significant positive coefficient

of ∆PLAG and the significant negative coefficient of ∆PLEAD indicates timing advantages

of I4. They increase (decrease) their stock holdings by 0.74 before prices rise (fall) by 100

basis points within the next 3 periods and they decrease (increase) their stock holdings after

prices have risen (fallen). For traders with average information levels I1 and I2 the coefficient

of ∆PLAG is significantly negative and ∆PLEAD shows a significant positive sign. They

decrease (increase) their stock holdings in the three periods before prices rise (fall) and increase

(decrease) their stock holdings after prices have risen (fallen). Uninformed traders, irrespective

of human or artificial, are independent and do not make systematic errors in estimating future

price changes. 34

Dependent Variableexpected changes stock holdings

Factor I1 I2 I3 I4

α -0.06 -0.04 0.08* 0.02(0.04) (0.04) (0.04) (0.02)

∆PELAG 1.26** -3.30*** -1.58*** 3.42***(0.57) (0.60) (0.49) (0.82)

∆PE0 -18.70*** -11.12*** 16.36*** 13.69***(1.23) (1.83) (1.36) (1.88)

∆PELEAD 1.72*** 5.01*** -1.43** -4.55***(0.65) (0.70) (0.69) (0.62)

#AR-terms 1 0 1 2R2 0.43 0.39 0.34 0.66n 128 136 128 120


Table 6: Panel regression with the dependent variable, ∆SFUNDj,k,m, the expected changes

in stock holdings according each information levels fundamental information. Leading and

lagging versions of the changes in equlibrium price, PEk,m, serve as independent variables:

∆PELAG represents the sum of lag(1) to lag(3) of changes in mean prices. ∆PE0 stands for

the unlagged changes in mean prices. ∆PELEAD indicates the relation of past prices (the

aggregate of the last 3 periods) and expected changes in stock holdings according information

level’s fundamental information. The data is presented for double-sided tests with standard

errors in parenthesis. The results are very similar to those in Table 5. Coefficient ∆PELAG

of I4 is highly significantly positive which will lead to an increase (decrease) in stock holdings

before prices rise (fall). For the average informed I2 coefficients of ∆PELAG show highly

significantly negative values. Coefficients of ∆PELEAD for I1, I2 and I4 exhibit the same

directions compared to table 5. This indicates that at the time the average informed trade

on the basis of their fundamental information it is already incorporated into prices due to the

actions of the better informed I3 and I4.

35

Factor Aggregate T1 T2

α 0.532*** 0.557*** 0.510***(0.030) (0.046) (0.039)

I2 0.063* 0.036 0.087*(0.044) (0.068) (0.055)

I3 0.059* 0.046 0.071*(0.043) (0.082) (0.055)

I4 0.157*** 0.082* 0.232***(0.044) (0.063) (0.057)

#AR-terms 3 3 3R2 0.08 0.06 0.10n 1774 810 964


Table 7: Panel regression with the dependent variable percentage of fundamental strategy,

%FS, and dummies for I2 to I4 as independent variables. As we expect that traders have

more confidence in their fundamental information with increasing information level, the data

is presented for single-sided tests. The standard errors are given in parentheses. All infor-

mation levels show ratios larger than 50%. I2, I3 and I4 significantly use more fundamental

information than traders with I1 with ratios of 59.5%, 59.1% and 68.9%.

36

Appendix

Experimental instructions

We welcome you to this experimental session and ask you to refrain from talking

to each other for the duration of the experiment

Background of the experiment

This experiment consists of a market in which ten traders trade the shares of a

fictitious company for 20-30 consecutive periods (months).

Market procedure

The market is characterized by an asymmetric information structure. The best

informed (I4) receive all relevant information on the company. The second

best informed (I3) receive the same information one period later. This process

continues until the worst informed, I1, receive the information, who have an

informational disadvantage of 3 periods compared to the insiders.

Trading will occur with a double auction market mechanism. The price of

the shares is determined by your and the other traders’ actions in the market.

You are free to submit as many bids and asks (in the range of 10 to 200 with

up to two decimal places) as you wish.

Total wealth

Your wealth is the sum of your money balance and the market value of your

shares (the number of shares you hold multiplied with the current price). Your

wealth will change during a period as the market price changes, even if you do

not trade; the most recent trading price will be used to value your shares.

Fundamental value and CV

All relevant information on the future development of the company are included

in the variable ”intrinsic value”, which stands for the fundamentally justified

37

valuation of the company at any time. The fundamental value starts at 40 and

will change randomly each period. The random change each period is +0.5%

with a standard deviation of 7.2%. Examples:

• The probability of the intrinsic value increasing by more than 14.9% =

2.3%

• The probability of the intrinsic value decreasing by more than 13.9% =

2.3%

• The probability for the intrinsic value increasing by more than 7.7% =16%

• The probability for the intrinsic value decreasing decrease by more than

6.7% =16%.

The intrinsic value is especially relevant at the end of the experiment, since

all shares will be bought back by the experimenter from you at that time at

this value. Each period you (as well as every other participant with exception

of I0) receive an estimate (CV) of the intrinsic value. Traders with information

level 4 (I4) get the most up-to-date information, i.e. the intrinsic value of the

stock in the current period. Traders with information level 3 receive the same

information with one period delay. Traders with information level 2 get the same

information as I4, just two periods later. Finally, investors with information

level I1 receive the same fundamental information as I4 with three periods

delay. As mentioned before, traders with I0 don’t get any information on the

fundamentals of the company.

The following table gives a brief overview on the number of traders per

information level and their initial endowments:

Information level Stocks Money No. traders Lag to intrinsic value

I0 40 1,600 2 no informationI1 40 1,600 2 3I2 40 1,600 2 2I3 40 1,600 2 1I4 40 1,600 2 0

Table E1: Overview of initial endowments and traders per information level.

38

0 500 1000 1500 200020

25

30

35

40

45

50

55

60

65

70

Time in sec.

Val

ue, V

; Con

ditio

nal v

alue

, CV

I1I2I3I4

Figure E1: Example of a realisation of intrinsic value/CV as a function ofinformation level

At the end of each period a history screen will give a short summary on your

endowments, past prices and trading activity on the market.

39

Figure E2: Trading screen

40

Figure E3: History screen

Some important details

• Each period lasts 100 seconds. The experiment will be terminated between

periods 20 and 30, with equal probability at each termination date.

• Final payment: At the end of the experiment you will be paid in EUR. At

this time all your stocks will be bought back at the intrinsic value (equal

to the estimate of I4 in the final period). Your money will be added to

the value of your stocks and this amount will be converted into EUR at

the rate of 1 EUR = 175 Taler. So, at the end of the experiment only I4

are perfectly informed on the intrinsic value of the stocks. The worse your

information level, the imprecise your estimate (CV) will be.

Example: If your final wealth is 3860 units of money you earn 3860/175

= 22.10

41

Plots of markets

T1

0 500 1000 1500 200020

25

30

35

40

45

50

55

60

65

70

Time in sec.

Val

ue, V

; Con

ditio

nal v

alue

, CV

; Pric

eT1_M1

I1I2I3I4Price

0 5 10 15 20 25 30 35 40−0.6

−0.4

−0.2

0

0.2

0.4

0.6

lag

AC

F R

etur

ns, |

Ret

urns

|

0 500 1000 1500 2000

−0.4

−0.2

0

0.2

0.4

Time in sec.

Ret

urns

T1_M1

Figure A1: T1 M1: Intrinsic value, conditional values (CV ) and prices as a function of

time - (top). Autocorrelation function of absolute log-returns (solid line with asterisks) and

of log-returns (solid line) - (bottom). The dashed lines represent the 95% confidence bounds.

42

0 500 1000 1500 200020

25

30

35

40

45

50

55

60

65

70

Time in sec.

Val

ue, V

; Con

ditio

nal v

alue

, CV

; Pric

e

T1_M2

I1I2I3I4Price

0 5 10 15 20 25 30 35 40−0.6

−0.4

−0.2

0

0.2

0.4

0.6

lag

AC

F R

etur

ns, |

Ret

urns

|

0 500 1000 1500 2000

−0.4

−0.2

0

0.2

0.4

Time in sec.

Ret

urns

T1_M2




43

0 500 1000 1500 200020

25

30

35

40

45

50

55

60

65

70

Time in sec.

Val

ue, V

; Con

ditio

nal v

alue

, CV

; Pric

e

T1_M3

I1I2I3I4Price

0 5 10 15 20 25 30 35 40−0.6

−0.4

−0.2

0

0.2

0.4

0.6

lag

AC

F R

etur

ns, |

Ret

urns

|

0 500 1000 1500 2000

−0.4

−0.2

0

0.2

0.4

Time in sec.

Ret

urns

T1_M3




44

0 500 1000 1500 200020

25

30

35

40

45

50

55

60

65

70

Time in sec.

Val

ue, V

; Con

ditio

nal v

alue

, CV

; Pric

e

T1_M4

I1I2I3I4Price

0 5 10 15 20 25 30 35 40−0.6

−0.4

−0.2

0

0.2

0.4

0.6

lag

AC

F R

etur

ns, |

Ret

urns

|

0 500 1000 1500 2000

−0.4

−0.2

0

0.2

0.4

Time in sec.

Ret

urns

T1_M4




45

0 500 1000 1500 200020

25

30

35

40

45

50

55

60

65

70

Time in sec.

Val

ue, V

; Con

ditio

nal v

alue

, CV

; Pric

e

T1_M5

I1I2I3I4Price

0 5 10 15 20 25 30 35 40−0.6

−0.4

−0.2

0

0.2

0.4

0.6

lag

AC

F R

etur

ns, |

Ret

urns

|

0 500 1000 1500 2000

−0.4

−0.2

0

0.2

0.4

Time in sec.

Ret

urns

T1_M5




46

0 500 1000 1500 200020

25

30

35

40

45

50

55

60

65

70

Time in sec.

Val

ue, V

; Con

ditio

nal v

alue

, CV

; Pric

e

T1_M6

I1I2I3I4Price

0 5 10 15 20 25 30 35 40−0.6

−0.4

−0.2

0

0.2

0.4

0.6

lag

AC

F R

etur

ns, |

Ret

urns

|

0 500 1000 1500 2000

−0.4

−0.2

0

0.2

0.4

Time in sec.

Ret

urns

T1_M6




47

0 500 1000 1500 200020

25

30

35

40

45

50

55

60

65

70

Time in sec.

Val

ue, V

; Con

ditio

nal v

alue

, CV

; Pric

e

T1_M7

I1I2I3I4Price

0 5 10 15 20 25 30 35 40−0.6

−0.4

−0.2

0

0.2

0.4

0.6

lag

AC

F R

etur

ns, |

Ret

urns

|

0 500 1000 1500 2000

−0.4

−0.2

0

0.2

0.4

Time in sec.

Ret

urns

T1_M7




48

0 500 1000 1500 200020

25

30

35

40

45

50

55

60

65

70

Time in sec.

Val

ue, V

; Con

ditio

nal v

alue

, CV

; Pric

e

T1_M8

I1I2I3I4Price

0 5 10 15 20 25 30 35 40−0.6

−0.4

−0.2

0

0.2

0.4

0.6

lag

AC

F R

etur

ns, |

Ret

urns

|

0 500 1000 1500 2000

−0.4

−0.2

0

0.2

0.4

Time in sec.

Ret

urns

T1_M8




49

T2

0 500 1000 1500 200020

25

30

35

40

45

50

55

60

65

70

Time in sec.

Val

ue, V

; Con

ditio

nal v

alue

, CV

; Pric

e

T2_M1

I1I2I3I4Price

0 5 10 15 20 25 30 35 40−0.6

−0.4

−0.2

0

0.2

0.4

0.6

lag

AC

F R

etur

ns, |

Ret

urns

|

0 500 1000 1500 2000

−0.4

−0.2

0

0.2

0.4

Time in sec.

Ret

urns

T2_M1




50

0 500 1000 1500 200020

25

30

35

40

45

50

55

60

65

70

Time in sec.

Val

ue, V

; Con

ditio

nal v

alue

, CV

; Pric

e

T2_M2

I1I2I3I4Price

0 5 10 15 20 25 30 35 40−0.6

−0.4

−0.2

0

0.2

0.4

0.6

lag

AC

F R

etur

ns, |

Ret

urns

|

0 500 1000 1500 2000

−0.4

−0.2

0

0.2

0.4

Time in sec.

Ret

urns

T2_M2




51

0 500 1000 1500 200020

25

30

35

40

45

50

55

60

65

70

Time in sec.

Val

ue, V

; Con

ditio

nal v

alue

, CV

; Pric

e

T2_M3

I1I2I3I4Price

0 5 10 15 20 25 30 35 40−0.6

−0.4

−0.2

0

0.2

0.4

0.6

lag

AC

F R

etur

ns, |

Ret

urns

|

0 500 1000 1500 2000

−0.4

−0.2

0

0.2

0.4

Time in sec.

Ret

urns

T2_M3




52

0 500 1000 1500 200020

25

30

35

40

45

50

55

60

65

70

Time in sec.

Val

ue, V

; Con

ditio

nal v

alue

, CV

; Pric

e

T2_M4

I1I2I3I4Price

0 5 10 15 20 25 30 35 40−0.6

−0.4

−0.2

0

0.2

0.4

0.6

lag

AC

F R

etur

ns, |

Ret

urns

|

0 500 1000 1500 2000

−0.4

−0.2

0

0.2

0.4

Time in sec.

Ret

urns

T2_M4




53

0 500 1000 1500 200020

25

30

35

40

45

50

55

60

65

70

Time in sec.

Val

ue, V

; Con

ditio

nal v

alue

, CV

; Pric

e

T2_M5

I1I2I3I4Price

0 5 10 15 20 25 30 35 40−0.6

−0.4

−0.2

0

0.2

0.4

0.6

lag

AC

F R

etur

ns, |

Ret

urns

|

0 500 1000 1500 2000

−0.4

−0.2

0

0.2

0.4

Time in sec.

Ret

urns

T2_M5




54

0 500 1000 1500 200020

25

30

35

40

45

50

55

60

65

70

Time in sec.

Val

ue, V

; Con

ditio

nal v

alue

, CV

; Pric

e

T2_M6

I1I2I3I4Price

0 5 10 15 20 25 30 35 40−0.6

−0.4

−0.2

0

0.2

0.4

0.6

lag

AC

F R

etur

ns, |

Ret

urns

|

0 500 1000 1500 2000

−0.4

−0.2

0

0.2

0.4

Time in sec.

Ret

urns

T2_M6




55

0 500 1000 1500 200020

25

30

35

40

45

50

55

60

65

70

Time in sec.

Val

ue, V

; Con

ditio

nal v

alue

, CV

; Pric

e

T2_M7

I1I2I3I4Price

0 5 10 15 20 25 30 35 40−0.6

−0.4

−0.2

0

0.2

0.4

0.6

lag

AC

F R

etur

ns, |

Ret

urns

|

0 500 1000 1500 2000

−0.4

−0.2

0

0.2

0.4

Time in sec.

Ret

urns

T2_M7




56

0 500 1000 1500 200020

25

30

35

40

45

50

55

60

65

70

Time in sec.

Val

ue, V

; Con

ditio

nal v

alue

, CV

; Pric

e

T2_M8

I1I2I3I4Price

0 5 10 15 20 25 30 35 40−0.6

−0.4

−0.2

0

0.2

0.4

0.6

lag

AC

F R

etur

ns, |

Ret

urns

|

0 500 1000 1500 2000

−0.4

−0.2

0

0.2

0.4

Time in sec.

Ret

urns

T2_M8




57

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Curse of mediocrity - On the value of asymmetric