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2.
506 K.Y. Szeto and L.Y. Fong
to introduce heterogeneous agents, but our focus is on the individuality of the agent,
with personal character which entails different psychological responses to other
agents. These two steps are by nature not easy to model, as human interactions and
psychological responses are themselves very challenging topics. Nevertheless, we
start by considering some techniques used by physicists. The first problem of
incorporating interactions can be modelled by the standard technique of mean field
theory, meaning that each trader will interact with the average trader of the market,
who is representative of the general atmosphere of investment at the time. This will
naturally incur some error as effects of fluctuation, or volatility of the stock market,
may not be adequately treated. Next, we like to consider the psychological response of
individual trader. We can introduce simple quantitative parameters to measure
individual characteristics of the trader, so that the response to the general atmosphere
of the market is activated according to these parameters. Our model includes
heterogeneous agents who are represented by different rules of investment as well as
different human characters. The interactions between agents are simplified into
interaction with a mean field, or the general atmosphere of the market. We model the
general atmosphere of the market in an ad hoc manner, in that we do not deduce it
from a model of microscopic interaction between agents, but rather by a source of
random news which will serve as a kind of external, uncontrollable stimulus to the
market. We understand that this simple model of stock market traders lacks the
generality of a realistic agent. However, the important thing to note is that refinement
can be introduced later to model better the interactions, while the heterogeneity of
agents can be tuned by introducing more parameters in describing their individualities.
We hope that this new approach of modelling the microscopic agents is a first step
towards building a more comprehensive model of the stock market and its complex
patterns. Our generic trader is an optimal rule in forecasting, using a genetic
algorithms framework [5-10], where the relative performance of the individual agents
(chromosomes) is compared in a finite population under the Darwinian principle of
the survival of the fittest. In such a model, by suitably defining a measure of fitness on
the level of individual agents and group of agents, self-organized behaviour in the
population during evolution emerges. Furthermore, automatic control of the diversity
of the population and increase in the average fitness of the entire population are
observed [8-10]. A selection of fit rule and the subsequent augmentation of individual
character of the agents will follow. Their performance is measured by the net asset
value of their portfolios after a given period.
2. Prediction as an Optimization Problem
In using Genetic Algorithm for forecasting [5-10], the problem can be considered as
pattern recognition and the subsequent optimisation of the rate of correct prediction.
Since the objective of this work is to test the effects of news on the performance of the
agents, we will employ a simple Genetic Algorithm for the forecasting of the time
series, and focus our attention on the performance of portfolios of the agents. We
perform training and testing for a given time series, x(t), with 2000 data points by first
dividing it into three parts. The first 800 points form the training set for extracting
rules. The next 100 points form the test set, used for evaluating the performance of the
set of rules obtained after training. The last 1100 points form the news set for
3.
How Adaptive Agents in Stock Market Perform in the Presence of Random News 507
investigating the performance of investors with different degree of greed and different
level of indifference to the random news. In the training set, we make the usual
assumption that at time t, the value x(t) is a function of the value at x(t-1), x(t-2),...,
x(t-k). Here k is set to 8. As to the rules of forecasting, we use the linear model of time
series and assume a relation between the predicted value x (t ) and its precedent:
∑
i= k
x (t ) =
ˆ β i x ( t − i ) . The objective is to find a set of { β i } to minimize the root
i =1
mean square error in x compared with the true value x. Here, we do not perform any
vector quantization on the series {x(t)}, so that each x(t) is a real value. Note that
these x(t) values can represent the daily rate of return of a chosen stock, with
| x ( t ) |≤ 1 . We also assume the same condition on β i , so that | β i |≤ 1, i = 1,.., k .
Since our objective is to look at performance of agents who buy and sell the particular
stock, we only care for the sign of x . What this means is that for x positive, the
agent predicts an increase of the value of the stock and will act according to his
specific strategy of trading. If x is non-positive, then he will predict either an
unchanged stock price or a decrease, and will also act according to his specific
strategy. We count the guess as a correct one if the sign of the guess value is the same
as the actual value at that particular time, otherwise the guess is wrong. If the actual
value is zero, it is not counted. The performance index Pc that measures the fitness
value of the chromosome is designed as the ratio: Pc = N c /(N c + N w ) . Here Nc is
the number of correct guess and Nw is the number of wrong guess. Note that in this
simple genetic algorithm, we do not worry about the absolute difference between x
and x , only paying attention to their signs. This feature can be refined by a more
detailed classification of the quality of the prediction. Furthermore, while most
investors make hard decision on buy and sell, the amount of asset involved can be a
soft decision. Indeed, when we introduce the greed parameter for the agent as
discussed below, the decision on the amount of asset involved in the trading of a stock
can be considerably softened. For the purpose of the present work, the prediction
based on signs will be sufficient to obtain general insights of the coupling between
agents and news, and the effect of this coupling on the global behaviour. Finally, we
should remark that agents do not predict when x is zero, corresponding to the
situation of holding onto the asset. We start with a set of 100 rules (chromosomes)
represented by {βi}. By comparing the performance of the chromosomes, the
maximum fitness value is the result found by genetic algorithm using a modification
of the Monte Carlo method that consists of selection, crossover and mutation
operators [5-10]. We will leave the details of the genetic algorithms in a separate
paper, here we just state the results. After several thousands of generations, we
observe a saturated value of Pc, and we choose the chromosome corresponding to this
Pc as the generic rule of prediction. We simply make use of the adaptive nature of the
different chromosomes in a Darwinian world to single out the best performing
chromosome to be the prototype of agents with different human characters. We
introduce two parameters to characterize different human nature of the best agent.
These two parameters are the greediness "g" and level of fear "f". The final set of
agents, all with the same chromosome (or rule), but with different parameters of greed
g and fear f, will be used for the performance evaluation in their portfolio
4.
508 K.Y. Szeto and L.Y. Fong
management in response to online news. In the news set (last 1100 data points), we
assign identical initial asset to the agents. For instance, we give each rule
(chromosome, portfolio manager, or agent) an initial cash amount of 10,000 USD and
a number of shares =100. The value of f and g ranged from 0 to 0.96 in increment of
0.04 will be used to define a set of 25x25=625 different agents. We will then observe
the net asset value of these 625 portfolios as they trade in the presence of news.
3. News Generation
For a given past pattern, a particular agent will first make a comparison of this data
with his rule and if the pattern matches his rule, then the prediction according to the
rule is made. Without the news, the prediction is definite, for the agent is supposed to
execute the action suggested by the rule. However, in the presence of the news, the
agent will have to re-evaluate his action, reflecting the changed circumstances implied
by the news. The present work treats `news' as a randomly generated time series. This
can of course be made more realistic by taking some kind of average of many real
series of news as the input stimulus to the agent. One can also include a more detailed
model of interaction of agents so that the input stimulus to the agent is neither an
artificial time series, nor an external time series of news, but an internally generated
series that reflect the dynamics of interacting agents. This will be studied in a future
paper. Next, we consider the interaction of an individual agent with the randomly
generated time series of news. The agent has to decide whether and how his/her action
should be modified in views of the news. In making these judgements, the agent must
anticipate certain probability of change, which reflects the `greed' and the `fear' of the
agent in his decision process. For example, when there is news that is good in
conventional wisdom, the stock market price is generally expected to increase. An
agent, who had originally forecasted a drop in the stock price tomorrow and planned
to sell the stock at today's price by taking profit, may change his plan after the arrival
of the `good' news, and halt his selling decision, or even convert selling into buying.
This is a reversal of his original decision that is solely based on historical data
analysis. Similarly, for an agent who originally wanted to buy the stock at today's
price, as his forecast for tomorrow is a rise in stock price, may halt his buying action
because `bad' news just arrives. Instead of buying today, he may sell or hold on to his
cash, for fear of a crash. This kind of reversal of buying action may in reality trigger
panic selling. These behaviours anticipate immediate effect of news, thereby often
reverse original decision based on rational analysis on historical data through pattern
matching. To incorporate these realistic features of the markets, we introduce two
additional real numbers to model the market. The following features now characterize
each agent. (1) An integer indicating the class of prediction. For this paper we only
use two classes, 1 for increases and 0 for decreases or unchanged stock price. (2) A
rule to recognize pattern in the time series. (3) A real number f to characterize the
level of fear of the agent in his original decision. If f is 0.9, then the agent has 90%
chance of changing his decision when news arrives that contradicts his original
decision. This denotes an insecure investor who easily changes his investment
strategy. If f is 0.1, then there is only 10% chance of the agent of changing his original
decision, a sign of a more confident investor. Thus, f is a measure of fear. (4) A real
5.
How Adaptive Agents in Stock Market Perform in the Presence of Random News 509
number g to characterize the percentage of asset allocation in following a decision to
buy or sell. This number can be interpreted as a measure of the greediness of the
agent. If g is 0.9, it means that the agent will invest 90% of his asset in trading, a sign
of a greedy gambler. On the other hand, if g is 0.1, the agent only invests 10% of his
asset in trading, a sign of a prudent investor. Thus, g is a measure of greed.
Algorithmically, we first choose a random number c between 0 and 1 and decide that
news is good if c > 0.5, otherwise it is bad. This model of random news may not be
realistic, but will serve as a benchmark test on the effect of news on the agents by
saying that there is equal chance of arrival of good news and bad news. There are four
scenarios for the agent with news. (1) News is good and he plans to sell. (2) News is
good and he plans to buy. (3) News is bad and he plans to sell. (4) News is bad and he
plans to buy. Note that there is no contradiction between the agent's original plan and
the news for case (2) and (3). But in case (1), the agent may want to reverse the selling
action to buying action due to the good news, anticipating a rise in stock price in the
future. Also, in case (4), the agent may decide to change his decision of buying to
selling today, and buying stock in the future, as the news is bad and the stock price
may fall in the future. Thus, in (1) and (4), the agent will re-evaluate his decision. He
will first choose a random number p. If p > f, he will maintain his prediction,
otherwise he reverses his prediction from 1 to 0 or from 0 to 1. Therefore f is a
measure of fear of the agent. The parameter g measures the percentage of the amount
of cash used for buying stock or the shares in selling stock. Large greed parameter g
implies that a big gambler, and will invest a large fraction of his asset following the
rules and the news, while a small g parameter characterizes prudent investors.
Fig.1 Final values in cash of the portfolio of the 625 agents. Initially all agents have
the same value at 19900. The time series for stock is Microsoft.
4. Results
We use several sets of time series, including the real stock value of Microsoft, the
long and short memory time series with controlled auto-correlation generated using
the inverse whitening transformation. All these time series show similar behaviour. In
6.
510 K.Y. Szeto and L.Y. Fong
Fig.1 we show the effects of news on the performance of the agents in terms of the
steady state or 'final' values of their portfolio. Empirically, we find that the net asset of
the portfolio, (cash plus stock) reaches a steady value after more than 1000 responses
to random news. From our numerical experiment with a ten days probation period,
(we then have 110 evaluations on the news set), we observe to our surprise similar
patterns to all the data sets. In Fig.1, we observe a trend of the portfolio measured in
net asset value in cash to rise at large g and small f. This is an interesting universal
behaviour that demands an explanation, which we leave it to a future paper. In a pool
of agent that are trained by historical data, and endowed with individual characters
like greed and fear in their investment exercises, the effects of news, generated
randomly, show universal behaviour. This universal behaviour suggests that greedy
(large g) and confident (small f) investors perform better.
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