This document discusses several theories of stock market fluctuations: 1) The efficient market hypothesis which states prices reflect all known information and movements are due to new information. 2) The random walk hypothesis which claims fluctuations are totally random and unpredictable. 3) Behavioral economics perspectives which emphasize the role of human psychology in driving mass movements. It also examines the work of Fama on market efficiency forms, Malkiel's refutation of fundamental and technical analysis, and Taleb's criticisms of attempts to explain movements with structured models. The document aims to statistically test and potentially refute these theories of market predictability.

1. Patterns of Price Change in the Dow Jones Industrial Average?
“Black Swans” as a Refutation of the Random Walk Hypothesis.
Patrick Moore
Economic Research
1

2. Explanation of stock market fluctuations has long been a crucial part of
economics. Many theories have been derived in an attempt to explain the complex
dynamics of market fluctuation. Amongst these theories are the random walk hypothesis,
and the efficient market hypothesis. Both theories use vastly different reasoning in an
attempt to accurately explain price movements in the stock market. A much more
unorthodox view of market function, held by Nassim Taleb, will also be examined.
In this paper I plan to assess the aforementioned theories on stock market
fluctuation and run a regression in an attempt to refute their claims using statistical
analysis and behavioral finance theory. Ultimately, I hope to uncover some form of
predictability amongst price movements in the stock market.
The first theory I wish to address is the efficient market hypothesis. This idea
states that prices of stocks directly reflect all known information. These prices are totally
unbiased due to the fact that they reflect the aggregate beliefs of all investors about future
prospects. The aggregate view of future prices based on current information is referred to
as rational expectations. Any price movements are considered to be the result of an influx
of new information (Shiller, 2003, 83). As a result any gains received are attributed solely
to luck. Because information throughout the market is perfect, it would be impossible for
investors to predict prices and continually outperform the market. This theory allows for
the overreaction or under reaction of individual agents in the market, however, the market
as an aggregate will always accurately represent all available information. This being the
case, the possibility of regularly outperforming the market by capitalizing on any
noticeable trends would not be possible.
2

3. A critical contributor to the expansion of the efficient market hypothesis was
Eugene F. Fama. His work refined prior views on the efficient market hypothesis and
offered three possible forms of an efficient market, all of which have different
implications of how the market works. These forms consist of weak form efficiency, semi
strong form efficiency, and strong form efficiency. Weak form efficiency claims that
current share prices are the best estimate of the value of any security and is based on
historical prices ( Fama, 383, 1970). Therefore, any technical analysis can not be used to
predict future prices. However, in weak form efficiency markets fundamental analysis of
a stock can lead to possible gains. Semi strong efficiency states current prices directly
reflect all publicly known information (Fama, 414, 1970). As a result, neither technical
nor fundamental analysis of a stock will produce abnormal gains. The only way to obtain
abnormal gains would be to have access to information that is not publicly known. Lastly,
the idea of strong form efficiency markets expresses how stock prices reflect both public
and private knowledge. Thus, abnormal gains are impossible to obtain regardless of the
information one has access to. Fama does point out that this model is rather extreme, and
best used as a benchmark against which the importance of deviations from market
efficiency can be judged (Fama, 414, 1970).
An interesting finding within Fama’s work is the existence of positive dependence
in day to day price changes. There is a serial autocorrelation within his data that is
positive, but extremely minute and non profitable due to commissions and transaction
fees(Fama, 393-394, 1970). The existence of such a pattern is in direct conflict with
components of other theories addressing market function, namely the random walk
hypothesis.
3

4. The random walk hypothesis was first addressed by the economist Burton
Malkiel. His book, A Random Walk Down Wall Street, examines the role of randomness
in the stock market. Essentially, this theory claims that all market fluctuation is totally
random. Random walk theory advocates the idea that with so many variables
contributing to changes in stock prices it is impossible accurately predict future prices. In
this text Malkiel examines the effectiveness, or lack thereof, of both fundamental and
technical analysis in the prediction of stock prices.
There are several fundamental determinants of stock prices. Malkiel defines these
determinants as expected growth rate, expected dividend payout, degree of risk, and the
level of market interest rates. He does recognize that stock prices do have an inherent
logic in relation to these fundamentals. However, he is quick to point out that the ability
to generate excess profits by understanding these fundamentals is not possible. A quote
from Malkiel further illustrates my point, “It looks like there may be a firm foundation of
value after all, and some jokers in Wall Street think you can make money knowing what
it is” (Malkier, 87, 1973). Even though these fundamental determinants do act as a gauge
for value, it is a very flexible and undependable one.
Malkiel elaborates on the undependability of fundamentals using an interesting
metaphor. He states that stock prices are anchored to their fundamentals, but that anchor
is easily pulled up and dropped in another place ( Malkiel, 91, 1973). This metaphor
illustrates how unknown events can alter the foundations of stock prices In conclusion he
finds that stock prices can’t be predicted using fundamental analysis and that market
function is heavily influenced by mass psychology, not concrete laws. Regardless of any
4

5. fundamental analysis investors will not have the ability to accurately forecast where that
anchor will next be dropped.
Malkiel holds similar views towards the effectiveness of technical analysis of
stocks. He points out that market fluctuation is purely random and no more predictable
than a toss of a coin ( Malkiel, 120,1973). In other words, past price movements have no
effect on future prices. He concludes that accurately foreseeing future stock prices based
on past movements is not possible. According to Makiel, “ Technical strategies are
usually amusing, often comforting, but of no real value.”(Malkiel, 134, 1973)
The findings of Makiel and the random walk hypothesis have helped lead to the
recognition of the significant role psychology plays in the stock market. Economists
during the classical period, such as Adam Smith, first recognized the link between
psychology and economics. In his work, The Theory of Moral Sentiments, he addressed
the psychological principles of individuals’ behavior and influences on decision making.
However, behavioral economics was placed on the back burner during the neo-classical
period as economists began to distance themselves from psychology in an attempt to
reshape economics as a natural science. The concept of “homo-economicus” was
developed and claimed that man was a totally rational being, continually trying to
maximize his well being through rational decision making.
A resurgence of psychology in economics occurred during the mid 20th
century.
The further understanding of human psychology played a vital role in its acceptance back
into economic thought. Viewing man as a more dynamic decision maker and
understanding his complex psychological makeup challenged earlier neo-classical views.
In fact, a study done by Kahneman and Tversky in 1979 used cognitive psychological
5

6. techniques that explained many documented divergences of economic decision making
from neo-classical theory. Kahneman and Tversky opened the eyes of economists to the
importance of psychology in economics and broadened the understanding of human
judgment and decision-making in the presence of risk.
The relevance of Kahneman and Tversky’s work to this research is their discovery
of how people view risk and reward. Their findings showed that humans have a
disproportionate emotional reaction to risk than to reward. This tendency of humans to
avoid any losses is referred to as loss-aversion. For example, when faced with the
opportunity of having a 50-50 shot at winning $105 or losing $100, the lose-averse
decision maker will turn down the bet. On the other hand, a completely rational agent
would undoubtedly accept this offer ( Kahneman ,164, 2003). Realistically speaking,
human emotional response to short term gains is much too strong to accept this
proposition. Such an experiment merely exemplifies the irrationally amidst the human
psyche.
The stock market crash of 1987 is an interesting example of the role psychology
plays within the stock market. On October 19, 1987 the Dow Jones Industrial average
plummeted 508 points, losing over 22 % of its value. It would be virtually impossible to
explain the significance of this crash to any particular event or news at the time. Instead,
many experts attribute the significance of this crash to the peculiarities of human nature
and their reaction to risk. Such an occurrence can reasonably be blamed upon humans’
view of losses and the fear of other investors having similar skeptical outlooks. In such a
case, it is fear itself that can cause an economic meltdown without any fundamental flaws
in the marketplace ( Guarino; Huck; Jeitschko,17, 2003).
6

7. The final and most controversial topic I am going to assess is the views of Nassim
Taleb. Formerly a full time trader, this self acclaimed philosopher and author has
developed some unusually unorthodox views on market function. Taleb faults prior
attempts to explain market fluctuation, including the random walk hypothesis, for their
shortcomings. Partially directing the blame on what he refers to as ludic fallacy. This
idea faults random walk hypothesis for assigning a set level of risk to particular
occurrence and using a game like structure to study the role of chance. He disagrees with
the ability to assign structured randomness into such a dynamic and absolutely
unpredictable environment such as the market.
Taleb is a strong advocate of limited human knowledge, moreover the
unwillingness of humans to admit this intellectual shortcoming. He makes a point to
illustrate the importance of particular events that have a substantial effect on the market.
He credits these events, also referred to as black swans, to complete randomness. More
specifically, he believes we create false explanations of these events after they have
occurred, also known as narrative fallacies. In essence, Taleb suspects that people form
explanations in an attempt to make the market something structured and comprehensible
when randomness is the true catalyst behind all market movements.
It is these completely random unforeseen events, black swans, that Taleb models
his unique investment strategy. He lacks such confidence in the accuracy of current
market predictions that he invests in speculation of the occurrence of a black swan some
time in the future. For example, Taleb is betting that the price of oil, now hovering
around $90 per barrel, will be at either $10 or $400 over the next several years. He will
be the first to admit that he does not know which extreme it will be, but thinks such a
7

8. massive change in oil price is possible (Stone,2005). Because the majority of other
traders don’t believe such drastic changes are realistically possible, Taleb can buy
options. In essence, options are contracts allowing the investor to purchase a security at a
certain price set in the future. He is willing to sacrifice many relatively small losses on
the expectation of a black swan on the horizon. Taleb has made a handsome living by
capitalizing on the market’s inability to predict such events.
Taleb labels many successful investors as “lucky fools” whose success is merely a
result of chance. These people are just statistical outliers who happened to pick and
choose the right investment at the right time, claiming that even Warren Buffet’s success
is attributable to luck alone. Taleb is quick to point out that these people trick themselves
into believing that their financial success is due to a precise occurrence they previously
predicted (Taleb, 1, 2004). The fact that a company, or investor, has shown successful
gains over the past years has no effect on the following year’s results, regardless of what
the data leads us to believe. He believes people underestimate the role of unexplainable
randomnesss and accuse economists, scientists, historians, policymakers and
businessmen of overestimating the value of rational explanations of past data. In an
attempt to contort the market into something structured and predictable these people
overlook the possibility of a black swan.
That being said, the question that arises is whether or not there is any
predictability in markets after these large fluctuations that Taleb previously mentions.
Large fluctuations will be defined as price movements of three percent or more. Price
increases of at least three percent will be referred to as “black swans” while price
decreases of at least three percent will be referred to as “neon falcons”. Such occurrences
8

9. are relatively rare and fluctuations this substantial may have an effect on trading the
following day. The goal of this research is to uncover any correlation amongst the day
following black swans in an attempt to refute the idea that price fluctuation is absolutely
random.
To test this idea of predictability a list of daily price changes from the Dow Jones
Industrial Average since 1980 was compiled. A regression analysis was conducted to
determine how much, if any, effect these black swans and neon falcons had on the
following day’s price movement. Using the percent difference in price from one day to
the next as the dependent variable and black swan’s effect, neon falcon’s effect, and the
lag variable as independent variables, the test was able to decipher what, if any, effect
these large fluctuations had on the market.
The results of this regression were somewhat surprising. It was discovered that
there actually is some statistical significance and pattern amongst these black swans. As
shown in the table, the t value of the coefficient for black swans is greater than two,
meaning statistical significance is present. On the contrary, absolutely no statistical
significance was present with the neon falcons. In other words, price increases of three
percent or greater have no effect on the market the following day, while price decreases
of at least three percent do have an effect on the next trading day. It seems as though
these black swans have a tendency to be self-correcting. These large price decreases will
often be followed by a price increase in an attempt for the market to correct itself. This
tendency for self correction of black swans is expressed graphically on page three of the
attached data.
9

10. This evidence of prices correcting themselves could be attributed to mean
reversion. This is a theory that suggests prices will eventually move back towards their
long run average value. Prices after an abnormally large fluctuation will often revert back
to this mean price over a period of time. A study done by Fama and French points out
that mean reversion occurs faster when profitability is below its mean, as may be the case
after a black swan ( Fama; French, 174, 2003).
Humans’ inherent nature to avoid losses leads me to believe that these black
swans may be a result of simultaneous overreactions of investors. Prior research has been
conducted that is in support of this claim and found that stock prices do overreact to such
events (Barberis; Shleifer; Vishny, 28,1998).The instant bad news is released investors
will not hesitate to remove their money from the market in an attempt to avoid any
further losses. This overreaction leads to a market which may be viewed as undervalued.
A possible explanation for the tendency of prices to show immediate mean reversion after
these black swans is the ability of the market to recognize its overreaction. With this
recognition investors will reinvest in an attempt to capitalize on the market’s mistake
resulting in the significant price increase on days following black swans. On the same
note, investors will be much more reluctant to sell after a sharp upswing in the market.
This obvious asymmetry amongst prices is directly correlated to the way in which people
view and react to risk and the potential for losses.
As previously stated this regression does show some pattern and predictability
after significant losses within the market and, as a result, directly refutes the idea of
absolute randomness. In addition, the evidence from this study discredits Malkiel’s view
on the complete inability of technical analysis to predict future price changes. Despite the
10

11. overwhelming amount of randomness in trading patterns there is slight amount of
predictability in how investors will react to these black swans. For the most part prior
assumptions on market fluctuation are correct; there is virtually no short term
predictability in the market. With an infinite number of variables effecting price changes,
accurately foreseeing short term fluctuations is impossible.
Unfortunately the magnitude of these predictable market fluctuations is rather
small. However, the correlation I discovered is significantly larger than the trend revealed
by Fama in daily stock price fluctuations. In both cases the level of predictability is too
small to significantly profit from. Transaction fees and short term capital gains tax will
eliminate most of the gains. In addition, the rarity of such events that cause black swans
trumps the possibility of using this technique to generate substantial profits.
With the continual attempt amongst herds of investors seeking methods to exploit
patterns within the market, the finding of any monumental patterns was unlikely. That is
not to say the discoveries of this research are insignificant. Any findings, no matter how
minute, can be beneficial to the further evolution of the field of economics and
understandings of market function. If nothing else, this research shows clear refutation
towards the fundamental structures of some pre-existing theories pertaining to market
fluctuation.
11

12. 3 1.1068585E11 3.6895284E10 8061852.2560413 <.0001
7016 32108913.1018989 4576.5269530
7019 1.1071796E11
DF Sum of Squares Mean Square F-Value P-Value
Regression
Residual
Total
ANOVA Table
Price vs. 3 Independents
7020
4
.9998550
.9997100
.9997099
67.6500329
Count
Num. Missing
R
R Squared
Adjusted R Squared
RMS Residual
Regression Summary
Price vs. 3 Independents
1.5625101 1.3646751 1.5625101 1.1449686 .2523
1.0000201 .0002038 .9997947 4906.6283393 <.0001
.0126629 .0030698 .0016132 4.1250226 <.0001
-41.1891952 20.6173606 -.0007807 -1.9977919 .0458
Coefficient Std. Error Std. Coeff. t-Value P-Value
Intercept
Pricet-1
BlackPast
BlackL1
Regression Coefficients
Price vs. 3 Independents
3468
3552
64002230.911805
1.993286
.003081
# >= 0
# < 0
SS[e(i) - e(i-1)]
Durbin-Watson
Serial Autocorrelation
Residual Statistics
Price vs. 3 Independents
12

13. Model Summary(b)
Model R R Square
Adjusted R
Square
Std. Error of
the Estimate Durbin-Watson
1 .060(a) .004 .003 .0103252 2.004
a Predictors: (Constant), BlackSwan, NeonFalcon, LagVariable
b Dependent Variable: dprice percent
ANOVA(b)
Model
Sum of
Squares df Mean Square F Sig.
1 Regression .003 3 .001 8.574 .000(a)
Residual .748 7016 .000
Total .751 7019
a Predictors: (Constant), BlackSwan, NeonFalcon, LagVariable
b Dependent Variable: dprice percent
Coefficients(a)
Model
Unstandardized
Coefficients
Standardized
Coefficients
t Sig.
Collinearity Statistics
B Std. Error Beta Tolerance VIF
1 (Constant) .000 .000 3.173 .002
LagVariable .034 .014 .034 2.387 .017 .713 1.402
NeonFalcon .020 .038 .007 .537 .591 .864 1.157
BlackSwan -.155 .032 -.064 -4.836 .000 .805 1.243
a Dependent Variable: dprice percent
13

14. -.25
-.2
-.15
-.1
-.05
0
.05
.1
.15
%dPrice
-.25 -.2 -.15 -.1 -.05 0 .05 .1 .15
%dPriceL1
2.000
1.000
0.000
This graph portrays daily fluctuations in the Dow Jones Industrial Average. The purple
diamonds mean either today or yesterday was a Black Swan, the red dot means neither
days were black swans, while the red cross shows two black swans in a row.
This illustrates that black swans do have a unique effect on market fluctuation and
exemplify the findings of the regression.
14

15. References
Barberis, Nicholas; Shleifer, Andrei; Vishny, Robert. “ A Model of Investor Sentiment.”
University of Chicago and Harvard University. (1998): 1-42
Fama, Eugene "Efficient Capital Markets: A Review of Theory and Empirical Work".
Journal of Finance 25(1970): 383-417
Fama, Eugene; French, Kenneth. “Forecasting Profitability and Earnings”. The Journal of
Business. 73.2 (2000): 161-175
Guarino, Antonio; Huck, Steffec; Jeitschko, Thomas.“Can Fear Cause Economic
Collapse? Insights from an Experimental Study”.(2003): 1-23
Ho, Chia-Cheng ; Sears, R. Stephen .“Is there conditional mean reversion in stock
returns?” Quarterly Journal of Business and Economics (2006): 1-6
Kahneman, Daniel “A Psychological Perspective on Economics”. The American
Economic Review ,93.2 (2003): 162-168
15

16. Malkiel, Burton. A Random Walk Down Wall Street. New York: W.W. Norton &
Company, 1973.
Shiller, Robert. “From Efficient Market Theory to Behavioral Finance.” Journal of
Economic Perspectives 17.1 (2003); 83-104.
Stone, Amy. “Profiting from the Unexpected”. BusinessWeek. Oct. 12, 2005. Dec 6,
2007< http://www.businesswee k.com/bwdaily/dnflash/o ct2005
/nf20051024_5234_db035.htm>
Taleb, Nassim. Fooled By Randomness: The Hidden Role of Chance in Life and in the
Markets. London: Texere, 2004.
“Tales of the Unexpected”. Wilmott Magazine http:// www.fooledbyrandomness
.com/0603_ coverstory.pdf : 30-36
"Verizon South Inc (VZC)." Yahoo Finance. 7 June 2004. http://finance.yahoo.co m/q?
s=VZC&d=t
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