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S&P 500 and Crises:
A Trace of Prior Knowledge of 9.11
Atsufumi Ichinoseki
May 30, 2012
INTRODUCTION
The purpose of the spectral analysis of a stock price index is to extract a trend from a randomly fluctuating stock price index in order to have a sense of direction. That is one way to characterize a stock market, classifying it as a rising market or a declining market. Since the spectral analysis derives a trend called “CPS determinate trend” so well, the deviation of the index from the trend also characterizes the market in a significant way. In what follows, this is demonstrated by unveiling common characteristics of the S&P 500 just before crises occurred. The crises considered are 9.11, the Lehman Shock, and the Euro debt crisis in 2011. In each case, the behavior of the S&P 500 is analyzed in terms of the deviation from the trend to see if there are common characteristics among them. Particularly, 9.11 is of interest, because, months before and after the sell-off of 9.11, the stocks were intensively sold as well. The analysis presented here decides whether the characteristics of these sell-offs are the same. Also considered is the Nikkei 225 just prior to March 11, 2011, when the devastating tsunami hit Japan after a gigantic earthquake off its northeastern coast and caused catastrophic melt-through of the Fukushima Daiichi nuclear power plant. The disaster of 3.11 helps ascertain the characteristic that signifies unforeseen crises.
CHARACTERISTICS OF STOCK PRICE FLUCTUATIONS
The characterizations to be used for analyzing the crises are presented immediately below. They are based on the extensive examination of the fluctuations of various stock price indexes and capture the nature of crises.
Strong closing price: A closing price of an index at time t is called “a strong closing price,” if it deviates from the CPS determinate trend by more than +ε(t).
A strong closing price represents intensive buying by bulls and/or short covering by bears. A strong closing price is indicated by a blue particle in the graphs below.
Weak closing price: A closing price of an index at time t is called “a weak closing price,” if it deviates from the CPS determinate trend by more than -ε(t).
A weak closing price reflects intensive selling by bulls and/or short selling by bears. A weak closing price is denoted by a red particle.
Neutral closing price: If a closing price of an index is neither a strong nor a weak closing price, it is called “a neutral closing price.”
A neutral closing price is shown by a grayish particle.
Pendulation: When there are at most 3 neutral closing prices, if any, between a strong and a weak closing price, the stock price index is said to have “a pendulation.”
A strong and a weak closing price must be the nearest pair in terms of time so that there are no other strong and weak closing prices between them. A pendulation represents the basic idea that the index should be considered volatile, if it has a strong and a weak closing price within a week of five trading days. A pendulation reflects a vehement battle between bulls and bears.
-Pendulation: If a strong closing price comes before a weak closing price, it is called “a negative pendulation” and denoted by -Pendulation. If -Pendulation starts at time t-4, it must end at time t at the latest.
The notation, -Pendulation, describes the condition that the bulls’ forceful attempt to push up the index is countered by the bears’ intensive short selling in an attempt to pull it down. In other words, bulls buy the stocks, thinking the prices are (already/still) low enough to go up, but bears short them later (probably on a rebound), thinking the prices are (still/already) high enough to go down. Or it may reflect the converse condition that bears, who think the stocks went down enough, cover the shorts, pushing up the index, while bulls, who want to get out of the market, find it a good chance to dispose of the stocks, pulling it down.
+Pendulation: If a weak closing price comes before a strong closing price, it is called “a positive pendulation and denoted by +Pendulation.
The notation, +Pendulation, describes the condition that the bears’ powerful attempt to pull down the index is countered by the bulls’ intensive buying in an attempt to push it up. In other words, bears short the stocks, thinking the prices are (already/still) high enough to go down, but bulls buy them later (probably on a pullback), thinking the prices are (still/already) low enough to go up. Or it may reflect the converse condition that bulls, who think the prices are reasonably high, take the profits, pulling down the index, while bears, who find it a good chance to get out of the market, cover the shorts, pushing it up.
If a positive pendulation comes within 5 trading days of a negative pendulation, for example, it is indicated by -+Pendulation. That is, if -Pendulation ends at time t, then +Pendulation must end at time t+4 at the latest.
The notations, +-+Pendulation and -+-Pendulation, imply that the index is unstable (level 3 unstable), whereas +-+-Pendulation and -+-+Pendulation imply that the index is very unstable (level 4 unstable).
Fall-off: The descent of a stock price index from time t-1 to time t is called “falling off” and the index is said to be “falling off the lower bound,” when the index at time t is below -2σ of the CPS determinate trend at time t. The index at time t is called “a fall-off.” If the CPS determinate trend does not exist, the index must be below -2σ of the CPS determinate trend of the immediate past. The notation for -Pendulation with a fall-off is (-)Pendulation. A negative pendulation ending with a fall-off has a strong downward pressure on the index.
Outburst: The ascent of a stock price index from time t-1 to time t is called “bursting out” and the index is said to be “bursting out of the upper bound,” when the index at time t is above +2σ of the CPS determinate trend at time t. The index at time t is called “an outburst.” If the CPS determinate trend does not exist, the index must be above +2σ of the CPS determinate trend of the immediate past. The notation for +Pendulation with an outburst is (+)Pendulation. A positive pendulation ending with an outburst implies a strong upward pressure.
Fall-offs and outbursts are indicated by х in the graphs below.
Free fall: At least 3 successive fall-offs are called “a free fall.”
Upsurge: At least 3 successive outbursts are called “an upsurge.”
Negative foresight term: A negative foresight term is a term preceding a free fall. It starts with -Pendulation and ends with -Pendulation just prior to a free fall.
Positive foresight term: A positive foresight term is a term preceding an upsurge. It starts with +Pendulation and ends with +Pendulation immediately before an upsurge.
The expression “a foresight term” refers to either a negative or a positive foresight term. A total number of strong and weak closing prices exceeding 20 is required for the length of a foresight term.
Relative bias of a foresight term (denoted by RB): The relative bias of a foresight term is given by a total number of strong closing prices during a foresight term divided by a total number of weak closing prices during the same period.
The stock index is “upward biased” if RB>1, which means the index tends to go up. If RB>1.4 , it is “strongly upward biased,” expressing the strong tendency of the index to climb.
The stock index is “downward biased” if RB<1, indicating the index tends to go down. If RB<0.6 , it is “strongly downward biased,” implying the strong tendency of the index to decline.
Downward reaction of a foresight term (denoted by DR): The downward reaction of a foresight term is given by a total number of negative pendulations during a foresight term divided by a total number of strong closing prices during the same period.
The downward reaction of a foresight term is designed to measure how intensely the bears counter the bulls’ strong attempt to raise the stock index during that term. It also appraises how high the bears consider the index is or how resolutely bears expect the descent of the index.
If DR≥0.5 , the index is said to be “downward reactive,” which means the bears tenaciously oppose the bulls’ vigorous attempt to push up the prices and that the bears earnestly think the index is high enough to go down.
Upward reaction of a foresight term (denoted by UR): The upward reaction of a foresight term is given by a total number of positive pendulations during a foresight term divided by a total number of weak closing prices during the same period.
The upward reaction of a foresight term is designed to measure how intensely the bulls counter the bears’ stout attempt to pull down the stock index during that term. It also appraises how low the bulls consider the index is or how intently bulls expect the ascent of the index.
If UR≥0.5 , the index is said to be “upward reactive,” which means the bulls are forcefully fighting back the bears’ tenacious attempt to pull down the prices and that the bulls earnestly think the index is low enough to go up.
The downward and the upward reaction can be interpreted in terms of the market. If the index is neither downward reactive nor upward reactive, bulls and bears do not have conviction. The market (both bulls and bears as a whole) is indecisive. Thus, the market does not possibly foresee a crisis. It does not foresee a soaring index, either. If the index is not downward reactive but upward reactive, bears do not have conviction while bulls are convinced that the index will rise. Again, the market does not possibly foresee a crisis. If the index is both downward reactive and upward reactive, bears firmly believe the index will decline considerably while bulls confidently deny such possibility. Hence, the market is unstable. If the index is not upward reactive but downward reactive, bulls do not have conviction while bears are confident that the index will fall substantially. The market does not foresee euphoria.
S&P 500 AND CRISES
The first crisis to consider is the Lehman Shock, because some, such as Professor Rogoff at Harvard University, expected or foresaw a crisis of the kind, while others thought the Fed would not allow large U.S. banks to collapse. [1] Since many were taken by surprise and thrown into chaos when Lehman filed for bankruptcy, there is a good reason to believe that bulls and bears had fought the battle intensely until Lehman collapsed. [2][3] Even a casual look at the next graph confirms this observation.
During the negative foresight term, from July 23 to September 29, the S&P 500 underwent a lot of pendulations, manifesting the considerable instability. It also suffered 5 fall-offs and 2 negative pendulations ending with a fall-off, displaying strong downward pressure. The index was downward reactive with the downward reaction of 0.6. Hence, bears firmly believed the index would go down. And then the index went into free fall as the Lehman Shock unfolded. Even if the negative foresight term is interrupted by -Pendulation just prior to the Lehman Shock, as is shown by a grey arrow in the above graph, the downward reaction was still 0.5, which implies bears foresaw a crisis such as the Lehman’s collapse with strong conviction. It was a defeat of the bulls and a victory for the bears. As the index was downward reactive, the bulls were badly hurt, and it took them quite a while to recover.
The second example is 3.11, because, unlike the Lehman Shock, hardly anyone expected natural calamities of that magnitude. As the next graph shows, just prior to 3.11, the Nikkei 225 seemed to be converging, waiting for an opportune time to soar or to nose-dive. Do bears and bulls have any convictions?
During the foresight term, the downward reaction was 0.25, while the upward reaction was 0.33: the Nikkei 225 was neither upward reactive nor downward reactive. The bulls did not strongly expect the index to soar, nor did the bears intensely anticipate the index would fall substantially. Both bulls and bears were indecisive. Therefore, from the perspective of downward reaction, the market (bulls and bears as a whole) did not foresee the sharp decline of the index. The downward reaction of the foresight term says the market cannot have foreknown the devastation of 3.11. The market simply reacted to the disaster as it happened. It was an instantaneous reaction. The market quickly bounced back from this instantaneous panic, as it had not been downward reactive.
The third example is the Euro debt crisis 2011, because, in sharp contrast with 3.11, the Euro debt crisis was already well-known in 2011, as it had manifested itself in 2008, when Iceland’s banking system collapsed, and in 2009, when Greek Prime Minister Papandreou disclosed the nation’s enormous hidden deficits were more than double the previous estimates. [4] On July 21, 2011, the Council of the European Union reached an agreement on measures aimed at solving the Greek debt crisis, only to fail to reassure the markets. Then, the S&P 500 plummeted for fear that the European banking system was on the verge of collapse and that the Euro debt crisis could spill into the US banking system as well. [5][6][7][8][9][10]
Did bears and bulls have any conviction before the nose dive? The first glance at the next graph may seem to provide an affirmative answer.
During the foresight term, the downward reaction was 0.256, while the upward reaction was 0.205. The S&P 500 was wavy, which was displayed by three pendulations of instability and two pendulations of strong downward pressure. The downward bias was 0.886. Thus, the anxiety for what was to come was prevailing to some extent. Yet, the index was neither upward reactive nor downward reactive. Neither the bulls nor the bears had confidence. They didn’t counter the opponent moves intensively. The sideway market’s sharp decline was an instantaneous reaction probably because of the disappointment with the solution presented by the Council of the European Union. The market (bulls and bears as a whole) did not foresee this disappointment with conviction. Since this was not fully priced into the S&P 500, the index took a steep dive. Although the disappointment lingered on for a while, the index recovered as it had not been downward reactive.
S&P 500 HAS A TRACE OF FOREKNOWLEDGE OF 9.11
Immediately after 9.11, the speculation was circulated that the terrorists with foreknowledge of 9.11, along with their associates, had shorted the airline and the insurance stocks in addition to the purchase of the related put options prior to the attacks. [11][12][13] The NYSE reported that, between August 10 and September 10, short sales of the parent company of United Airlines had increased 40 percent and that of American Airlines 20 percent. [12] Professor Cox at Duke University pointed out that the terrorists had set out not only to destroy capitalism, but also to beat capitalists at the capitalists’ own game. [14] Columbia University law professor John Coffee asserted that those terrorists were sophisticated strategists trying to pay for future terrorist activities by profiting from their past terrorist activities. [14]
Governments around the world began investigating the possibility that the terrorists and their associates had profited from advance knowledge of the 9.11 attack. After almost two weeks of their investigation, no evidence was found. A number of officials suspected it was unlikely a terrorist group, having worked for months to orchestrate its attack, would be reckless enough to create even a subtle signal of its plans by shorting stocks or buying put options. [15] Furthermore, the 9/11 Commission Report says, on page 172, “Exhaustive investigations by the Securities and Exchange Commission, FBI, and other agencies have uncovered no evidence that anyone with advance knowledge of the attacks profited through securities transactions,” attributing, on page 499, much of the seemingly suspicious trading in American Airlines on September 10 to a specific U.S.-based options trading newsletter which recommended the trades. [16]
Since the publication of the 9/11 Commission Report, its conclusions have been widely criticized. Dr. McDermott at Charles Sturt University protested that the 9/11 Commission Report overlooked what the terrorists had targeted, saying, “The World Trade Center was the nerve center of the global financial system, so the attacks were a major disruption to business. … many investment banks had head offices in or around the World Trade Center.” [17] University of Illinois professor Poteshman states that the statistical examination of the option trading leading up to September 11 reveals an unusually high level of put buying, which is consistent with informed investors having traded options in advance of the attacks. [18] Some options professionals insist that conspirators may actually have profited more from a plunge in the entire market, not just specific shares. [19] Professors working at RMI report their statistical findings that there was abnormal trading in S&P 500 index options prior to the September 11 attacks and discredited the possibility of abnormal volume due to declining market, which, they conclude, is consistent with insiders anticipating the 9.11 attacks. [20] Therefore, it may make more sense to focus on the behavior of the S&P 500, although the initial investigations were centered on the individual stocks.
The downward reaction is designed to perceive how intensely bears counter bulls’ powerful attempt to push up stocks. Hence, in the case of the 9.11 attacks, the downward reaction of the S&P 500 foresight term prior to 9.11 is a good gauge of how persistent terrorists are in their attempt to pull down stocks. The next graph clearly and simply reveals what it testifies.
During the negative foresight term, from May 22 to August 29, the S&P 500 underwent 10 pendulations, manifesting the considerable instability. It also suffered 7 fall-offs, displaying strong downward pressure. Actually, the S&P 500 was strongly downward biased with the relative bias of 0.5. Since the downward reaction was 0.545, the index was downward reactive. Hence, the bears firmly believed the index would go down. In this case, the bears foresaw the crisis. Those who had prior knowledge of 9.11 actively countered the powerful moves to raise the index. The S&P 500 foresight term has the trace of a prior knowledge of 9.11. The terrorists’ main target must have been the capitalism with its financial headquarters and markets.
As the next graph shows, there were sell-offs months before and after 9.11. Did the terrorists actively counter the attempts to push up the index?
During the declining market between September 5, 2000 and April 4, 2001, two free falls occurred, making it possible to define a negative foresight term, as the following graph shows.
A negative foresight term must start with -Pendulation and end with -Pendulation just before a free fall. Therefore, the foresight term during the declining market is from October 24, 2000 to February 2, 2001. During the foresight term, the relative pressure is 1.45, which implies the index was upward biased. With the downward reaction of 0.207, the index was not downward reactive. The bears did not actively counter the strong moves to raise the index and the market as a whole did not foresee the free fall and the subsequent descent with conviction. The terrorists may have accumulated the short positions during and after the foresight term, consequently causing a nose dive. If that’s the case, they didn’t intensely resist the strong moves to push up the S&P 500 during the negative foresight term, as they had foreknowledge that the real crisis would be far ahead.
Another sell-off was the declining market from March 19, 2002 to July 26, 2002, during which a negative foresight term can be defined. It starts on March 19 and ends on July 9, as the next graph shows.
During the foresight term, the relative pressure is 0.234, which implies the index was strongly downward biased. With the downward reaction of 0.545, the index was downward reactive. The bears intensely countered the bulls’ vigorous attempts to raise the index. This bears’ move is consistent with the terrorists’ tenacious attempts to devastate capitalism and its capitalistic markets. It is a significant fact that, from March 19, 2002 to July 9, 2002, the bears desperately tried to pull down the S&P 500 by persistently countering the powerful moves to raise the index. The Bush Administration, on September 24, 2001, declared the president’s executive order to freeze the assets of terrorist organizations and individuals. [21] The fact that the bears were vigorously countering the powerful attempts to raise the index in 2002 suggests that the Executive Order to seize the terrorists’ assets did not prevent terrorists from smashing the stock markets. Were they sophisticated strategists as Professor Coffee asserted? [14] Even the 9/11 Commission Recommendation admits that many have questioned the feasibility of separating terrorist organizations from their assets. [22] Professor Gomez at University of Granada reported that the international community had not succeeded in cutting off many of Al-Qaeda’s sources of financing. [23] The Fletcher School adjunct professor Warde insists that going after terrorist funding is expensive, time consuming and unproductive. [24] The finding that the S&P 500 was downward reactive even in 2002 probes into more details: There is a strong possibility that neither the measures to track down terrorists transactions nor the Executive Order to freeze terrorists’ assets stopped terrorists and their associates from crashing the stock markets.
CONCLUSION
This paper has shown that the characterizations of markets in terms of upward and downward reaction help understand the nature of crises. The characterizations were made possible by the conception of the CPS determinate trend derived from spectral analysis of stock market indexes. The characterizations are applied to the S&P 500 in crisis. The results are summarized by the table below.
Downward and Upward Reaction of the S&P 500 Foresight Term
The Lehman Shock, 9.11, and the sell-off in 2002 after 9.11 have a common characteristic that the S&P 500 was downward reactive during the foresight term. Those crises are clearly distinguished from the Euro debt crisis in 2011, 3.11, and the sell-off before 9.11 by the downward reaction. If the index is downward reactive, it has a trace of bears’ massive counterattack against strong moves to raise the index: The bears foresee upcoming crises, have conviction that the index will fall substantially, or try to make the index nose-dive. The characteristic that the S&P 500 was downward reactive just prior to 9.11 implies that the bears with foreknowledge of the crisis tenaciously countered the vigorous moves to push up the index. The fact that the S&P 500 was downward reactive during the foresight term of 2002 implies that the bears desperately wanted to crash the market even after 9.11. Who were those bears? Did bulls completely yield to the bears of terrorists, acknowledge the defeat by abandoning the stocks in spite of the worldwide movement to fight against terrorists, and run a risk of being identified with the terrorists’ associates? Or were they the terrorists and their associates who persistently tried to devastate capitalism and its capitalistic markets? The bears have left their traits, as the downward reaction during the foresight term of 9.11 and that in 2002 were the same. In aggressively countering bulls' strong moves to push up the index, the bears could not possibly hide their disposition. The spectral analysis presented in this paper candidly asserts that neither the investigations to track down terrorists’ transactions nor the Executive Order to freeze their assets could prevent the terrorists and their associates from crashing the stock markets that symbolize capitalism.
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