Evidence of market manipulation in the financial crisis

Abstract

We provide direct evidence of market manipulation at the beginning of the
financial crisis in November 2007. The type of manipulation, a "bear raid,"
would have been prevented by a regulation that was repealed by the Securities
and Exchange Commission in July 2007. The regulation, the uptick rule, was
designed to prevent manipulation and promote stability and was in force from
1938 as a key part of the government response to the 1929 market crash and its
aftermath. On November 1, 2007, Citigroup experienced an unusual increase in
trading volume and decrease in price. Our analysis of financial industry data
shows that this decline coincided with an anomalous increase in borrowed
shares, the selling of which would be a large fraction of the total trading
volume. The selling of borrowed shares cannot be explained by news events as
there is no corresponding increase in selling by share owners. A similar number
of shares were returned on a single day six days later. The magnitude and
coincidence of borrowing and returning of shares is evidence of a concerted
effort to drive down Citigroup's stock price and achieve a profit, i.e., a bear
raid. Interpretations and analyses of financial markets should consider the
possibility that the intentional actions of individual actors or coordinated
groups can impact market behavior. Markets are not sufficiently transparent to
reveal even major market manipulation events. Our results point to the need for
regulations that prevent intentional actions that cause markets to deviate from
equilibrium and contribute to crashes. Enforcement actions cannot reverse
severe damage to the economic system. The current "alternative" uptick rule
which is only in effect for stocks dropping by over 10% in a single day is
insufficient. Prevention may be achieved through improved availability of
market data and the original uptick rule or other transaction limitations.

Full text

Evidence of market manipulation in the financial crisis∗
Vedant Misra,Marco Lagi, and Yaneer Bar-Yam†
New England Complex Systems Institute
238 Main Street Suite 319, Cambridge, Massachusetts 02142, US
(Dated: January 4, 2012)
Abstract
We provide direct evidence of market manipulation at the beginning of the financial crisis in
November 2007. The type of market manipulation, a “bear raid,” would have been prevented by
a regulation that was repealed by the Securities and Exchange Commission in July 2007. The
regulation, the uptick rule, was designed to prevent market manipulation and promote stability
and was in force from 1938 as a key part of the government response to the 1929 market crash and
its aftermath. On November 1, 2007, Citigroup experienced an unusual increase in trading volume
and decrease in price. Our analysis of financial industry data shows that this decline coincided
with an anomalous increase in borrowed shares, the selling of which would be a large fraction of the
total trading volume. The selling of borrowed shares cannot be explained by news events as there
is no corresponding increase in selling by share owners. A similar number of shares were returned
on a single day six days later. The magnitude and coincidence of borrowing and returning of shares
is evidence of a concerted effort to drive down Citigroup’s stock price and achieve a profit, i.e., a
bear raid. Interpretations and analyses of financial markets should consider the possibility that the
intentional actions of individual actors or coordinated groups can impact market behavior. Markets
are not sufficiently transparent to reveal or prevent even major market manipulation events. Our
results point to the need for regulations that prevent intentional actions that cause markets to
deviate from equilibrium value and contribute to market crashes. Enforcement actions, even if
they take place, cannot reverse severe damage to the economic system. The current “alternative”
uptick rule which is only in effect for stocks dropping by over 10% in a single day is insufficient.
Prevention may be achieved through a combination of improved transparency through availability
of market data and the original uptick rule or other transaction process limitations.
∗A report on preliminary results from this work was transmitted to the House Financial Services Committee
and sent by Congressman Barney Frank and Congressman Ed Perlmutter to the SEC on May 25, 2010.
†Corresponding author: yaneer@necsi.edu
1
arXiv:1112.3095v3 [q-fin.GN] 3 Jan 2012

I. INTRODUCTION TO BEAR RAIDS AND MARKET MANIPULATION
On July 6, 2007, the Securities and Exchange Commission (SEC) repealed the uptick rule,
a regulation that was specifically designed to prevent market manipulations that can trigger
market crashes. While it is widely accepted that the causes of the crash that began later
that year were weaknesses in the mortgage market and financial sector, the close proximity
of the repeal to the market crash suggests that market manipulation may have played a role.
Here we present quantitative evidence of a major market manipulation, a “bear raid,”
that would not have been possible if the uptick rule were still in force. The timing of the
bear raid, in autumn 2007, suggests that it may have contributed to the financial crisis. Bear
raids are an illegal market strategy in which investors manipulate stock prices by collectively
selling borrowed shares. They profit by buying shares to cover their borrowed positions at a
lower price. While bear raids are often blamed for market events, including financial crises
[1,2], this paper is the first to demonstrate the existence of a specific bear raid.
The sale of borrowed shares, called short selling, is a standard form of market trading.
Short sellers sell borrowed shares, then buy them back later and return them to their owners.
This practice yields profits when prices decline. In a bear raid, investors engage in short
selling with the addition of market manipulation. Instead of profiting from a natural decline
in the fundamental value of a company stock, the executors of a bear raid themselves cause
the price to decline. Large traders combine to sell shares in high volume, “driving” the price
down [3,4].
A bear raid is profitable if other investors are induced to sell their shares at the lower
price. This may happen for two reasons: margin calls and panic. Margin calls occur when
brokerages force investors to liquidate their positions. Investors who are confident in the
rising price of a stock may buy shares on borrowed funds, called “buying on margin,” using
the value of the shares themselves as collateral. When prices decline, so does the value of
the collateral and at some point brokerages issue “margin calls,” requiring shares to be sold
even though the owners would prefer not to. Panics occur when investors, fearing further
losses, sell their shares. The executors of a bear raid profit from the price decline by buying
back the shares they borrowed—“covering” their short positions—at the lower market price.
In the aftermath of the 1929 market crash, Congress created the Security and Exchange
Commission (SEC). Recognizing the dangers of short selling, Congress specifically required
2

the SEC to regulate short selling [5]. The regulation that was instituted in 1938, the uptick
rule, states that borrowed shares may only be sold on an “uptick”—at a price that is higher
than the immediately preceding price. The rule was designed to limit the intentional or
unintentional impact of short selling in driving prices down, and specifically to prevent bear
raids. The uptick rule was repealed in July, 2007 by the SEC on the basis of arguments that
markets were transparent and no longer needed the protection of the uptick rule [6]. SEC
claims that the uptick rule had no significant effect on market stability, even in absence
of specific manipulation, have been refuted [7–9]. Our results implying a bear raid in
November 2007 contradict the assertion of market transparency.
Our evidence points to a bear raid on the large financial services company Citigroup. On
November 1, 2007, Citigroup’s stock experienced an unusual increase in trading volume and
decrease in price. To analyze this event, we studied financial industry short trading data
(see Appendix A), which reveal the total number of borrowed shares (short interest) at the
end of each trading day. Using these data, we show that the increase in trading volume on
November 1 coincides with an increase in borrowed shares. Six days later, a comparable
number of short positions were closed during a single trading day. News events to which
these events might normally be attributed cannot account for the difference between trading
in borrowed shares and trading by owners of shares. The magnitude and coincidence of short
activity is evidence of a concerted effort to drive down Citigroup’s stock price and achieve
a profit, i.e., a bear raid.
II. CITIGROUP ON NOVEMBER 1 AND 7, 2007
On November 1, 2007, Citigroup experienced large spikes in short selling and trading
volume. The number of borrowed shares—short interest—increased by approximately 130
million shares to 3.8 times the 3-month moving average. The total trading volume jumped
from 73 million shares on the previous day to 171 million shares, 3.7 times the 3-month
moving average. The ratio of the increase in short positions to volume was 0.77. This is the
fraction of the total trading that day that may be attributed to short positions held until
market closing. The total value of shares borrowed on November 1 was approximately $6.07
billion. Adjusted for the dividend issued on November 1, 2007, Citigroup stock closed on
November 1 down $2.85 from the previous day, a drop of 6.9%.
3

The number of positions closed on November 7, 202 million, was 53% larger than the
number opened on November 1. The short interest before the increase on November 1 and
after November 7 are virtually identical, the larger decrease corresponding to an additional
increase in short interest between these dates. The mirror image one-day anomalies in short
interest change suggest that the two are linked. We can conservatively estimate the total
gain from short selling by multiplying the number of short positions opened on November 1
by the difference between the closing price on November 1 and closing price on November 7
($4.82), which yields an estimated gain for the short sellers of $640 million.
The total decrease in short interest on November 7 exceeds the total trading volume
on that day, 121 million, by 82 million shares. This indicates that the reported decrease
in borrowed shares is not fully accounted for by recorded trading on the markets. The
difference may result from off-market transfers, which may be advantageous to short sellers
in not causing the price to increase. Alternatively, despite the usual coincidence of borrowing
and selling, this may be due to shares that were borrowed and returned without being sold
short. Further investigation of transaction data is necessary to explain the difference in
returned shares and trading volume.
Figure 1shows daily stock price, volume, and short sale data for Citigroup over a two-
year period starting January 1, 2007. Short sale data includes short interest—the number
of shares borrowed at the end of each day—and the daily change in short interest. During
much of 2007-2009, the daily change in short interest did not exceed a small fraction of the
total trading volume. The largest single-day increase in short interest occurred on November
1 and is marked with arrows in Figure 1. Figure 2shows an enlarged view of the period
around that date.
In Appendix B we analyze quantitatively the probability of the events on November 1 and
November 7. Often probabilities are estimated using normal (Gaussian) distributions that
underestimate the probability of extreme events (“black swans”) that are better represented
by long-tailed distributions [11,12]. We directly fitted the long tails of the distributions and
estimated the probability of the events based upon these tails to be p= 2 ·10−5and 8 ·10−9,
respectively. Given 250 trading days in a typical year, it would take on average 200 years
and 500 thousand years, respectively, to witness such events. Moreover, the probability of
these two events occurring 6 days apart is p= 1 ·10−12, corresponding to 4 billion years,
comparable to the age of the Earth. Figure 3shows that these events are outside the general
4

10
20
30
40
50
Price ($)
Jan 2007 Apr 2007 Jul 2007 Oct 2007 Jan 2008 Apr 2008 Jul 2008 Oct 2008 Jan 2009
20
15
10
5
0
5
10
15
20
25
30
Demand Quantity
(tens of millions of shares)
Total Short Interest
Volume
Change in Short Interest
FIG. 1: Market activity for Citigroup over a two-year period starting January 1, 2007. Top panel
shows vertical bars for the daily high and low stock price. Lower panel shows total short interest
(yellow), trading volume (gray), and daily change in short interest (red). Arrows indicate November
1, 2007 [10].
behavior of the market. We emphasize that our estimates of the probabilities of these events
reflects the higher probabilities of extreme events in long-tailed distributions.
Changes in investor behavior are often explained in terms of specific news items, without
which it is expected that prices have no reason to change significantly [13,14]. The press
attributed the drop of Citigroup’s stock price on November 1 to an analyst’s report that
morning [15,16]. This report, by an analyst of the Canadian Imperial Bank of Commerce
(CIBC), downgraded Citigroup to “sector underperform” [17]. Any such news-based expla-
nations of investor behavior on November 1 (similarly for November 7) would not account for
the difference in behavior between short sellers and other investors. Under the assumptions
of standard [14] capital asset pricing models, all investors act to maximize expected future
wealth [18], and should therefore respond similarly to news. Furthermore, it has been shown
empirically that the ratio of short sales to total volume remains nearly constant, even around
5

30
35
40
45
Price ($)
Sep 2007 Oct 2007 Nov 2007 Dec 2007 Jan 2008
20
15
10
5
0
5
10
15
20
25
30
Demand Quantity
(tens of millions of shares)
Change in Short Interest
Total Short Interest
Volume
FIG. 2: Market activity for Citigroup over a five-month period starting on August 15, 2007. Top
panel shows bars for daily high and low stock price (adjusted for dividends). Lower panel shows
daily change in short interest (red bars), total short interest (yellow lines), and trading volume
(gray bars). Arrows indicate November 1, 2007 [10].
news events [19]. In the literature, analysis of the residual small differences in the behavior
of short and long investors has been interpreted to indicate that short sellers have an infor-
mational advantage or that short sellers are able to anticipate lower future returns [19–23],
rather than cause them. Still, these studies do not show that large differences in trading
generally occur between short and long sellers. Thus, the existence of such a difference is
indicative of specific trader action.
Our evidence points to a bear raid during a period of financial stress [24,25] to which
the Federal Reserve Bank responded in August 2007 by announcing that they would be
“providing liquidity to facilitate the orderly function of markets” because “institutions may
experience unusual funding needs because of dislocations in money and credit markets” [26].
Shortly afterwards, the Dow Jones Industrial Average achieved its historical peak—14,167
points on October 9—three weeks prior to November 1, the date our evidence suggests a bear
6

FIG. 3: Scatter plot of the daily volume of trading divided by the three month prior average (volume
ratio), and the increase in number of borrowed shares divided by the volume (short interest change
ratio), for Citigroup over a two-year period starting January 1, 2007. Arrows indicate Citigroup
on 1 November 2007 and 7 November 2007. These two points are well outside of the behavior of
daily events even during the period of the financial crisis in late 2007 and throughout 2008. The
two measures are described in Appendix A.
raid occurred. Bear raids may have long-term price impact if decision makers infer investor
confidence from price movements and act on that basis [27,28]. Citigroup CEO Charles
Prince’s resignation on November 4 after an emergency board meeting [29] may reflect such
an effect. The months after November 1 saw the beginning of the stock market turmoil of
2008-2009 as well as many significant events of the financial crisis, such as the purchase of
Bear Stearns by JP Morgan Chase in March 2008 and the bankruptcy of Lehman Brothers
in September 2008.
III. CONCLUSIONS AND POLICY IMPLICATIONS
The 2007–2011 financial crisis resulted in widespread economic damage and introduced
questions about both our understanding of economic markets and about the practical need
for regulations that ensure market stability. The Financial Crisis Inquiry Commission
7

(FCIC) reported that over 26 million Americans were unemployed or underemployed in
early 2011, and that nearly $11 trillion in household wealth evaporated. Moreover, the
FCIC concluded that the crisis was avoidable and was caused in part by “widespread fail-
ures in financial regulation and supervision [that] proved devastating to the stability of the
nation’s financial markets” [30]. Regulatory changes that preceded the financial crisis in-
clude the June 2007 repeal of the uptick rule, which was implemented in 1938 to increase
market stability and inhibit manipulation [5–8,31].
Within the resulting deregulated environment, it is still widely believed that the crisis was
caused by mortgage-related financial instruments and credit conditions, and that individual
traders did not play a role [32–35]. Our analysis demonstrates that manipulation may have
played a key role. Methods for detecting manipulation and its effects are necessary to both
inform and enforce policy.
When the SEC repealed the uptick rule on July 6, 2007, one of its main claims was that
the market was transparent, and that such regulations were not needed to prevent market
manipulation [6]. Our results suggest that, not long after the uptick rule was repealed,
a bear raid may have occurred and remained undetected and unprosecuted. Our analysis
reinforces claims that lax regulation was an integral part of the financial crisis [30].
In response to requests for reinstatement of the uptick rule after the financial crash,
the SEC underwent extended deliberations and finally implemented an alternative uptick
rule, which allows a stock to fall by 10% in a single day before limitations on short selling
apply [36]. This weaker rule would not have affected trading of Citigroup on November 1,
2007, as its minimum price was just 9% lower than the close on October 31. Subsequent
day declines until November 7 were also smaller than 10%.
The existence of a major market manipulation should motivate changes in market models,
analysis, regulation and enforcement. In particular we conclude that:
•Large traders may have a significant influence on the market. Scientific analysis and
models should recognize the role of large traders and consider both past events and
potential future events they may cause. For example, market time series analysis that
does not specifically consider the effect of manipulation may be unable to discover it,
because manipulation events may not manifest in averages and distributions that are
usually considered.
8

•Improved access to data can enable the detection of market manipulation. This would
foster transparency in the markets, which has been lauded but not realized. Regulatory
agencies should mandate the increased availability of relevant data for the detection
of manipulation. If these data cannot be made available in real-time or for public use,
they may be provided with time delays or only for scientific use. Data of importance
include not only the opening of short positions but also their closing, as aggregate
short sale activity cannot be determined when only opening trade data are available.
These data should be made available at the transaction level.
•Current legislation, which focuses on retroactive penalties, is ineffective due to the
discrepancy between the timescale of enforcement response and that of market manip-
ulation. Severe failures in the financial system may include cascading global market
crises and numerous takeovers and bankruptcies, making the disentanglement of indi-
vidual events difficult if not impossible. Regulatory agencies should adopt preventive
measures such as the uptick rule, which would be more effective than punitive ones.
The uptick rule was designed to minimally restrict trader’s actions while simultane-
ously providing underlying stability for the financial system and inhibiting particular
forms of manipulation, including bear raids.
•The limitations of our data prevent definitive conclusions about individual events or
their attribution to individual investors. Enforcement agencies should perform inves-
tigations into specific candidate events, including the candidate event we identified on
November 1, 2007.
•Until effective regulations and enforcement are in place, market price changes may not
reflect economic news. They may reflect market manipulation.
The complexity of financial markets and their rapid dynamics suggest that data analysis
and market models are increasingly necessary for guiding decisions about setting market
regulations and their enforcement [37–39]. Independent of the role it may play in financial
crises, understanding market manipulation may be important for characterizing market dy-
namics. Recent decades have seen significant advances in financial market theory, including
the mean-variance portfolio theory [40], the capital asset pricing model [18], arbitrage pricing
theory [41], and the theory of interest rates [42]. However, the financial crisis and anoma-
9

lous events such as “flash crashes” [43] demonstrate limitations in existing approaches. More
recent efforts seek to explain market phenomena via methods such as agent-based model-
ing [44–49] and analysis of the long-tailed distributions of price fluctuations [11,50–53].
While these methods have been successful in describing some aspects of market behavior,
they generally do not consider the impact of individual traders who have the ability to sig-
nificantly impact the market [54–60]. Current approaches, whether analytical or statistical,
may not reveal isolated—or even frequent—instances of trader influence.
Among the possible forms of individual trader influence, intentional actions—including
manipulation—are of particular relevance, as they undermine the role of markets in setting
prices so as to reflect economic value. Market manipulation is illegal under Section 10 of
the Securities Exchange Commission Act of 1934 [5]. Some forms of manipulation are well
documented, including indirect price manipulation through the generation of false news [61].
Direct price manipulation through market transactions is also commonly thought to occur [1,
2,54], but methods for its detection that are based on statistical analysis [62,63] are limited
by their inability to independently account for news events and other anomalies. No direct
evidence of recent price manipulation has been presented based upon these methods.
The timing of the event we identified raises questions about the potential role it may have
played in the financial crisis. Understanding the wider impact of such an event requires that
we consider the vulnerability of the overall market.
Whereas a highly stable system is not vulnerable to any but the largest impacts, a vul-
nerable system can be destabilized by much smaller shocks [64,65]. This is a general aspect
of the behavior of complex interdependent systems, not just of financial markets. Specific
events can have large effects if the underlying physical, biological or social system is vul-
nerable. For example, while mass extinctions have been shown to coincide with meteor
strikes [66], underlying vulnerabilities are thought to contribute to the severity of extinction
events [67]. Similarly, market manipulation during a period of instability and high intercon-
nectedness, such as before the financial crisis [24,25,68], may exacerbate or even trigger a
collapse. The financial system can be expected to exhibit this general property of complex
systems, in which the coincidence of underlying vulnerability and extreme events can trigger
crises.
We thank Yves Smith and Matt Levine for helpful comments. This work was supported
by the New England Complex Systems Institute.
10

Appendix A: Methodology: Data and Event Detection
It is generally difficult to characterize the investments of individual traders, especially
for short positions. Unlike those who own large stakes in companies, those with large short
positions are not required to report their holdings [69]. Short interest data is publicly
available by ticker symbol at two-week intervals for a rolling 12-month period [70]. This
time resolution is too low to detect the bear raid candidate we will describe, and does not
include historical data for the period of the financial crisis. The recent availability of off-
market transaction systems that enable large volume transactions, such as crossing networks
[71,72], makes it difficult, if not impossible, to trace intentional large short sale transactions
using market data. A short sale transaction between cohorts on a crossing network may
allow one trader to execute a short sale while the other trader accumulates a long position.
This long position can then be sold on the open market without leaving a signature of its
short sale origins.
Our study is based on industry data on daily securities lending. While this data does
not identify the individuals borrowing the shares, the time resolution proved sufficient to
provide evidence of a bear raid.
We obtained price and volume data from Thomson Reuters Datastream. Short interest
data was obtained from Data Explorers and included a daily record of the value and quantity
of loaned securities as reported by brokerages. These included separate time series for
the total number of borrowed securities (total demand quantity) and for daily incremental
changes in the number of borrowed shares. Daily incremental changes were approximately
given by day-to-day differences in total demand quantity, with small corrections arising from
the addition and removal of reporting organizations from the data set. The reconstruction
of short selling data from security lending data is an inexact process, because borrowed
securities may be used for purposes other than short selling, including tax arbitrage, dividend
arbitrage, and merger arbitrage. Furthermore, reported data may be incomplete, because
not all lenders supply data to industry data providers. Nevertheless, because short selling
is the predominant reason for securities lending, securities lending is a reasonable proxy
for short selling [73,74]. We also were able to eliminate the possibility of the most likely
alternative explanation to a bear raid, dividend arbitrage, as described in Appendix C.
The signature of a successful bear raid is an anomalous spike in the number of shares
11

of a company’s stock that are sold short, followed by a price decline, then a corresponding
large spike in the number of positions that are covered—a decrease in the number of short
positions. A sufficiently large increase in short selling would also increase the total volume
of trades, so we monitored also the total daily trading volume.
We searched data for several prominent companies to identify candidate events, and
calculated two ratios, Rand Q, for each trading day. Ris the ratio of the change in short
interest to daily volume,
R(t) = ∆S(t)
V(t),(1)
where ∆S(t) = S(t)−S(t−1) is the change in short interest, Vis trading volume, and tis the
date. A large absolute value of Rindicates that a high proportion of trading is accounted
for by securities lending activity—that the volume of borrowed shares was a substantial
fraction of the total volume, and that short sales might have affected the stock price. A
high positive value indicates that shares were borrowed, and a high negative value indicates
short covering. Note that if a large number of short positions were opened and closed on
the same day (i.e. an intraday bear raid), it would not be revealed by daily short interest
data. We cannot exclude the possibility of intraday bear raids occurring during this period.
Qis the ratio of the trading volume to the three month moving average,
Q(t) = V(t)
V(t),(2)
where Vis the prior 3-month (63 trading day) moving average of volume. A value of Q
substantially greater than one indicates an anomalously high trading volume. The event we
analyzed was identified by a high absolute value of Rand high value of Q, indicating that
the increase in borrowed shares was large in comparison to trading activity, and that total
trading activity increased dramatically.
Appendix B: Rand Qdistributions
In this appendix we present our analysis of the distributions of R(the ratio of the change
in short interest to daily volume, see Eq. 1) and Q(the ratio of the trading volume to the
three month moving average, see Eq. 2) for Citigroup, from January 2007 through December
2008. The analysis allows us to obtain a probabilistic estimate of the inherent likelihood of
12

Rand Qvalues for each day, and in particular for the events on November 1 and 7, 2007.
The positive and negative tail cumulative distributions for Citigroup for Rare plotted in
Fig. 4. The two sides of the distribution behave differently: while the positive tail follows
a power law distribution (top panel), the negative tail is well described by a Laplacian
distribution (bottom panel). The distribution for Q, shown in Fig. 5, has a power law
tail. November 1 and 7, 2007 are omitted in the plots, but this does not affect the fitted
distributions. From the fitted distributions we extracted the expected probabilities of the
two events.
Appendix C: Tests and Technical Notes
We have tested a number of alternative explanations of the data:
•Is it possible that the borrowed shares were used to receive a dividend payment, i.e.
dividend arbitrage?
Sometimes borrowing shares provides benefits of dividends to the borrower rather than
to the owner. In such cases the borrower may not necessarily sell the shares short,
which precludes a bear raid.
The date on which shares were borrowed, November 1, was an “ex-dividend” date, i.e.
a date on which ownership determines dividend payments. In order for borrowers to
receive the benefit of dividends they are required to hold the shares at the prior day’s
closing. Thus, there was no dividend paid to shares borrowed on November 1.
•Is it possible that the reported dates for borrowed shares is delayed so that the actual
date of borrowing is a different date than what is reported (for example, could it be
reported on the date of settlement three days after a market transaction)?
We verified the agreement of reported borrowing and short selling date by looking at
the period of the short sale ban starting in September 2008. The dates of the start
and stop of borrowing coincide with the dates that they should for the ban, which
shows that there is no delay in reporting.
•Does commercial market transaction data corroborate the short selling?
13

0.001
2
4
6
8
0.01
2
4
6
8
0.1
2
Cumulative Distribution
2 3 4 5 6 7 8 9
0.1 2 3 4 5 6
R
Citigroup R (positive tail)
Power Law
0.001
0.01
0.1
1
Cumulative Distribution
5 6 7 0.01 2 3 4 5 6 7 0.1 2 3 4 5 6 7
- R
Citigroup R (negative tail)
Laplacian
FIG. 4: Citigroup Rdistribution - Cumulative distribution functions (CDF) of the short interest
change ratio for Citigroup, for 2007 and 2008. Top panel: Positive tail of the distribution, blue
line is the best fit power law (CDF(R)∼Rα, with α=−1.35). Bottom panel: Negative tail of
the distribution, blue line is the best fit Laplacian distribution (CDF(R)∼1 + sign(R−β)(1 −
exp(−|R−β|/γ)), with β= 0.11 and γ= 0.048).
14

0.001
0.01
0.1
1
Cumulative Distribution
2 3 4 5 6 7 8 9 12 3 4 5 6 7 8
Q
Citigroup Q
Power Law
FIG. 5: Citigroup Qdistribution - Cumulative distribution function (CDF) of the volume
ratio for Citigroup for 2007 and 2008. Blue line is the best fit power law (CDF(Q)∼Qα, with
α=−3.34).
We have studied commercially available NYSE short selling data [75] from these dates,
and found it to be unreliable because the transactions reported are inconsistent with
reported trade and quote data [76] at the transaction level. Despite dialog with the
NYSE staff we have not received an explanation of the inconsistency. For the present
analysis, the inconsistency inhibits our efforts to use this data to cross-validate the
results in this report. More generally, it raises questions about the reliability of market
provided short sale data.
•Is it possible that the analyst report downgrading Citigroup that morning was released
in collusion with the bear raid?
We have no specific evidence, but such collusion would be consistent with strategies
used by those who manipulate stocks [1,2,54,61].
•Is it possible that those who engaged in the bear raid also used trading in options to
increase their profits by buying put or selling call options?
15

Our estimate of the profits made on the bear raid are conservative.
•Is it possible that the large block trades on November 1 and 7 represented trading
based upon information that was not yet available to the public on November 1?
Our evidence suggests that a single individual or group of individuals traded a large
volume of borrowed shares on November 1 and November 7. If this represented po-
tentially illegal insider trading, the traders would have avoided attracting attention.
Neither the large trading volume nor the abrupt price drop on November 1 at the
opening of the market appear to be consistent with a low-profile trading approach.
The rapid price drop is also inconsistent with the expected behavior of insider traders,
which is to maximize profits by selling gradually to avoid affecting prices until the neg-
ative news becomes public. Both the large volume of trading and the rapid drop are
consistent with trading intended to affect prices, i.e. a bear raid. While the intentions
of traders can only be determined from a more detailed inquiry once those traders are
identified, the available information strongly supports a bear raid over the possibility
of insider trading per se. It is possible that traders with insider information chose to
help matters along by performing a bear raid at the same time as they were trading
on insider information.
Addendum: Additional Tests and Technical Notes
Following the release of this paper, we were contacted by the NYSE with additional
information about the NYSE short selling transaction data [75] described in Appendix C.
The new information enabled us to reconcile the short sale and trade data [76] by aggregating
and shifting the times of multiple transfers to correspond with market transactions. There
are residual issues with a small minority of transactions that are being resolved, but these
issues appear to be irrelevant to conclusions about the volume of trading.
The additional information enables us to identify with some confidence the reported short
sale volume on the NYSE on November 1 and other dates. The short sale volume is not
unusual as a proportion of total volume, constituting about one quarter of the total volume
on this market. NYSE transactions constituted 30% of the total market volume on November
1, 2007. This limits the volume of reported short selling on the markets, and diminishes the
16

likelihood that the reported increase in borrowed shares was directly reflected in reported
short sales.
Absent an alternative interpretation, if shares were sold in a way that concealed their
origin as borrowed shares the data sets would be consistent. One method to achieve this,
using “short to buy” transactions, was reported in Senate investigations of the Pequot
Capital hedge fund in 2009 [77]. In this approach a single trader moves shares from one
account to another, creating a short position in one and a long position in the other. Since
there is no change in beneficial ownership, such transactions may be reported in a way that
is not consistent with standard reporting requirements, resulting in share borrowing without
a market record. Long positions created this way may be sold on any market without being
identified as short sales, even though in doing so a net short position is created.
This method appears to have been developed to hide short selling at a time when the
uptick rule was in effect. Short to buy transactions require a close relationship with a
broker dealer. The necessary access to market trading systems, called “sponsored” or “direct
market” access, needed to perform the short to buy transaction is not available to most
traders but constitutes a significant fraction of reported trading [78,79]. Only recently,
beginning in 2011, were brokers required to apply standard regulations to transactions of
traders using sponsored access [80,81]. Previously, non-compulsory self-regulation was in
effect [82]. In the absence of oversight, market data may not properly record the volume of
short selling.
An explanation in these terms for the events in November of 2007 is also consistent with
the observation that there was a larger volume of returned shares on November 7 than the
trading volume. In the “short to buy” scenario, residual positions can be closed through
“back office” transactions and may never be recorded on the market.
The new information we received implies that the sale of borrowed shares reflected in the
increase in borrowed shares on November 1 and the corresponding decrease on November 7
may have been done in a way that would not have been prevented by the uptick rule. A
more detailed inquiry into the means by which such selling could have been done is beyond
the current work.
17

We thank Steven Poser and Wayne Jett for helpful discussions.
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