A contribution to solving an old puzzle: why different trading strategies persist in competitive markets.

ABSTRACT

A simulation study is used to explore, how valuable information in a market is and how useful different trading strategies are. While earlier work in this field covered this question only with two levels of information I use ten different levels to control carefully for the influence of additional information. The analysis shows that additional information is mostly useless and sometimes even harmful for low and average informed investors. It can be shown, that trading strategies exhibit kind of a 'decreasing marginal return', i.e. the more agents use a specific strategy, the worse its results are. This leads to the general conclusion that different information levels should use differing trading strategies--there is no single optimal strategy in financial markets.

1. INTRODUCTION

Everybody is talking about the 'information society' we are living in, but rarely does anybody ask, how valuable information really is. It has become kind of a paradigm to assume that information can never be harmful. Especially with respect to financial markets it is widely believed that traders with more information make better decisions and therefore gain higher profits. However, game theory reveals that "having more information ... can make a player worse off (Gibbons, 1992, 63). Even though the game-theoretical properties of markets are widely realized, little attention has been paid to potential consequences of these properties. With this paper I want to shed some light on this still quite dark field of research.

Apart from the efficient market hypothesis (Fama 1970) in its strongest form the existing literature, models, and experiments covering the value of information in markets mostly conclude, that additional information will make the possessor of information better off (for literature see below). For all of these studies I see a major shortcoming: they compare only two levels of information--uninformed vs. informed. Their common result, that the informed can outperform the uninformed traders, is no surprise. Until now, little consideration has been given to the impact of heterogeneously informed traders on the relation of information and return in capital markets. Yet it is a fundamental characteristic of modern stock markets that different agents receive different information signals and signals of different quality.

The rest of the paper is organized as follows: in Chapter 2 the basic intuition of the paper is given. In Chapter 3 the research question will be clarified before turning to the design of the market. Next I will examine the used trading strategies and then present the results of the simulation study. The analysis will be continued by changing trading strategies in the simulation to derive an equilibrium. The paper is concluded by summing up the major results in Chapter 5.

2. INTUITION AND RELATED LITERATURE

A market can be segmented into different groups after to the information level they possess: on the top end we have the insiders, who are the best informed and who can presumably outperform the market. This has been shown in theoretical, empirical and experimental work (e.g. Jaffe (1974); Seyhun (1986); Lin/Howe (1990); Lakonishok/Lee (2001); Ackert et al. (2002)).

Apart from insiders we have the vast field of 'low to average' informed traders. This includes most private investors but also the managers of actively managed funds. Finally there is a significant group of people who chose not to process any information but to either act randomly or buy an index paper. When asked about the performance of theses groups in the market most people would probably answer, that the return should increase with growing information level. We generally think that effort should and will be rewarded and that processing information will thereby help a trader to improve his performance in the market.

However, I object to this simple assumption--I also think that Insiders outperform the market, but I think that a random trader is on average more successful than an average informed investor. I agree with Malkiel (2003a, p.2), who argues, that "clearly all stocks have to be held by someone and if certain investors achieve above-average returns, then it must be the case that other investors are achieving below average performance ... after accounting for the additional expenses of active management, most investors must underperform the market average." But which ones are underperforming the market to which extent--and what can they do about it?

This leads to the starting point of this research: if the random walk hypothesis holds, a trader who does not gather any information but trades randomly can expect to earn the market return. There is no reason to assume any systematic over- or underperformance, if she really chooses her shares randomly, e.g. by throwing a dart arrow at a quotations list.

This leads to a puzzling situation: if Insiders gain above average returns and uninformed investors earn the market return, who is below the average? The only possible answer is: the average informed. A stylized fact supporting this is the performance of professionally managed funds: most high-paid funds managers are regularly not able to beat a broad market index, as shown in studies across the globe. On average about 70 percent of actively managed stock market funds were outperformed by the market over a ten-year period. Over the past ten years the median actively managed fund has produced annual returns 175 basis points lower than the index (Malkiel, 2003a, 4 and 9). Here we have highly-trained people trying to beat the market by processing information, but most of them achieve no better result than "a blindfolded monkey throwing darts at a newspaper's financial pages." (Malkiel, 1996, 24).

The intuition behind this stunning result is quite simple: whenever an average informed agent trades in a market he takes a bet against a better informed person. As a consequence he will loose on average. In a market context this means being below the average return. The mentioned relationship is well established in game theory: if I play against a person who is able to foresee my moves better than I can predict hers, I should make myself unpredictable by playing randomly. The same is true for markets, and making himself unpredictable is exactly, what an uninformed trader does: he chooses his stocks randomly. Consequently there is nothing foreseeable and therefore nothing exploitable in his trading strategy. Again, the below-average performance of professional investment funds managers, which are in most cases not able to beat a broad market index, suggest that gathering information could, in fact, be futile to a large extent (Malkiel, 2003a and 2003b).

In this paper I want to examine how the return of heterogeneously informed traders depends on their information level and the trading strategy they choose. No broadly accepted analytical or experimental study that I am aware of examines market dynamics when there are more than two levels of information. Reality, however, most definitely is characterized by a multitude of different information levels of individuals. Here I see a major shortcoming in present studies and the purpose of this paper is to extend this line of research by introducing more than two levels of information.

One author covering the relationship of information and return in a market with more than two levels of information is Schredelseker. He approaches the problem analytically (Schredelseker, 1984) and with a simulation study (Schredelseker, 2001). His starting point is the above-average return of insiders: if we have a less than strong form efficient market, insiders will be able to gain above average returns. As we saw above, a random trader can expect the average market return and therefore the average informed have to be below the market.

Strong and Walker (1987) also examine the relationship between information level and return, but their argumentation is not as explicit as Schredelsekers'. Their result, however, is quite close to his, as they state, after finding that the low informed investors systematically loose to better informed agents, that low informed traders have two ways to avoid these losses: "They can refuse to trade with the more informed individual and/or insulate themselves from the trading activities of the more informed by adopting a passive 'buy and hold' strategy." (Strong/Walker, 1987, 91).

Is it best for them to leave the market? Not necessarily: they are just below the market return, but not necessarily loosing money. As long as they earn more than the risk-free rate it may be advantageous for them to stay in the market. If the risk-free rate is for example 3 percent and the average return in the stock market is 8 percent, traders have an incentive to stay in the market, as long as their underperformance relative to the market is less than 5 percent, as their net return will then still be better than the alternative. Strong and Walker (1987) also argue that by refusing to trade on information (i.e. adopting a passive strategy) a trader can improve his situation. Such a move can be interpreted as shifting from an average information level (earning less that the average return) to a strategy using no information (with an expected return equal to the market return).

3. RESEARCH QUESTION AND MARKET DESIGN

With this study I want to explore how useful information is in a market and which information processing strategy is best for each of ten discrete information levels. To answer these questions a simulation study is conducted extending the model developed by Schredelseker (2001). His model seems very well suited to investigate the return of heterogeneously informed agents in a market with more than two different information levels as it allows to carefully control the information and to change trading strategies.

3.1. Design of the market

To investigate the usefulness of information in a market I chose the simplest market design that is still suited to capture the main characteristics needed to answer the research questions. There is only one asset in the market that can be traded by the agents by going long or short in each period. The periods are independent, and each period consists of four steps: first the traders are endowed with information about the intrinsic value of the asset. Then they post their reservation price (henceforth 'bid') for the asset. In a third step the ten bids are sorted from the highest to the lowest. To clear the market the median becomes the market price and all traders with a lower bid are sellers (short), while all traders with a higher bid are buyers (long). If a bid equals the market price the respective agent is neutral in this period. To ensure the zero-sum property of the market and to make sure, that the net supply of papers is zero, scale selling is used if the number of buyers and sellers is not equal. This design reflects a double-auction market without spreads, where all traders act as market makers. The market price thereby aggregates supply and demand and is an endogenous variable. In the fourth step of each period the individual payoff is calculated by comparing the market price with the intrinsic value according to the formula

[R.sub.j,k] = [Bid.sub.j,k] - [P.sub.k]/[absolute value of [Bid.sub.j,k] - [P.sub.k]] x [[V.sub.k] - [P.sub.k]].

[R.sub.j,k] stands for the return of trader j in period k, [Bid.sub.j,k] is the posted bid of trader j in period k, [P.sub.k] is the market price and [V.sub.k] the intrinsic value in period k. A buyer makes a profit if the intrinsic value is higher than the market price. If the intrinsic value is below the market price, he makes a loss. A seller receives a positive payment, if the intrinsic value is below the market price, and vice versa. For example, if the market price is 5 and the intrinsic value is 6, each buyer gains 1, while each seller looses 1.

3.2 The intrinsic value and the information system:

In each period the intrinsic value of the asset is given by the sum of ten Laplace-coins showing either 1 or 0 with the same probability of 0.5. The coins represent different brackets of the total information. The distribution of the intrinsic value is thus generated by a binomial process of ten steps leading to a binomial distribution with a mean of 5 and a standard deviation of 1.58.

The ten coins are used because it allows me to create a heterogeneous information structure among the agents. Trader Ix knows x of the ten coins, with x [member of] {0, 1, ..., 9}. I0 therefore knows none of the coins, I1 knows the realization of the first coin, I2 knows the first and the second coin, etc. until I9 who knows nine of the ten coins. The information system of this market is cumulative--a better informed trader always knows all the coins a worse informed trader knows plus some additional information. If the coins are understood as representing different brackets of all the factors relevant for a share price (e.g. the first coins representing inflation outlook, economic growth, industry sales outlook, etc.; and the last few coins representing secret product developments or the retirement of a key executive), it seems rational and realistic, that the low informed traders tend to have similar information (from newspapers, newsletters and TV), represented by a cumulative information system, than all having strongly diverging information represented by an independent information system. As Figlewski (1982) points out, an "independent information is not likely to be an adequate description of real-world speculative markets".

3.3 Trading strategies

In the simulation only two different trading strategies were used to keep the analysis as simple as possible. The most straightforward strategy is for each trader to use the information he has to estimate the intrinsic value of the asset. This strategy, which I call "active information processing strategy", can be considered the equivalent to the fundamental analysis widely used in real stock markets. The trader sums up the value of all the coins he knows and adds the expected value of all other coins. If the six coins I6 sees show for example 100111, he knows that the intrinsic value is between four (if the four coins he does not see all show 0) and eight (if they all show 1). The expected value of the four unknown coins is two (0.5 times four), so his best estimate of the intrinsic value is six. This can be generalized for all information levels:

[Bid.sub.j,k] = [j.summation over i=1][c.sub.i,k] + [(n - j)x0.5],

with [Bid.sub.j,k] representing the bid for the trader j in period k, [c.sub.j,k] the coins known to trader j in period k, and n the maximum number of coins (in this study 10).

The second trading strategy considered in this paper is to act randomly ('random strategy'). Here several approaches would be possible--for example choosing each value from 0 to 10 with a probability of 1/11, or choosing only 0, 5 or 10 with 1/3 probability each. I decided to use the simplest strategy available: a random player posts a bid of zero or ten, each with p=0.5. With this he only decides whether to go long (10) or short (0)in the market.

I want to stress several design features, before we turn to the results of the simulation: (i) the information level of each agent was kept constant during the whole session. (ii) There are no information or transaction costs. (iii) Each agent was required to post a bid each period. It was therefore not possible to abstain from trading. (iv) The market is a pure zero-sum game where zero is the benchmark (the market return) for each trader. All profits/losses reflect only the result from market trading. If information costs were included, the return of better informed traders would drop depending on the extent of information costs, while uninformed traders would pay nothing for information, so their result would stay the same.

4. SIMULATION RESULTS

For the results of the simulation study presented below the average returns of all [2.sup.10] = 1024 possible sets of coins have been calculated. All of the results presented show the average of twenty simulation runs to reduce the influence of chance in the data of random traders.

As the sum of the ten coins gives the intrinsic value, and as a coin is never shown wrong, everybody will agree, that the more coins a trader knows, the higher is his information level. It is obvious, that a person knowing five of ten coins is better informed, that a person knowing none. The question I want to answer first is, whether the better informed can expect a higher return in the market than the uninformed. Then we will turn to the question what the underperformers can do to improve their result.

In Table 1 we see the resulting expected returns for the ten information levels when all agents process their information actively (for I0 who does not possess any information this means always posting a bid of 5). The assumption of a positive additional value of information holds for the third and all additional coins, but it is obvious, that the first two coins can not improve the return of the trader, but worsen it. I4 is the first who is able to outperform the uninformed I0. Not the worst informed trader (I0), but the low to average informed I2 has the lowest return in the market.

Confronted with this result the question arises, how additional information can worsen the return of I1 and I2 compared to the return of I0. The key to solving this puzzle is 'skewed' information. If information is unskewed, a part of the information shows basically the same picture as the total information. If the ten coins show for example 0101011010, an uninformed trader estimates a value of five, a trader knowing the first four coins (0101) also estimates five, and the same holds for a participant knowing the first eight coins if the traders use active information processing. In cases of unskewed information, as above, most traders estimate the same price, which will also be the market price. At this price nobody will loose or gain a lot and the information is basically useless. While most sets of coins are of this type, some are cases of skewed information.

Here a part of the information shows a different picture than the total information. Let us consider an extreme case where the coins show 0000011111. As in the example above the intrinsic value is five, but some traders may be mislead by the information they get. As this is one of the core points of the study let us take a close look at every single trader and his bid with active information processing. The only information I0 has is the number of coins. He therefore estimates the intrinsic value as 0.5x10=5. I1 knows the first coin and her bid is therefore 0.5 lower at 4.5. Subsequent estimates of the value decrease until I5 who has the lowest estimate of 2.5 as he sees five times '0'. I6 to I9 see additional coins showing '1', so their bids are higher.

The market clearing price with these bids is 3.75. Five traders (I0, I1, I2, I8 and I9) have posted bids higher than this price and are therefore buyers, while the other five traders sell the asset. Here the asset is underpriced and all sellers loose to the buyers, as they sold the asset too cheap.

The average informed traders all process the same information (the first few coins) and are thereby systematically mislead, lowering the price to their own disadvantage. We could speak of an 'information risk' that traders take, when they gather information, as this information could be skewed. The information risk is zero for uninformed traders, increases with additional information until a certain extent of information is reached, where the information risk becomes lower again, as the information known is a very large part of the total information, so it has to be representative and can not be strongly skewed.

A similar result has recently been derived analytically by Rossi (2004). He shows that additional information has two different effects on expected returns: information reduces uncertainty and thereby increases returns, but is also carries a "covariance-risk" that reduces returns. He shows that additional information is harmful for the first few units of information, while it has a positive net effect for higher levels of information.

We can conclude, that an uninformed trader knows too little to be systematically mislead, while the well informed know enough to be on the right side of the market. Only the average informed traders who all use the same information make the same estimation errors and influence the market price to their own disadvantage. For them information is either useless (when it is unskewed) or harmful (when it is skewed). Even though cases of skewed information are rather rare, they contribute greatly to the final outcome, as the profits and losses in these cases are quite large.

4.1 Changing trading strategies

Traders are neither stupid nor do they like to loose money systematically. In real markets they will try to improve their results by switching to other information processing and trading strategies. Here we will just consider one alternative strategy: random trading. Instead of active information processing a trader can choose a bid of 0 or 10 with probability 0.5 each.

Table 3 shows the resulting return distribution when 10 switches to a random strategy. While he lost -0.33 with information processing his loss is only -0.11 with a random strategy. The returns of other traders also change a little.

This result is remarkable for two reasons: we see an improvement of the return which is in line with the intuition given at the beginning, but contrary to the assumption stated above a random strategy does not generate the market return (which would be zero) but a somewhat lower result. This is due to the thinness of the market: with only ten traders in the market each trader has considerable market power and therefore influences the price. Whenever our random trader selects '0' he lowers the median and therefore the price, while a bid of '10' increases the price. These price changes are always to his disadvantage and in total this reduces his net return from 0 to -0.11. In a market where a single trader does not have market power the net return should really be zero.

Other players may also wish to improve their result: if a random player looses just -0.11, while for example I3 looses -0.36 by using the information content of her three coins, she will at some point just stop using her information and switch to a random strategy as well. The result of this change in her information processing strategy is shown in Table 4: by ignoring her (correct) information, the trader can significantly improve her performance in the market. She is even able to outperform the better informed I4 and I5. By ignoring her information, I3 becomes a second random trader, as signified by "rand." in the table.

The rationale behind this result has already been outlined above: I3 surely knows more than a random trader, but when trading in the market she is always betting against still better informed traders, who can systematically exploit her mistakes. Her limited information (equivalent probably to the information provided by newspapers, stock market TV and newsletters) does not show the whole picture and may therefore be skewed. As we have seen above, especially the average informed traders fall into this trap, while a random player is not exploitable. Sometimes she will be right, sometimes wrong, but she does not make systematic mistakes. This result is in line with Malkiel (2003a, p. 10), who concludes that "Investors are likely to achieve far higher returns by employing a passive indexing strategy than they are likely to achieve from active portfolio management." A passive indexing strategy is just another way not to process any information and leads to similar results as a random strategy.

In time more and more traders will realize, that their return is below the market average and some will switch from information processing to a random strategy. Table 5 shows, what happens if all traders who lost money in Tables 3 and 4 (I0 to I5) start trading randomly: they all loose approximately the same amount of money, but with an average of -0.40 the loss is much larger than it is for the single random trader in the basic scenario. The losses of the random traders are now even higher, than the highest loss is in the basic scenario (-0.38 for I2). On the other hand the profit for I9 increases from 0.62 in the basic scenario to 0.86 when six traders act randomly.

We see that the informed traders are now able to exploit the random traders even more than they could with average informed active traders. This is due to the fact that random trader produce "noise" in the market and when the number of random traders increases (here 60 percent of the market act randomly!), the price becomes noisier and insiders can exploit mispricings even better.

What we see here is a phenomenon that I call a 'decreasing marginal return' of a trading strategy: when just one or two traders act randomly they can improve their position, but when more and more traders start to use the strategy its usefulness decreases. For the random strategy the net loss increases from -0.11 when one participant trades randomly to -0.12 for two traders and a staggering average loss of -0.40 with six traders acting randomly. This shows that to profit from a random strategy it is important, that not too many traders use this strategy. Later I will show that this decreasing marginal return also exists for other trading strategies (and presumably for all strategies).

Let us take this comparative-statically analysis one step further: some of the random traders may realize, that they now loose even more money than they did before. By switching back to information processing they can probably improve their situation. If, for example I3 decides to start processing her information again, her losses of -0.40 change to even a small profit of 0.03. The resulting returns for all traders are displayed in Table 6.

Apart from the significant improvement for I3 it is also remarkable, that the return of the five remaining random traders improves from -0.40 to -0.29 on average, while the best informed have lower profits than before. This is due to a decreasing degree of noise in the market when I3 switches back to processing her information.

While processing information was damaging for I3, when all traders did it, it is beneficial to her, in case that many traders act randomly. This shows, how dependent the optimal strategy and the result of one trader is on what other participants in a market are doing at the same time. A rough rule for low to average informed agents that one could derive from this analysis would be to "use a different strategy than all the others do." If most traders process information, it is beneficial to use a random strategy, but if many traders use a random strategy, it is better to process information even if a trader has only a rather low information level. For insiders it is a dominant strategy to use their information.

4.2 Deriving an equilibrium

The logical question is, whether an equilibrium exists, where no trader can improve his situation given the strategies of all other traders. It is clear, that the situation shown in Table 6 is not an equilibrium, as traders like I4 or I5 can hope to improve their return by switching back to an active information processing strategy.

Above I mentioned the decreasing marginal return for the random strategy. It should be noted, that the same can be found for the active information processing strategy: if only one agent (the best informed) uses information, while the nine others trade randomly, his profit is 1.20. The average profit drops to 1.12 when two agents process their information actively, 0.93 for three agents and a modest 0.09 if six agents process their information actively. For this analysis I started with the best informed agent I9 and subsequently added always the next best informed agent using his information actively. As we have a zero-sum-game the average profit is naturally zero, if all traders process information actively.

Table 7 shows the complete set of average and marginal returns for both strategies depending on the number of traders using the strategy. For the active information processing strategy the marginal return is lower than the average, as the last (marginal) trader switching to active information processing is always worse informed than the ones that already use the strategy. For the random strategy marginal and average returns are always equal, therefore only one line is displayed.

Remember that the sum of traders using the active or the random strategy is always ten, as we have ten traders in the market, lf each of four traders processing their information actively earns 0.60 on average, each of the six other traders (acting randomly) looses -0.40 for the zero-sum property to hold.

Let us examine an example to make the results shown in the table very clear: if three traders use a random strategy each of them faces an expected average loss of -0.13. The seven other traders, who process their information actively, make an average profit of 0.05. But not all of them win. The worst informed active trader makes a loss of -0.27 (shown in the marginal return of the seventh active trader). If this agent decides to switch to a random strategy (becoming the fourth random trader) he and the other random traders now have an expected loss of-0.15, while the average return of the remaining six traders actively processing information increases to 0.09.

To derive an optimal strategy for herself a participant has to compare the marginal returns of each strategy. For the random strategy marginal and average returns are the same, while the marginal return with active information processing is regularly lower than the average. It is obvious that not all traders will act randomly, as the first active trader will be able to earn a profit of 1.20. Several other agents will use their information until we reach the sixth agent. When trading randomly he would loose -0.22 (as the fifth random trader) each period, if he processes his information the loss would increase slightly to -0.24 (as the sixth active information processor). The sixth agent (and all subsequent ones) should therefore trade randomly and we find an equilibrium in our setting with only two allowed strategies with the first five participants trading randomly, while the five best informed traders process their information actively. It is remarkable that the marginal returns of both strategies are almost equal in this equilibrium with -0.22 for the random strategy and -0.24 from the information processing strategy. Both strategies (and many others that are not show here) have their place in the market as they offer their users a better return than the alternatives. The resulting returns in equilibrium are shown in Table 8.

This result can be considered a rational expectation equilibrium as no agent can improve his situation by changing his strategy and prices are market clearing for each possible realization of the coins.

If we would allow more strategies (passive, contrarian, technical trading strategies), the task of deriving an equilibrium would become more complicated, but there should always exists at least one in this sort of closed market. The decreasing marginal return shown for active as well as random trading strategies could also be shown for other strategies. This leads to the conclusion, that in a market with numerous traders we have an equilibrium with some traders processing information, while others trade randomly, and again others may follow any other rule that you can think of. In equilibrium the marginal returns for all strategies should be the same and slightly below the market average. Only a few insiders will be able to gain excess returns. In real markets several factors make the analysis probably too complex to test it empirically: traders do not necessarily stay in the same information level, they may improve over time. The permanent entry and exit of traders in the market increases the dynamic further. In addition a precise study would require a separate analysis for every single asset, as some traders being extremely good informed about one asset may know little or nothing about other assets.

5. CONCLUDING REMARKS

In this paper I explored a field, yet little covered in finance--the relationship of information level and return in a market with more than two information levels and the usefulness of different trading strategies in such a market. In addition to the "usual" result of informed traders outperforming uninformed ones, I find an area where additional information is of no value or even harmful for traders. In this context financial markets are understood as a game, where heterogeneous agents interact. In their attempts to outsmart each other only the best informed are able to gain above average returns. Average informed traders who rely on their information can be exploited by their better informed opponents, while random traders can expect almost the average return, as they are not exploitable.

By changing trading strategies of underperforming agents in the simulation an equilibrium is derived where no trader can improve his situation by changing his trading strategy. In this equilibrium well informed traders process their information actively, while low to average informed traders act randomly. In equilibrium the marginal return of the different trading strategies is approximately the same.

A remarkable finding is, that trading strategies show a phenomenon known from economics as decreasing marginal returns and also common in game theory: a strategy that is useful for one agent may be harmful if many traders use it. This has been shown for a simple random strategy, where the results deteriorate when more and more traders use it. A simple rule for low and average informed agents one could derive from this is to use a different trading strategy, than the others ("never follow the herd"). However, this is obviously difficult to do, as it is not possible what the others are doing at the same time.

TABLE 1: RETURN PER INFORMATION LEVEL
IF ALL TRADERS ACTIVELY PROCESS INFORMATION

Information     I0      I1      I2      I3      I4
net return    -0.33   -0.37   -0.38   -0.37   -0.30

Information     I5      I6      I7      I8      I9
net return     0.03    0.23    0.38    0.50    0.62

TABLE 2: MARKET ANALYSIS WITH SKEWED INFORMATION COINS SHOW 0000011111)

                  I0      I1      I2      I3      I4

bid              5       4.5     4       3.5     4
market side *      B       B       B      S       S
profit / loss    1.25    1.25    1.25   -1.25   -1.25

                  I5      I6      I7      I8      I9

bid              2.5     3       3.5    4       4.5
market side *     S       S       S       B       B
profit / loss   -1.25   -1.25   -1.25   1.25    1.25

TABLE 3: RETURN PER INFORMATION LEVEL WHEN I0 ACTS RANDOMLY

Information   rand.   I1      I2      I3      I4
net return    -0.11   -0.29   -0.33   -0.36   -0.31

Information   I5      I6      I7      I8      I9
net return    -0.11   0.14    0.33    0.47    0.60

TABLE 4: RATE OF RETURN PER INFORMATION LEVEL WITH I0 AND I3 TRADING
RANDOMLY

Information   rand.   I1      I2      rand.   I4
net return    -0.12   -0.29   -0.31   -0.12   -0.31

Information   I5      I6      I7      I8      I9
net return    -0.12   0.09    0.29    0.44    0.58

TABLE 5: RATE OF RETURN PER INFORMATION LEVEL WITH I0 TO I5 TRADING
RANDOMLY

Information   rand.   rand.   rand.   rand.   rand.
net return    -0.40   -0.39   -0.40   -0.40   -0.41

Information   rand.   I6     I7      I8      I9
net return    -0.40   0.39   0.51    0.67    0.86

TABLE 6: RATE OF RETURN PER INFORMATION LEVEL IN THE SIMULATION WITH
13 SWITCHING BACK TO INFORMATION PROCESSING

Information   rand.   rand.   rand.   13      rand.
net return    -0.28    -0.3   -0.29    0.03   -0.29

Information   rand.    I6      I7      I8      I9
net return    -0.29    0.11    0.29    0.47    0.62

TABLE 7: AVERAGE AND MARGINAL RETURN OF TRADING STRATEGIES
WITH RESPECT TO THE NUMBER OF TRADERS USING THE STRATEGY

# of traders using strategy     1       2       3       4       5

average return active          1.20    1.12    0.93    0.60    0.22
marginal return active         1.20    1.06    0.78    0.38    0.02
return random (avg=marg.)     -0.11   -0.12   -0.13   -0.15   -0.22

                                6       7       8       9      10

average return active          0.09    0.05    0.03    0.01   0.00
marginal return active        -0.24   -0.27   -0.30   -0.31   0.00
return random (avg=marg.)     -0.40   -0.40   -0.28   -0.13   0.00

TABLE 8: RATE OF RETURN PER INFORMATION LEVEL
IN THE SIMULATION APPROACH WITH EQUILIBRIUM STRATEGIES

Information    rand.    rand.    rand.    rand.    rand.     I5

net return     -0.22    -0.23    -0.22    -0.21    -0.22    -0.05

Information     I6       I7       I8       I9

net return     0.02     0.18     0.39     0.56

REFERENCES

Ackert, Lucy F., Church, Bryan K., Zhang, Ping, "Market behaviour in the presence of divergent and imperfect private information: experimental evidence from Canada, China and the United States", Journal of Economic Behavior & Orqanization, Vol. 47, 2002, 435-450.

Fama, Eugene, "Efficient Capital Markets: A Review of Theory and Empirical Work", Journal of Finance, Vol. 45, 1970, 383-417.

Figlewski, Stephen, "Information Diversity and Market Behavior", Journal of Finance, Vol. 37 (1), 1982, 87-102.

Gibbons, Robert, A Primer in Game Theory, Prentice Hall, Gosport, 1992.

Jaffe, J.F., "The effect of regulation changes on insider trading", Bell Journal of Economics and Management Science, Vol. 5, 1974, 93-121.

Lakonishok, J, Lee, I. "Are Insider Trades Informative?", The Review of Financial Studies, Vol. 14, 2001, 79-111.

Lin, Ji-Chai, Howe, John, "Insider Trading in the OTC Market", Journal of Finance, Vol. 45 (4), 1990, 1273-1284.

Malkiel, Burton G., A Random Walk Down Wall Street, W.W. Norton & Company, New York, 1996.

Malkiel, Burton G., "Passive Investment Strategies and Efficient Markets", European Financial Management, Vol. 9 (1), 2003a, 1-10.

Malkiel, Burton G., "The Efficient Market Hypothesis and Its Critics", Journal of Economic Perspectives, Vol. 17 (1), 2003b, 59-82.

Rossi, Andreas, Zum Wert von Information fur Investoren auf Finanzmarkten, Thesis, Innsbruck, 2004.

Schredelseker, Klaus, "Anlagestrategie und Informationsnutzen am Aktienmarkt" Schmalenbachs Zeitschrift fur Betriebswirtschaftliche Forschunq, Vol. 36/1, 1984, 44-59.

Schredelseker, Klaus, "Is the usefulness approach useful? Some reflections on the utility of public information" in Contemporary Issues in Accounting, McLeay, Stuart and Riccaboni, Angelo (Eds.), 2001, 135-153.

Seyhoun, H.N., "Insiders' profits, cost of trading, and market efficiency", Journal of Financial Economics, Vol. 16, 1986, 189-212.

Strong, Norman, Walker, Martin, Information and Capital Markets. Worcester, Basil Blackwell, 1987.

Author Profile

Dr. Juergen Huber, studied in Austria and the U.S. (Tulane University), he earned two Ph.D., one in Finance, one in Political Sciences, currently he works as Assistant Prof. at the Department of Corporate Finance, University of Innsbruck, Universitaetsstrasse 31/8/32, A-6020 Innsbruck, Austria, Tel.: [phone], e-mail: juerqen.huber@.uibk.ac.at