Modeling Decision Making Biases in the C ontext of a Market
Kawika Pierson
MIT Sloan School of Business PhD Student
305 Memorial Drive #207
Cambridge MA, 20139
617-838-2888
kawika@ mit.edu
Keywords: Decision making biases, Market, Overconfidence, Availability, Trading
Abstract
The effects of two behavioral decision making biases are evaluated within the
context of a system dynamics model of a market for a commodity, overconfidence and
availability. Overconfidence is modeled as an increase in the percent of a trader’s
capital they are willing to commit to any trade and is found to have the effect of
increasing profits for traders with good information relative to traders with poor
information, as well as increasing the volatility of the returns for traders with good
information more than for traders with poor information. The Availability Bias is
modeled as a overweighting of information easily available to a trader and is found to
have the effect of increasing the returns of traders with good information easily available
to them and decreasing the returns of traders with poor information easily available.
Introduction
Quantifying the effects of decision making biases on trader's profits is a difficult
problem. Complexities arise from several angles, including difficulties inherent in
running controlled experiments in continuously shifting market conditions, difficulties in
finding trading firms willing to provide access to their traders and also from difficulties
isolating and quantifying when, where and how these biases intervene in trading
decisions. Because of these difficulties, system dynamics lends itself naturally as a tool
for accomplishing this goal.
With this goal in mind, this paper starts by constructing a system dynamics model
of a market with functionalities inherent in it that will allow us to run detailed tests of
several hypotheses about the effect these biases might have on traders. The model allows
us to run repeated, controlled experiments over underlying market conditions that are
identical in each case, as well as isolate the exact mechanism and size of the biases in
each case. We then lay out the experimental framework for how we will test these
hypotheses and display and analyze our results.
Model Structure
Supply, Demand and the Market
The basic engine behind the model is a pair of supply and demand curves that
solve for the correct price with twin delays. These two table functions that lookup price
and read out what the values of supply and demand ought to be function exactly like
supply and demand curves familiar with economists, demand decreases with price
increases and production reacts in the other direction. Supply and demand can not
instantly respond to the signals price is sending them however. As in the real world,
supply and demand in the model adjust to their price indicated values with some delay.
In general the delay time for price effecting supply will be different than the delay time
for price effecting demand, therefore the model allows for these constants to be set
separately. The values for supply and demand above feed back into the model’s
determination of price.
While none of the tests conducted in this paper utilize this functionality, the
model has implemented parameterization of these table functions that allow the user to
test more complicated supply and demand relationships such as sudden shocks to
producers cost functions or gradual decreases in consumers consumption habits due to
viable alternatives coming to market. This implementation was created along the lines of
that found in Repenning’s “Dynamics of Implementation” paper (Repenning 2001).
Each unit of the commodity that is produced must be hedged by selling a contract
on the market and every unit of the commodity that is demanded must be hedged by
buying a contract on the exchange. The model then compares the number of contracts
long (buying) to the number of contracts short (selling) in the market at any one time and
based on which number is higher and the size of the difference adjusts price at the next
time step within some limited range. The exact mechanism of this price adjustment is
accomplished with a table function. The ratio of the residual contracts [abs(long-short)]
to the total number of contracts traded is the input to the table function which then
outputs the magnitude of the price change resulting from that trading. In the absence of
speculative trading these contracts would be the only ones traded on the exchange, and
would provide the mechanism through which production and consumption decisions
could feedback through price onto future decisions. Thus, when demand is much larger
than supply more contracts will come to the market long, price will move up and over
time demand will slack, production will grow and the market will come into balance. A
symmetric description is true for the case of production being higher than demand.
Figure one shows this base case result of the model. Price, supply and demand are
initially in disequilibrium, they quickly adjust, but oscillate around their goal, coming
into equilibrium by the end of the model run.
Price
“ Production and Demand
, o 10 2 3 4 50 6 70 80 90 100
100 ‘Time (Day)
. 0 20 0 40 so 60 7 a 9 100
Tine (Das) Amount Produced : Cures. ———__________—ammountDay
Prioe : Cuan; dotargeontract Demand : Curent —————————__ ammount/Day
Figure 1. Price, Supply and Demand in the base case of the model with no trading
This mechanism for price discovery is substantially different from the actual
process of discrete bids and offers within a market, but a case can be made for it
approximating that process. On an exchange, individual bids and offers may respond
independently of the total order flow in any one direction; however the bids and offers
given by floor traders are very sensitive to their interpretation of how much outside order
flow is coming from the long side as opposed to the short. If there is a great imbalance in
one particular direction the price that floor traders offer moves to correct that imbalance.
This is the process that the price discovery mechanism in the model mirrors. This
implementation has the advantage of capturing the underlying dynamics of how a market
discovers price without having to model the sometimes messy discreteness found in the
actual bid matching process.
Speculation
There are two strategies available to traders in the model, fundamental strategies
and technical strategies. These two classes correlate well with the major classifications
of trading strategies practicing traders would identify. Technical traders in practice follow
a range of strategies which all posit that past prices contain some information about what
future prices will be. Some are essentially trend followers, while others trade a variety of
other indicators. Within the model, one of the most popularly used indicators, the
moving average cross rule, is used as the decision rule of technical traders. Essentially,
this rule works by making each trader compute two different smoothes of price, one of
which uses a shorter averaging time than the other. When the value of the short moving
average rises above the value of the long moving average the decision rule says that the
market situation is bullish and the trader should get long, when the value of the short
moving average is below the value of the long moving average, the decision rule says that
the situation is bearish and the trader should get short. This decision rule works because
the short moving average reacts more quickly to the trend of price then the long moving
average, and thus their relative values will signal the short term direction of the trend in
price. In this model, the values that the traders use for the long and short averaging time
cascade in order to represent more fully the wide spectrum of trend following techniques
employees in modern markets.
The Finance community has largely shunned technical analysis due in part to the
influence of the Efficient Markets hypothesis’ random walk theory; see for instance
Fama’s survey. (Fama 1970) One of the seminal revelations of the hypothesis was that
markets fully discount all relevant information, which means that forward prices can not
be projected from past price data and thus the primary approach used by technical
analysts could not possibly work. More recent work has suggested flaws in this theory
however, Lo and MacKinlay published one example, in which the authors find that the
random walk theory can not be upheld, since stock prices have a small autocorrelation.
(Lo and MacKinlay 1998) Despite this debate however, there is ample evidence that the
existence of technical trading is a behaviorally realistic fact about modern capital
markets, and thus there is a compelling argument for including its effects in a model of a
market.
Fundamental traders look to supply and demand to make their determination of
price direction. They cannot obtain this information themselves in the detail they need,
therefore they rely on a network of opinion makers to provide them with opinions of the
market direction based on fundamental information. Each opinion maker samples a
noisy value of the carry out and the demand every “observation interval” days. The size
of the noise component of the signal they receive is easily controllable within the model
and can be varied independently for each opinion maker creating a situation where
certain opinion makers will in general be more correct about the actual value of supply
and demand than others. The noise added to these observations is pink in spectrum, and
is implemented with a standard pink noise generator. These observations are then used
by the opinion maker to compute the forward value of the carry out to use ratio, the trend
of which becomes the opinion maker's opinion on the direction of price. If the trend of
the carry out to use ratio is growing then stocks are building and price should go down,
whereas if the carry out to use ratio is shrinking then stocks are being used and price
should rise. This mimics almost exactly the method employed by commodity analysts,
although it neglects the effect of the absolute level of the carry out. Adding in the effect
of the absolute level of the carry out is a goal of future extensions of our model.
erties: vemana =—— Carry uur
Make an
Observation?
<Make an _
opselvation / — : Observation? |
“ene { Current Value of i Current Value of
Observed Demand observed Carry Out
sos
a] Bemeng yn &
cant” Readout Reet “ee”
step> Demand dime 0 <rine ry
\ Stee | <TIME
| <time | STEP>
<Time>| STEP> ctimie>:
thes TIMES
Figure 2. Opinion Makers’ sampling of demand, a non-standard formulation
The sampling mechanism employed to approximate the fact that real world
opinion makers can only observe static pictures of the demand and consumption of
consumers is the only non-standard formulation in this portion of the model. From a
spectral analysis standpoint the harder cutoff represented by this sampling differs
substantially from the softer low pass filtering of a smooth. Since a smooth is also used
in the formulation to represent the time lag inherent in opinion makers updating their
views of supply and demand one might suggest that these two effects be combined into
one longer smooth. However this modification significantly alters the spectrum of noise
that is passed from the “noisy observations” on through the system to price and greatly
reduces the plausibility of the price series’ created in the model. For this reason, and also
because the sampling mechanism is behaviorally plausible from the author's viewpoint
there is significant evidence to warrant using this non-standard structure in the model.
The opinions created by these fundamental analysts are then given to the traders,
after passing through an awareness screen which allows information to be known by
some traders and not others. The traders then weight each of the market direction
opinions representing the degree to which the trader trusts that opinion maker to correctly
analyze the market, and then each trader takes the weighted average of these opinions.
The sign of this number is the direction the trader thinks the market is moving and the
size of the number if how confident the trader ought to be if they were completely
rational and actually weighed each opinion in the proportions implied by the model. The
confidence of each trader affects the fraction of their total capital committed to each bet
they make, so a confidence of 1 will cause the trader to bet 100% of his available capital.
Once traders make a decision using one of these two strategies the model will
notice that the trader wishes to make a trade and record the value of price that the trader
traded. These trading flags are then used along with the size of the positions each trader
took to calculate the number of contracts coming to the market long or short in any given
time period. This number then is used to compute price in the same way as described
above for the base case except that now the flows of contracts to the market come not
only from producers and users but also from speculators.
There is also significant model structure dedicated to tracking the profit or loss
over time from each of the trader’s trades and adjusting the level of capital each trader
has due to this profit or loss. The data collected in this way will allow us to evaluate the
effect of biases on the profits enjoyed by traders.
Decision Making Biases
There is ample evidence within the decision making literature that people are
generally overconfident in the correctness of their views. In their paper on Naive
Realism, Ross and Ward note that “[In] prediction, for example, failure to make sufficient
allowance for the possibility that the situation facing the actor actually will be quite
different than the way we are construing it (and/or the possibility that the relevant actors
construal of it will be quite different from our own) breeds unrealistically high levels of
confidence, and ill advised gambles.” This tenant of naive realism is undoubtedly a bias
which is present within the context of a market. (Ross and Ward 1996) With the many
sources of often contradictory information available to traders, a surprising number of
them will have highly confident views on the direction of the market at any given time.
Within the model this tendency towards overconfidence can be analyzed by
measuring the effect of the constant additive modifier of confidence that explicitly makes
each trader more confident than they would have been otherwise. This overconfidence
then translates within the model into the trader committing a higher percentage of their
total capital to each trade than they otherwise would have. The base case for a world
where everyone is exactly as confident as they ought to be given the information
available to them is when this variable is set to zero, high values of the variable
correspond to greater levels of overconfidence by the trader.
Hypothesis 1 - The natural tendency of traders to be overconfident will produce
higher profits for traders with relatively good information and less of an increase in
profits for traders with relatively poor information.
This hypothesis is plausible because over the long term, traders with better
information will probably be paid by the market to be overconfident since their
confidence will let them profit more from their information. Their overconfidence will
simply make their already good bets larger and so more profitable. This is likely not the
case for traders using comparatively poor information about supply and demand, since
increasing the size of their trades will on balance cause them to make less money than
their better informed counterparts.
Kahneman and Tversky present several decision making biases in there seminal
paper. One explored in this model is “Availability,” the thrust of which is that people
tend to be biased towards information that is more available to them. In the model, we
can evaluate the effect of this bias by separating the traders into three groups, ten traders
in firm 1, ten in firm 2 and ten independent. We will then compare the size of the
trader’ s cumulative profits in the case of all traders valuing all information equally to the
case of traders overweighting information available to their firm. (Kahneman and
Tversky 1988)
Hypothesis 2 - The availability bias will have a net negative effect on trader's
profit unless the information easily available to them is better than the information that
would be possible, but difficult to observe.
This is likely to be the case since overweighting information from particular
opinion makers will cause traders to rely too heavily on one set of opinions which on
balance are more likely to be incorrect than a more evenly weighted average of all
available opinions. If it were the case that the information easily available to the trader
provided a much better picture of price’s likely direction than the other information the
trader could access with more effort, then it would be likely that this bias would work in
favor of the trader, but that is the only case where this would be the effect. The trader
would have better information, and the good practice of heavily overweighting that
information. .
Results
In order to test the effect of overconfidence on traders profits, the traders were
split into two groups, one that relied on opinions with noise standard deviations between
30 and 50 added to the observations of supply and demand, and one that relied on more
accurate opinions ranging from 10 to 30 in noise standard deviation. Two hundred
simulations were run for each value of the overconfidence factor, with the noise seed
varied for each simulation and the results were averaged and recorded in the table below:
A verage of Profits
\Overconfidence
Factor 0 0.05 0.1 0.2 0.3 0.4 0.5
Good Information 64871 {90194 {113592 [181808 |256134 {302064 {262960
Poor Information 86508 |33076 {66071 [111957 |169173 {204953 191190
Difference 28363 [41626 {47521 {69850 {86961 {97111 _ [71770
Standard Deviation of Profits
|Overconfidence
Factor (0. 0.05 0.1 0.2 0.3 0.4 0.5
|Good Information [19657 [33076 [38566 62492 {102136 [144680 [119785
Poor Information [12850 |19081 |27779 [47539 {85108 _{103996 {103930
ISD as% of AVG 80.30% |36.67% 33.95% |34.37% |39.87% 47.90% |45.55%
35.20% |39.29% |42.04% |42.46% [50.31% [50.74% [54.36%
Figure 3. Results for the Monte Carlo simulation of the Overconfidence Bias
The results confirm hypothesis one, but show a slightly more nuanced picture.
For one thing, the profits of both traders with poor information and good information
increased for increases in the overconfidence factor up to and including 0.4. This is due
primarily to the fact that the sums bet by both groups of traders were larger with larger
levels of overconfidence and on average the trades recommended by fundamental
analysis were profitable. Thus larger sums of money risked on profitable trades will
result in more money made. One reason why the profits of both groups actually dropped
for the change from 40-50% overconfidence is that by the time the model was running at
40% overconfidence only very few trades were being executed at less than 100% of
capital committed. These were the trades that were affected by the increase in
confidence, and consequently the increase in capital committed actually decreased the
profits of traders because the increase capital was placed on losing trades.
As hypothesis one would suggest, the overconfidence bias helped traders with
good information more than traders with poor information for all increases in the
overconfidence factor up to and including 0.4. This can be seen from the increase in the
value of “Difference” in figure three. For higher levels of overconfidence, this difference
shrank, as more and more of the less profitable bets for each class of trader were
undertaken with large amounts of capital.
The standard deviation of the profits for each class of trader also tells an
interesting story. As can be seen in the lower half of figure three the standard deviation
of the profits for traders with both good and bad information, as a percent of their average
profits, increased substantially from the base case to the cases with high overconfidence.
This data suggests that in the real world overconfidence may increase the volatility of
retums for traders, suggesting an interesting area for research into the effects of these
biases that could serve as a test of the model’s results.
In testing the effect of the availability bias on traders profits a similar set of tests
were conducted. In these simulations the opinion makers and traders were each separated
into three groups. The first three opinion makers had noise with standard deviations
ranging from 5 to 15, the second group ranged from 70 to 90 and the last four opinion
makers had noise standard deviations ranging from 20 to 50. These groups were
designated as firm one’s proprietary information, firm two’s and public information
respectively. The traders were then divided into three groups, with the first ten belonging
to firm 1, and heavily overweighting their proprietary information, the second ten
belonging to firm 2 and heavily overweighting their proprietary information and the last
ten trading only on the information available publicly. In the cases where a trader had
access to proprietary information, the public information was also a part of their decision
making process, but was underweighted compared to the information easily available to
them from within their firm.
Using this setup, two hundred simulations were run varying the noise seed for the
opinion makers’ observations and the average profit for each group of traders was
recorded. The base case is the case where each trader is approximately as likely to
weight proprietary information heavily as they are to weight publicly available
information heavily. The results are shown in this table:
Average Profits Base Case Biased Case Percent Change
Firm 1 (Good) $38352 $39621 3.31%
Firm 2 (Poor) $22345 $16536 -26.00%
Independent $38529 $26517 -32.18%
Figure 4. Average Profits of traders for the test of the Availability Bias
The results above confirm hypothesis two, since the profits for traders with good
information rose, while the profits for traders with poor information fell. Two things
about the data stand out however. One is the fact that the increase in profits for firm 1 is
a good deal smaller than what one might have guessed would be the case given the
superiority of the information they were using to make their trades. Results very similar
to this were observed for repeated runs with different noise seeds, so the increase is likely
nota statistical artifact, but its size sheds some doubt on the hypothesis that the
availability bias has a measurable positive effect on traders with relatively good
information in the real world. If there is any such positive effect it is likely very small.
The negative effect of the availability bias for traders with poor information is
evident beyond any doubt looking at the data, what is surprising though is the extent to
which the independent third of traders had their profits reduced by the other firms trading
with the bias. Since the weights each independent trader placed on each information
source did not change between the two runs one might be tempted to say that there must
be some flaw in the model's formulation. However the fact that these trader’ s profits
change even though their weightings did not is a plausible outcome of the other traders
changing their weights. Since the weights used by the other traders influence their
trading decisions which in tum influence the price traded on the exchange, which in tum
influences supply and demand decisions which in turn further influence prices as well as
the signals being sent by the opinion makers in the model we would expect some change
in the profits of the independent traders given changes in the weights of the other twenty.
In fact, this insight gives us another angle to consider the data from. If we were
willing to say that the Independent traders were a “control” group in that the weights that
they placed on the incoming sources of information did not change, then we might be
willing to say that the market returns for each of the groups should thought of as
competing against a benchmark change of -32.18 percent in the control. This thinking
would increase the returns exhibited by the group one traders, and edge the returns of the
group two traders to become slightly positive. However the dynamics of the situation are
complex enough that this sort of linear thinking is rarely the correct heuristic to apply to
these situations, and so for the purposes of this paper the unadjusted results will be taken
as final. Efforts to study more in depth the mechanisms and effects of the availability
bias in markets are needed, and potential avenues for future research.
Conclusions and Ideas for Future Research
The results from our simulations uphold and extend the hypotheses outlined in the
decision making biases section. The effect of the overconfidence bias within the model
was to amplify the effects of the relative information quality of the trader up to a limit.
At this limit, the trader’s overconfidence caused them to enter into marginally poor trades
with such a large percentage of their capital that the positive effect of overconfidence for
traders with good information was undercut. Further, the volatility of profits for all
traders, as a percentage of their average profits, increased with increases in
overconfidence. This result suggests a potentially fruitful avenue for research into the
effect of these biases in actual trading settings, though the usual difficulties with access
and quantification of parameters will arise.
The effect of the availability bias was negative for all groups, except for the group
with relatively good information. Traders who were fortunate enough to have high
quality information about the markets easily available to them were slightly more
profitable, but in general overweighting information that was easily obtainable had a
strong negative effect on profits.
Some ideas for further applications of the model include fleshing out the supply
and demand sectors of the model, potentially by incorporating it with the Sterman’s
Commodity Cycle model. (Sterman 2000) This would allow for a richer picture of how
speculators effect decisions about what to produce and consume through the feedbacks
from price onto supply and demand, as well as increase how realistic the market
conditions faced by speculators in the model are. Additionally, the price setting
mechanism in the model is only an approximation of the actual process that takes place
within a market. An extension of this mechanism to mirror the discrete bid ask process
of amodem market could be helpful for increasing the realism of the results, although at
the time scales considered by the model, the approximation used is adequate. Also,
extending the model to capture the effect that the absolute level of the carry out to use
ratio has on fundamental traders’ opinions of price direction will help to bring the model
closer to the actual decision processes employed in the market.
Cited Works
Fama, Eugene F. 1970. Efficient Capital Markets: A Review of Theory and Empirical
Work. Journal of Finance: 383-417
Lo, and MacKinlay. 1988. Stock Market Prices do not follow random walks: evidence
from a simple specification test. The Review of Financial Studies: 41-66
Repenning, Nelson. 2003. A Simulation-Based Approach to Understanding the Dynamics
of Innovation Implementation. Organization Science 13: 109
Ross, L. and Ward, A. 1996. Naive realism in everyday life: Implications for social
conflict and misunderstanding. In Values and Knowledge, ed. E.S. Reed and E.
Turiel, 103-35. Mahwah NJ: L. Erlbaum Associates.
Sterman, John. 2000. The Invisible Hand Sometimes Shakes: Commodity Cycles. In
Business Dynamics: Systems Thinking and Modeling for a Complex World,
Chapter 20. McGraw- Hill/Irwin.
Tversky, and Kahneman. 1974. Judgment under uncertainty: Heuristics and Biases.
Science 185: 1124-31
Appendix A - Weights given by traders in Tests of Hypothesis 1
1,3,1,1,1,0,0,0,0,0; 1,2,1,1,2,0,0,0,0,0; 2,1,1,1,3,0,0,0,0,0; 3,1,2,1,2,0,0,0,0,0;
3,1,3,1,2,0,0,0,0,0; 3,1,2,2,1,0,0,0,0,0; 2,1,1,1,2,0,0,0,0,0; 2,1,3,1,2,0,0,0,0,0;
2,2,3,3,3,0,0,0,0,0; 1,2,1,3,1,0,0,0,0,0; 2,3,2,3,1,0,0,0,0,0; 2,3,2,1,1,0,0,0,0,0;
1,1,1,2,3,0,0,0,0,0; 1,1,2,2,2,0,0,0,0,0; 3,1,2,1,2,0,0,0,0,0; 0,0,0,0,0,2,3,1,2,1;
0,0,0,0,0,1,1,2,1,3; 0,0,0,0,0,2,1,3,1,2; 0,0,0,0,0,1,1,1,2,2; 0,0,0,0,0,1,2,2,2,1;
0,0,0,0,0,1,1,1,1,1; 0,0,0,0,0,3,1,2,1,2; 0,0,0,0,0,3,3,3,1,1; 0,0,0,0,0,1,2,1,1,2;
0,0,0,0,0,2,1,2,1,2; 0,0,0,0,0,1,1,1,2,3; 0,0,0,0,0,2,1,2,2,1; 0,0,0,0,0,3,1,3,3,1;
0,0,0,0,0,3,2,2,1,2; 0,0,0,0,0,3,3,2,1,2;
Appendix B - Weights given by traders in Tests of Hypothesis 3
11,1
Lil
1,2,9,0,0,0,1,1,1,1; 9,4,7,0,0,0,1,1,1,1; 0,0,0,9,6,3,1,1,1,1; 0,0,0,5,9,8,1,1,1,1;
1,1,1
11
0,0,0,0,0,0,9,7,5,3; 0,0,0,0,0,0,7,5,3,1; 0,0,0,0,0,0,5,7,5,3; 0,0,0,0,0,0,5,9,5,3;
0,0,0,0,0,0,1,3,7,3; 0,0,0,0,0,0,2,5,9,5; 0,0,0,0,0,0,1,3,5,7; 0,0,0,0,0,0,3,5,7,9;
0,0,0,0,0,0,1,1,1,1; 0,0,0,0,0,0,4,8,4,8;
9,4,6,0,0,0,7,3,8,1; 7,3,8,0,0,0,9,4,6,1; 9,8,9,0,0,0,1,7,3,8; 4,7,6,0,0,0,4,6,1,1;
9,5,5,0,0,0,1,4,6,1; 4,8,4,0,0,0,2,9,5,3; 9,3,4,0,0,0,7,6,2,1; 7,6,2,0,0,0,3,2,9,5;
1,2,9,0,0,0,9,4,9,5; 9,4,7,0,0,0,9,8,9,1; 0,0,0,9,6,3,3,9,4,6; 0,0,0,5,9,8,6,1,5,3;
0,0,0,2,7,9,1,9,5,3; 0,0,0,7,6,3,1,9,8,9; 0,0,0,9,5,3,1,7,6,2; 0,0,0,2,4,6,1,5,3,2;
0,0,0,8,3,2,6,3,1,9; 0,0,0,5,3,2,9,5,3,1; 0,0,0,1,2,3,5,3,2,1; 0,0,0,4,6,1,9,6,3,3;
0,0,0,0,0,0,9,7,5,3; 0,0,0,0,0,0,7,5,3,1; 0,0,0,0,0,0,5,7,5,3; 0,0,0,0,0,0,5,9,5,3;
0,0,0,0,0,0,1,3,7,3; 0,0,0,0,0,0,2,5,9,5; 0,0,0,0,0,0,1,3,5,7; 0,0,0,0,0,0,3,5,7,9;
0,0,0,0,0,0,1,1,1,1; 0,0,0,0,0,0,4,8,4,8;
