Is more information always better? Experimental financial
markets with cumulative information#
Jürgen Huber†,#, Michael Kirchler† and Matthias Sutterª,‡,*
†
University of Innsbruck, Department of Banking and Finance, Universitaetsstrasse 15, A-6020
Innsbruck, Austria. Phone: +43 512 507 7555, Fax: +43 512 507 2846, e-mail:
michael.kirchler@uibk.ac.at
#
Yale University, School of Management, 135 Prospect Street, P.O. Box 208200, New Haven,
Connecticut 06520-8200, USA. Phone: 001 203 432 5799, Fax: 001 203 433 0342, e-mail:
juergen.huber@uibk.ac.at
ª University of Innsbruck, Department of Economics, Universitaetsstrasse 15, A-6020 Innsbruck, Austria.
Phone: + 43 512 507 7152, Fax: +43 512 507 2970, e-mail: matthias.sutter@uibk.ac.at
‡
University of Cologne, Department of Economics, Albertus Magnus Platz, D-50923 Köln, Germany.
Phone: +49 221 470 5761, Fax: +49 221 470 5068, e-mail: msutter@uni-koeln.de
Final version: 18th April 2006
______________________________________________________________________
Abstract
We study the value of information in financial markets by asking whether having more
information always leads to higher returns. We address this question in an experiment
where information about an asset’s intrinsic value is cumulatively distributed among
traders. We find that only the very best informed traders (i.e. insiders) significantly
outperform less informed traders. However, there is a wide range of information levels
(from zero information to above average information levels) where additional
information does not yield higher returns. The latter result implies that the value of
additional information need not be strictly positive.
JEL-classification: C91; D82; D83; G1
Keywords: Cumulative information, Experimental economics, Value of information
__________________________________________________________________________________________________________
#
*
We would like to thank Matthias Bank, Michael Hanke, Florian Hauser, Rudolf Kerschbamer, Klaus
Schredelseker, two anonymous referees and an associate editor for their very helpful comments on
earlier versions of this paper. We also received useful suggestions from conference participants at
WEHIA 2003 and 2004, ELAB 2003, ESA 2004, and Verein fuer Socialpolitik 2004. Debra Dove
helped us in editing the paper. Financial support from the Raiffeisen-Landesbank Tirol and the Center
for Experimental Economics at the University of Innsbruck is gratefully acknowledged.
Corresponding author: Department of Economics, University of Cologne, Albertus Magnus Platz, D50923 Köln, Germany. Phone: +49 221 470 5761. e-mail: msutter@uni-koeln.de
1 Introduction
This paper addresses the question whether having more information than others is
always advantageous when trading on financial markets. More precisely, we study
whether traders who are better informed about the intrinsic value of an asset can expect
to earn higher returns than traders with less information. If the answer to that question
were positive, then we might conclude that having more information has generally a
positive marginal benefit. In individual decision-making tasks this is typically the case,
as has already been pointed out by Blackwell (1951). However, in an interactive context
such as trading on financial markets, the answer to our question is less obvious and
might not necessarily be positive for all information levels. Game theory, for instance,
shows that “having more information (or, more precisely, having it known to other
players that one has more information) can make the player worse off” (Gibbons 1992,
63).1
We will present an experimental study to examine the marginal value of additional
information for traders in financial markets. Traders will have different levels of
information about the intrinsic value of a tradable asset. The distribution of information
is cumulative, meaning that a better informed trader knows everything that a less
informed trader knows, plus a little extra. By implementing such a cumulative
information system and holding all other conditions constant, it is possible to analyze
the marginal value of additional information. The two features of (i) considering more
than two different information levels and (ii) having a cumulative information system
distinguish our paper from almost all previous studies. Most experimental papers on the
value of information have considered two distinct information levels only, showing that
informed traders outperform uninformed ones (see, e.g., Copeland and Friedman 1992,
Ackert et al. 2002). Yet two information levels (in particular in the binary context of
informed versus uninformed traders) are not enough to conclude that more information
is always better. There are several theoretical papers on the value of information when
more than two traders have different information. These models, which will be related
1
Bassan et al. (1997) provide some nice examples for situations in which having more information is
actually detrimental to a player’s payoffs in a two-person game (see also the related paper of
Kamien et al. (1990)). In the context of financial markets one might refer to Cowles (1933, 1944)
who was the first to show that financial advisors and professionals are almost without exception not
able to outperform the market. Hence, the (presumably) better information of financial experts need
not yield higher returns. A related argument is made by Malkiel (2003a, 2003b) who shows that 80
percent of professionally managed funds do worse than the market average.
1
more specifically to our paper in section 2, are typically characterized by a combination
of public information about an asset and private information, with the latter being
idiosyncratic for each trader. Although these models provide very useful insights into
asset pricing, they are not suitable for answering the question of whether more
information leads to better results (in terms of trading profits) than less information,
because no trader has more information than another trader in these models, just
different information. This led Figlewski (1982, 99) to claim that “independent
information is not likely to be an adequate description of the information structure of a
real-world speculative market” Rather, we think it is more realistic to assume that
information is cumulatively distributed, meaning that some traders know more than
others by having the same plus some extra information. For instance, there may be some
investors relying exclusively on information from newspapers or TV. Such information
is, of course, also available to better informed investors who also take into account
companies’ fundamentals such as their public financial statements or revenue outlook.
Finally, there may be some very well informed traders (insiders) having all the
previously mentioned information, but also knowing some important details (such as a
planned merger or a product innovation) that are not publicly known.
Given that there is no empirical evidence on the value of additional information
when information is cumulatively distributed, we have opted for an experimental
approach. In the laboratory we are able to control carefully a trader’s information about
the value of an asset. In particular, we can easily assign to single traders different levels
of information in a cumulative way, such that better informed traders know everything
that less informed traders know, plus an additional amount. By implementing such a
cumulative information system and holding all other conditions constant, we can track
down the marginal value of additional information.
The rest of the paper is organized as follows. In section 2 we will relate our
research question to the literature on the value and on the processing of information in
markets. Section 3 presents our experimental study. Section 4 offers a concluding
synopsis.
2
2 Markets and the marginal value of additional information
The question of whether better informed traders can earn higher returns than worse
informed traders is intimately related to the issue of how markets process information.
Fama’s (1970) efficient market hypothesis (EMH) has become one of the milestones in
the finance literature. In a nutshell, the EMH claims that prices “fully reflect all
available information at all times” (Fama, 385). As a consequence of this claim,
gathering information seems superfluous, as all information is already incorporated in
the market prices. A related finding is that market prices may reveal to traders all
available information. Radner (1979) shows that when traders have different
information about the assets to be traded, then the market price may reveal to some
traders information that was originally only available to other traders. A rational
expectations equilibrium is possible when traders have a certain ‘model’ of how
equilibrium prices are related to initial information2 and when the alternative states of
initial information are finite. Both conditions together imply that market prices fully
reveal the information of traders. As a consequence, there is no reason to expect better
informed traders to perform better than worse informed traders, but there is also no
incentive to gather any information. According to this line of reasoning it remains a
puzzle how prices could reflect all available information, as Grossman (1976)
formulated in his information paradox. Grossman and Stiglitz (1980) as well as
Diamond and Verrecchia (1981) have suggested models to solve the information
paradox. Grossman and Stiglitz assume asymmetric information of traders and costs of
gathering information. Due to some noise in the market, gathering additional
information can increase the returns from trading, yet when players play their
equilibrium strategy, the extra return from additional information matches exactly the
costs of gathering the additional information. As a result, the net return after accounting
for information costs is the same for all traders. Although it is not explicitly addressed
in the paper by Grossman and Stiglitz, their model also implies a strictly positive value
of additional information if one assumes that gathering additional information has
strictly positive marginal costs at any information level.
Another way to tackle the information paradox is the approach by Diamond and
Verrecchia. They develop a market model with a large number of heterogeneously
2
Recently, Allen et al. (2006) have shown, however, that when asset prices depend on higher order
expectations of others’ information, then there is a bias in the prices such that they are overly
sensitive to public information, whereas traders underweight their private information.
3
informed traders who observe public as well as (differential) private information. In the
noisy rational expectations equilibrium of the model, prices do not fully reflect a
trader’s own information. Due to this only partially revealing nature of the market price,
traders have a private incentive to collect information, and the information affects the
price through supply and demand. Note that the information system in the model of
Diamond and Verrecchia is not cumulative, but stochastically independent, as each
trader receives different private information. The precision of information is identical
across traders since each trader has the same prior beliefs and is endowed with private
information of the same precision. Under such conditions, it is not possible (and it was
not the intention of Diamond and Verrecchia, as we should stress) to analyze whether
more information leads to higher returns.
Schredelseker (1984) addresses the possible relationship between a trader’s level of
information and his profit by assuming a continuum of information levels, ranging from
complete ignorance to insider knowledge. Traders with a higher information level have
complete knowledge of what traders with a lower information level know, but not vice
versa. Schredelseker does not consider information costs, though their inclusion would
not change his main argument, which runs along the following lines: If one accepts that
markets are not fully efficient in processing information3 then it seems very reasonable
to acknowledge that on the one hand, the best informed market participants (i.e.
insiders) can gain above average returns4 while the other hand, the least informed
traders who do not gather any information, but trade purely randomly, can be expected
to earn the market return on average if their portfolio is as diversified and as risky as the
index of the market.5 If uninformed traders earn the average market return and insiders
above-average returns, it follows that some traders with an intermediate information
level need to earn below average returns, as is shown in Figure 1. As a consequence,
3
4
5
A series of anomaly effects (such as calendar effects) suggest that markets are less than fully efficient
(Hirshleifer 2001, Shiller 2003).
There is quite some evidence supporting this claim; see Jeng et.al. (2003), Lin and Howe (1990),
Lakonishok and Lee (2001), Krahnen et.al. (1999). Jeng et al., for instance, show that insider
purchases yield excess returns of about 6% per year. Lakonishok and Lee show that insiders are
better able to predict market movements, in particular with respect to the returns of relatively
smaller firms, which makes insider trading so profitable.
One might argue that the least informed traders should not trade at all, as in a zero-sum game they
should recognize that they will lose for sure when betting against better informed traders (no trade
theorem). Yet since the well-established equity premium puzzle (Mehra and Prescott 1985) rests on
the fact that there is a systematic and significantly positive margin between the returns of risky
assets and those of risk-free ones, even an underperforming trader may have an incentive to trade as
long as he is willing to accept the risk associated with the expected positive margin between risky
and risk-free assets.
4
there will be at least some information levels where more information is associated with
lower, instead of higher, returns. The intuition for that claim is that medium informed
traders sometimes receive skewed signals on which they put too much weight and to
which they ascribe too much precision when taking positions on the market.6
return
average return
information level
Fig. 1. Rate of return per information level as assumed by Schredelseker (1984, 51)
3 Experiment
We study the marginal value of additional information in three separate treatments
that differ either with respect to the mechanism used to determine the market price
(either a call market or a continuous double auction market7 with open order book) or
with respect to the type of information about an asset’s intrinsic value (being
determined either by a sequence of random binary variables or by a series of dividend
streams to be paid out in the future). Treatment T1 is motivated by the argument of
Schredelseker (1984) and based on the model developed in Schredelseker (2001). Since
prices are only ex-post observable in T1, the results in T1 might be affected by this
feature of the market. As the literature discussed in section 2 has shown, it is important
that the market price is observable in order to be able to make some inference about
other traders’ information. As a control for the possibility that results in T1 depend
crucially on the price mechanism, we have designed treatment T2 where everything is
6
In section 3.1.2 we will come back to this issue of skewed signals in the context of our experimental
market. Schredelseker (2001) provides a simulation on the effects of skewed signals for trading
profits in a market with cumulative information. Schredelseker claims that at least one equilibrium
of strategies should exist where each trader chooses his best response to other trader’s actions. In
this equilibrium most traders (except insiders) do not condition their bids on their available
information, but make random bids and, consequently, earns profits slightly below the average. Only
insiders are able to outperform the market.
5
kept constant with the exception of using a continuous double auction where all bids
and asks are public information and observable for all market participants in real time
(i.e., also before they make bids). Treatments T1 and T2 use a binomial process to
determine the tradable asset’s intrinsic value. One might object to using such a process,
claiming that the intrinsic value of an asset is, basically, the net present value of its
future dividends and redemption value. Treatment T3 is intended to come closer to this
concept of intrinsic value by letting traders know the future dividends of the asset, with
better informed traders knowing the dividends of a longer time horizon than worse
informed traders do. By using such a stream of dividends, T3 moves from the rather
static settings of T1 and T2 to a dynamic setting of the asset price mechanism, which
seems a reasonable approximation of real-world financial markets. For the sake of
clarity, we will present each treatment, its design and its results separately and offer a
concluding synthesis of all experimental results in section 4 (The Appendix is available
on the JEBO website).
3.1
Treatment T1 – Call market with binomial process
3.1.1 Experimental design
We have set up a market with 10 traders who can buy or sell an asset. The asset’s
intrinsic value is determined by the sequential random draw of 10 binary variables that
can either take the values “0” or “1” with equal probability. The sum of the 10 random
variables is the intrinsic value of the asset.8 Each trader knows how the intrinsic value is
determined, but has a different information level about the actually realized outcomes of
the 10 random draws. The trader with information level zero (denoted as I0) knows
none of the realized outcomes. The trader with level I1 knows the realization of the first
random draw, the trader with level I2 the realizations of the first two random draws, and
so on. Finally, the trader with level I9 knows the realized values of the first nine out of
ten random draws. It is common knowledge in the market that a trader with information
level Iy knows precisely what all traders with level Ix know, if y > x, yet a trader with
level Iy has only a subset of the information available to a trader with level Iz, if y < z.
7
Many major stock exchanges in the world (like Eurex in Frankfurt, Euronext in Paris, Brussels and
Amsterdam, or SETS in London) have an opening call auction when trading starts and later on a
continuous double auction market.
8
Of course, the expected value is 5. If one considers all 210 = 1024 possible realizations of the 10 binary
variables, the standard deviation of the expected value is 1.58.
6
Given their information level, traders can make bids for the asset.9 As usual in a
call-market one price per period is clearing the market. In our market bids are collected
and arranged in ascending order and the median of bids becomes the market price. For
instance, if the bids are 0-3-4-4-5-6-7-7-7-8, the market price is 5.5. All traders whose
bid is lower than the market price are sellers, while the other traders are buyers.10
Traders’ payoffs depend upon the relation of the market price to the intrinsic value of
the asset. A buyer makes a profit if the intrinsic value is higher than the market price
and a loss otherwise. A seller gains (loses) from trading if the intrinsic value is below
(above) the market price. The profit Ri for trader i from trading can then be calculated as
follows, where V denotes the intrinsic value, P the market price, and Bi trader i’s bid,
Ri =
Bi − P
⋅ [V − P ] , with Ri = 0, if Bi = P.
Bi − P
(1)
There are 20 trading periods in the experiment. For each period, the sequence of the
ten random draws (and, thus, the asset’s intrinsic value) has been determined randomly
in advance of the experimental sessions. Then they have been randomly ordered from
period 1 to period 20. Finally, this order has been fixed for each group (of 10 traders) in
order to make the experimental conditions perfectly comparable between the different
groups. The distribution of the intrinsic value of the asset in the experiment has been
chosen such that it matches the whole distribution of the 210 = 1024 possibilities as
closely as possible. Table 1 indicates the absolute and relative frequencies of a given
intrinsic value (in the possible range from zero to ten) both for the experimental
sessions as well as for the whole distribution.
9
The ‘bids’ in treatment T1 represent separation prices. This implies that if the market price is below this
bid traders would buy; else they would sell the asset. In treatments T2 and T3 prices are no longer
separating, and a ‘bid’ is an offer to buy and a ‘ask’ is an offer to sell,.
10
Traders having bid the median are neither sellers nor buyers. As a consequence, it is possible that the
number of sellers is not equal to the number of buyers. In such cases scale selling applies in order to
satisfy the zero-sum property of the market. Consider a set of bids such as 0-2-3-3-4-4-4-5-6-7 that
yields 4 as the market price. There are 4 sellers and 3 buyers. Assume that the intrinsic value of the
asset were 6; then each of the 3 buyers would make a profit of 2 units of money, whereas each of the
4 sellers would have a loss of 1.5 units of money.
7
Table 1. Absolute and relative frequencies of intrinsic values in the experiment
Intrinsic value
0
1
2
3
4
5
6
7
8
9
10
Absolute frequency
Experiment
0
1
0
2
4
5
4
3
1
0
0
Set of 210 possibilities
1
10
45
120
210
252
210
120
45
10
1
Experiment
0.0
5.0
0.0
10.0
20.0
25.0
20.0
15.0
5.0
0.0
0.0
Set of 210 possibilities
0.1
1.0
4.4
11.7
20.5
24.6
20.5
11.7
4.4
1.0
0.1
Relative frequency (%)
At the beginning of sessions, participants have been randomly assigned to an
information level from I0 to I9. This assignment has been kept fixed for the whole
session, as has been the group composition of ten traders. Therefore, we have a group of
ten traders as independent unit of observation. In total, we have 7 of these groups in
T1.11 The experimental sessions were fully computerized (using z-Tree of Fischbacher
1999) and were run in June 2002 at the University of Innsbruck. Sessions lasted on
average 75 minutes, with subjects earning on average 14 €.12
Before we present our experiment results, we would like to introduce one possibly
prominent trading strategy that we call active information processing strategy. If we
assume that a trader forms his bid by adding to the number of known random draws
with “1” the expected value of the unknown draws, then trader i’s bid Bi can be
calculated as follows:
i
Bi = ∑ bk + [(n − i ) ⋅ 0.5]
(2)
k =0
with n = 10 denoting the total number of random draws, i denoting the number of
draws of which trader i knows the outcome and bk denoting an indicator variable with
value zero if draw k yielded a “0” and value one if draw k yielded a “1”. Consider the
example where trader I6 knows the following realizations of the binomial process:
110101. The expected value of the four unknown random draws is 2, so trader I6’s bid
is assumed to be 6. Bids calculated as in equation (2) will serve as useful benchmark for
our analysis, even though we do not suggest that such bids are optimal.
11
Note that the trader with information level I0 was computerized (bidding randomly either zero or ten).
Given that one of the referees cast doubt about this practice, we abstained from this practice in
treatment T2 and T3.
12
At the beginning of the experiment, subjects received an initial endowment that was not specified in the
instructions and was only private knowledge. Trader I0 received the highest initial endowment of 19
€. For each additional information we subtracted 1 €, yielding 10 € for I9.
8
3.1.2 Experimental results in T1
The diamonds in Figure 2 represent the average profit of a single trader with a
given information level in one of our 7 independent groups. The bold line shows the
average profit across the 7 markets for a given information level. The overall average
returns of traders with levels I0 to I5 all lie in the narrow range from -0.14 to -0.21 and
are not significantly different from each other. Hence, in this range of information levels
additional information has no significantly positive value. Rather, additional
information seems to be irrelevant for returns, yet we probably should stress that
additional information is not detrimental (i.e. it never leads to significantly lower
profits). Hence, our Figure 2 does not support the stylized argument of Schredelseker
(1984, see Figure 1 above). Only from an intermediate information level onwards do we
find a clearly positive relation between information and profits. More precisely, average
profits are significantly increasing from I5 to I9 (p < 0.05, Friedman-test, N = 7).
Average profit per information level in treatment T1
1.20
average profit
0.60
0.00
-0.60
-1.20
I0
I1
I2
I3
I4
I5
I6
I7
I8
I9
information level
Fig. 2. Average profit per information level in treatment T1
Table 2 yields more insights into the actual use of available information in the
experiment. It reports the Pearson correlation between a trader’s actual bid and the bid
we would expect with active information processing according to equation (2).13 The
13
Note that the correlation for I0 cannot be calculated, as the variance of the expected bid (according to
equation (2) that always gives a result of 5) is zero. Therefore the correlation coefficient is not
defined (division by zero).
9
correlation is significantly increasing (with p < 0.05, Page test for ordered alternatives,
N = 7), showing that better informed traders use their information more actively in the
sense that they condition their actual bid more systematically on the available
information about the realizations of the binary random draws.
Table 2. Correlation coefficients between actual and expected bid
under active information processing in treatment T1
Information level
Correlation
I1
I2
I3
I4
I5
I6
I7
I8
I9
-0.03
0.38
0.40
0.40
0.58
0.81
0.78
0.74
0.85
Even though traders I2 to I5 condition their bids more on their available
information (see Table 2) than traders with I0 or I1, they do not earn systematically
higher profits on average (see Figure 2). Hence, using their information must have
drawbacks for traders I2 to I5, at least sometimes. A thorough analysis of our data
reveals that this hinges on what the sequence of the random draws looks like. Let us call
a sequence alternating when the sum of two consecutive draws is always one. The
following sequence is an example for an alternating one: 0101011010. In the case of
alternating sequences, it is noteworthy that traders’ bids (according to equation (2)) are
more or less insensitive to their information level because smaller bits of the whole
sequence yield almost the same bid as when a trader knows the whole sequence. In such
cases, most traders post the same bid, which will become the market price. At this price
most traders will neither win nor lose much, and, hence, their profits are basically
independent of their information level.
The situation is different when the sequence of random draws is skewed such that
it contains many identical outcomes in a row. An extreme example for such a
consecutive sequence would be 0000111111.14 In such cases active information
processing according to equation (2) leads to unfavorably low bids of medium informed
traders (e.g. trader I4 would bid 3), which drives the market price (4.25) below the
intrinsic value (6), causing losses for traders with information levels I2 to I6 as they sell
the asset too cheap. Hence, only the very well informed traders (I7 to I9) and the
uninformed or poorly informed traders (I0 and I1) would gain from trading in such
14
Of course, the probability for any specific sequence is always the same, 0.510.
10
situations, provided every trader would actively use his information and bid according
to equation (2). Table 2 has indicated that this is less the case for worse informed
traders. The latter seem to be able to discard misleading information in consecutive
sequences, at least to a certain extent, which actually helps them prevent losses.
As a final aspect to be considered in this treatment we look at the average profits
across the 7 markets in both halves of the experiment.15 As we can see from Table 3,
average profits are on average higher in the periods 11-20 than in periods 1-10 for the
less informed traders. Even though the increase in profits is only significant for traders
with information level I4, we can take this as tentative evidence that less informed
traders can slightly increase their performance in the course of the experiment. This is
mainly due to a shift in their information processing strategy since the correlation
between their actual bid and the one in case of active information processing is
decreasing from periods 1-10 to periods 11-20. Since trading in our market satisfies a
zero-sum property, the increase of profits of less informed traders comes at the cost of a
decrease of profits for better than average informed traders.
Table 3: Average profits in periods 1-10 and periods 11-20 in treatment T1
Information level
I0
I1
I2
I3
I4
I5
1) Periods 1 – 10
-0.15
-0.22
-0.19
-0.22
-0.47
2) Periods 11 – 20
-0.13
-0.18
-0.13
-0.13
0.05
Difference 2) – 1)
0.02
0.04
0.05
0.09
0.52
3.2
I6
I7
I8
I9
-0.19
0.19
0.16
0.44
0.65
-0.21
0.00
0.10
0.24
0.39
-0.02
-0.19
-0.06
-0.20
-0.26
Treatment T2 – Double-auction market with binomial process
3.2.1 Experimental design
Treatment T2 differs from treatment T1 only in a single aspect, the price
mechanism. In T2 we used a continuous double auction where all traders could post as
many bids and asks for buying or selling the asset as they wished. All bids and asks
were public information. A trade was realized as soon as another trader accepted an
offer to buy or sell at a given price. The market prices of all trades within one period
15
It seems noteworthy that the average absolute deviation of the market price from the intrinsic value
decreases from an average of 1.36 in the first ten periods to 0.84 in the second half of the
experiment. If we take this measure as an indicator for the market’s efficiency, we might conclude
that market efficiency is higher in periods 11-20 than in periods 1-10.
11
were also observable for all other traders. At the end of each period participants saw a
“history screen” displaying information on past prices, values, and own profits.
This sort of price mechanism yields two important differences in comparison to
treatment T1. First of all, prices become observable (whereas they are only set ex post in
T1). The observability of prices, though, is one of the key elements of the theoretical
models discussed in the previous section such that traders can infer something about the
other traders’ information only when they can observe the market price. Second, traders
are no longer forced to trade, but rather they can deliberately abstain from trading by not
making any asks or bids.
Each of the 20 periods in the experiment lasted 150 seconds in which traders could
make and accept bids and asks. Each trader could realize at most 3 trades per period,
whereas there was no restriction on the number of bids and asks. In order to induce
trading, we provided an incentive to trade by paying a small premium for each realized
trade.16
We used exactly the same random draws in T2 as in T1 in order to keep all other
conditions as comparable as possible. In total, we had 80 participants in T2, that is 8
independent groups of 10 traders each. None of the participants had taken part in a
session of treatment T1. The computerized sessions were run in April 2004, lasted about
70 minutes and yielded average payoffs of 14 € per participant.
3.2.2 Experimental results in T2
Figure 3 shows the average profits per period contingent on traders’ information
levels. A Friedman-test reveals that the profits per trade are not significantly different
for traders with information levels I0 to I7. Only traders with information levels I8 and
I9 have significantly higher profits than all other traders (p < 0.05). Hence, even when
market prices are fully observable and determined in a double auction, there is a wide
range of information levels where additional information does not lead to higher profits.
Note that the average profits of traders with information level I0 are only marginally
lower than those with information level I6, for instance.
16
The premium was 1 Taler per trade (see the instructions in Appendix A2), reflecting the risk premium
in real markets. Note that the premium was much lower than the potential losses from trading.
12
Average profit per information level in treatment T2
1.20
average profit
0.60
0.00
-0.60
-1.20
I0
I1
I2
I3
I4
I5
I6
I7
I8
I9
information level
Fig. 3. Average profit per information level in treatment T2
Since traders could strike more than one deal per period, we are interested in the
relation of trading activity and information level. Table 4 reports the average number of
trades, respectively bids and asks per period, contingent on a trader’s information level.
Traders with information levels I0 to I7 make on average between 1.53 and 1.78 trades
per period, with no significant differences between these traders. Only traders with I8
and I9 make significantly more trades than the other traders (p < 0.05, Friedman test, N
= 8). Hence, they actually use their superior information to make more trades. The best
informed traders also make the most bids and asks per period. However, due to a large
variance in the number of bids and asks there is no significant difference between any
information levels.
Table 4. Number of trades and bids and asks per period in treatment T2
Information level
I0
I1
I2
I3
I4
I5
I6
I7
I8
I9
Trades per period (Average)
1.64
1.58
1.72
1.61
1.78
1.56
1.53
1.66
2.06
2.38
Bids and asks per period (Average)
4.56
4.93
4.19
3.85
4.83
3.43
4.48
4.69
6.14
6.51
As in treatment T1 we find that the better informed traders make more use of their
information when making bids and asks. We correlate the average price of a trader’s
transactions per period with his fictitious bid that would arise from active information
processing (see equation (2)). This correlation is significantly increasing in the
information level (p < 0.05, Page test for ordered alternatives, N = 8) (see Table 5).
13
Table 5. Correlation coefficient between average price of a trader’s transactions per
period and expected bid under active information processing in treatment T2
Information level
Correlation
I1
I2
I3
I4
I5
I6
I7
I8
I9
0.45
0.53
0.60
0.65
0.79
0.76
0.78
0.79
0.84
When we look at intertemporal developments we find that the number of trades per
period is decreasing from 9.04 in periods 1-10 to 8.48 in periods 11-20. The decrease is
not significant (p = 0.12;Wilcoxon signed ranks test; N = 8), nor is the increase in the
average number of bids and asks per period from the first to the second half of the
experiment (36.6 vs. 41.2; p = 0.16). However, the ratio of bids and asks to the actual
number of trades is, in fact, significantly increasing from periods 1-10 to periods 11-20
(4.0 to 4.9; p < 0.05). This indicates that subjects are less willing to accept offers in the
latter part of the experiment. In particular, they hesitate to accept the very first offers
placed in a trading period. As a consequence, the variance of prices decreases
significantly from periods 1-10 to periods 11-20 (p < 0.01; Wilcoxon signed ranks test),
as is shown in Figure 4, where the bold line indicates the overall average. Whereas the
variance of prices decreases, profits do not change significantly from periods 1-10 to
periods 11-20.
Variance of prices across periods in treatment T2
3.0
variance of prices
2.5
2.0
1.5
1.0
0.5
0.0
1
2
3
4
5
6
7
8
9
10
11
12
13 14
15
16
17
18
19
20
period
Fig. 4. Development of the variance of prices across periods in treatment T2
14
3.3
Treatment T3 – Double-auction market and dividend process
3.3.1 Experimental design
Treatment T3 also relies on a double auction with open order book for setting the
prices of the tradable asset. However, contrary to the previous treatments, the asset’s
value in T3 is determined by a dividend stream. The different information levels of
traders are implemented by varying the traders’ knowledge about future dividends.17 In
general, trader Ix knows the dividend of this and the next (x-1) periods. For instance, a
trader with information level I1 knows this period’s dividend only, whereas a trader
with level I9 knows the dividends of this and the next 8 periods. For the sake of
simplicity we assume that traders know the exact value of the future dividends.
At the end of each period the current dividend is paid out for each stock owned. In
the next period the information on dividends is updated, such that the former dividend
for period t+1 is now the dividend of period t. The dividend stream follows a random
walk and is determined as follows:
Dt = Dt −1 + ε ;
(3)
Dt denotes the dividend in period t, D0 was set to 0.2, and ε is a normally
distributed random term with a mean of zero and a variance of σ² = 0.0004.
As in the previous treatments, the sequence of dividends was randomly determined
before running the experimental sessions and was, then, kept constant in order to
guarantee identical conditions in all sessions. All subjects started with an endowment of
1600 units of money (Taler) and 40 stocks with an initial price of 40 Taler each (see the
instructions in Appendix A3). Trading time was 100 seconds per period. In total, we had
30 periods18, after which subjects’ accounts were exchanged into money at the rate of
200 Taler = 1 €.
At the start of each period subjects received information on the future dividends
according to their information level. In addition we displayed to each trader the net
present value of the stock given this information. The net present value was derived
17
Such a situation, though with only two information levels, was first studied theoretically by Hellwig
(1982).
18
The results to be reported below would remain qualitatively identical if we considered only 20 periods,
which is the length of treatments T1 and T2. We opted for 30 periods because the dividend stream
process implies that trader I9 already knows the dividends for the first 9 rounds at the beginning of
the experiment. In order to have also the best informed trader getting about 20 times new
information (as in T1 and T2) we extended the duration to 30 periods in T3.
15
using Gordon’s well-known formula, discounting the known dividends and assuming
the last one to be a continuous, infinite stream that was also discounted,19
E (V | I j ,t ) =
Dt + j −1
(1 + re )
j −2
⋅ re
+
t + j −2
Di
∑ (1 + r )
i =t
i −t
;
(4)
e
E (V | I j ,t ) denotes the conditional expected value of the asset in period t, j
represents the index for the information level of trader Ij and re is the risk adjusted
interest rate that was fixed at 0.5%. The expected growth rate of the dividend was set as
zero and is therefore not shown in the formula.
In each round, traders could make as many bids and asks as they wished. If any of
them were accepted the subjects’ accounts were adapted accordingly. Contrary to the
previous treatments we let cash holdings earn a small interest of 0.1% per period.20
Trader j’s wealth in period t, Wt,j, is then calculated as the sum of cash and wealth in
stocks, with the latter being calculated by multiplying the number of stocks with the
current price (i.e. the price of the last transaction).
By using a dividend stream to determine an asset’s intrinsic value and by allowing
for cash holdings that earn a fixed interest rate, we regard our treatment T3 as the one
closest to the conditions in real markets. Therefore, we think that treatment T3 is the
hardest test of whether more information is always better for traders.
The experimental sessions for treatment T3 were implemented in July 2004 with a
total of 7 independent groups of 9 subjects. Each of the 9 subjects had a different
information level ranging from I1 to I9.21 The average duration of the sessions was 90
minutes, with average earnings of 18 €.
3.3.2 Experimental results in T3
Figure 5 shows the individual and average returns (bold line) for different
information levels.22 The returns are calculated according to the following formula,
19
Subjects were informed in the instructions how the net present value was calculated and that it
depended on the information level, particularly on their last known dividend.
20
The periods were assumed to be roughly a month in the real world. The respective annual interest rates
would be approximately 1.2 percent for the risk-free and 6.2 percent for the risky asset.
21
We economized on subjects (9 instead of 10), because one referee argued that one should expect that all
traders in a market have at least some minimal level of information, which implies that there should
be no traders with zero information (I0).
22
Two outliers with information level I2 (with average returns of +52%, respectively –31%) are not
included in Fig. 2.
16
where RT,T-X,j denotes trader j’s return from period T-X (with wealth WT-X,j) to period T
(with wealth WT,j);
RT ,T − X , j =
WT , j − WT − X , j
(5)
WT − X , j
Individual and average returns per information level
45%
return
30%
15%
0%
-15%
I1
I2
I3
I4
I5
I6
I7
I8
I9
information level
Fig. 5. Individual and average returns per information level in treatment T3
As in the other two treatments we find that the best informed agents earn on
average the highest returns, but that there is no generally positive relationship between a
trader’s information level and his return. Average returns range from 7.1% for traders I5
to 22.2% for traders I9. Due to a relatively high variance in single traders’ returns23 a
Friedman test shows that there is no significant difference in the returns of traders with
different information levels (p = 0.11; two-sided Friedman test including all information
levels, N = 7). Only when we look for pairwise differences do we find that the average
returns are significantly higher for traders with level I9 than for traders with either level
I3, I4 or I5 (p < 0.05 in each pair wise test, Wilcoxon signed ranks test, N = 7). Hence,
our results in treatment T3 confirm our findings from the previous treatments, indicating
that there is a broad range of information levels where additional information has no
significantly positive influence on returns and that only the very best informed traders
can actually outperform (some of) the less informed ones.
23
Overall, 22 out of 63 traders exceeded the expected return of the stock of 16.1%. Traders with all nine
different information levels are among those 22 traders. 9 out of 63 traders ended up with a return
17
So far, we have only considered the final wealth of subjects and their returns from
trading over all 30 periods. It might be interesting to check whether information levels
and returns are somewhat differently (or even positively) related in earlier periods of the
experiment. To do so, we compare the average wealth per information level with the
initial wealth W0,j of information level j. From that we can calculate the average return
RT,0,j according to equation (5). The results are displayed in Figure 6.
Two features of Figure 6 are particularly noteworthy. First, we see that the
performance of traders across time is remarkably stable. The insiders I8 and I9 have the
best performance from the beginning to the end of the experiment. Similarly, the finally
worst performing traders I5 and I3 are already lagging behind after the first few periods.
In general, there are very few intersections in Figure 6. Rather the differences increase
over time; I9 wins more and more, while I5 falls back relatively more and more. The
distribution of final average returns (see Figure 5) is therefore not due to a few periods,
but it is the result of different performance throughout the experiment.
Development of average returns over time
25%
20%
I1
I2
average return
15%
I3
I4
10%
I5
I6
I7
5%
I8
I9
0%
-5%
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
period
Fig. 6. Development of average returns RT,0,j over time in treatment T3
Second, Figure 6 also shows an important feature of the dividend stream. While the
zero-sum property of treatments T1 and T2 necessarily implied some traders win and
others lose in the same period, the dividend stream process makes it possible that the
that was lower than the risk free rate (of 3.0% in 30 periods). 7 of these 9 traders actually suffered
losses from trading.
18
wealth of all traders can be positively aligned in a given period such that they all get
richer (see, e.g., periods 1 to 9) or all get poorer (see, e.g., periods 10 to 14), depending
upon the prospects for the asset’s dividends.
In Figure 7 we plot the asset’s dividends in each period (see left-hand scale and
solid line24) and the average price of the asset across all seven groups of traders (see
right-hand scale and broken line). It seems that during the most part of the experiment
average prices are leading dividends by about 5 periods,25 which is exactly the
information level of the median informed trader I5.26 However, prices show a smoother
path with smaller variance than dividends do. This is a result of all but one trader in the
market knowing more than just the current dividend.
Development of dividends and prices over time
0.30
60
0.25
50
40
0.15
30
0.10
20
0.05
10
0.00
price
dividends
0.20
0
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
pe riods
Dividends
Price
Fig. 7. Development of dividends and average prices over time
Next we are interested in how traders reacted in buying and selling stocks on the
information about the asset’s dividends. In particular, we have checked the relative
frequency with which traders with a given information level bought (or sold) stocks
when the present value they saw was higher (or lower) than the current transaction
price. If trading did not depend on the relation between present value and current price,
24
25
Recall that the dividends were identical across all seven groups of traders.
Spearman-Rho coefficients of average prices per period and dividends of 5 periods later are
significantly positively correlated in all but one session. Correlation coefficients range from 0.56 to
0.83.
19
one would expect roughly a rate of 50%. Yet on average we find a relative frequency of
about two thirds, indicating that traders react significantly to their available information
(p < 0.01; Binomial test). Better informed traders typically react stronger to the relation
between the net present value and the current price because traders with information
levels I6 to I9 buy (respectively sell) on average in 70% of cases where the net present
value is higher (lower) than the current price, whereas the corresponding figure is 63%
for traders with information level I1 to I5 (see bottom line of Table 6).
Table 6. Frequency of trading
Information level
I1
I2
I3
I4
I5
I6
I7
I8
I9
6.60
8.23
3.80
3.17
5.53
5.27
7.00
4.97
5.63
0.61
0.63
0.65
0.64
0.60
0.70
0.77
0.61
0.72
Average number of transactions per
period
Relative frequency of buying (selling) if
net present value > (<) current price
Finally, we would like to address how trading activity is related to the information
level. Overall, there are about 20 transactions per period. Table 6 provides the average
number of transactions per period, contingent on the information level. Obviously
trading activity is not correlated with a trader’s information level, but the information
level has an influence on when traders buy or sell shares. Figure 8 shows the average
number of stock holdings in the course of the experiment.27 The best informed trader I9
is the first one to start buying actively (and at relatively low prices), because he is the
first one to realize that dividends are steadily increasing from period 5 to period 12 (see
the solid line in Figure 7). Alternatively, when prices are high and prospects for
dividends deteriorating, trader I9 is the first to sell. Overall, the correlation of trader I9’s
stock holdings and his conditional expected value of the asset is 0.92. Traders I5 who
have the lowest average returns are the most eager ones to sell stocks at the beginning of
the experiment, as they have the lowest estimates of the present value. These stocks are
quite frequently bought by traders I9. When traders I5 realize around period 6 that
26
This finding is somewhat related to Kyle’s (1985) finding. Although his model is constructed in a very
different way, he also finds that market prices reflect exactly half of the best informed traders’
(insider) information.
27
For the sake of clarity we have selected only the uneven information levels in Figure 8. A separate
figure with the stock holdings of traders with an even information level shows a very similar pattern
and is available upon request.
20
dividends increase in the future they start buying stocks actively (and at a relatively
high price), supposedly in the hope that the price will maintain its upward trend. Yet
this is not the case, leading in sum to the relatively bad performance of traders with
information level I5. The worst informed traders with level I1 begin to buy actively
when prices are relatively low (around period 15; compare Figure 7 above).
Average stock holdings by uneven information levels in
treatment T3
70
60
stock holdings
50
40
30
20
10
0
1
3
5
7
9
I1
11
13
I3
15
17
I5
19
21
I7
23
25
I9
27
29
pe riod
Fig. 8. Average stock holdings of selected traders
4 Conclusion
We have studied in an experiment the value of additional information in financial
markets. The combination of two specific features of our experiment distinguishes our
paper from previous ones. First, we consider more than two information levels. Second,
we use a cumulative information system. Both features seem to mirror the conditions of
financial markets quite reasonably. It is particularly the second feature that we deem
important because very well informed traders can be expected to have at least a good
guess of what less informed traders know (from newspapers, TV, corporate reports,
etc.).
Though our three experimental treatments T1, T2, and T3 differ in some notable
ways, their main results are remarkably similar, indicating that the results are not driven
by some peculiarities of a particular treatment. The most important result is the fact that
more information is not always better for traders on financial markets, even though it
pays to have insider (i.e. far above average) information. Whereas the benefit of insider
information has been documented before, our design and analysis provides the first
21
evidence that there is a broad range of information levels (ranging from basically
uninformed traders to traders with an average information level) where additional
information does not lead to higher returns or profits from trading. Of course, we should
stress that we have not found that having more information leads to significantly lower
returns or profits. This latter finding is clearly inconsistent with the model of
Schredelseker (1984) that would predict that additional information can, in fact, be
harmful. Given that our findings have proved robust in three different experimental
markets28, the difference between Schredelseker’s model and our results does not seem
to depend on the type of market. Rather, it might be that the number of participants is
critical. In markets with a large number of traders in which the price and an unbiased
estimate of the value of an asset are known, Schredelseker’s theory may hold because
the uninformed traders can always buy or sell at the market price and make zero
expected profit. In all of our markets, however, we have found that uninformed traders
actually suffer losses. This could have been due to the fact that in our markets with
relatively few participants any bid introduces some noise in the price, which is then no
longer an unbiased estimate of the asset’s value.
Nevertheless, we deem it an important finding that more information does not lead
to higher returns or profits in a wide range of information levels. This result seems to be
related to the market as an institution where traders take bets with other traders on the
future development of a stock price (besides taking into account the current
fundamentals such as profits or revenue). Medium informed traders may have some
information, but they often take bets against even better informed traders, thereby losing
money quite frequently. The information that medium informed traders get may also be
rather skewed, causing a bias in the conditional expectation of the asset’s value.
Completely uninformed traders cannot suffer from such a bias, given that they have no
information. Seen from this perspective, it even might seem surprising that medium
informed traders did not perform significantly worse than uninformed traders. This
might be due to medium informed traders knowing the possible distribution of values
(in treatments T1 and T2) and becoming aware of the fact that their partial information
might be misleading. The latter conjecture can be supported by the observation that
trading becomes less active in the latter part of the experiment.
28
The robustness across three different kinds of markets should also remove doubts that our results
depend on the sample sizes used in our three treatments.
22
More generally, our key result on the (often zero) value of additional information
seems to question the widespread assumption that having more information is always a
good thing, even in a world where information is costless, as we have assumed
throughout the paper. Actually, the introduction of positive marginal costs for additional
information can be expected to strengthen our results that having more information need
not be positive for a trader’s overall profits (including information costs). However, we
leave it open for future research to corroborate this conjecture.
23
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25
Appendix (The following instructions are translated from German.)
A1. Experimental instructions for treatment T1
We welcome you to the experiment and ask you
not to talk to other participants during the whole experiment
Experiment background
The experiment is a replication of a stock market, where 10 participants trade a
virtual asset. The experiment consists of 20 independent periods. Each
participant has a different information level about the intrinsic value of the asset.
Individual goal
Your personal goal is to maximize your personal profit. The higher your profit in
the experiment, the higher your final monetary payment at the end of the 20
periods will be.
Composition of ONE period
Information levels and the intrinsic value of the asset
To derive the intrinsic value of the asset each period ten coin flips are made,
showing either “1” or “0” each with probability 0.5. The intrinsic value is the sum
of these ten coins.
Example:
Information level
Coin set 1
Coin set 2
…
0
1
1
0
2
1
1
3
0
0
4
1
0
5
0
0
6
0
1
7
1
1
8
0
0
9
1
0
10
1
0
value
6
3
Each trader has a different information level: some know many of the ten coins,
others know just a few. Specifically trader I1 knows the first coin, I2 knows the
first and the second coin, etc. until trader I9 who knows the first nine of the ten
coins. In addition, there is a computer-simulated trader I0 knowing nothing. This
trader chooses a bid of 0 or 10 randomly.
Trader I6 knows in coin set 1 that the first six coins show 1, 1, 0, 1, 0, 0 and he
also knows that he does not know the other four coins. In addition he knows
that e.g. trader I4 knows only the first four of these coins.
Entering a separation price
Each period you estimate the intrinsic value, which is the
sum of the ten coin flips. How you get this estimate, is up to you!
Some important information on the intrinsic value:
The maximal value is 10
The minimal value is 0
If you enter a separation price of 0 you are a sure seller in this period
If you enter a separation price of 10 you are a sure buyer in this period
26
Deriving a price and market positions
The ten separation prices entered by the ten traders are ordered from the
lowest to the highest and the median (between 5th and 6th separation price) is
the market price for this period. All traders who have posted a separation price
below the market price are sellers in this period, those who have posted a
higher separation price are buyers. Those who have posted exactly the market
price are neutral in this period.
Example: the arranged separation prices of the traders are 0-3-4-4-6-7-7-7-7-8. The market
price is therefore 6.5 (median of 5th and 6th price). The traders with separation prices 0, 3, 4,
4, 6 are sellers, while the other five are buyers.
Individual payment per period
The difference (market price minus intrinsic value) gives the profit/loss per
period:
If the separation price > market price you are buyer
If the separation price < market price you are seller
If the separation price = market price you are neutral
If you are buyer you make a profit of (intrinsic value minus market price)
if the intrinsic value > market price, else you loose this amount
If you are seller you make a profit of (market price minus intrinsic value)
if the intrinsic value < market price, else you loose this amount
Neutral traders have neither profits nor losses
Example: If the intrinsic value is 7 and the separation prices are 4-4-5-5-5-6-7-7-8-10, then
the market price is 5.5 and the five traders having posted lower separation prices are
sellers. The other five traders are buyers. As the intrinsic value is higher than the market
price each buyer earns a profit of 1.5 (the difference of 7-5.5), while each seller looses this
amount.
Example: The separation prices are 0-3-4-5-6-6-6-6.5-7-7.12. The 5th, 6th and 7th separation
prices are all “6”, which therefore is the market price. The three traders with these
separation prices are neutral in this period and have neither profits nor losses. We therefore
have 4 sellers and 3 buyers. As the sum of profits and losses has to be equal (zero-sumgame) we use scale selling: If the value is 7, then each buyer gets his profit (=1), while the
four sellers loose only 0.75 (= 1*3/4) instead of 1.
Time
Each period you have 45 seconds to enter your separation price. After each
trading period you have 30 seconds to write a short description how you came
up with the separation price (protocol).
Final Payment
Your payment at the end of the experiment is derived as follows:
Sum of profits/losses per period
+ Starting money (depends on your information level; see first screen)
= Final payment
27
A2. Experimental instructions for treatment T2
We welcome you to the experiment and ask you
not to talk to other participants during the whole experiment
Experiment background
The experiment is a replication of a stock market where 10 participants trade a
virtual asset. In order to be able to trade you get an initial endowment with
money depending on your information level. Each money unit represents one
Euro and at the end of the session you get paid your total earnings in cash. The
experiment consists of 20 independent periods.
The intrinsic value of the asset
To derive the intrinsic value of the asset each period ten coin flips are made
(representing relevant information for the asset value: inflation, economic
growth, etc.), showing either “1” (good) or “0” (bad) each with probability 0.5.
The intrinsic value is the sum of these ten coins.
Example:
Information level
Coin set 1
Coin set 2
…
0
1
1
0
2
1
1
3
0
0
4
1
0
5
0
0
6
0
1
7
1
1
8
0
0
9
1
0
10
1
0
value
6
3
Each trader has a different information level: One trader (I0) knows none of the
coins. Trader I1 knows the first coin, I2 knows the first and the second coin, etc.
until trader I9 who knows the first nine of the ten coins.
Trader I6 knows in coin set 1 (see example above) that the first six coins show
1, 1, 0, 1, 0, 0 and he also knows that he does not know the other four coins. In
addition he knows that e.g. trader I4 knows only the first four of these coins.
Trading
Trading takes place in a double auction. This means that each trader can be
buyer and seller. Each trader can post as man bids and asks between 0 and 10
as he wants. The trading screen has several sectors. On the very left you find
your information. Next you have the possibility to post your asks and to accept
offers by other traders. In the middle you see the prices of this period and on
the right you can accept or post bids.
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Your information
in this period
Open asks, arranged
from the highest to the
lowest. The last offer is
the best
Here you post the price
at which you would sell
and confirm below
If you push this button you
buy the marked offer
Open bids, arranged
from the lowest to the
highest. The last offer
is the best
Prices of all
transactions in this
period. The last price is
always last in the list
Here you post the
price at which you
would buy and
confirm below
If you push this button you
sell the marked offer
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Profit and loss
At the end of each period the intrinsic value is revealed and profits and losses
are calculated. You make a profit, if you sold the asset at a higher price than the
intrinsic value or if you bought it cheaper than the intrinsic value.
Profit buyer = intrinsic value – price (negative, when price > intrinsic value)
Profit seller = price – intrinsic value (negative, when price < intrinsic value)
Important details
• Each round you may make up to three transactions. You may, however,
post as many bids and asks as you want.
• Each trading period lasts for 150 seconds (2.5 minutes)
• In each period when you make at least one transaction you get a risk
premium of 1 Taler.
History Box:
At the end of each period you get an overview in the history box. Each period
you see the most relevant data (intrinsic value, trading, profit, etc.). The history
box will be shown for 30 seconds after each period.
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A3. Experimental instructions for treatment T3
We welcome you to the experiment and ask you
not to talk to other participants during the whole experiment
Background of the experiment
This experiment is concerned with replicating asset markets where 9
participants in a group can trade the stocks of a fictive company for 30
consecutive periods (months). With trading you can increase your wealth and at
the end you will receive a cash payment depending on your wealth.
Characteristics of the market
Each trader is endowed with 1600 Taler (experimental currency) and with 40
stocks worth 40 at the beginning of the experiment. The only fundamental
information you receive is the dividend of the stock (monthly dividend equals
monthly profit). Changes of the dividend per period have an expected value of
zero and will fluctuate randomly at maximum +/- 50%. The market is
characterized by an asymmetric information distribution. Worst informed traders
are informed only about the dividend of the current period, while better informed
ones know the dividend of the company a few months in the future. The best
informed trader knows this periods dividend and the dividends of the coming 8
periods.
At the end of each period (which lasts 100 seconds) you will receive the current
dividend for each stock you own. A risk free interest rate of 0.1% is paid for the
cash holdings in each period. The risk adjusted interest rate for evaluation of
the stock equals 0.5%.
Trading
The trading mechanism is implemented by a double auction. This means that
each trader can buy or sell stocks freely. Therefore you can enter as many
bids/asks as you wish within the range of 0 and 200 (with at maximum one
decimal place).
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Overview of stock and
cash holdings; Wealth =
money + [stock*current
price]
Your dividend
information for this
period with „t“
denoting the current
period and “-1.000”
standing for no
information.
Conditional
expected value of
the stock.
Overview of own
transactions in the
current period.
Calculator
History Box: „Average price“
denotes the average price of
the past periods.
SELLIING AREA
You can either insert
your own asks and
confirm them with
clicking on the „ASK“
button or accept an
open bid of another
trader with clicking on
the “SELL” button. All
bids are sorted from the
lowest to the highest.
BUYING AREA
You can either insert
your own bids and
confirm them with
clicking on the „BID“
button or accept an
open ask of another
trader with clicking on
the “BUY” button. All
asks are sorted from
the highest to the
lowest.
Chronological
history of prices of
the current period.
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Calculation of the conditional expected value (present value, PV)
Generally it is up to you on what kind of information you will trade and how you
will evaluate the stock. If you use your fundamental information you can see the
present value (PV) of all future dividends (of course only those you can estimate
on the basis of your information level) on the bottom left side of the trading
screen. Your PV is derived using Gordon’s well-known formula, discounting the
known dividends and using the last one as a continuous, infinite stream which
was also discounted as a company is basically designed for infinity.
PV0 = i=0Σn-1Di/(1.005)i + Dn/0.005/(1.005)n with n denoting the last period
Example: The dividends of this and the next 2 periods are 0.191; 0.214; 0.202. So, the PV on
basis of this information level is calculated as follows: 0.191 + 0.214/1.005 + 0.202/0.005/1.0052
= 40.40. This PV is shown on the bottom left side of the trading screen.
Wealth
Your wealth is the sum of your cash holding and the product of your stock
holdings multiplied with the current price. If you are buying a stock your cash
holdings are reduced by the price you paid and at the same time your stock
holdings are enlarged by one stock. Generally, for evaluation of your wealth the
current price on the market is being used, so your wealth will change even if
you have not participated in the last transaction. After expiration of each trading
period (month) an interest rate of 0.1% per month is paid for the current cash
holdings, and the dividends for your stocks are being added to your cash.
Example: If you own 1600 in cash and 40 stocks with a price of 40 and the dividend equals
0.215 at the end of a period, so your wealth is increasing from 3200 to 3210.2 (Hence, the
increase is wealth consists of +1.6 for interest earnings (= 1600*0.001) +8.6 for dividend
earnings (= 40*0.215)).
Important details
• Per period you can trade as much as you wish (of course, only within the
boundaries of your cash and stock holdings). Negative cash holdings are
not possible.
• Trading time per period is 100 seconds, which is being displayed at the
top right side of the trading screen.
• Your payment at the end of the experiment depends on your wealth in
the last period.
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