Download Naked Short Selling

Fails-to-Deliver, Short Selling, and Market
Quality
Abstract
We investigate the aggregate market quality impact of equity shares that fail to deliver (“FTDs”). For a
sample of 1,492 NYSE stocks over a 42-month period from 2005 to 2008, greater FTDs lead to higher
liquidity and pricing efficiency, and their impact is similar to our estimate of delivered short sales.
Furthermore, during the operative period of an SEC order mandating pre-short-sale stock borrowing, the
securities affected display relatively lower liquidity and higher pricing errors. Finally, we do not find any
evidence that FTDs caused price distortions or the failure of financial firms during the 2008 financial
crisis.
Keywords: Naked Short Selling, Short Selling, Failure to Deliver
JEL classification: G10, G14, G18
This version: March 10, 2014
1.
Introduction
Trades in US stock markets are settled on a three-day cycle: for trades on day t, if the net delivery
obligations of a clearing member are not fulfilled on day t+3, any undelivered position becomes a
“failure-to-deliver” (or “FTD”). Regulators and financial journalists have widely perceived FTDs, and
specifically “naked” short sales, as having a very negative impact on markets.1 For example, a report in
Time Magazine (“Watch out, they bite”, November 9, 2005), quoting estimates by a former Under
Secretary of Commerce, alleges that that naked short selling has “cost investors $100 billion and driven
1,000 companies into the ground”; and an article in Euromoney (“Short selling: the naked truth”,
December 2008) claims that, “Fails to deliver in the US equity market have exacerbated the sharp
declines in share prices of financials. Although the SEC is clearing up the mess caused by naked shortselling, more drastic measures might be needed to restore confidence.” In this context, this paper
investigates the overall net impact (on day t+1) of the change in the open interest of undelivered positions
(i.e., the change in FTDs) generated collectively by trades on day t (and observed on day t+3). First, we
analyze the effect of FTD changes on pricing efficiency and liquidity. Second, we examine whether FTD
changes played a causal role in the major price declines or the demise of financial institutions during the
2008 financial crisis.
Settlement on U.S. stock exchanges is done electronically through the Depositary Trust and
Clearing Corporation, its subsidiaries, and associated agencies (hereafter collectively referred to as the
“DTCC”). Ownership records are largely held, tracked, and transferred electronically through the DTCC,
with more than 99.9% of all trades involving only electronically held securities (Morris and Goldstein,
2009). The DTCC becomes the central counterparty of all duly-matched error-reconciled trades, and
electronically checks and updates relevant stock ownership accounts. If the stock ownership accounts
associated with a clearing member with a net delivery obligation do not actually include the stock needed
1
The term “naked short sale” is used (in this paper) to describe a short sale that, irrespective of any intent
considerations, fails to deliver because of the short seller not making timely stock borrowing arrangements.
1
for delivery on settlement day, the undelivered position becomes a FTD.2 FTDs can potentially arise from
both short and “long” sales (i.e., sales of duly owned stock). In a short sale, such a delivery shortfall arises
when the stock is not borrowed in time to credit the stock ownership account by settlement day.3 In a long
sale, a delivery shortfall arises, for example, when (duly-owned) sold stock has been lent out and not
returned to the stock ownership account in time for settlement; or because the broker has not ensured
electronic recording of a paper certificate prior to the trade; or in conjunction with oversubscribed
securities at security issuance.
There has been a strong regulatory focus on reducing FTDs. In January 2005, Regulation SHO
introduced requirements to “locate” stock prior to every short sale to reduce FTDs due to stock borrowing
delays; it also forced firm pre-short-sale stock borrowing arrangements in “threshold-list” stocks (that is,
securities with high levels of FTDs) unless existing FTDs were “closed-out”. In July/August 2008, a
temporary SEC Order mandated stock borrowing arrangements prior to short selling in select financial
stocks to “eliminate any possibility that naked short selling may contribute to the disruption of markets”
(SEC Release 58166, 2008). After Lehman’s collapse in September 2008, through Rule 204T (later made
permanent), FTDs arising from short-sales were virtually eliminated by requiring borrowing or
purchasing by the broker by the morning after the failure day; FTDs arising from long sales or market
maker FTDs were given three additional days. Similarly, in November 2012, new EU rules instituted a
2
A delivery failure by an individual client account will not become a FTD at DTCC level if another client account
held with the same clearing member lends the stock explicitly, or implicitly because of being due to receive
delivery. Due to such “netting”, a FTD at DTCC level cannot generally be uniquely attributed to a specific trade or
trader; nor is it possible to identify whether it originated from a short or long sale.
3
The Regulation SHO “locate” requirement introduced in January, 2005 requires broker-dealers to ensure (prior to a
short sale) that there are “reasonable grounds” to believe that the security could be borrowed for timely delivery,
rather than identify a separate bloc of shares for each specific short-sale. As a consequence, a lender may indicate to
multiple potential borrowers that shares are available, but be unable to meet all demands. The requirement could
also often be fulfilled by using published lists of easy-to-borrow securities (Welborn, 2008).
2
pre-trade borrowing requirement for short sales. Regulatory concerns have been further exacerbated by
the widespread allegations and the extensive litigation about FTDs being used manipulatively by naked
short sellers. Such “abusive” naked short selling is widely alleged to have contributed to the financial
crisis by precipitating sharp price declines of financial firms.4 Notwithstanding extensive concerns, the
SEC (in Report 450, March 2009) says that “there is hardly unanimity in the investment community or the
financial media” on the dangers involved, and “despite its assertions regarding the potential of danger...
the [SEC] Report can cite to no [relevant] bona fide studies” on the associated market impact.
In the context of the strong regulatory focus, we begin by examining whether changes in FTDs
are followed by changes in prices, pricing errors, intraday volatility, bid-ask spreads, and order
imbalances. Our main sample consists of all the 1,492 NYSE ordinary common-share issues for which all
relevant data is available over the period January 2005 to June 2008. For robustness, we replicate our core
analysis on a similarly constructed sample of 2,381 NASDAQ ordinary common-share issues over the
same period. First, we analyze liquidity and pricing efficiency for securities in different portfolios based
on the number of FTDs. Second, we utilize OLS regressions and Granger-causality tests to investigate the
link between FTD changes and market quality. Third, given the complex and endogenous
interrelationships between market quality metrics and other market variables, we fit vector autoregressive
models and test these relationships using impulse response functions. Fourth, we examine whether FTDs
by market makers affect securities differently from FTDs by other “public traders”, by using a proxy
4
Over a two-year period leading up to the 2008 financial crisis, the SEC received more than 5,000 complaints in this
regard (Wall Street Journal Asia, March 20, 2009), and a Factiva search shows over 4,600 printed English-language
articles on the subject. Several investor associations and high-profile CEOs lobbied aggressively. The huge volume
of litigation alleging associated stock price manipulation led to “naked” short selling being called the “Holy
Grail….bigger than tobacco” for plaintiffs’ lawyers (Stokes, 2009). Examples of lawsuits include The Biovail
lawsuit against Stephen Cohen, Gradient, and others; the Overstock lawsuit against Rocker Partners, Gradient, and
others; and the The NFI lawsuit against Bank of America (the Specialist) and the Prime Brokers.
3
based on the reduction in FTDs subsequent to SEC Rule 204T in September 2008, which selectively
precluded public-trader FTDs but not market-maker FTDs.
We find that, during our sample period, FTDs affect about 95% of NYSE securities. For this
NYSE sample, we conclude that an increase in FTDs equivalent to 0.1% of the number of outstanding
shares leads to a 3% reduction in the magnitude of positive and absolute pricing errors; a 0.2% decline in
intraday volatility; a 1.7% reduction in bid-ask spreads; and a 0.70% reduction in order imbalances. Each
of these changes is statistically significant and not subject to significant subsequent corrections. Similar
results are obtained in sub-samples of securities affected by high levels of FTDs, or by persistent FTDs.
Further, the beneficial impact on pricing efficiency and liquidity is driven by FTDs of both marketmakers and public traders. Overall, our results are consistent with failing-to-deliver traders acting as value
arbitrageurs and liquidity suppliers, enhancing pricing efficiency and providing liquidity as needed.
We observe that the regulatory focus on reducing FTDs has been particularly concerned with
FTDs arising from short sales, despite extant literature documenting that short sales have a beneficial
overall impact on pricing efficiency and liquidity by enabling value-traders to more effectively bring
prices of overpriced securities in line with their true value, and facilitating financial intermediaries in
providing liquidity more expeditiously.5 This suggests an underlying regulatory belief that short sales that
fail to deliver have an impact on liquidity and pricing efficiency that is different from the corresponding
impact of short sales that result in timely delivery. However, from an economic perspective, that should
arguably not be the case. First, short sales that fail to deliver might not differ from timely delivered short
sales at the time of the trade since a short seller need not definitively know on day t of the trade whether
or not she will deliver or fail on settlement day t+3. This is because that decision may rationally be taken
5
While there are some dissenting opinions, there is broad agreement behind an extensive literature finding that short
selling leads to improvements in pricing efficiency and liquidity (Diamond and Verrecchia, 1987; Abreu and
Brunnermeier, 2002 and 2003; Miller, 1977; Bris et. al. 2007; Diether et al., 2009; Boehmer et al., 2008).
4
only on day t+3 on the basis of the rebate rates in the OTC stock-borrowing market on day t+3.6 The
short seller may want to borrow and deliver if these rebate rates are positive and fail if they are negative.
Second, as explained by Culp and Heaton (2008), a FTD results either in automatic stock borrowing at
zero rebate rates from a pool of voluntary lenders under the DTCC Stock Borrow Program, or in forced
stock borrowing at zero rebate rates from a randomly assigned broker with a long stock position – and
little incentive to enforce delivery by forcing a “buy-in” from the market, since the random assignment
potentially changes every day (Putniņš, 2010). As far as the market is concerned, since the stock is being
temporarily borrowed anyway (voluntarily or otherwise), there should not be any functional consequences
arising from whether a short sale ultimately results in a FTD or not. Hence, any FTDs that arise from
short sales should contribute to price discovery and liquidity on the day of trade in the same way as timely
delivered short sales. In the context of the above, we extend our empirical analysis (on the impact of FTD
changes on pricing efficiency and liquidity) to also examine the corresponding impact of delivered short
sales, and test whether that impact is different. We find strong evidence that the impact on our marketquality metrics of daily changes in FTDs, and of daily changes in short interest net of FTDs (our proxy
for delivered short sales), is similar in both magnitude and significance.
To focus on FTDs more likely to originate from short sales, and to control for any omitted
variables, we investigate the securities affected by an exogenous event: the imposition of a temporary
SEC Emergency Order (Release 58166 dated July 15, 2008) that remained in force between July 21 and
August 12, 2008. This order required pre-borrowing arrangements prior to all short sales in 19 selected
financial stocks and hence did not directly affect any FTDs arising from “long” sales. We find that during
the order validity period, reported FTDs for the affected securities reduce to about 12% of their pre-order
6
Since stock borrowing arrangements are ordinarily accompanied by same day delivery, it is economically not
rational for short sellers to borrow prior to the delivery date and pay extra borrowing fees (Geczy et al., 2002).
Evans, et al. (2009) show that short sellers fail to deliver when rebate rates are negative. Boni (2006) offers evidence
of correlation between fails and borrowing costs, which she interprets as indicative of “strategic” fails.
5
average within one week, to about 2% of their pre-order average within three weeks, and finally, on the
last day of the order period, reported FTDs are below the minimum reportable threshold for each and
every affected security. We also find that securities affected by the order display a significant increase in
intraday volatility, absolute pricing errors, and bid-offer spreads while the order was in force: i.e., the preshort sale stock-borrowing mandate designed to reduce FTDs significantly worsened pricing efficiency
and liquidity. While this natural experiment may not be generalizable because very few securities in the
same industry and during a particularly turbulent time are affected, our results indicate that FTDs for
these firms appear to arise largely from short sales, and contribute beneficially to market liquidity and
pricing efficiency.
In the context of the extensive concerns articulated in the press, and by investor groups and
company CEOs, the final section of our empirical analysis investigates whether FTDs caused price
crashes and distortions for specific securities during the 2008 financial crisis period.7 Since FTDs have
been blamed for the price crashes of Bear Stearns Companies Inc. (“Bear Stearns”), Lehman Brothers
Holdings Inc. (“Lehman”), Merrill Lynch & Co. Inc. (“Merrill”), and American Insurance Group
(“AIG”), we test for high levels of FTD changes prior to the large price declines in the stock prices of
those companies. We find that FTDs were too few for any significant stock price distortions on most
days, and when FTDs did become abnormally high, it was after price declines, not before. In each case,
FTDs were responding to information about the firms, rather than being responsible for triggering price
declines. Overall, we find no evidence that FTDs played a causal role in the demise of financial
institutions or in generating price distortions during the 2008 financial crisis.
7
Press sentiment is exemplified by statements such as “when Bear and Lehman made their final leap off the cliff of
history, both undeniably got a push — especially in the form of a flat-out counterfeiting scheme called naked short
selling” (Rolling Stone, October 2009). Concerned investor associations include The Movement for Market Reform,
National Coalition against Naked Short Selling and Coalition for the Reform of Regulation SHO. An example of a
crusading high-profile CEO is Patrick Byrne of Overstock.com, which filed several lawsuits against alleged nakedshort sellers and financial institutions they accused of facilitating “naked-shorting”.
6
This research contributes to the literature on settlement systems and delivery failures. Fails are
not actual “failures” of delivery, but delays (with a median age of three days as per Boni, 2006). Evans, et
al. (2009) show that “the alternative to fail is valuable and important to the pricing and trading of
options.” Our results additionally and importantly show that the ability to fail has a beneficial impact on
liquidity and pricing efficiency of equity markets as well. Earlier, Merrick, et al. (2005) have shown that
the ability to fail is an important release valve for settlement-related pressures and manipulative
distortions. Similarly, the difficulty of borrowing shares when short selling demand is high leads to costly
frictions which negatively impact market quality; and the ability to fail is a release valve that helps to
protect traders from the worst effects of these frictions: it is particularly valuable when stock-borrowing is
so costly that short selling rebate rates become negative, which is exactly when liquidity is most needed in
the stock-borrowing market (Evans, et al., 2009).8 Hence, regulatory removal of the ability to fail for all
public traders is debatable when progressive fines for settlement delays can arguably be effective without
being an extreme solution. It is more important for regulators to focus on removing the economic
incentives for delivery failures by improving the liquidity, transparency, and regulation of the stock
borrowing market.
This research also contributes significantly to the short selling literature. First, extending the
extant evidence on the market-quality benefits of short selling, our results suggest that short sales that fail
to deliver are as beneficial for market quality as short sales that deliver on time. Second, our findings have
important implications for the extensive press coverage of naked short selling, and the strong regulatory
response to it. Finally, we extend the literature on the impact of short sales restrictions: the ban on FTDs
8
These frictions are well documented by Kolasinski, Reed, and Ringgenberg (2013): they find that high levels of
stock borrowing demand lead to dramatic increases in loan fees and search costs related to supply constraints.
7
in some stocks in July 2008 was effectively an additional constraint on short selling and our evidence
shows that it had predictably negative consequences on market quality.9
The remainder of the paper is structured as follows. Section 2 outlines the data, the variables and
the measures utilized. Section 3 presents empirical results on the impact of FTD changes on pricing
efficiency and liquidity. Section 4 investigates the role of FTD changes in creating price distortions
during the 2008 financial crisis. Finally, Section 5 offers concluding remarks.
2.
Data, variables, and measures
2.1
Data and sample
The main sample consists of all NYSE listed common stocks in CRSP share codes 10 and 11 for
which complete data are available. By restricting the analysis to share codes 10 and 11, we exclude ETFs
(in case FTDs are caused by delays in the creation of units) and other securities that are not common
stocks. We thereby exclude securities classified by CRSP as certificates, American trust components,
ADRs, SBIs and units such as “depositary units” and “units of limited partnership interest”, as well as
securities issued by other types of entities such as foreign firms, closed-end funds, and REITs. We also
restrict the sample to securities that are listed for at least six months during the sample period (in order to
have adequate data to fit vector autoregressive models) and that have been trading for at least one year
prior to the sample period. Having a year of trading data allows for the estimation of pricing errors as
discussed later in this section. We further require that the number of shares outstanding does not vary by
more than 10% over any single day, to control for the unusual volumes of FTDs around primary market
transactions documented by Edwards and Hanley (2010); though our results are robust to resampling
9
Several recent papers examine short selling restrictions in 2008: Boulton and Braga-Alves (2010) and Kolasinsky,
et al. (2012) examine aspects of the July/August 2008 SEC Emergency Order that we investigate in this paper. Other
papers - Battalio and Schultz (2011), Boehmer, et al. (2013), Autore, et al. (2011) and Beber and Pagano (2011) –
focus on the subsequent September 2008 short selling ban, which we do not examine.
8
without this constraint. In view of the potentially confounding influence of the July 2008 SEC Emergency
Order and the restrictions on short selling and FTDs subsequently imposed in September and October
2008, we confine our analysis to the period up to June 30, 2008. The main sample thus consists of 1,492
NYSE securities over January 2005 to June 2008. For robustness tests, we construct a comparable sample
of 2,381 NASDAQ securities for the same period. Short interest data are from www.shortsqueeze.com
and short sales data (available from January 2005 onwards) are from the NYSE. The number of shares
outstanding is from CRSP. Market quality measures are based on NYSE TAQ data.
2.2
Outstanding Fails-to-Deliver Ratio (OFR) and Outstanding Delivered Shorts Ratio (ODR)
Our metric for FTDs is the Outstanding Fails-to-Deliver Ratio (OFR), defined for each day t as
the number of outstanding failed positions reported on day t+3 scaled by the total number of shares
outstanding of the firm. We obtain data on the number of shares outstanding from the Center for Research
in Security Prices (CRSP), while data on outstanding FTDs have been made available by the SEC under
the Freedom of Information Act (FOIA) since March 22, 2004. Reported raw FTD data from the SEC
represents the open interest of failed-to-deliver trades that occurred up to three days prior. For each day t,
we look at the number of outstanding FTDs on day t+3, as we are interested in investigating the impact of
FTD changes on the market on the day on which the transaction actually occurs (day t), rather than on the
day on which the resulting failures are disclosed (day t+3). Hence, OFR on day t is equal to the number of
FTDs for day t+3, scaled by shares outstanding on day t. Our approach of scaling the number of FTDs by
the number of shares outstanding is similar in spirit to previous literature that relies on measures of
“relative short interest” (DeChow et al., 2001; Desai et al., 2002; Chen and Singal, 2003), and mirrors
recent studies using FTD-based data (for example, Boulton and Braga-Alves, 2010). FTD changes are
measured as the daily change in OFR.
Over our sample period, the SEC reports the number of outstanding FTDs only for a trading day
on which it exceeds 10,000 shares of a particular security. Accordingly, on a day on which no figure is
reported for a particular security, we are unable to determine the true number of outstanding FTDs – we
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simply know that it is less than 10,000 shares. In the absence of reported data, we record the number of
FTDs as zero. Our approach is consistent with extant literature using FTD data (for example, Boulton and
Braga-Alves, 2010). Accordingly, reported figures somewhat understate the true extent of fails. To put
this into perspective, we note that the average number of shares outstanding for the securities in our
NYSE sample is about 212 million. Further, over the days on which non-zero FTDs are reported, the
average number of reported FTDs is 97,068 shares, which is well in excess of the minimum reporting
threshold. In terms of our tests regarding the market impact of FTDs, this data bias makes our findings
more conservative, rather than less. First, by inducing a level of noise, it is lowering the statistical power
of our tests. Second, it is arguably unlikely that securities with low levels of FTDs would suffer from
distortions in market quality due to failed trades, given that we find that securities with high levels of
FTDs do not display such problems.
In order to examine whether claims regarding the market impact of “naked” short selling are
valid, we construct a control variable, the Outstanding Delivered Shorts Ratio, or ODR, which is the
estimated short ratio net of FTDs. The Outstanding Delivered Shorts Ratio is intended to be the open
interest of timely delivered short sales positions scaled by the number of shares outstanding. We estimate
the open interest of timely delivered short sales by the difference between the estimated short interest and
the number of outstanding failed positions. The implicit assumption in this estimate of delivered short
sales is that all FTDs arise from short selling. Additionally, while we have daily data on short sales from
TAQ, short interest data is bi-weekly; accordingly, we calculate the short interest on a day within a biweekly period as the sum of the short interest reported at the start of the period and the cumulative daily
changes in short interest since the start of that period. The daily change in short interest is calculated as
the difference between the daily total short sales and an estimate of the daily short positions covered.
Following Deither, et al. (2008), we assume that the number of shares covered on each day of the biweekly interval is equal to the total short sales over the period minus the change in short interest over that
period, divided by the number of trading days in that period. We use the daily change in ODR as our
measure of timely delivered short sales.
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2.3.
Pricing error
We define the “pricing error” on any day as the difference between the observed price on that day
and the estimated information-efficient price for the same day. The unobservable daily estimate of the
information-efficient random-walk or “fundamental” price of the security, a latent stochastic variable, is
estimated for each sample security using a Kalman-filter methodology as in Hamilton (1985). The
procedure involves establishing two equations. The first equation dictates the evolution of the latent
variable, and in our case we assume, in the spirit of Hasbrouck (1993), that the logarithm of the stock’s
underlying or information-efficient value, F (t ) , follows a random walk with a drift,  , and a white
noise innovation,  (t ) , with mean zero and variance  2 :
F (t )    F (t  1)   (t ),
 ~ N (0,  2 )
(1)
The second equation relates the observed and latent variables, i.e., specifies the pricing error
process. We assume that the pricing error Y(t) follows a mean-reverting process around zero, with α, the
rate of mean-reversion, ranging between 0 and 1. Pricing errors correct fully in one period when α is
equal to one, and not correct at all when α is equal to zero.
Y (t )   Y (t  1)   (t),
 ~ N (0,  2 )
(2)
The observed log of stock price S (t ) is the sum of the fundamental price and pricing error:
S (t )  F (t )  Y (t )
Hence, S (t )    (1   )S (t  1)  F (t  1)   (t ) ,  (t )   (t )   (t )
(3)
(4)
The Expectation Maximization (EM) algorithm (Dempster, et al., 1977) is employed to compute
the Maximum Likelihood (ML) estimate of the unobservable variable, F(t), based on data relating to the
observed variable, S(t). Hamilton (1985) employs such an approach to estimate expected quarterly
inflation, the latent variable, based on observed actual inflation. In exactly the same way, we utilize the
observed daily stock prices to infer the daily unobserved fundamental price, and hence the daily pricing
error, using daily closing price data from CRSP. The state-space representation of the system is as
follows:
11
M easurement Equation
Transition Equation
 S (t ) 
S (t )  1 0 0  F (t )
 (t ) 
 S (t )  (1   ) 
 F (t )   0
1

 
 (t )   0
0
  S (t  1)   (t )
0  F (t  1)   (t ) 
0  
1
(5) and (6)
  0 
To test the bias and efficacy of the pricing error estimation process, we run 500 simulations of
both fundamental price and pricing error for a hypothetical stock over 252 trading days assuming a range
of volatility parameters and mean reversion parameters. In each case, we add the fundamental price and
the pricing error to arrive at the equivalent of a simulated “observed” price. Then, we run our Kalmanfilter estimation procedure on this observed price series to determine our Kalman-filter estimate of the
originally simulated fundamental price. Finally, we run a regression of changes in the originally simulated
fundamental price on changes in our Kalman-filter estimate of that fundamental price. In each and every
case, the regression intercept is not significantly different from zero, and the regression slope is not
significantly different from one; and the root mean square error in the estimated fundamental price is
economically small in magnitude.
We employ three measures of pricing efficiency related to pricing errors. First, we use duly
signed pricing errors as estimated. Second, we use the absolute values of pricing errors, which given the
zero-mean distribution of pricing errors, are also a direct measure of the volatility of pricing errors.
Finally, given that the impact of FTDs on pricing errors could be asymmetric, we use a dummy for
positive pricing errors to distinguish between positive and negative pricing errors.
2.4
Liquidity measures and other variables
The liquidity measures we use are relative order imbalance, bid-ask spread, and trading volume
defined as in Table 1. Our measure of volatility is the intraday volatility computed as the daily standard
deviation of five-minute stock returns. The definitions of all of our variables are based on extant empirical
literature analyzing NYSE TAQ data, and are summarized in Table I.
12
3.
Empirical results: FTDs, pricing efficiency, and liquidity
3.1.
Preliminary descriptive analysis of overall sample
We sort securities into ten deciles based on mean OFR, computed over the entire sample period
(January 1, 2005 to June 30, 2008). In Table II, we report means, medians, and standard deviations of the
main variables, for the overall sample and for the top and bottom deciles. We find that overall mean OFR
is about 0.04%. By construction, OFR varies by decile: the mean is less than 0.01% in decile 1 and about
0.29% in decile 10. ODR is similarly higher in decile 10 (13.35%) than in decile 1 (4.08%), with an
almost monotonic positive relationship between mean OFR and mean ODR across (OFR-based) deciles of
different securities. However, even though securities with higher mean OFR tend to also have a higher
mean ODR, the average time-series correlation between ODR and OFR of a particular security is, in
contrast, extremely small – only 0.08. Securities in deciles 1 and 10 do not differ significantly in terms of
mean pricing errors. Securities with higher OFR display significantly higher positive pricing errors and
absolute pricing errors, which is consistent with FTDs intensifying when securities are overpriced –
although we should not infer causality from this correlation. Similarly, higher OFR is associated with
higher and positive order imbalances and higher intraday volatility, but lower spreads. Our results also
indicate that FTDs are significantly more common for smaller firms, as average market capitalization for
firms in decile 1 (USD 9.2 billion) is almost six times larger than for firms in decile 10 (USD 1.6 billion).
As discussed in Section 2.2, FTD reporting is subject to a minimum threshold of 10,000 shares.
It is reasonable to conjecture that this reporting threshold is relatively more onerous for securities with
smaller market capitalization and, likely, a lower number of shares outstanding. That is not actually so.
The proportion of security-days with no reported FTDs is 97.6% in OFR-decile 1, and drops
monotonically across deciles to 48.0% for securities in decile 10; the daily average number of
outstanding FTDs for the days on which FTDs exceed the 10,000 shares reporting threshold ranges from
29,031 for securities in decile 1 to 357,238 for securities in decile 10. Since securities with smaller mean
market capitalization generally have higher mean OFR, they also have a relatively larger average
number of reported FTDs (in number of shares) on the days on which FTDs are reported, and a lower
13
proportion of days with no reported FTDs.
3.2.
Portfolio approach
As a first test of the relationship between FTD changes and subsequent market quality, on each
day t in our sample spanning January 2005 to June 2008, we group the 1,492 securities into nine
portfolios based on changes in OFR and ODR. We start by estimating the daily time-series standard
deviation in OFR by security. On each day, we include securities with a one-standard deviation or greater
decrease in OFR into a “FTD Decrease” portfolio and, similarly, securities with a one-standard deviation
or greater increase in OFR into a “FTD Increase” portfolio. We include all remaining securities into a
“FTD Constant” portfolio. In order to control for the extent of timely delivered short sales, we replicate
the same procedure on the basis of timely delivered short sales, proxied by changes in ODR, thus forming
the portfolios “Delivered Short Sales Decrease”, “Delivered Short Sales Constant”, and “Delivered Short
Sales Increase”. Finally, we intersect those groups of securities, forming nine final portfolios. For each
portfolio, we compute average changes in our metrics of price levels, intraday volatility, market liquidity,
pricing errors, absolute pricing errors, and order imbalances for the following day (t+1). All variables are
standardized and winsorized (at three standard deviations) by security. We compute next-day average
changes for the portfolios “FTD Decrease, Delivered Short Sales Constant” and “FTD Increase, Delivered
Short Sales Constant” and we further test for differences between these averages.
Our interest lies in changes in OFR. We form portfolios on changes in ODR to control for the
impact of estimated delivered short sales on liquidity and pricing efficiency. We present results for the
two key portfolios (the ones including low and high levels of FTD changes while experiencing normal
levels of delivered shorts), rather than for the full set of nine portfolios, primarily for the sake of brevity.
Our focus on the portfolios with high or low levels of FTD changes and “normal” levels of delivered
shorts, allows us to draw inferences about FTD changes under “normal” short selling conditions. Also,
the samples with abnormal levels of both FTDs and estimated delivered shorts vary greatly in size,
leading to comparisons of data samples of dramatically different sizes.
14
The results of this analysis are presented in Table III. For the portfolio “FTD Increase, Delivered
Short Sales Constant”, we find that, on the following day, there is a 4.2% reduction in absolute pricing
error, a 0.1% decrease in spreads, a 0.4% decrease in order imbalances, and a 0.67% decrease in intraday
volatility – all results being statistically significant at the 1% level, except for the result on order
imbalances, which is significant at 5%. We also find a decrease in price and pricing error, but estimates
are not statistically significant. For the portfolio “FTD Decrease, Delivered Short Sales Constant”, we
similarly observe a decrease in absolute pricing error, but the magnitude of the estimated effect is smaller
(0.18%). We further investigate the differences in next-day metrics between the two portfolios. The “FTD
Increase” portfolio, compared to the “FTD Decrease” portfolio, displays lower absolute pricing errors,
spreads, order imbalances, and intraday volatility, with all results being statistically significant at the 1%
level.
This initial analysis offers evidence that large FTD changes are followed by next day
improvements in market liquidity and pricing efficiency. Given the limitations of this univariate
framework, in the following section we employ OLS regressions to investigate the relationship between
FTD changes and subsequent market quality while controlling for timely delivered short sales and
relevant systematic factors.
3.3. Panel OLS regressions
We next estimate panel regressions to investigate the relationship between FTD changes and
next-day market quality metrics. Accordingly, we estimate six separate regressions, with changes in
pricing errors, absolute pricing errors, prices, intraday volatility, spreads, and order imbalances as
responses. Our main explanatory variable is the previous-day change in OFR. Given the regulatory focus
on reducing FTDs arising from short sales, and the well-documented impact of short sales on liquidity
and pricing efficiency, our empirical tests aim to control for the estimated impact of delivered short sales
on market quality. Accordingly, we also add the previous day change in ODR to the model. As further
controls, we include, in each regression, previous-day changes of the dependent variable, to account for
15
possible autocorrelations. In addition, to control for systematic effects, we include market averages of the
changes in the same quality metrics. Finally, when modeling changes in pricing errors, we add interaction
variables between previous-day changes in OFR and ODR and a binary variable identifying positive
pricing errors, to allow for an asymmetric impact of fails on pricing errors. All regressions contain
security fixed-effects. The models estimated are:
PE i ,t  0,i  1 OFRi ,t 1  2 ODRi ,t 1  3 OFRi ,t 1 * Positive _ PE _ Dumi ,t 1 
4 OSRi ,t 1 * Positive _ PE _ Dumi ,t 1  5 PE M ,t  6 PE i ,t 1   i ,t
PE _ Volatility i ,t   0,i   1 OFRi ,t 1   2 ODRi ,t 1   3 PE _ Volatility M ,t
  4 PE _ Volatility i ,t 1   i ,t
Volatility i ,t   0,i   1OFRi ,t 1   2 ODRi ,t 1   3 Volatility M ,t   4 Volatility i ,t 1   i ,t
(7)
(8)
(9)
Spread i ,t   0,i  1 OFRi ,t 1   2 ODRi ,t 1   3 Spread M ,t   4 Spread i ,t 1   i ,t
(10)
OIBi ,t   0,i   1 OFRi ,t 1   2 ODRi ,t 1   3 OIBM ,t   4 OIBi ,t 1   i ,t
(11)
Logmid i ,t   0,i  1 OFRi ,t 1   2 ODRi ,t 1   3 Logmid M ,t   4 Logmid i ,t 1   i ,t
(12)
We estimate the above parameters with OLS regressions using daily data and standard errors are
time-clustered. Variables definitions are included in Table I; the i and t subscripts index, respectively,
securities and days. The M subscript indicates a “market” equally weighted average computed over our
entire sample. Δ is used to identify daily changes (for example, ΔOFRt= OFRt - OFRt-1)
Results for the overall sample are presented in Table IV. As reported, an increase in OFR is
associated with a next-day decrease in absolute pricing errors, spreads, order imbalances, and intraday
volatility (all significant at 1%). We find no significant relationship between increases in FTDs and price
levels, nor with positive and negative pricing errors, when those are separately modeled.
This second set of results is highly consistent with our previous findings: an increase in FTDs is
related to improvements in liquidity and pricing efficiency. We recognize that the correlations
documented in this analysis are not proof of causation. Hence, we attempt to gain insights into the
direction of causality in our system by first testing for Granger causality. For each metric of interest, we
16
test both directions of Granger causality: that is, we test whether previous-day FTD changes “Grangercause” next-period market quality metrics. We first find that FTD changes Granger-cause absolute pricing
errors, spreads, order imbalances, and intraday volatility. Yet, when testing the other side of causality, we
find it equally meaningful, as each of those variables Granger-causes FTD changes as well. FTD changes
and market quality metrics Granger-cause each other – and the whole system displays feedback effects
over time. Hence, it is necessary for us to investigate the impact of FTD changes within a statistical model
that allows us to control for inter-temporal interdependency amongst all metrics. Accordingly, in the next
section, we present results from vector autoregressive (VAR) models, duly accounting for endogenous
interrelationships between market quality metrics, FTD changes, and timely delivered short sales.
3.4. Vector autoregressive framework
In a third set of tests, we control for endogenous interrelationships using three vector
autoregressive (VAR) models, with additional exogenous variable(s) added as controls. The system of
equations underlying each of these models is formally described in Table V. In VAR Model 1, the
variables included are changes in OFR, ODR, Pricing Error, Intraday Volatility, Spread, and Order
Imbalance. We add, as predictors in the pricing error equation, (1) an interaction between lagged changes
in OFR and a lagged binary variable set equal to one when pricing error is positive and (2) an interaction
between lagged changes in ODR and a lagged binary variable set equal to one when pricing error is
positive. Accordingly, we are able to separately estimate the impact of FTD changes and delivered short
sales on pricing error when the pricing error is positive in contrast to when the pricing error is negative.
We add two more predictors to each of the equations in which the change in OFR or ODR are the
response variables: (3) a lagged binary variable set equal to one when order imbalance is positive and
zero otherwise and (4) a lagged binary variable set equal to one when pricing error is positive and zero
otherwise. Finally, in each equation we add, as an exogenous variable, the market-wide equally-weighted
average of the dependent variable, to control for possible systematic effects. In VAR Model 2, we replace
Pricing Error by Absolute Pricing Error; given that we do not model pricing error here, we do not
17
include the interaction-variables described above in points (1) and (2). VAR Model 3 is similar to Model
2, but we replace Pricing Error by Price.
We estimate VAR Models 1, 2, and 3 separately for each security. The results we report in Table
V are obtained by first standardizing all variables by subtracting the security-specific mean and dividing
by the security-specific standard deviation, and then winsorizing at three standard deviations from the
mean. Based on an analysis of the Schwarz information criteria (SIC), we determine that, for all models,
it is most appropriate to use a VAR of order one. In order to draw inferences about the true population
parameters, we average coefficient estimates obtained for each security as in Fama and MacBeth (1973).
In significance testing, we use cross-sectional estimates of standard errors. For robustness, we also
estimate all three models without standardizing variables, but we face problems with the convergence of
our maximum likelihood estimation algorithm, likely driven by the extreme differences in magnitude
across our variables. For those securities for which we manage to obtain results without standardizing
variables, our results are qualitatively similar to those reported.
We estimate VAR Models 1, 2, and 3 for both our “entire market” sample and for a subset of the
sample containing only the 10% of securities with the highest level of FTDs based on mean OFR over the
sample period, January 2005 to June 2008 (the same sub-sample described as “decile 10” in Table II). We
focus on this subset of securities with the highest FTDs to find whether the impact of FTD changes differs
when they occur most frequently. We find that the sign and the significance of the various interrelationships involved are economically reasonable for both samples. For compactness, ease of
interpretation and to preserve the focus on the specific equations of interest to us, we report in Table V
only those relationships that are relevant to the issues addressed in the paper. In particular, we report, for
all three models and for both samples, the coefficient estimates related to the effects of FTD changes and
timely delivered short sales on each of the market quality metrics. We present estimated coefficients and
related statistical significance in Table V, Panels A and B.
First, and most importantly, irrespective of the measure used as proxy for pricing efficiency or
liquidity, increases in FTDs lead to higher liquidity and improve pricing efficiency. In particular:
18
1.
Increases in FTDs significantly reduce positive pricing errors, consistent with those traders acting
as value arbitrageurs when stocks are overpriced (statistically significant at 1%).
2.
Increases in FTDs significantly reduce absolute pricing errors, consistent with an increase in
pricing efficiency (statistically significant at 1%).
3.
Increases in FTDs significantly reduce intraday volatility, consistent with improved market
stability (significant at 1% in five models and at 5% in the sixth).
4.
Increases in FTDs significantly reduce order-imbalances, consistent with an improvement in
liquidity (significant at 1% for the overall sample, but not for the sample of securities with most
fails).
5.
Increases in FTDs reduce spreads and thus lower trading costs (significant at 1% in five models
and at 5% in the sixth).
6.
The impact of changes in FTDs on prices is not significant overall.
Second, we find that the direction and significance of all results relating to the impact of FTD
changes is qualitatively similar to the direction and significance of all results relating to the impact of
delivered short sales. The main differences lie in the fact that delivered short sales appear to have a
statistically significant impact on prices, while the results are not statistically significant for FTD changes.
Our main analysis does not include any measure of trading volume, as trading volume is highly
correlated with other market quality metrics. Nevertheless, for robustness, we add to the VAR models a
measure of trading volume based on the daily number of trades for the security of interest. The core
results describing the relationship between FTD changes and metrics of market liquidity and pricing
efficiency are unaffected, while we find that an increase in OFR is related to lower subsequent trading
volume. We also obtain similar results by utilizing a different metric of trading volume based on the
monetary value of shares traded daily. The results are not included in tables for brevity.
19
3.5.
FTD changes vs. timely delivered short sales
Overall, when comparing the impact of FTD changes with the impact of delivered short sales, the
direction and significance of the results are virtually identical, with the exception of the impact on stock
prices. That said, the coefficients measuring the impact on market quality in Table V, Panels A and B are,
in most cases, larger in magnitude for delivered short sales relative to FTD changes. This is arguably what
we should expect given that the vector autoregressive models we employ are based on standardized
variables, and the average standard deviation of delivered short sales is much greater than that of FTD
changes, as reported in Table II. Hence, a one standard deviation change in delivered short sales
predictably results in a much greater volume of trades relative to a one standard deviation change in FTDs
and should arguably have a greater impact on market quality. In this context, we next examine the
economic significance of the market-quality impact of an equal size (in terms of the number of shares
outstanding) of FTD changes and delivered short sales. The results are reported in Table V, Panels C and
D for the impact of FTD changes and delivered short sales respectively.
Based on the Model 1 estimates for the “entire market” sample, we find that an increase in FTDs
corresponding to 10 basis points of the total number of outstanding shares – approximately equal to a onestandard deviation increase in total short interest – leads to a 3.2% reduction in the magnitude of positive
pricing errors, a 3.2% reduction in absolute pricing errors; a 0.2% point decline in intraday volatility; a
1.7% reduction in spreads; and a 0.7% reduction in order imbalance. The impact on prices, aside from not
being statistically significant, is tiny, with a reduction of less than 0.01%. In comparison, again based on
the “entire market” sample, we find that delivered short sales corresponding to 10 basis points of the total
number of outstanding shares leads to about a 4.5% reduction in the magnitude of positive pricing error; a
6.8% reduction in absolute pricing error; a 0.6% decline in intraday volatility; a 0.6% reduction in
spreads; a 1.2% reduction in order imbalance. The impact on prices is again small, with a reduction of
approximately 0.01%. We test for the statistical significant of differences between the coefficients
20
estimated for OFR (Panel C) and ODR (Panel D) and find that those are, in all cases, not statistically
significant.10
Overall, the economic significance of the estimated impact of FTD changes and delivered short
sales is of roughly similar magnitude. Inferences based on the sample with the highest FTD changes are
weaker (the same quantum of FTD changes leads to smaller market-wide reactions). This suggests that a
further increase in FTDs has a weaker impact when existing levels of outstanding FTDs are higher. The
bottom-line is that the market-quality impact of FTD changes is economically significant and very similar
to that of timely delivered short sales. Both types of trades appear to have a positive effect on market
quality, first by enhancing pricing efficiency through correction of security overvaluation and reduction of
intraday volatility, and second by providing and improving liquidity through a reduction of orderimbalances and spreads.
3.6. Impulse-response functions
To further investigate the impact of FTD changes on pricing efficiency and liquidity, we compute
impulse response functions based on the vector autoregressive models of Table V. We estimate
accumulated impulse response function parameters for each security and then present cross-sectional
means of the parameter estimates. We construct confidence intervals using cross-sectional estimates of
standard errors. We present the results related to accumulated impulse response functions depicting the
impact of one-standard deviation increase in OFR on pricing error volatility, intraday volatility, spreads,
and order imbalances in Figure 1. We opt to utilize accumulated rather than orthogonalized impulse
response functions because, consistent with econometric literature in this regard, the latter are extremely
sensitive to the ordering of variables in the model, thus adding a level of arbitrariness to the estimation
procedure. For comparison, we present a similar set of impulse response functions for the impact of
10
We do not separately report all the estimated t-statistics related to the tests for significance because all tests
uniformly fail to reject the null hypothesis that the mean difference between estimated coefficients is zero.
21
delivered shorts in Figure 2. As the impulse response functions depict, the impact of FTD changes on
market quality metrics documented in Table V occur over the following day. On subsequent days,
accumulated responses are mostly flat, indicating no further correction or reversal. Given the very close
similarities in the estimated VAR coefficients, we only report impulse response functions related to the
VAR models with pricing error volatility, and omit the other models including pricing errors and prices.
We observe very similar patterns for changes in ODR, thus providing additional evidence that delivered
short sales have a similar impact on market quality.11
3.7. Robustness check: threshold-list securities
The impact of FTD changes could be different when failures are persistent or long-lived.
Accordingly, we separately focus on a sample of securities which displays persistent FTDs – securities
that appear on the NYSE Threshold List. In accordance to the SEC Regulation SHO, “threshold
securities” are securities for which the aggregate FTD position for five consecutive settlement days at a
registered clearing house totals 10,000 shares or more and equals at least 0.5% of the total number of
shares outstanding for the issuer. From our sample, we select all securities which appear on the NYSE
Threshold List for at least one day during the period spanning January 1, 2005 to June 30, 2008: we
identify 175 such securities. Accordingly, we re-estimate the VAR model for this subset of securities –
with the addition of a binary variable, equal to one for each day on which a security is included on the
threshold list, as a predictor in each equation. Results, reported in Table V, Panel E, are largely consistent
with what previously reported: coefficient estimates are of similar magnitude to those obtained with the
data subset containing the securities with the highest level of FTDs. While we do not report the
11
Given the different magnitude of the estimated coefficients, which reflect the scaling issues described in Section
3.5, the scale used in the vertical axes in the plots in Figure 1 and Figure 2 differ. Such unavoidable differences in
scaling render a visual comparison of the magnitude of the estimated responses and of the related confidence
intervals difficult: while the confidence intervals associated with OFR appear wider than those associated with
ODR, they are, in reality, narrower.
22
coefficients on the “threshold” binary variable in tables for brevity, we note that inclusion on the
threshold list is associated with higher spreads, higher intraday volatility, and higher prices.12 Overall,
these results are consistent with inclusion on the threshold list hampering liquidity (as, under regulation
SHO, shorting without pre-borrowing of securities on the threshold list is curtailed), while leading to
higher prices, perhaps due to the resulting buying pressure of traders forced to close their non-delivered
positions.
3.8. Robustness check: NASDAQ securities
As a further robustness test, we re-estimate the VAR model with a sample of securities with
NASDAQ as a primary exchange. We apply the same filters in creating the sample as we did for our
overall, NYSE-based, sample: we focus on securities with share codes 10 and 11 in CRSP, for which we
have at least 18 months of continuous trading data and with no significant changes in the number of
shares outstanding; we obtain a full sample of 2,983 securities. Results are presented in Table V, Panel F.
The total number of securities for which we are able to estimate the models presented in Table V, Panel F
ranges from 2,983 to 2,223. Estimation is not possible for some securities because of inadequate number
of positive pricing errors, or negative pricing errors, or order imbalances. In this data subset, similar to
our NYSE results, we find that increases in FTDs lead to a next-day decline in positive pricing errors and
absolute pricing errors, intraday volatility, and in spreads, but we also find an increase in prices. We also
find a decline in order imbalances, but results are statistically significant in only one of three models.
However, in this context, it is relevant to recognize data limitations, particularly liquidity metrics, for
NASDAQ securities.13 Most importantly in the context of this paper, while NYSE has played the
12
This test is based on a time-series analysis and, thus, should be interpreted as indicative of changes to market
quality affecting a specific security at threshold-list inclusion.
13
The fragmentation of trading across several different platforms and systems on NASDAQ has led in the past to
difficulty in observing and reacting to short-term changes in market variables. For example, quote adjustment has
23
dominant role in our sample period in the supply of liquidity for stocks with NYSE as their primary
exchange, this has not been so for stocks with NASDAQ as their primary exchange. For example,
Diether, Lee, and Werner (2009) document that, while NYSE accounted for almost 80% of shares sold
short in NYSE stocks, NASDAQ accounted for less than 35% of the shares sold short in NASDAQ
securities. Hence, our estimated order-imbalances can potentially be a noisy proxy of the overall orderimbalances of NASDAQ stocks.
3.9.
FTD changes: market makers vs. public traders
The SEC has regarded the use of FTDs by market-makers as bona fide and positive for market
liquidity. SEC Report "Key Points about Regulation SHO", April 11, 2005, updated 2008 says: “because
it may take a market maker considerable time to purchase or arrange to borrow the security, a market
maker engaged in bona fide market making, particularly in a fast-moving market, may need to sell the
security short without having arranged to borrow shares”. In a similar vein and context, SEC Report No.
450, March 18, 2009 states that the SEC “has repeatedly stressed the fact that the practice can provide
needed market liquidity in certain circumstances”.
It is therefore conceivable that the beneficial effects on market quality of FTDs arise due to such
market-making activities, and that there are no beneficial effects from FTDs of public traders. We define
the term “public trader” in this context to mean all market participants other than registered marketmakers. Notably, it is these public traders that have been the primary focus of negative media and
regulatory attention. If there are no beneficial effects of public-trader FTDs, the estimated FTD-related
improvement in market quality will be relatively stronger for securities that have a relatively greater
been documented to be slower (Jones and Lipson, 1999) and time stamps of trades and quotes on NASDAQ could
not always be matched (Schultz, 2000). More recently, Pastor and Stambaugh (2003) and Watanabe and Watanabe
(2008) do not use NASDAQ data in their pricing of liquidity studies apparently because of problems in using
NASDAQ-based liquidity measures.
24
proportion of market-maker FTDs. To gain insights into the impact of public-trader FTDs relative to the
impact of market-maker FTDs, we classify securities based on the proportion of FTDs originating from
market makers. In order to accomplish that, we employ an exogenous event – an SEC ban in September
2008 that affected only public-trader FTDs but not market-maker FTDs: SEC temporary rule 204T (later
made permanent).
SEC rule 204T required all market participants other than registered market makers to purchase
or borrow securities to close out their FTD position by the beginning of day t+4, effectively banning
FTDs for anyone other than a market maker. Hence, we compute average FTDs across our entire sample
of NYSE securities for two periods: pre-204T from January 1, 2005 to June 30, 2008; and post-204T from
January 1, 2009 to December 31, 2010. We intentionally omit the period July to October 2008 because of
multiple short selling rule changes, and omit November and December 2008 to allow outstanding FTD
positions to fully clear and thereby enable accurately gauging the impact of post-204T FTDs. Consistent
with a 2009 SEC report, we find a drop in average OFR of approximately 71% across all securities,
suggesting that, on average, about 29% of all FTDs were due to market-makers prior to September 2008.
For each sample security, we use the proportional change in mean OFR between the two subperiods as our proxy for FTDs by public traders. Our underlying assumption here is that the number of
market-maker FTDs is fairly constant over time.14 We accordingly rank securities on the basis of this
proportional decline and allocate securities to terciles. Table VI presents results for the two terciles
corresponding to “high proportion of estimated market maker trades” (i.e., securities with the lowest
decline in mean OFR) and “low proportion of estimated market maker trades” (i.e., securities with the
highest decline in mean OFR).
14
A brief example can be useful in clarifying our methodology: if, for a given security, average OFR in the pre-
204T period is 1% and OFR in the post-204T period is 0.25%, then we estimate that 75% of FTDs are due to public
traders and 25% are due to market makers.
25
For the “low proportion of estimated market maker trades” sub-sample, despite the sample size
being much smaller than the overall sample, all previously documented results remain strong and
statistically significant, with the exclusion of the coefficient estimates associated with order imbalance.
For the “high proportion of estimated market maker trades” subsample, we observe statistically
significant parameter estimates for the impact on spreads, but not for the other variables. Our overall
results indicate that, if anything, the impact of FTD changes is stronger for the subset of securities with a
relatively low involvement of market makers. Hence, at the very least, our results are inconsistent with
the hypothesis that the beneficial effects of FTD changes arise entirely from market-makers. Our intuition
is that, while market-maker trades contribute to an improvement in liquidity (and, hence, lead to lower
spreads), they do not lead to an improvement in pricing efficiency – which is consistent with market
makers not engaging in price arbitrage.
3.10.
The market quality impact of restrictions on FTDs.
As discussed in the introduction, FTDs can plausibly originate from both short and long sales. In
this sub-section, we use a natural experiment based on an exogenous regulatory change to focus on FTDs
most likely arising from short sales. In particular, we look at the imposition on July 15, 2008 by the SEC
of an Emergency Order selectively mandating pre-short-sale borrowing requirements and applicable only
to the stocks of a select group of 19 publicly traded financial institutions from July 21 to August 12, 2008.
The SEC order required that “no person may effect a short sale in these securities… unless such
person or its agent has borrowed or arranged to borrow the security or otherwise has the security
available to borrow in its inventory prior to effecting such short sale.” (SEC Release 58166, 2008). The
only regulatory change affecting these stocks during this period was this order mandating firm stockborrowing arrangements prior to executing short sales. Any FTDs arising from “long” sales should clearly
not be affected by this order. The overall effect of the SEC order in relation to FTDs should therefore be
driven by FTDs arising from short sales. We employ an event study methodology to investigate the
26
variation in FTDs and in market quality around this mandate requiring pre-short-sale stock borrowing
arrangements.
Data for 17 of the 19 securities (the “event sample”) affected by the order are available from
CRSP. We construct a matched control sample: for each of our affected 17 affected securities, we identify
the firm that is not affected by the order, but shares the same 4-digit SIC code and has the closest market
capitalization (least absolute deviation) as of January 1, 2008. Overall, the securities affected by the ban
have a higher mean and median market capitalization, but the differences are not statistically significant.
Then, we analyze the number of reported FTDs (duly scaled by the number of shares outstanding) and
relevant market quality variables for both event and control samples, over the following periods: 1) a preOrder period from January 1 to July 14, 2008 ending on the day prior to the announcement of the
Emergency order; 2) the Order period – July 21 to August 12, 2008 – for which the Emergency order was
in force; and 3) a post-Order period from August 13 to September 9, 2008 following the order and ending
before Lehman’s bankruptcy. We do not include the four trading days on July 15, 16, 17, and 18, 2008, in
the pre-Order period to avoid any potentially confounding effects arising from the announcement of the
order on July 15, 2008.
We report our results on FTDs in Table VII. Reported FTDs (as a proportion of shares
outstanding) for the 17 securities in our sample average 4.78 basis points (“bp”) during the pre-order
period. After the order, FTDs reduce rapidly to about 0.57 bp, or 12% of their pre-order average within
one week; to about 0.12 bp, or 2% of the pre-order average, within three weeks; and, on the last day of the
order period, reported FTDs are below the reporting threshold of 10,000 shares for each and every
affected security. In contrast, reported FTDs for control sample securities increase during the first week of
the ban, slightly decrease over the second week of the ban and show no significant change during the
third week of the ban. As soon as the temporary order period expires, reported FTDs of affected securities
again increase monotonically and significantly. The difference in reported FTDs between event and
control firms is positive and significant prior to the mandate period, negative and significant during the
mandate period, and again positive and significant after the mandate is lifted. Given that reported FTDs
27
cannot fall immediately to zero because of the time required for fails outstanding from prior to the SEC
order to clear (Boni, 2006), this natural experiment suggests that, at least for these particular securities
and around this specific period, a very large portion of FTDs originated from short sales.15
We report our results on market quality in Table VIII. To test the impact of the order on market
quality, we analyze Absolute Pricing Error, Return, Intraday Volatility, Spread, and Order Imbalance
over each of our three sub-periods. We average each of these six variables across securities to obtain a
daily mean for the affected and control samples. We compare differences in means between the orderperiod (July 21 to August 12, 2008) and the “pre and post order” (January 1 to July 14 and August 13 to
September 9) periods for both sample and control securities. Our results are presented in Table VIII.
Comparing securities during the benchmark “pre and post order” period, we note that “event sample”
securities display larger pricing errors, lower returns, higher intraday volatility and lower spreads than
“control sample” securities. While these results are indicative of the difficulty of obtaining perfect
matches, we mitigate the impact of these differences by employing a “difference-in-difference”
methodology: we compute the difference between the “order” and the “pre and post order” periods for
both “event sample” and “control sample” securities and then compute the difference between those
differences. We find that, while both samples display higher absolute pricing errors, intraday volatility,
and spreads during the “order” period, the increase for the “event sample” securities is larger and the
“difference-in-difference” tests are all statistically significant – at the 1% level for absolute pricing errors
and for intraday volatility and at the 10% level for spreads. The impact of the SEC order on returns and
order imbalances is not statistically significant. In robustness tests (that are not reported for brevity), we
replicate a similar analysis excluding the period subsequent to the order from the benchmark, and obtain
virtually identical results.
15
For our larger NYSE sample, we also find that new FTDs on day t+3 are significantly (p-value<<0.01) and
positively related only to the daily trading volume arising from short sales on day t, and not the daily trading volume
arising from “long” sales on day t.
28
Boulton and Braga-Alves (2010) also document a negative impact of the July 2008 Emergency
order on liquidity, i.e., higher bid-ask spreads and lower trading volume relative to a matched sample of
financial firms. However, an SEC Office of Economic Analysis (“OEA”) memorandum dated January 14,
2009 titled “Analysis of the July Emergency Order Requiring a Pre-Borrow on Short Sales” examines
selected market quality variables around the July 2008 Emergency order, but is unable to conclude
statistically significant differences between their “event” and “control” samples for any of the market
quality variables they examine. There can be several reasons for the difference in our conclusions. First,
except for returns (for which our conclusions are the same), the OEA do not examine the variables that
we analyze all through this paper, or their variable is defined in a materially different way: 1) they do not
examine absolute pricing errors and order imbalances; 2) as against our intraday volatility measure
(computed daily over 5-minute intervals), they examine daily close-to-close or open-to-close volatility
(over several weeks); and 3) as against our relative spreads (i.e., dollar spreads scaled by price), they
examine dollar spread (which also means that their averages implicitly give higher weight to higher
priced securities.) Second, while we use a control sample of financial firms that are as closely matched to
the affected securities as possible, the OEA uses two control samples – a sample of all financial firms and
a sample of all non-financial firms – none of which are specifically matched with the affected securities.
Third, the OEA uses a benchmark period prior to the Order that is constructed by randomly selecting only
20 trading days over the previous nine months – the small number of days and the randomness may
arguably increase the standard errors of their estimates, besides making it impossible for us to replicate
their results or more fully explain any differences. The longer benchmark period we utilize, our closelymatched construction of the control sample, and the higher frequency of some of our variables, are all
reasons why our tests are likely to have greater power, and hence potentially accounts for the fact that we
detect significance in tests in which the OEA may not.
Overall, our results indicate that mandating stock-borrowing arrangements prior to executing a
short sale leads to a sharp drop in overall FTDs to almost zero (as it would if FTDs arose largely from
short sales over the sample-period), but at the same time, there is also a significant adverse impact on the
29
stock’s liquidity and its price discovery process. Banning FTDs should also arguably lead to an upward
pressure on stock-lending rates as short sellers scramble to make stock borrowing arrangements at short
notice, and thereby also concomitantly increase costs for all short sellers. Kolasinsky, Reed and Thornock
(2013) and the OEA memo cited above document that this is indeed the case with rebate rates for orderaffected securities becoming negative on the first day of order-validity and remaining negative for several
days thereafter. While our results clearly show that restricting FTDs reduces market quality, this could
result directly from the absence of FTDs, or because informed short selling decreases due to
consequential increase in stock-lending rates, or both. In this context, we examine short interest of our
event and control sample securities over our pre-Order period and Order-period, and find, consistent with
similar findings of the OEA memo cited above, that the short interest of event sample securities over the
Order-period is not significantly different from the short interest over the pre-Order period: the mean
short interest for event firms reported on July 15 is 5.07% (of shares outstanding) and, by the end of the
order period, on August 15, it is 5.45%; the slight increase is not statistically significant and neither it is if
we measure it relative to the control sample. Given that FTDs arising from short sales decrease sharply
during the ban while the short interest does not change significantly, we conjecture that the adverse
market quality impact is likely to be related at least partially to the absence of failing-to-deliver short
sales. Irrespective, our results show that restricting FTDs reduces market quality.
That said, our results in this sub-section should be interpreted or generalized with caution. First,
this Emergency Order affected only a few securities, all from one industry, and during a fairly unique
period of time. Second, while Kolasinsky, Reed and Thornock (2013) note that it is sensible to analyze
the impact of a short selling regulation during a crisis, as that is exactly when short selling regulation is
most likely to be operational, the OEA memo cited above suggested a “Hawthorne effect”, whereby
“firms could have been on their best behavior during the time of the Emergency Order because of the
likelihood of intense scrutiny by regulators of failed positions.”
30
4.
Empirical results: FTDs and the 2008 Financial Crisis
In the wake of the 2008 financial crisis, it has been widely alleged that short sellers have, by
failing to deliver, caused or accelerated sharp declines in stock prices, particularly of financial firms, in
order to profit from eventual collapse of the financial institutions involved. For example, in relation to
Bear Stearns, a former Under-Secretary of Commerce, has been quoted as saying that “… the pace of the
collapse of the stock price was clearly accelerated by the enormous naked short sale activity”
(Euromoney, December 2008). Similarly, Richard Fuld, former CEO of Lehman Brothers, in his October
2008 testimony before the US House of Representatives Committee on Oversight and Reform, stated that
“naked short selling […] dealt a critical, if not fatal, blow to Bear Stearns” and “contributed significantly”
to the collapse of Lehman Brothers. In this context, we examine whether significant increases in FTDs
preceded (and hence potentially triggered) the price crashes associated with the four major casualties of
the 2008 financial crisis, i.e., Bear Stearns, Lehman, AIG and Merrill, or did significant increases in FTDs
take place after these price crashes and in response to negative public news.
The first large financial casualty of the 2008 financial crisis was Bear Stearns, the fifth largest
investment banking firm in the nation at the time of its demise. We analyze OFR on the days preceding
and immediately following the dramatic loss of market value that led to the demise of the firm. Figure 3
provides a time-line about the crisis. Outstanding suspicions about liquidity problems at Bear Stearns
were reported in the media from March 10 onwards, along with news that the company’s management
was repeatedly denying rumors about such problems. The first major price-crash took place on Friday,
March 14, when the price per share dropped from $57 to $30 after a 9 a.m. announcement that Bear
Stearns would receive an unprecedented loan from the Federal Reserve System; and two days later, on
Sunday March 16, JP Morgan Chase proposed buying Bear Stearns for $2 per share (Wall Street Journal,
March 15, 2008; J.P. Morgan News Release, March 16, 2008). When markets opened on March 17, a
second major price crash materialized, and the price dropped to a close of $4.81. We compute OFR for
Bear Stearns on each trading day from January 1 to March 28, 2008. We also compute, as a control
variable, an equal weighted average OFR for four other financial institutions – Raymond James Financial
31
Corporation, Ameritrade Holdings Corporation, Ameriprise Financial Inc. and Charles Schwab
Corporation – with the same primary SIC code as Bear Stearns, and with the closest market value as of
the end of the fiscal year 2007. We test for the statistical significance each day of the difference, i.e. the
“abnormal” OFR of Bear Stearns. To construct a t-statistic for the difference in means, we compute the
standard error of this difference over the period January 1 to February 15, 2008. Results are presented in
Table IX, Panel A.
Even though negative media attention started on March 10, Table IX, Panel A and Figure 3 show
that, while OFR for Bear Stearns was greater than for the benchmark securities, its small magnitude
(below 0.1%) indicates that fails were unlikely to have a significant economic impact up to March 11.
While OFR did increase significantly on March 12 and 13, the increase was still relatively tiny from an
economic perspective relative to the total number of shares outstanding, to the typical overall short
volume, and to what took place on or after March 14: OFR was only 0.32% of shares outstanding until
market close on March 13. OFR increased to 0.90% on March 14, but increased massively only on March
17, reaching 5.84%. Importantly, given that the Fed announcement was at the start of trading on March
14, even the (relatively small) increase in OFR on March 14 was clearly subsequent to the public release
of tangibly negative news in the form of the announcement and the consequent immediate precipitous
price-drop. By the time OFR spiked on March 17, the company was already in an open distress sale. The
evidence clearly shows that the abnormal incidence of increases in FTDs did not precede the price decline
but followed it; and the decline in stock price was triggered by other well-identified negative economic
news. Consistent with our previous results, short sellers appear to be facilitating price discovery, rather
than increasing pricing errors.
The second notable casualty of the financial crisis of 2008 was Lehman. In Figure 4A we present
the relationship between OFR and stock price for the period from January 2008 to Lehman’s bankruptcy
on September 15, 2008. We present a closer look at the period surrounding Lehman’s bankruptcy in
Figure 4B. It is clear that OFR remained minuscule in magnitude all through till September 10; and till
September 9, the firm’s stock price had already lost approximately 87% of its value as of the beginning of
32
the year. There were some “spikes” in OFR over the period, but these were too small to be economically
relevant – for example, OFR increases on June 27 just prior to an 11% drop in share price on the next
trading day of June 30, but this “spike” is just 0.06%, and ostensibly linked, according to an article in
Bloomberg (March 19, 2009), to a rumor about Barclays PLC buying Lehman for a 25% discount to
market value. The biggest single-day price drop – about 45% – occurred on September 9, again following
news that talks with the Korea Development Bank (previously rumored to be considering a 25% stake in
Lehman) had failed. The OFR on the days immediately surrounding the dramatic price fall on September
9, 2008, is presented in Table IX, Panel B. The table indicates very low OFR – below 0.01% – in the days
leading to September 9. While OFR increases on September 9, it still remains less than 0.09% of shares
outstanding. Abnormal OFR increased more dramatically only after September 10, well after widespread
coverage of negative news about Lehman and the associated price crash. On September 11, as
shareholders rejected a management rescue plan, the stock price fell by an additional 42% and OFR
further increased to 1.63%. Over the following days, talks of a possible acquisition by Bank of America
and Barclays failed, triggering further declines in stock price and an increase in OFR to 2.37%. Lehman
announced its bankruptcy on September 15, and OFR increased beyond 3.6% on September 17. In sum,
our analysis shows that the incidence of increases in FTDs occurred only after the large price drops on
and after September 9, not before.
We report the relationship between OFR and the stock price for Merrill and AIG in Figure 5 and
Figure 6 respectively. In both cases, the stock price declines were fairly gradual through the year and not
accompanied by any significant increase in FTDs. For Merrill, OFR reached its highest value of only
0.09% on October 10, 2008, well after the Merrill had lost most of its value. AIG had also lost about 40%
of its market value by the end of August 2008, and the largest single-day price drop was on September 15,
2008 when S&P cut AIG’s credit rating. Following the announcement, the company’s stock price
dropped by about 60% and, on the following day, OFR climbed to its highest value up to that point, at
0.13%; OFR reached its highest value only a fortnight later on September 29, 2008, and even this highest
33
value was only 0.14%. Given that OFR remained so low all through the financial crisis period for both
firms, we do not engage in any further statistical testing.
5.
Conclusions
Recent regulatory action has focused on eliminating settlement day delivery failures in equity
markets, particularly delivery failures arising from short sales, even though the alternative to fail has been
shown to be valuable and important for pricing and liquidity (Evans, et al., 2009; Merrick, et al., 2005);
and notwithstanding the extensive evidence on the beneficial effect of short sales on market quality
(Diamond and Verrecchia, 1987; Abreu and Brunnermeier, 2002 and 2003; Miller, 1977; Bris et. al. 2007;
Diether et al., 2009; Boehmer et al., 2008). In this context, we investigate the aggregate impact on pricing
efficiency and liquidity of changes in FTDs, i.e., the market quality impact of the set of trades over the
day that collectively affect the open interest of undelivered positions.
For samples of both NYSE and (in robustness checks) NASDAQ securities, we find that
increases in FTDs lead to a reduction in pricing errors, intraday volatility, spreads, and order imbalances.
Further, consistent with our expectation that the effect on market quality of a short sale will not depend on
whether or not the short sale finally results in timely delivery at settlement, we also find that the positive
impact of FTD changes on pricing efficiency and liquidity is similar to the beneficial impact of our
estimate of delivered short sales.
We then focus specifically on FTDs most likely arising from short sales by examining the effect
of a July 2008 temporary SEC order restricting FTDs by mandating pre-short-sale stock-borrowing
arrangements in select financial securities. We find that, while the SEC order banning FTDs arising from
(naked) short sales did lead (as expected) to a drastic reduction in FTDs, it also led to a significant
increase in absolute pricing errors, relative bid-ask spreads, and intraday volatility. These findings are
consistent with other studies documenting a negative impact on market quality associated with regulatory
34
restrictions on short sales in general – for example, Battalio and Schultz (2011), Boehmer, et al. (2013),
Autore, et al. (2011), and Beber and Pagano (2011).
In the context of the widespread allegations that FTDs arising from (naked) short sales
contributed to the collapse of major financial firms, we find that large abnormal increases in FTDs took
place after and not before their major stock price declines and associated negative news; and hence FTDs
were responding to information about the firms, rather than triggering the observed price declines.
Overall, our results indicate that, contrary to media and regulatory perceptions about naked short selling,
FTDs did not precipitate the collapse of major financial firms in 2008.
Our findings have important implications for regulatory policy. While we do not advocate
tolerance for FTDs tied to manipulative episodes, we find no evidence indicating that FTDs, in aggregate,
systematically and manipulatively precipitated price declines, even in the extreme situation of the 2008
financial crisis. Instead, the gently regulated FTD regime that existed after Regulation SHO up to mid2008 was net beneficial for pricing efficiency and market liquidity. In this context, the removal of the
ability to fail for the vast majority of market participants is very questionable, since the ability to fail
arguably reduces stock borrowing costs at the time when such costs are the highest, and thereby protects
traders from the lack of liquidity sometimes seen in the less regulated stock borrowing market. This
ability to fail is valuable for markets also because it can prevent distortions in the stock borrowing and
lending market leading to serious pricing and liquidity distortions in the mainstream stock market.
Regulators could alternatively consider progressive fines for settlement delays rather than a blanket
removal of the alternative to fail. Importantly, regulation should focus on how best to generate liquidity
and transparency in the stock borrowing market.
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37
Table I - Variable Definitions
Table I lists the variables used in the analysis and provides definitions. All variables are daily, unless otherwise
specified.
FTDs and Short Selling
Outstanding Fails-to-Deliver Ratio
(OFR)
Outstanding Delivered Shorts Ratio
(ODR)
For each day t, ratio of the number of outstanding fails to
deliver reported on day t+3, over total shares outstanding on
day t.
Ratio of the estimated number of outstanding delivered shorted
shares over total shares outstanding.
Pricing Error
Pricing Error (PE)
Negative Pricing Error (Negative PE)
Positive Pricing Error (Positive PE)
Absolute Pricing Error (Abs PE)
Positive PE Dum
The non-random walk component of a daily return series
estimated using a Kalman filter methodology.
A variable set equal to the pricing error when pricing error is
negative, to zero otherwise.
A variable set equal to the pricing error when pricing error is
positive, to zero otherwise.
The absolute value of the pricing error.
A binary variable set equal to one if pricing error is positive, to
zero otherwise.
Liquidity
Order Imbalance (OIB)
Positive OIB Dum
Spread
Volume
The daily sum of the 5-minute difference between the market
value of shares traded in buyer initiated trades and the market
value of shares traded in seller initiated trades, divided by total
daily dollar trading volume.
A binary variable set equal to 1 if OIB is positive and to zero
otherwise.
The daily average of the ratio of the difference between bid and
ask and the mid-quote.
Daily number of shares traded.
Other
Price
The natural log of the daily average of the 5-minute midquote.
Return
The daily stock price return.
Intraday Volatility
The daily average of standard deviation of the 5-minute stock
price return.
The number of shares outstanding multiplied by the closing
price for the day.
Market Value
38
Table II - Summary Statistics
All variables are as defined in Table I. The Outstanding Fails-to-Deliver Ratio (OFR) is computed for all NYSE common stock of US-based firms (CRSP share codes 10 and
11) listed for at least 18 months over the interval January 1, 2005 to June 30, 2008, and with no large daily change (>10%) in the number of shares outstanding and for which
all required data is available (n= 1,492). Securities are ranked by mean OFR and allocated to decile 1 (lowest) through 10 (highest). Daily statistics are computed by security,
security averages are further averaged over deciles and for the entire sample. This table reports mean, median and standard deviation for the sample, means for deciles 1 and
10 and the difference between those, along with results of a t-test for differences in means across deciles 1 and 10. “*”, “**”, and “***” indicate significance at the 10%, 5%
and 1% level respectively.
Outstanding Fails-to-Deliver Ratio
Outstanding Delivered Shorts Ratio
Pricing Error
Positive Pricing Error
Abs Pricing Error
Price (Log)
Intraday Volatility
Return
Spread
Order Imbalance
Market Value (US$ M)
Obs
Mean
0.04%
5.46%
-0.15%
0.51%
1.18%
3.3001
0.21%
0.07%
0.18%
6.72%
$8,223.33
1,492
Sample
Median
<0.01
4.34%
<0.01%
0.10%
0.21%
3.4171
0.20%
0.06%
0.11%
6.92%
$2,087.97
1,492
Std
0.18%
5.32%
4.33%
1.47%
4.96%
0.7631
0.08%
0.11%
0.27%
5.71%
$24,212.97
1,492
OFR Decile Means
OFR D1
OFR D10
<0.01
0.29%
4.08%
13.35%
<0.01%
-0.55%
0.37%
1.06%
0.74%
2.66%
3.1484
2.9121
0.21%
0.28%
0.05%
0.03%
0.39%
0.26%
4.00%
8.26%
$9,128.81
$1,598.89
149
150
Difference
OFR D10-D1 p-value
0.29%
<0.01
9.27%
<0.01
-0.55%
0.35
0.68%
<0.01
1.92%
<0.01
-0.2363
0.03
0.08%
<0.01
-0.02%
0.26
-0.13%
<0.01
4.26%
<0.01
-$7,529.91
<0.01
149
***
***
***
***
**
***
***
***
***
39
Table III – FTDs and Market Quality, Portfolio Approach
All variables are as defined in Table I. All variables are standardized and winsorized by security. The sample includes all NYSE common stock of US-based firms (CRSP
share codes 10 and 11), listed in the CRSP and TAQ databases for at least 18 months over the interval January 1, 2005 to June 30, 2008, and with no large changes (>10%) in
the number of shares outstanding. The resulting sample includes 1,492 securities. On each day t between January 2005 and June 2008, securities with a one-standard
deviation or greater decrease in OFR are allocated to a “FTD Decrease” portfolio and, similarly, securities with a one-standard deviation or greater increase in OFR to a
“FTD Increase” portfolio. All remaining securities are allocated to a “FTD Constant” portfolio. The same procedure is repeated on the basis of the intensity of delivered short
selling, proxied by changes in ODR, thus forming the portfolios “Delivered Short Sales Increase”, “Delivered Short Decrease”, and “Delivered Short Sales Constant’. Those
portfolios are intersected, forming nine final portfolios. Averages of next-day (t+1) changes in returns, return volatility, market liquidity, pricing errors and order imbalances
are computed. The table presents results for the “FTD Increase, Delivered Short Sales Constant” and the “FTD Decrease, Delivered Short Sales Constant” portfolios, along
with results of a test for differences between them. p-values are from two-sided t-tests. “*”, “**”, and “***” indicate significance at the 10%, 5% and 1% level respectively.
FTD Increase,
Delivered Short
Sales Constant
∆Price(t+1)
∆PE(t+1)
∆Abs PE(t+1)
∆Spread(t+1)
∆OIB(t+1)
∆Intraday Volatility(t+1)
N (days)
2.31%
-0.28%
-4.20%
-0.10%
-0.40%
-0.67%
844
p-value
0.31
0.41
<0.01
<0.01
0.01
<0.01
***
***
**
***
FTD Decrease,
Delivered Short
Sales Constant
-0.15%
-0.04%
-0.18%
<0.01%
-0.09%
-0.01%
849
p-value
Difference
0.36
0.36
<0.01 ***
0.22
0.12
0.14
2.46%
-0.24%
-4.02%
-0.10%
-0.31%
-0.66%
844
p-value
0.75
0.77
<0.01
<0.01
<0.01
<0.01
***
***
***
***
40
Table IV – FTDs and Market Quality, OLS Regressions
Coefficient estimates and p-values (in italics) from panel regressions with firm fixed effects and time-clustered standard errors. Metrics of market quality (in column
headings) are regressed on lagged values of the predictors (listed in the first column). All variables are standardized and winsorized by security, and defined as in Table I. The
sample includes all NYSE common stocks of US-based firms (CRSP share codes 10 and 11), listed in the CRSP and TAQ databases for at least 18 months over the interval
January 1, 2005 to June 30, 2008, and with no large changes (>10%) in the number of shares outstanding. The resulting sample includes 1,492 securities and 1,001,656 firmdays. The “Market” variable on day t is obtained by averaging the related variable across all securities on day t. Δ is used to identify changes (for example, ΔOFRt= OFRt OFRt-1). “*”, “**”, and “***” indicate significance at 10%, 5% and 1% level respectively.
∆OFR(t-1)
∆ODR(t-1)
∆Pricing Error (t-1)
∆OFR(t-1)*Positive PE(t-1)
∆ODR(t-1)*Positive PE(t-1)
∆Pricing Error(t)
∆Abs PE(t)
∆Price(t)
0.0019
0.4127
0.1932
<0.01 ***
-0.3489
<0.01 ***
-0.0048
0.1375
-0.4240
<0.01 ***
-0.0069
<0.01 ***
-0.2733
<0.01 ***
<0.0001
0.9718
-0.0042
0.03 **
∆Abs PE(t-1)
∆Intraday
Volatility(t)
-0.0068
<0.01 ***
-0.0721
<0.01 ***
∆Spread(t)
∆OIB(t)
-0.0125
<0.01 ***
-0.1008
<0.01 ***
-0.0093
<0.01 ***
-0.2599
<0.01 ***
-0.3763
<0.01 ***
∆Price(t-1)
-0.0255
<0.01 ***
∆Intraday Volatility(t-1)
-0.1937
<0.01 ***
∆Spread(t-1)
-0.3214
<0.01 ***
∆OIB(t-1)
∆ Market Pricing Error(t)
∆ Market Abs PE(t)
∆ Market Price(t-1)
∆ Market Intraday Volatility(t)
∆ Market Spread(t)
∆ Market OIB(t)
-0.4480
<0.01 ***
0.8559
<0.01 ***
0.8363
<0.01 ***
0.9971
<0.01 ***
0.9150
<0.01 ***
0.8751
<0.01 ***
0.8016
<0.01 ***
41
Table V - FTDs and Market Quality, VAR Analysis
Results for the estimation of three vector autoregressive models of order one used to investigate the impact of
changes in OFR and ODR: VAR with Pricing Error (Model 1), VAR with Pricing Error Volatility (Model 2), and
VAR with Price (Model 3). All variables are defined in Table I and are standardized and winsorized by security.
The “entire market” sample includes all common stock of US-based firms (CRSP share codes 10 and 11) with
NYSE as the primary exchange, listed in the CRSP and TAQ databases for at least 18 months over the interval
January 1, 2005 to June 30, 2008, and with no large changes (>10%) in the number of shares outstanding. For the
“most FTDs” sample, securities from the sample described above are ranked by mean OFR and allocated on that
basis to decile 1 (lowest) through 10 (highest); the securities included in decile 10 constitute the “most FTDs”
sample. The VAR models are defined below; the subscripts M and t indicate, respectively, the market-wide average
of the variable of interest and day t; Δ is used to identify changes (for example, ΔOFRt= OFRt - OFRt-1)
M odel1 : ΔY1t  c1  β1ΔY1t 1  M1t  S 1t  S 2t  ε1t
ε1t ~ i.i.d. N (0, Ω)
M odel 2 : ΔY2t  c2  β2ΔY2 t 1  M2 t  S 1t  ε2t
ε 2t ~ i.i.d. N (0, Ω)
M odel 3 : ΔY3 t  c3  β3ΔY3 t 1  M3 t  S 1t  ε3t
ε3t ~ i.i.d. N (0, Ω)
 OFRt



 ODRt

 PE

t

Y1 t  
Volatility t 


 Spreadt 
 OIB

t


ψ1  OFRM ,t



 2  ODRM ,t

 3  PE

M ,t

M1t  
 4  Volatility M,t 


 5  Spread M,t 
 6  OIB

M,t


 OFRt



 ODRt

 Abs PE 
t 
Y2 t  
Volatility t 


 Spreadt 
 OIB

t


ψ7  OFRM ,t



ψ8  ODRM ,t

 9  Abs PE

M ,t

M2 t  
 10  Volatility M,t 


 11  Spread M,t 
 12  OIB

M,t


 OFRt



 ODRt

 Price

t

Y3 t  
Volatility t 


 Spreadt 
 OIB

t


ψ13  OFRM ,t



 14  ODRM ,t

 15  Price

M ,t

M3 t  
 16  Volatility M,t 


ψ17  Spread M,t 
ψ18  OIB

M,t


 1  Positive OIB Dumt-1   2  Positive PE Dumt-1 
 3  Positive OIB Dum   4  Positive PE Dum 
t-1
t-1 

0

S 1t  

0

0



0

0

0



 5  ( Positive PE Dumt -1  OFRt 1 )   6  ( Positive PE Dumt -1  ODRt 1 )
S 2t  

0

0



0

X t  X t - X t -1
42
Table V Panels A and B are extracts of estimates of the parameters in Models 1, 2 and 3 above and report results pertaining to the impact of, respectively,
OFR and ODR. Reported parameter estimates are averages of parameters estimated by security. The p-values from two-sided t-tests are in italics below the
parameter estimate. “*”, “**”, and “***” indicate significance at the 10%, 5% and 1% level respectively.
Panel A - Impact of FTDs
Δ PE
A: Overall
1,407 Securities
B: Most FTDs
150 Securities
A: Overall
1,407 Securities
B: Most FTDs
150 Securities
A: Overall
1,407 Securities
B: Most FTDs
150 Securities
0.0045
0.20
0.0451
<0.01 ***
Δ PE
(incremental effect
when lag PE > 0)
-0.0168
<0.01 ***
-0.0785
<0.01 ***
Δ Abs PE
Δ Price
-0.0077
<0.01 ***
-0.0361
<0.01 ***
0.0002
0.70
<0.0001
0.99
Δ Intraday
Volatility
Δ Spread
Δ OIB
-0.0054
<0.01 ***
-0.0121
0.11
-0.0071
<0.01 ***
-0.0189
0.01 **
-0.0049
0.02 **
-0.0133
0.08 *
-0.0126
<0.01 ***
-0.0204
<0.01 ***
-0.0095
<0.01 ***
-0.0168
<0.01 ***
-0.0103
<0.01 ***
-0.0192
0.05 **
-0.0093
<0.01 ***
-0.0130
0.31
-0.0071
0.04 **
-0.0115
0.37
-0.0068
0.05 **
-0.0140
0.28
Δ Intraday
Volatility
Δ Spread
Δ OIB
-0.9128
<0.01 ***
-0.9759
<0.01 ***
-0.9594
<0.01 ***
-1.0141
<0.01 ***
-0.9126
<0.01 ***
-0.9872
<0.01 ***
-0.2267
<0.01 ***
-0.0690
0.06 *
-0.2104
0.09 *
-0.0615
0.09 *
-0.2106
<0.01 ***
-0.0762
0.04 **
-0.7665
<0.01 ***
-0.6021
<0.01 ***
-0.7629
<0.01 ***
-0.6035
<0.01 ***
-0.7628
<0.01 ***
-0.6079
0.01 **
Panel B - Impact of Delivered Short Selling
Δ PE
A: Overall
1,407 Securities
B: Most FTDs
150 Securities
A: Overall
1,407 Securities
B: Most FTDs
150 Securities
A: Overall
1,407 Securities
B: Most FTDs
150 Securities
0.5414
<0.01 ***
0.8416
<0.01 ***
Δ PE
(incremental effect
when lag PE > 0)
-1.3759
<0.01 ***
-1.4300
<0.01 ***
Δ Abs PE
Δ Price
-0.8516
<0.01 ***
-0.7913
<0.01 ***
-0.0221
<0.01 ***
-0.0196
0.04 **
43
Table V Panels C and D present the effect on the market quality metrics included in Models 1, 2 and 3 of an increase in Outstanding FTD Ratio (OFR)
and Outstanding Delivered Shorts Ratio (ODR) equivalent to 10 basis points of the number of outstanding shares. The panels report the impact on the
response variable as a proportion of the mean of the response variable. Percentages presented in bold are significant at 10% or lower.
Panel C: Impact of a Change in Outstanding FTD Ratio (OFR) equal to 10 Basis Points of the number of outstanding shares
Response Variable
Positive PE
Abs PE
Price
Intraday Volatility
Spread
OIB
Model 1
(PE)
Overall Sample
Model 2
(Abs PE)
Model 3
(Price)
-3.24%
Model 1
(PE)
Model 3
(Price)
-2.59%
-3.00%
-0.18%
-1.68%
-0.73%
Most FTDs Sample
Model 2
(Abs PE)
-0.24%
-1.27%
-0.53%
-3.84%
<0.01%
-0.17%
-1.77%
-0.55%
-0.12%
-0.70%
-0.35%
-0.18%
-0.58%
-0.31%
<0.01%
-0.13%
-0.66%
-0.38%
Panel D: Impact of a Change in Outstanding Delivered Shorts Ratio (ODR) equal to 10 Basis Points of the number of outstanding shares
Response Variable
Positive PE
Abs PE
Price
Intraday Volatility
Spread
OIB
Model 1
(PE)
Overall sample
Model 2
(Abs PE)
Model 3
(Price)
-4.52%
Model 1
(PE)
Model 3
(Price)
-2.39%
-6.78%
-0.63%
-0.62%
-1.23%
Most FTDs Sample
Model 2
(Abs PE)
-0.66%
-0.58%
-1.22%
-3.49%
-0.01%
-0.63%
-0.58%
-1.22%
-0.49%
-0.09%
-0.96%
-0.51%
-0.08%
-0.96%
-0.01%
-0.50%
-0.10%
-0.97%
44
Table V Panels E and F are extracts of estimates of the parameters in Models 1, 2 and 3 above and report results pertaining to the impact of OFR. Panel E
presents results from a subset of the “entire market” dataset discussed in panels A-D; the sample includes all common stock of US-based firms (CRSP share
codes 10 and 11) with NYSE listed as the primary exchange, listed in the CRSP and TAQ databases for at least 18 months over the interval January 1, 2005
to June 30, 2008, with no large changes (>10%) in the number of shares outstanding and that appear, for at least one day, on the NYSE-published list of
Threshold Securities. Panel F presents results from a dataset including NASDAQ securities: all common stock of US-based firms (CRSP share codes 10
and 11) with NASDAQ listed as the primary exchange, available in the CRSP and TAQ databases, listed for at least 18 months over the interval January 1,
2005 to June 30, 2008, and with no large changes (>10%) in the number of shares outstanding. Reported parameter estimates are averages of parameters
estimated by security. Significance is tested employing a cross-sectional estimate of the standard error of the parameter estimate. The p-values from twosided t-tests are in italics below the parameter estimate. “*”, “**”, and “***” indicate significance at the 10%, 5% and 1% level respectively.
Panel E - Impact of FTDs, Threshold Securities
Δ PE
163 Securities
Δ PE
(incremental effect
when lag PE > 0)
Δ Abs PE
Δ Price
Δ Intraday
Volatility
Δ Spread
Δ OIB
0.0409
-0.0857
-0.0176
-0.0158
-0.0142
<0.01 ***
<0.01 ***
0.02 **
0.01 **
0.23
-0.0268
-0.0223
-0.0137
-0.0150
0.02 **
<0.01 ***
0.02 **
0.25
175 Securities
175 Securities
-0.0024
-0.0171
-0.0146
-0.0178
0.24
0.02 **
<0.01 ***
0.17
Δ Price
Δ Intraday
Volatility
Δ Spread
Δ OIB
Panel F - Impact of FTDs, NASDAQ Sample
Δ PE
2223 Securities
2983 Securities
2983 Securities
Δ PE
(incremental effect
when lag PE > 0)
Δ Abs PE
0.0069
-0.0162
-0.0053
-0.0048
-0.0054
0.10
<0.01 ***
0.02 **
0.07 *
0.04 **
-0.0135
-0.0059
-0.0042
-0.0029
<0.01 ***
0.09 *
0.09 *
0.46
0.0019
-0.0025
-0.0045
-0.0004
0.02 **
0.48
<0.01 ***
0.93
45
Table VI – Impact of FTDs for Securities with High/Low Proportion of FTDs by Market Makers
This table provides results for the estimation of three vector autoregressive models of order one: VAR with Pricing Error (Model 1), VAR with Pricing
Error Volatility (Model 2), and VAR with Price (Model 3), as described in Table V. All variables are standardized and winsorized by security, and are as
defined in Table I. The sample includes all NYSE common stock of US-based firms (CRSP share codes 10 and 11), listed in the CRSP and TAQ databases
for at least 18 months over the interval January 1, 2005 to June 30, 2008, and with no large changes (>10%) in the number of shares outstanding. The
resulting sample includes 1,492 securities. Mean OFR is computed for all securities included in the sample for the period preceding the introduction of Rule
204T (January 1, 2005 to June 30, 2008) and for a period following (January 1, 2009 to December 31, 2010). Securities are ranked according to the
proportional change in Mean OFR. Securities are then allocated to three quantiles – those with the highest decline in Mean OFR are allocated to the “Low
Proportion of Estimated Market Maker Trades” sample, while those with the lowest decline in Mean OFR are allocated to the “High Proportion of
Estimated Market Marker Trades” sample. Reported parameter estimates are averages of parameters estimated by security. Significance is tested employing
a cross-sectional estimate of the standard error of the parameter estimate. The p-values from two-sided t-tests are in italics below the parameter estimates.
“*”, “**”, and “***” indicate significance at the 10%, 5% and 1% level respectively.
Low/High Proportion of Estimated
Market Maker Trades
A: Low
340 Securities
B: High
329 Securities
A: Low
340 Securities
B: High
340 Securities
A: Low
340 Securities
B: High
340 Securities
Δ PE
Δ PE
(incremental effect
when lag PE > 0)
0.0216
<0.01 ***
-0.0094
0.30
-0.0287
<0.01 ***
-0.0033
0.74
Δ Abs PE
Δ Price
-0.0169
<0.01 ***
0.0036
0.47
-0.0018
0.09 *
0.0007
0.52
Δ Intraday
Volatility
Δ Spread
Δ OIB
-0.0085
0.03 **
-0.0003
0.95
-0.0114
<0.01 ***
-0.0070
0.15
-0.0090
0.02 **
-0.0050
0.30
-0.0152
<0.01 ***
-0.0105
<0.01 ***
-0.0142
<0.01 ***
-0.0119
<0.01 ***
-0.0147
<0.01 ***
-0.0127
<0.01 ***
-0.0082
0.15
-0.0108
0.05 **
-0.0079
0.16
-0.0104
0.11
-0.0074
0.21
-0.0099
0.13
46
Table VII – FTDs and Short Sales
This table presents the average number of fails-to-deliver (FTDs) scaled by the contemporaneous number of shares outstanding for “Event Sample” and
“Control Sample”. Securities in the “Event Sample” are 17 stocks that were subject to the imposition of the SEC Order requiring pre-short sale stock
borrowing arrangements between July 21, 2008 and August 12, 2008, i.e., the “Order Period”. While the order affected 19 securities, data is available for 17
of these: Bank of America Corporation, Barclays, Bear Stearns Companies Inc., Citigroup Inc., Credit Suisse Group, Deutsche Bank Group AG, Allianz
SE, Goldman, Sachs Group Inc, Royal Bank ADS, HSBC Holdings PLC ADS, J. P. Morgan Chase & Co., Merrill Lynch & Co., Inc., Mizuho Financial
Group, Inc., Morgan Stanley, UBS AG, Freddie Mac, and Fannie Mae. “Control Sample” securities are 17 market capitalization and industry matched
stocks that were not subject to any relevant regulatory changes during the “Order Period”. The “Pre-Order Period” refers to the interval January 1, 2008 to
July 14, 2008. The “Post-Order Period” refers to the interval August 13, 2008 to September 9, 2008. The number of FTDs scaled by shares outstanding is
reported in basis points and computed on a daily basis over the interval January 1, 2008 to August 12, 2008. Reported p-values are for a test of differences
in mean FTDs (scaled by shares outstanding) between the indicated order sub-periods and the “Pre-Order Period” and between “Event Sample” and
“Control Sample”. “*”, “**”, and “***” indicate significance at the 10%, 5% and 1% level respectively.
Event Companies
Period
Mean (bps)
Pre Order
4.78
Order, 1st Week
0.57
(Order, 1st Week) - Pre Order
-4.22
Order, 2nd Week
0.17
(Order, 2nd Week) - Pre Order
-4.61
Order, 3rd Week
0.12
(Order, 3rd Week) - Pre Order
-4.67
Order, Last Day
0.00
(Order, Last Day) - Pre Order
-4.78
Post Order
1.12
(Post Order) - (Order, 3rd Week)
1.01
Control Companies
p value
Mean (bps)
Event-Control
p value
0.47
2.79
<0.01
***
2.32
<0.01
***
0.46
<0.01
***
-0.01
0.72
0.48
<0.01
***
0.01
0.21
0.23
<0.01
***
-0.24
0.03
**
-0.31
<0.01
0.18
0.51
***
Mean (bps)
p value
4.31
<0.01
***
-2.23
<0.01
***
-6.54
<0.01
***
-0.29
0.53
-4.60
<0.01
-0.36
0.43
-4.68
<0.01
-0.23
0.61
-4.55
<0.01
***
0.95
0.04
**
1.31
<0.01
***
***
***
47
Table VIII –The Impact of Restrictions on FTDs imposed by the SEC between July 21, 2008 and August 12,
2008.
The table presents means of Absolute Pricing Error, Return, Intraday Volatility, Spread, and Order Imbalance, as
defined in Table I. The SEC mandated pre-borrowing prior to short selling 19 securities during the period spanning
July 21 to August 12, 2008 (the “Order” period). The “Order” affected 19 securities, but data is available for 17 of
these (the “Event Sample”): Bank of America Corporation, Barclays, Bear Stearns Companies Inc., Citigroup Inc.,
Credit Suisse Group, Deutsche Bank Group AG, Allianz SE, Goldman, Sachs Group Inc, Royal Bank ADS, HSBC
Holdings PLC ADS, J. P. Morgan Chase & Co., Merrill Lynch & Co., Inc., Mizuho Financial Group, Inc., Morgan
Stanley, UBS AG, Freddie Mac, and Fannie Mae. Securities in the “Control Sample” are market capitalization and
industry matched stocks that were not subject to any relevant regulatory changes during the “Order” period. Means
during the “Order” period are compared to variable means computed over a period surrounding the “Order”, the
“Pre and Post Order” period, as indicated in the table. The p-values from two-sided t-tests for the significance of
mean differences are in italics below the parameter estimates. “*”, “**”, and “***” indicate significance at the 10%,
5% and 1% level respectively.
Abs PE
Return
Intraday
Volatility
Spread
OIB
Pre and Post Order
(Jan 1-Jul 14 & Aug
13-Sep 9, 2008)
Order
(Jul 21 -Aug 12,
2008)
Difference
(Order - Pre and
Post Order)
Event Sample
20.47%
28.08%
Control Sample
1.34%
1.48%
Difference
(Event-Control)
Event Sample
19.13%
<0.01 ***
-0.37%
26.60%
<0.01 ***
-0.27%
Control Sample
-0.14%
0.46%
Difference
(Event-Control)
-0.24%
0.06 *
-0.73%
0.07 *
7.61%
<0.01 ***
0.14%
0.24
7.47%
<0.01 ***
0.10%
0.93
0.59%
0.49
-0.49%
0.26
Event Sample
0.33%
0.44%
Control Sample
0.29%
0.37%
Difference
(Event-Control)
Event Sample
0.03%
<0.01 ***
0.10%
0.08%
<0.01 ***
0.15%
Control Sample
0.17%
0.21%
Difference
(Event-Control)
Event Sample
-0.07%
<0.01 ***
1.78%
-0.06%
<0.01 ***
-0.16%
Control Sample
0.18%
-0.34%
Difference
(Event-Control)
1.59%
<0.01
0.18%
0.90
0.11%
<0.01 ***
0.07%
<0.01 ***
0.04%
<0.01 ***
0.05%
<0.01 ***
0.04%
<0.01 ***
0.01%
0.07 *
-1.94%
0.33
-0.53%
0.71
-1.41%
0.37
48
Table IX– Outstanding Fails-to-Deliver Ratio (OFR) of Bear Stearns (Ticker: BSC) and of Lehman Brothers Holdings Inc. (Ticker: LEH) in 2008.
The Outstanding Fails-to-Deliver Ratio (OFR) is computed as the ratio of outstanding fails to deliver and shares outstanding. Index OFR is calculated as the equal weighted
average of OFR of common stock of 4 firms that are matched on primary SIC and market capitalization as of the end of the fiscal year 2007 to BSC in Panel A and to LEH in
Panel B. Tests for significance and related t-statistics are computed using the standard error of the OFR difference over the time interval January 1, 2008 to February 15, 2008
for BSC and over the time interval January 1, 2008 and ending 20 trading days prior to September 9, 2008 for LEH; p-values are two-sided. “*”, “**”, and “***” indicate
significance at the 10%, 5% and 1% level respectively.
Panel A: Bear Stearns
Panel B: Lehman Brothers Holdings Inc.
BSC OFR
Index OFR
Difference
in OFR
03/03/08
BSC
Stock
Price
(USD)
79.86
LEH OFR
Index OFR
Difference
in OFR
08/25/08
LEH
Stock
Price
(USD)
13.45
0.0580%
0.0003%
0.0577%
0.52
03/04/08
77.32
0.0069%
0.0000%
0.0069%
<0.01
***
0.0010%
0.0001%
0.0009%
0.89
08/26/08
14.03
0.0017%
0.0000%
0.0017%
0.79
03/05/08
77.17
0.0154%
0.0062%
0.0092%
<0.01
***
08/27/08
14.78
0.0000%
0.0016%
-0.0016%
0.79
03/06/08
75.80
0.0634%
0.0008%
0.0626%
03/07/08
69.90
0.0574%
0.0017%
0.0558%
0.66
08/28/08
15.87
0.0070%
0.0027%
0.0043%
0.50
0.47
08/29/08
16.09
0.0008%
0.0016%
-0.0008%
0.90
03/10/08
70.08
0.0082%
0.0001%
0.0081%
<0.01
03/11/08
62.30
0.0854%
0.0010%
0.0845%
0.64
09/02/08
16.13
0.0045%
0.0015%
0.0030%
0.63
09/03/08
16.94
0.0038%
0.0000%
0.0038%
0.55
03/12/08
62.97
0.5284%
0.0249%
0.5035%
<0.01
03/13/08
61.58
0.3175%
0.0041%
0.3134%
<0.01
***
09/04/08
15.17
0.0009%
0.0038%
-0.0029%
0.64
***
09/05/08
16.20
0.0000%
0.0095%
-0.0095%
0.13
03/14/08
57.00
0.8979%
0.0155%
0.8824%
<0.01
***
09/08/08
14.15
0.0023%
0.0005%
0.0018%
0.78
03/17/08
30.85
5.8383%
0.0174%
03/18/08
2.00
5.3300%
0.0004%
5.8209%
<0.01
***
09/09/08
7.79
0.0786%
0.0055%
0.0731%
<0.01
***
5.3296%
<0.01
***
09/10/08
7.25
0.4232%
0.0084%
0.4148%
<0.01
***
03/19/08
5.91
4.9694%
03/20/08
5.26
3.2489%
0.0031%
4.9663%
<0.01
***
09/11/08
4.22
1.6291%
0.0161%
1.6130%
<0.01
***
0.0180%
3.2310%
<0.01
***
09/12/08
3.65
2.3673%
0.0167%
2.3506%
<0.01
***
03/24/08
6.39
3.9550%
0.0030%
3.9520%
<0.01
***
09/15/08
0.21
2.0212%
0.0202%
2.0010%
<0.01
***
03/25/08
03/26/08
11.25
5.2488%
0.0240%
5.2248%
<0.01
***
09/16/08
0.30
2.1495%
0.0777%
2.0718%
<0.01
***
10.94
1.9806%
0.0076%
1.9730%
<0.01
***
09/17/08
0.13
3.6041%
0.0797%
3.5244%
<0.01
***
03/27/08
11.21
2.3933%
0.0110%
2.3823%
<0.01
***
03/28/08
11.23
2.7779%
0.0000%
2.7779%
<0.01
***
03/31/08
10.78
1.1950%
0.0000%
1.1950%
<0.01
***
Date
p-value
***
Date
p-value
49
Panel A: Absolute PE
Panel C: Spread
Panel B: Intraday Volatility
Panel D: Order Imbalance
Fig 1. Plots of accumulated impulse response functions depicting the impact of a one-standard deviation shock in
the Outstanding Fails-to-Deliver Ratio (OFR). The VAR model used for estimation is Model 2 and the sample is
the ‘overall market’, as described in Table VI. The response variables in the four panels are, respectively, Absolute
Pricing Error, Intraday Volatility, Spread, and Order Imbalance, as defined in Table II. The horizontal axis are
time periods (days), following the initial shock (day 0). All variables are standardized and winsorized by security.
Impulse response coefficients are estimated by security; mean values are depicted. 5% confidence intervals are
computed using cross-sectional standard error estimates.
50
Panel A: Absolute PE
Panel C: Spread
Panel B: Intraday Volatility
Panel D: Order Imbalance
Fig 2. Plots of accumulated impulse response functions depicting the impact of a one-standard deviation shock in
The Outstanding Delivered Shorts Ratio (ODR). The VAR model used for estimation is Model 2 and the sample is
the ‘overall market’, as described in Table VI. The response variables in the four panels are, respectively, Absolute
Pricing Error, Intraday Volatility, Spread, and Order Imbalance, as defined in Table II. The horizontal axis are
time periods (days), following the initial shock (day 0). All variables are standardized and winsorized by security.
Impulse response coefficients are estimated by security; mean values are depicted. 5% confidence intervals are
computed using cross-sectional standard error estimates.
51
Fig 3. Plot of Outstanding Fails-to-Deliver Ratio and Return Index related to Bear Sterns Companies Inc. common stock (ticker: BSC) against calendar date. The Return
Index is set to 1 on the 1st of January, 2008; Return Indexi 
i
 (1  R
j 1
BSC , j
) . RBSC , j is the observed total return for BSC on day j, from the CRSP database.
52
Fig 4A. Plot of Outstanding Fails-to-Deliver Ratio and Return Index related to Lehman Brothers Holdings Inc. (ticker: LEH) against calendar date. The Return Index is set to
1 on the 1st of January, 2008; Return Index i 
i
 (1  R
j 1
LEH , j
) . RLEH , j is the observed total return for LEH on day j, from the CRSP database.
53
Fig 4B. Detail of Plot of Outstanding Fails-to-Deliver Ratio and Return Index related to Lehman Brothers Holdings Inc. (ticker: LEH) against calendar date. The Return
i
Index is set to 1 on the 1st of January, 2008; Return Index i   (1  RLEH , j ) .
RLEH , j is the observed total return for LEH on day j, from the CRSP database.
j 1
54
Fig 5. Plot of Outstanding Fails-to-Deliver Ratio and Return Index related to Merrill Lynch & Co., Inc. (ticker: MER)
against calendar date. The Return Index is set to 1 on the 1st of January, 2008; Return Index i 
i
 (1  R
j 1
MER , j
) . RMER , j
is the observed total return for MER on day j, from the CRSP database.
Fig 6. Plot of Outstanding Fails-to-Deliver Ratio and Return Index related to American International Group (ticker:
AIG) against calendar date. The Return Index is set to 1 on the 1st of January, 2008; Return Index i 
i
 (1  R
j 1
AIG , j
).
R AIG , j is the observed total return for AIG on day j, from the CRSP database.
55