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## Abstract

This study examines battles between short sellers and firms. Firms use a variety of methods to impede short selling, including legal threats, investigations, lawsuits, and various technical actions intended to create a short squeeze. These actions create short sale constraints. Consistent with the hypothesis that short sale constraints allow stocks to be overpriced, firms taking anti-shorting actions have in the subsequent year very low abnormal returns of about −2% per month.

Short selling can be expensive, difficult, and risky. Impediments to shorting include the expense and difficulty of borrowing stock, legal and institutional restrictions, and the risk that the short position may be involuntarily closed due to recall of the stock loan. If these short sale constraints are sufficiently binding, stocks may become overpriced and thus have low future returns until the overpricing is corrected. By identifying stocks with particularly high short sale constraints, one can identify stocks with particularly low future returns. These constraints are difficult to measure, however, and researchers have struggled to find appropriate data to test the overpricing hypothesis.

In this article, I test whether overpricing increases when firms deliberately raise the level of short sale constraints. Firms can take a variety of actions to impede the short selling of their stock. Firms take legal and regulatory actions to hurt short sellers, such as accusing them of crimes, suing them, hiring private investigators to probe them, and requesting that the authorities investigate their activities. Firms take technical actions to make shorting difficult, such as splits or distributions specifically designed to disrupt short selling. Firms can coordinate with shareholders to withdraw shares from the stock lending market, thus preventing short selling by causing loan recall. These battles between short sellers and firms can be extraordinarily acrimonious. The following statement from the sample used in this article gives a flavor of the attitudes toward short sellers: “Your activities are mean, shameful and loathsome. They are motivated by appalling avarice and greed, and they will not be permitted to go unanswered” (Fulman 1998).

Solv-Ex, a firm claiming to have technology for economically extracting crude oil from tar-laden sand, is an example of the type of actions studied here. Short sellers claimed that Solv-Ex was a fraud. On February 5, 1996, Solv-Ex sent a letter to shareholders stating: “To help you control the value of your investment … we suggest that you request delivery of the Solv-Ex certificates from your broker as soon as possible” (Weiss 1996). This suggestion by the management of Solv-Ex, which appears to be legal, was intended to disrupt the stock lending system and orchestrate a short squeeze (the mechanics of stock lending are described in Section 1).

If a Solv-Ex shareholder took delivery of physical share certificates, these shares would have necessarily been removed from the stock lending market, potentially forcing short sellers to cover their positions. On February 2, 1996, before the letter, the share price of Solv-Ex stock was $24.875. By February 21, 1996, the price had risen to$35.375, perhaps due to Solv-Ex's attempted squeeze. Solv-Ex took other action against short sellers as well. Later in 1996, Solv-Ex said that it had hired private investigators to find out who was spreading misinformation about the firm, and subsequently it filed suit against a well-known short seller, claiming he had spread false information. However, in this case it was Solv-Ex that was engaged in illegal activities, not the short sellers. Solv-Ex delisted at July 1, 1997, at $4.25 per share; it entered Chapter 11 bankruptcy in 1997. In 2000, the court ruled that the firm had indeed defrauded investors. The sharp decline in Solv-Ex's share price is consistent with the hypothesis that Solv-Ex was overpriced as of February 1996. This article examines stock returns for a sample of 266 similar firms that threaten, take action against, or accuse short sellers of illegal activities or false statements. The sample is constructed using publicly observable actions from media reports and firm press releases. The article's main result is that firms have very low returns in the year subsequent to taking anti-shorting action: they trail the market by about 2% per month. Thus, the evidence is consistent with the idea that short sale constraints allow very substantial overpricing, and that this overpricing gets corrected only slowly over many months. As a secondary issue, this article also examines the behavior of short interest and prices around anti-shorting actions. There is weak evidence at best that deliberate short squeezes can temporarily raise stock prices. The idea that short sale constraints can prevent negative information or opinions from being expressed in stock prices comes from Miller (1977). Although constraints are necessary in order for mispricing to occur, they are not sufficient. Constraints can explain why a rational arbitrageur fails to short the overpriced security, but not why anyone buys the overpriced security. To explain that, one needs investors who are willing to buy overpriced stocks. Thus, two things, trading costs and some investors with downward-sloping demand curves, are necessary for substantial mispricing. This willingness to hold overpriced stocks can be interpreted as either reflecting irrational optimism by some investors, or rational speculative behavior reflecting differences of opinion. The underlying theory is further discussed in Section 1. This article is organized as follows. Section 1 discusses the general issues of short sale constraints and reviews related research. Section 2 describes how the sample was constructed. Section 3 describes the sample characteristics. Section 4 examines long-run returns for sample stocks. Section 5 examines shorting costs and short interest around anti-shorting events. Section 6 looks at short-term price movements around attempted short squeezes. Section 7 summarizes, discusses out-of-sample evidence, and presents conclusions. ## 1. Background and Literature Review ### 1.1 Mechanics of shorting stock In order to short sell a stock, one must first borrow the stock. Since stock lending in the United States occurs in a decentralized market, sometimes borrowing shares can be difficult or impossible. In order to borrow, an investor needs to find an institution or individual willing to lend. These lenders receive a daily lending fee from the borrowers, determined by supply and demand in the lending market. Brokers have the ability to lend shares of their customers, provided customers have given written permission. Once a short seller has initiated a position by borrowing stock, the borrowed stock may be recalled at any time by the lender. If the short seller is unable to find another lender, he is forced to close his position. This possibility leads to recall risk, one of many risks that short sellers face. There are several reasons that a shareholder might initially refuse to lend stock, or might later withdraw his shares from the stock lending market. First, if the lender sells his stock, he must recall his stock loan so that he can deliver his shares to the buyer. Second, in some unusual cases (which are studied here), firms devise technical actions that force shareholders not to lend. For example, one firm required shareholders to send their stock certificates to the firm's transfer agent in order to receive a distribution. An owner cannot send in the certificate unless he has physical possession of it. Third, shareholders may refuse to lend their stock because they fear that by helping short sellers, they will be helping drive stock prices down. This idea (the basis of the Solv-Ex example) obviously makes no sense in a competitive market where no individual investor is big enough to affect prices. Fourth, for individual investors, brokers typically only have the ability to lend out of margin accounts, not cash accounts. Fifth, some institutions do not have stock lending programs at all, perhaps because the income generated by lending would not be enough to compensate for the fixed cost of setting up a lending program. Generally, it is easy and cheap to borrow most large cap stocks, but it can be difficult to borrow stocks that are small, have low institutional ownership, or are in high demand for borrowing. A somewhat paradoxical description of the stock lending market is that it usually works very well, except when you want to use it, in which case it works terribly. In other words, it can be difficult or expensive to short stocks that many people believe are overpriced and many people want to short. Of course, this point is the essence of the overpricing hypothesis: stocks are only overpriced when informed investors are unable or unwilling to short them. No one would want to short them if they were not overpriced, and they would not be overpriced if they were not hard to short. Since the data-collection strategy is based on public anti-shorting actions taken by firms (and, in the case of lawsuits, depends on firms being able to identify short sellers), it is useful to consider the conflicting incentives for secrecy faced by short sellers. Short sellers sometimes attempt to remain anonymous, while at other times they publicize their activities. On the one hand, when shorting a stock, one has the incentive to publicize the opinion that the stock is overpriced. The sooner one can convince other investors that the stock price is too high, the sooner the price will fall, minimizing holding costs and price risk. On the other hand, recall risk, and more generally the cost of maintaining a short position, gives short sellers an incentive for secrecy, since holding costs generally rise when other investors are also trying to short. For stocks that are hard to short, a short seller would like the stock price to go down, but he may not want other people to short the stock. The cost and difficulty of shorting is determined by supply and demand in the securities lending market. If more people try to short a stock, the cost of shorting might rise and existing stock loans may be called in by the stock lender. In addition, secrecy might be preferred if the short seller wants to avoid being sued or harassed by the firm he is shorting. ### 1.2 Other short sale constraints Equity markets in the United States are not set up to make shorting easy. Over time, a variety of regulations and procedures have inhibited short selling or the stock lending market (e.g., actions taken by the SEC, the Federal Reserve, the various stock exchanges, underwriters, and individual brokerage firms). Legal and institutional constraints also inhibit investors from selling short. For example, Almazan et al. (2004) find that only about 30% of mutual funds are allowed to sell short, and only 2% actually do sell short. Historically, short sellers have also faced hostility from the society at large. Policymakers and the general public seem to have an instinctive reaction that short selling is morally wrong. Short selling has been characterized as inhuman, un-American, and against God (Proverbs 24:17: “Do not rejoice when your enemy falls, and do not let your heart be glad when he stumbles”). Hostility against short selling is not limited to the United States. In 1995, the Finance Ministry in Malaysia proposed mandatory caning as the punishment for short sellers (the beating “will be light, similar to the punishment carried out on juveniles”; Jayasankaran 1995). Like other oppressed minorities, short sellers face periodic waves of harassment, usually in times of crisis. Short sellers are often thought to be in league with enemies of the United States. The general idea seems to be that short selling is bad, and when bad things happen (such as war) it probably involves short sellers in some way. For example, the New York Stock Exchange imposed special short selling regulations during World War I (in November 1917), in response to both a substantial market decline and a fear that Kaiser Wilhelm II of Germany would send enemy agents to drive down stock prices. Jones and Lamont (2001) and Jones (2008) discuss another historical episode following the stock market crash of 1929. This historical pattern has continued in recent years, following the terrorist attacks of September 11, 2001; the more general market fall starting in 2000; and the recent financial crisis, which reached its peak in September 2008. ### 1.3 Overpricing: Theory Harrison and Kreps (1978) construct a model with rational investors where differences of opinion, together with short sale constraints, create a “speculative premium” in which stock prices are higher than even the most optimistic investor’s assessment of their value (see also Duffie, Garleanu, and Pedersen 2002). These differences of opinion can be interpreted as arising from different prior beliefs, which rationally converge as information arrives (Morris 1996), or as irrational overconfidence (Scheinkman and Xiong 2003). In any case, short sale constraints generate a pattern of overpricing leading to subsequent low returns. Here is an example that illustrates Harrison and Kreps (1978). In the model of Miller (1977), short sale constraints cause stock prices to reflect only the views of the optimists. The Harrison and Kreps (1978) model extends Miller (1977) to suggest that stock can be priced even higher than the most optimistic assessment of its true value. In their model, investors agree that stocks are overpriced but are still willing to hold them. Suppose investor A and investor B have different beliefs about the prospects for a risky asset. Each one knows what the other one believes, but they agree to disagree, so there is no asymmetric information. Assume a simple setup with three dates: date 0, 1, and 2. For simplicity, also assume risk-neutral agents behaving competitively, a discount rate of zero, and a sufficient number of type A and type B investors for each type to hold all the asset by themselves. Suppose it is currently date 0, and both A and B believe that the asset is worth$200 today. Specifically, they both believe that at date 2 it will be worth $300 with 50% probability and$100 with 50% probability. At date 1, a publicly observable signal occurs, and the two agents disagree on its meaning. Investor A thinks that the signal resolves all uncertainty, while B thinks the signal is completely uninformative and that no relevant news is released until date 2. This belief about when news gets released is the only disagreement between A and B (it is not necessary to state who, if either, is right in their belief). The Harrison and Kreps (1978) model has the remarkable property that in the presence of short sale constraints, both A and B would be willing to hold the asset at $250 at date 0, despite the fact that they both think it is only worth$200.

To get to this result, work backward from date 1, using the principle that with short sale constraints the optimist always sets the price. At date 1, if good news has arrived, then A will value the asset at $300 while B still thinks it is worth$200, thus the price will be $300 (A will hold all the asset; B will hold none of it). If bad news arrives at date 1, the price will be$200 (B will hold all of it). Since these two states happen with 50-50 probability, the date-0 expected price for date 1 is $250. Thus, at date 0, both A and B are willing to hold the asset at a price of$250. Although everyone thinks it is overvalued at date 0, they are willing to buy at date 0 because they believe they are following a dynamic trading strategy that will take advantage of the other investor. This example formalizes the notion of the “greater fool” theory of asset pricing. Note that everyone agrees that long-term expected returns between date 0 and date 2 are low (as the value is expected to fall from $250 to$200), and thus a buy-and-hold strategy is a bad idea. Volume is a key part of the story. Since everyone is following a dynamic trading strategy, there is lots of trading at date 1 as traders try to take advantage of one another. Without volume, there would be no overpricing.

### 1.4 Overpricing: Evidence

A variety of empirical evidence confirms the prediction that binding short sale constraints lead to low returns, although much of the evidence is circumstantial because it is hard to observe the level of short sale constraints for different stocks. One can test this hypothesis by either finding stocks with higher constraints (if constraints vary across stocks), or finding stocks with higher unexpressed shorting demand (if the demand for shorting varies across stocks). The basic idea of looking at shorting demand is that some investors want to short a stock but are impeded by constraints, and thus the stock is overpriced. If one can estimate the size of this group of investors, one can measure the extent of overpricing. In practice, measures of shorting constraints and shorting demand tend to be highly correlated, since both are reflecting the same mechanism that constraints prevent informed investors from immediately correcting overpricing.

The cost of shorting reflected in the stock loan market is one measure of short sale constraints. Recent articles examine the market for borrowing stocks (D’Avolio 2002; Geczy, Musto, and Reed 2002; Mitchell, Pulvino, and Stafford 2002; Ofek and Richardson 2003; Reed 2007; Cohen, Diether, and Malloy 2007), unfortunately using sample periods of short duration. Jones and Lamont (2002), using a longer sample of shorting costs, show that stocks that are expensive to short or that enter the lending market have high valuations and low subsequent returns. Indirect costs of shorting can come from options as in Figlewski and Webb (1993), Sorescu (2000), Lamont and Thaler (2003), and Ofek, Richardson, and Whitelaw (2004).

Proxies for shorting demand include breadth of ownership (Chen, Hong, and Stein 2002), dispersion of beliefs (Diether, Malloy, and Scherbina 2002), or the level of short interest (Figlewski 1981; Figlewski and Webb 1993; Dechow et al. 2001). Unfortunately, using short interest as a proxy for shorting demand is problematic, because the quantity of shorting represents the intersection of supply and demand. The quantity of shorting should respond to both the cost and benefit of shorting the stock, so that stocks that are very costly to short will have low short interest. Stocks that are impossible to short have an infinite shorting cost, yet the level of short interest is zero. Lamont and Thaler (2003), for example, examine a sample of technology carve-outs that appear to be overpriced. In one case they study, the apparent overpricing and the implied cost of shorting fall over time, while the level of short interest rises. Thus, short interest can be negatively correlated with shorting demand, overpricing, and shorting costs. The problematic nature of short interest leads to weak empirical results.

### 1.5 Reaction to news

Another strand of literature looks at the reaction of prices to news about short sales. In rational models such as Diamond and Verrecchia (1987), informed investors sell short, but once short interest is announced stock prices should immediately adjust to take into account the negative information. Consistent with this idea, Aitken et al. (1998) find that stock prices fall immediately in response to announced increases in short interest.

The anti-shorting actions studied here might reveal something about both the presence of informed pessimists, and the information possessed by the firm. For example, perhaps only firms that believe themselves to be overpriced engage in anti-shorting actions, since underpriced firms know that the market will eventually recognize their true worth. As in the Solv-Ex case, empirically many firms accuse short sellers of fraud, but are in fact themselves guilty of fraud (“The lady doth protest too much, methinks,” Hamlet, Act III, Scene 2). One short seller in the sample noted that “we can look at a company that is attacking us. When we have the goods on that company, it tells us we are onto something. The louder they scream, the better the short” (Pender 1989).

While the information revealed by anti-shorting actions is an interesting topic, it is not explored here. Rather, the hypothesis tested is whether anti-shorting actions lead to predictable low returns. Under the hypothesis of efficient markets with no frictions, prices should immediately adjust to new information, and post-event returns should be unpredictable. The empirical question studied here is not reaction to news, but rather long-term returns based on lagged public information.

## 2. Constructing the Sample

Searches were conducted in LexisNexis, Dow Jones Interactive, and other text sources using key words such as “short seller,” “lawsuit,” “conspiracy,” and so forth. I looked for episodes featuring reported disputes between short sellers and firms, ending in June 2002. These sources contained newspaper and magazine articles, newswire items, transcripts of broadcast media, and press releases. “Firms” were in most cases firm management, but in a few cases were large shareholders of the firm. Finding the relevant events was a time-consuming and labor-intensive process. Coding the events sometimes required judgment calls, and information was often incomplete or ambiguous.

The resulting sample has 327 events from 266 different firms from March 1977 to May 2002. Media coverage is thinner in earlier years, and 77% of the events occur after 1990. In addition to events, I also have (up to June 2002) returns, market equity, and volume from CRSP, book values from Compustat, and short interest from the NYSE (from 1992 to 2001) and NASDAQ (from 1995 to 2001). To get in to the sample, a firm must be common stock in CRSP with data available within the first 12 months after the event (this excludes OTCBB stocks, which are the source of many extraordinary anti-shorting episodes). Cases involving merger arbitrage or convertible securities arbitrage have been excluded.

To get into the sample, the firm must mount some sort of defense against short sellers, or accuse short sellers of wrongdoing (and thus implicitly raise the threat of legal action). The sample includes nine types of events, sorted into three categories. The first category is belligerent statements about short sellers, ranging from threats of legal action to detailed refutations of short sellers’ claims. The second category is taking legal or regulatory action against short sellers. The third category is taking technical action to prevent short selling. Table 1 lists the different types of events.

Table 1

Distribution of events

Description Comment Number Number
Events Firms
Claims conspiracy Conspiracy/bear raid/manipulation/illegal 29 29
Alleges lies Lies/rumors/planting stories/inaccurate statements 125 125
Considering options Consider options or conducting investigation using outside counsel or private investigator 21 21
All belligerent  175 159

Requests investigation Requests investigation by authorities (usually SEC or exchange), or claims one is underway, or media reports that authorities are investigating shorters 66 66
Lawsuit Announcement of lawsuit or of retraction based on litigation 35 35
All legal All legal 101 98

Exchange switch Exchange switch/seeking exchange switch
Urge not lend Urges (or “suggests”) that shareholders not lend shares to shorters 29 29
Friendly owners CEO sets up system to buy own stock, or firm announces repurchase explicitly in response to shorters, Friendly owners withdraw shares from lending market, lending by firm to shareholders, or employee stock ownership plan buying shares
Other technical Split/distribution/halt
All technical  51 43

All events  327 266
Description Comment Number Number
Events Firms
Claims conspiracy Conspiracy/bear raid/manipulation/illegal 29 29
Alleges lies Lies/rumors/planting stories/inaccurate statements 125 125
Considering options Consider options or conducting investigation using outside counsel or private investigator 21 21
All belligerent  175 159

Requests investigation Requests investigation by authorities (usually SEC or exchange), or claims one is underway, or media reports that authorities are investigating shorters 66 66
Lawsuit Announcement of lawsuit or of retraction based on litigation 35 35
All legal All legal 101 98

Exchange switch Exchange switch/seeking exchange switch
Urge not lend Urges (or “suggests”) that shareholders not lend shares to shorters 29 29
Friendly owners CEO sets up system to buy own stock, or firm announces repurchase explicitly in response to shorters, Friendly owners withdraw shares from lending market, lending by firm to shareholders, or employee stock ownership plan buying shares
Other technical Split/distribution/halt
All technical  51 43

All events  327 266

The sample is firms which have at least one monthly return in the 12 months following the event.

The first category, belligerent statements, is when the firm claims that short sellers are acting improperly to cause the stock price to go down. This category includes cases when the firm expends some effort refuting or denouncing short sellers, but falls short of taking specific actions. Belligerent statements often contain explicit or implicit threats of legal action against short sellers. Belligerent statements themselves do not impede short sellers, although they do indicate a greater likelihood that the firm will take some anti-shorting action in the future. Belligerent statements include any case in which firms explicitly accuse the short sellers of making illegal or improper actions, or disseminating false information. Cases where the firm mentioned short sellers but did not accuse them of improper action are excluded.

Belligerent statements come in three types. The first is when the firm claims some sort of conspiracy by short sellers, and includes claims of illegal shorting or stock price manipulation. A typical statement is “We continue to firmly believe that … stakeholders have been victimized by stock manipulators” (Knight 1998). This category also includes claims that short sellers were harassing or manipulating customers, investors, or suppliers.

The second type (which was often difficult to distinguish from the first) was the claim that the short sellers were spreading misinformation about the firm. Typical cases claimed lies, rumors, or planting negative stories in the media. To get into the database, firms had to either explicitly discuss the role of short sellers in spreading these lies, or be rebutting someone who was publicly acknowledged to be shorting the stock. A typical statement is “These false rumors regarding both the company and its products have been spread by short sellers of the company's stock” (System Software Associates Inc. 1995).

Third, firms state that they are considering their legal options and thus threaten potential legal action against short sellers or critics. A typical statement is “The Board of Directors has directed legal counsel to protect the Company's integrity and reputation and they will be assessing the legal remedies which the Company may pursue” (Quigley Corporation 1997). This category also includes cases where the firm states that they are undertaking their own investigation of short sellers, including hiring outside counsel or hiring private investigators.

### 2.1 Legal actions

Legal or regulatory actions are divided into two types of events. The first is when firms publicly announce that they are requesting an investigation by regulatory authorities, usually the relevant exchange or the SEC. This category also includes cases where the firm claims the SEC is already investigating short sellers. It is sometimes the case that when short sellers claim the SEC is investigating the firm for accounting shenanigans, the firm will respond by claiming that the SEC is investigating the short sellers for price manipulation.

This category also contained five cases when the media (as opposed to the firm) reports that the SEC or a stock exchange is investigating short sellers. Although not every case reveals that the firm alleged wrongdoing, in each of the cases the reports occur after other anti-shorting activities by the firm. It seems reasonable to infer that the firm complained to regulators. This category also includes eight cases involving 1989 Congressional hearings about short selling. Media reports indicated that the hearings were initiated by disgruntled firms (these hearings are discussed further in Section 7).

The second type of legal action is lawsuits initiated by the firm or by shareholders against short sellers or critics. Sometimes these lawsuits were against short sellers or brokers, and sometimes against media outlets or analysts. Of the 35 lawsuits, 7 were “cybersmear” lawsuits involving electronic postings by unknown persons. These lawsuits usually speculated that the posters were short sellers: “In its libel suit, Hollis-Eden alleges the defendants, named only by their screen aliases, could be disgruntled former employees and shareholders or people working with short sellers to manipulate the stock” (Crabtree 2001).

### 2.2 Technical actions

Firms take a variety of actions to disrupt the ability to borrow their shares. One technical action taken by firms in the sample was to switch stock exchanges from the NASDAQ to AMEX or NYSE. For much of the sample period, NASDAQ was perceived as being more lax in its short selling rules (it did not adopt the uptick rule until 1994). The sample includes six firms announcing that they were changing or applying to change exchanges explicitly to impede short selling (event dates range from 1988 to 1996).

Another type of action, as in the example of Solv-Ex, is when firms urge or suggest that shareholders collectively withdraw their shares from the stock lending market. Firms attempt in a variety of ways to get shares into the hands of friendly owners, who presumably will not lend their shares. I require that the stated action be explicitly in response to short sellers or taking place within the context of a battle with short sellers. Two cases are when the CEO announces that he is setting up an entity to buy and sell firm shares, using his own personal money. Three are when the firm announces it is repurchasing its own shares (I require that the announcement specifically mention short sellers). One is when it is announced that a large shareholder is withdrawing his shares from the lending market. One is when a firm announces that the employee stock ownership plan is acquiring shares. A last is when a firm offers to lend money to its shareholders to replace margin loans, so that they can place their stock in cash accounts (brokers typically can lend shares of their customers in margin accounts but not cash accounts).

The last category of technical actions contains miscellaneous trading-related activities to impede short selling. There are six cases where firms do splits or distributions that are apparently designed to force short sellers to close out their positions. For example, one firm required holders to send their stock certificates to the firm's transfer agent to be eligible to receive a stock dividend. Another firm did what was effectively a 1.1-for-1 stock split, with the same intention.

In three other cases, firms initiated trading halts explicitly in response to short sellers. The policy of the New York Stock Exchange is that firms should warn the NYSE ten minutes prior to major announcements. Sometimes the NYSE halts trading for a brief period, often 10 or 20 minutes, while the information is disseminated. One of these cases is described by Asensio (2001). After Asensio (a short seller) had released a negative report on a firm, the firm informed the NYSE that a major announcement was forthcoming and trading stopped at 10:44 a.m. Trading did not finally resume until 3:52 pm, eight minutes before the exchange closed, and in those eight minutes the price rose. According to Asensio, “someone had done a helluva job rallying the troops … By that time the institutions had galvanized enough buyers to run up the stock.” The firm did not make a major announcement, but only released a press release denouncing Asensio.

### 2.3 Limitations of the database

The database is surely an incomplete record of anti-shorting action taken by firms. First, it does not reflect private anti-shorting actions, such as private lawsuit threats made by firms. Many events only appear in the sample because they are deemed interesting or newsworthy. It is undoubtedly the case that many anti-short-selling actions do not get into the database because they are not reported in the media. As a result, the database is only a partial reflection of reality, and in particular it is likely that when firms take multiple actions, only some of them are reflected in the database. Coverage is particularly incomplete in the early years of the sample.

Some firms appear multiple times in the database since they took multiple actions. For this reason, the totals in the rightmost column of Table 1 are not always the sum of the individual categories. My coding strategy is to stop collecting belligerent statements on the first date that technical or legal events take place, so by construction the sample contains no belligerent statements after a legal or technical event. Probably many of the firms making belligerent statements subsequently take technical/legal actions that are not reflected in the database because they are not reported in the media. In addition, in each subcategory I collect only the first event and so subsequent instances are ignored.

### 2.4 Excluded cases

I exclude a variety of other forms of harassment of short sellers and suppression of criticism, since these anti-shorting actions were difficult to systematically classify. These cases range from the farcical to the tragic.

According to sworn testimony, Charles Keating Jr. (of the famous Keating Five) wanted to buy every copy of Forbes sold near branches of his Lincoln Savings, because the magazine contained critical comments (Dallas Morning News 1991). In other cases, firms attempt to prevent short sellers from asking questions at conference calls or annual meetings. In one case, when a short seller tried to ask a question at the annual meeting of Cineplex Odeon, he was drowned out by a “prolonged and very loud coughing fit,” which made his question inaudible (Hubbard 1990). Both Keating’s firm and Cineplex are included in the sample because of other reported incidents.

There are various reports of short sellers (and sometimes journalists or analysts) receiving death threats, requiring bodyguards, and arming themselves. In at least one case, someone may have been killed because of short selling. The case involves Tel-Com Wireless Cable TV, whose official spokesperson was Ivana Trump. On December 14, 1998, Barron’s reported that “several terrified investors told Barron's and the police that their families had been threatened by convicted criminals who accused the investors of selling short” (the firm gets in the sample, not because of this accusation, but because of the firm’s subsequent rebuttal). A year later, on November 1, 1999, Barron’s reported that one of the threatened individuals had been found murdered, execution-style, in Colts Neck, New Jersey.

The sample includes only explicit anti-shorting actions. I exclude from the sample some events that seemed to be anti-shorting but where the participants denied trying to hurt short sellers. For example, octogenarian potato tycoon J. R. Simplot was a major shareholder of Micron Tech, and also controlled an unrelated firm, the J. R. Simplot Company. He offered to his workers at Simplot the following employee benefit: “Mr. Simplot will make whole any loss” on Micron shares they buy (essentially giving employees a put option as long as they bought shares) (Lowenstein 1989). Although it was speculated in the media that this was intended to hurt short sellers (by increasing share prices and putting more shares into friendly hands), the J. R. Simplot Company denied this allegation.

In addition to the public manipulation of the stock loan market discussed previously, there are also allegations of private manipulation by institutional owners. One such accusation (Browning 1996) is that Fidelity Investments deliberately withdrew its shares of Chesapeake Energy from the stock loan market in order to drive up the price. Fidelity denied this allegation.

An extreme example of stock loan manipulation is the “corner.” Suppose B borrows shares from A and sells them short. Now A acquires 100% of the shares (or at least 100% available in the market) of the stock and demands that B return the shares. In this case, the only way B can return the shares is to buy them (at an inflated price) from A. Corners probably occurred (in U.S. equity markets) more frequently in the late nineteenth and early twentieth centuries, a prominent late case being the Stutz Motor corner of 1920 (Meeker 1932). Two recent cases in the United States occurred in the late 1980s. The president of Southland Communications was tried and convicted for driving his stock price up by cornering the firm's stock through secret trades (Lansner 1998). In another case, the SEC determined that two individuals had orchestrated a corner in Chase Medical and that they controlled 109% of the public float (Siconolfi 1989). Neither of these cases are reflected in the sample since they were not public anti-shorting actions.

## 3. Characteristics of the Sample

Table 2 shows the characteristics of the 266 firms in the sample. It shows the characteristics of the firms in the month prior to the month in which the first event takes place. For example, in the “all events” row, the statistics are for the month-end preceding the first event, even if multiple events take place. The table shows the percentile ranking of the variable relative to all stocks in CRSP in the same month.

Table 2

Characteristics of event firms (percentiles) in month prior to event

Number Percentiles

Firms Size M/B Volume Rt-12,t-1 Rt-1,t Short interestratio
Claims conspiracy 29 68 78 95 71 49 89
Alleges lies 125 72 75 88 68 53 88
Considering options 21 78 81 89 61 60 86
All belligerent 159 72 76 89 67 52 88

Requests investigation 66 67 81 85 69 58 86
Lawsuit 35 60 84 86 56 49 92
All legal 98 64 82 85 65 54 88

Exchange switch 67 96 68 42 76 82
Urge not lend 29 55 71 81 47 43 87
Friendly owners 76 66 84 75 75 74
Other technical 46 83 89 71 58 76
All technical 43 56 77 81 56 52 81

All events 266 67 77 87 64 53 86
Number Percentiles

Firms Size M/B Volume Rt-12,t-1 Rt-1,t Short interestratio
Claims conspiracy 29 68 78 95 71 49 89
Alleges lies 125 72 75 88 68 53 88
Considering options 21 78 81 89 61 60 86
All belligerent 159 72 76 89 67 52 88

Requests investigation 66 67 81 85 69 58 86
Lawsuit 35 60 84 86 56 49 92
All legal 98 64 82 85 65 54 88

Exchange switch 67 96 68 42 76 82
Urge not lend 29 55 71 81 47 43 87
Friendly owners 76 66 84 75 75 74
Other technical 46 83 89 71 58 76
All technical 43 56 77 81 56 52 81

All events 266 67 77 87 64 53 86

Percentile variables in the month prior to event, compared to the universe of CRSP firms. For firms that do not have data for the month prior to the event, the characteristic is from the month preceding the first return observation. Size is market equity. M/B is market-to-book ratio (market value of equity divided by Compustat book value of equity). The timing of M/B follows Fama and French (1993) and is as of the previous December year-end. Volume is monthly turnover (volume divided by shares outstanding) minus the median turnover of all stocks on the same exchange. Short interest ratio is the ratio of short interest to shares outstanding.

Looking first at size, the average ranking for all events is 67%, so that event firms are above median relative to the universe of firms in CRSP. This characteristic may reflect the fact that larger firms are more newsworthy. Market-to-book ratios show that event firms are growth firms, since they are in the upper quartile of valuation. Strikingly, event firms have very high trading volume in the month before the event (trading volume is measured as share turnover relative to other stocks on the same exchange). Part of this high volume of 87th percentile may reflect information released around the event date. However, 12 months before the event month, it is still the case that event firms have percentile turnover of 77%. One interpretation is that volume proxies for differences in opinion (agents trade when they disagree), and thus these are firms where investors have very dispersed opinions. Under short sale constraints, high volume may predict low future returns (e.g., Diether 2004). Looking at pre-event returns, the differences are less dramatic. Prior-one-year returns are slightly above median, and prior-month returns are about the same as the median stock. Thus events do not seem to be triggered by extreme stock price movements at the monthly or yearly level. Finally, looking at the ratio of short interest to shares outstanding, it is not surprising to see that immediately prior to the event, firms have very high short interest relative to the other stocks.

In summary, event firms are high volume, high short interest growth firms of above median size.

## 4. Long Run Returns

### 4.1 Event time returns

The overpricing hypothesis predicts that post-event returns should be low. Table 3 shows monthly returns subsequent to the event, for different time horizons. It shows event time returns with a very simple risk-adjustment procedure: returns are market-adjusted by subtracting out the return on the CRSP value-weighted index (later I show calendar time returns with different risk adjustments). The table shows average monthly returns earned by buying the event stock on the last day of the month in which the event is publicly observed. Thus, it measures post-event long-term performance.

Table 3

One month

Three month

One year

Three years

2 to 3 Years

t to t + 1  t to t + 3  t to t + 12  t to t + 36  t + 12 to t + 36
Claims conspiracy −2.64 (0.33) −2.28 (0.68) −4.37 (2.73) −2.77 (2.54) −1.63 (1.22)
Alleges lies −1.62 (0.67) −2.08 (1.61) −1.71 (1.96) −1.31 (2.03) −1.06 (1.55)
Considering options −5.10 (0.63) −8.19 (2.48) −5.79 (3.44) −2.76 (2.53) −0.82 (0.62)
All belligerent −2.63 (1.00) −2.70 (2.08) −2.28 (2.86) −1.62 (2.73) −1.19 (1.93)

Requests investigation −4.59 (1.52) −1.30 (0.66) −1.99 (2.17) −1.19 (1.73) −0.72 (0.81)
Lawsuit −3.48 (1.15) −3.30 (1.03) −2.65 (1.72) −1.44 (1.48) −0.59 (0.48)
All legal −4.22 (1.87) −1.89 (1.09) −2.24 (2.59) −1.31 (2.04) −0.73 (0.92)

Exchange switch 3.54 (0.47) −1.69 (0.38) 0.12 (0.06) −2.84 (2.37) −4.26 (2.95)
Urge not lend −4.55 (1.00) −4.66 (1.82) −3.17 (1.65) −2.66 (2.29) −2.14 (1.54)
Friendly owners −11.46 (0.87) −10.07 (1.66) −4.96 (1.90) 0.23 (0.07) 3.01 (0.60)
Other technical −8.17 (1.35) −12.39 (2.93) −8.54 (2.61) −5.60 (2.23) −1.52 (0.40)
All technical −3.86 (1.08) −5.19 (2.62) −2.66 (1.95) −2.04 (2.13) −1.50 (1.14)

All events −3.09 (1.85) −2.58 (2.63) −2.34 (3.69) −1.48 (2.80) −0.89 (1.51)
One month

Three month

One year

Three years

2 to 3 Years

t to t + 1  t to t + 3  t to t + 12  t to t + 36  t + 12 to t + 36
Claims conspiracy −2.64 (0.33) −2.28 (0.68) −4.37 (2.73) −2.77 (2.54) −1.63 (1.22)
Alleges lies −1.62 (0.67) −2.08 (1.61) −1.71 (1.96) −1.31 (2.03) −1.06 (1.55)
Considering options −5.10 (0.63) −8.19 (2.48) −5.79 (3.44) −2.76 (2.53) −0.82 (0.62)
All belligerent −2.63 (1.00) −2.70 (2.08) −2.28 (2.86) −1.62 (2.73) −1.19 (1.93)

Requests investigation −4.59 (1.52) −1.30 (0.66) −1.99 (2.17) −1.19 (1.73) −0.72 (0.81)
Lawsuit −3.48 (1.15) −3.30 (1.03) −2.65 (1.72) −1.44 (1.48) −0.59 (0.48)
All legal −4.22 (1.87) −1.89 (1.09) −2.24 (2.59) −1.31 (2.04) −0.73 (0.92)

Exchange switch 3.54 (0.47) −1.69 (0.38) 0.12 (0.06) −2.84 (2.37) −4.26 (2.95)
Urge not lend −4.55 (1.00) −4.66 (1.82) −3.17 (1.65) −2.66 (2.29) −2.14 (1.54)
Friendly owners −11.46 (0.87) −10.07 (1.66) −4.96 (1.90) 0.23 (0.07) 3.01 (0.60)
Other technical −8.17 (1.35) −12.39 (2.93) −8.54 (2.61) −5.60 (2.23) −1.52 (0.40)
All technical −3.86 (1.08) −5.19 (2.62) −2.66 (1.95) −2.04 (2.13) −1.50 (1.14)

All events −3.09 (1.85) −2.58 (2.63) −2.34 (3.69) −1.48 (2.80) −0.89 (1.51)

Average monthly market-adjusted returns in percents. Market-adjusted returns are returns minus the return on the CRSP value-weighted index. The t-statistics, in parentheses, use standard errors adjusted for the clustering of dates in calendar time.

First, looking at the all-event, one-year cell, Table 3 shows that event firms have very low returns.1 In the twelve months subsequent to any event, firms have returns that are a whopping 2.34% per month lower than the market, and this difference is highly statistically significant. In terms of the magnitude, the 2% per month is in the same ballpark as the large estimates found in other cases of extreme short sale constraints. Jones and Lamont (2002) found that highly constrained firms had abnormal returns of −1% per month in the year subsequent to becoming constrained, for the period 1926–1933. Lamont and Thaler (2003) find abnormal returns of −10% per month over an approximately six-month period for a sample of six cases involving short sale constraints, for the period 1998–2001. Ofek, Richardson, and Whitelaw (2004) and Cohen, Diether, and Malloy (2007) find abnormal returns of about −2% per month for a sample of short sale constrained stocks for a few years around the year 2000.

Examining the different time horizons, two facts emerge. First, the low returns are highly persistent, and continue for years. In the 36 months after any event, the market-adjusted returns are −1.48% per month, so that the cumulative fall is 42%. The last column shows that, even after excluding the first year (so that the sample is firms that had an event in the past three years but not in the last year), market-adjusted returns are −0.89% per month. While this number has a t-statistic that is less than two, partially because the sample contains fewer observations since many have gone bankrupt or been delisted, it is economically large. Thus, the time pattern is consistent with overpricing that is only slowly corrected through time. The effect is not primarily a short-term under reaction to bad news that gets quickly corrected. Rather, it is a long-term overpricing phenomenon, with a time pattern similar to the value effect.

Second, returns are lowest immediately after the event, and gradually the effect weakens over time. Thus, there is no evidence in Table 3 to support the idea that one should buy stocks after an event occurs, in anticipation of a short squeeze. (Section 6 examines in more detail a subset of these events, and looks at daily returns around event dates.)

Turning now to the different types of events, there does not seem to be much difference in mean returns in the different rows of Table 3. In drawing inferences about the effect of short sale constraints, the legal and technical categories may be more reliable, since the belligerent statement category is somewhat more ambiguous. Belligerent statements are just cheap talk, and require researcher judgment to define the event. In contrast, technical and legal events are tangible actions. Since all three categories of events predict large and statistically significant underperformance of returns in the subsequent year, it is not necessary to use the belligerent category to draw inferences about the effect of events. Even excluding belligerent statements, there is strong evidence that anti-shorting events are followed by very low returns. In regressions not shown, there is no statistically significant difference in returns between the three classes of events (belligerent, legal, and technical). Measurement error may be responsible for some of these similarities, since some belligerent firms probably also take unobserved legal or technical actions. Since there are not detectable differences between the categories, the discussion focuses on the “all events” row in Table 3 only.

The effect is robust to different methods. First, the calculations in Table 3 include the effects of delisting returns: 30 of the 266 firms delist in the twelve months after the event. Excluding these delisting returns, the average market-adjusted return at the one-year horizon is −2.05 instead of −2.34.2 Second, the effect is large and significant both before and after 1990. Third, the results do not appear to be caused by a few large outliers. The median monthly market-adjusted return at the one-year horizon is −3.47 (again compared to the mean of −2.34), and 59% of the monthly market-adjusted returns are negative.

### 4.2 Calendar time

Table 4 reports calendar time portfolio returns for the one-year horizon, showing both market-adjusted returns and two other adjustment methods. One should be cautious using calendar time returns here, since in the early years there are very few firms per month in the event portfolios, often only one. As it turns out, calendar time and event time calculations give about the same answer. The first column shows market-adjusted returns. For all events, market-adjusted returns are −2.85% per month over the 257 months of the sample, slightly higher than Table 3’s number.

Table 4

Calendar time portfolio returns for one-year horizon returns

Claims conspiracy 166 −3.33 (2.22) −2.77 (2.05) −2.06 (1.32)
Alleges lies 229 −2.06 (2.22) −1.09 (1.32) −1.76 (1.79)
Considering options 125 −5.46 (3.37) −4.66 (3.05) −4.90 (2.91)
All belligerent 251 −2.26 (2.66) −1.36 (1.85) −1.94 (2.31)

Requests investigation 220 −2.67 (2.94) −2.04 (2.47) −2.11 (2.17)
Lawsuit 179 −3.07 (2.06) −1.95 (1.39) −2.93 (1.88)
All legal 241 −2.82 (3.32) −1.91 (2.48) −2.55 (2.89)

Exchange switch 53 0.58 (0.27) 1.32 (0.70) −0.83 (0.33)
Urge not lend 132 −4.52 (3.07) −4.55 (3.18) −4.00 (2.48)
Friendly owners 51 −4.69 (1.82) −3.15 (1.25) −6.95 (2.19)
Other technical 58 −8.81 (2.45) −7.26 (1.99) −9.93 (2.42)
All technical 180 −2.79 (2.36) −1.97 (1.87) −2.90 (2.33)

All events 257 −2.85 (4.32) −1.88 (3.41) −2.40 (3.81)

All events, value weighted 257 −1.31 (1.81) −1.23 (1.72) −1.95 (3.22)
Claims conspiracy 166 −3.33 (2.22) −2.77 (2.05) −2.06 (1.32)
Alleges lies 229 −2.06 (2.22) −1.09 (1.32) −1.76 (1.79)
Considering options 125 −5.46 (3.37) −4.66 (3.05) −4.90 (2.91)
All belligerent 251 −2.26 (2.66) −1.36 (1.85) −1.94 (2.31)

Requests investigation 220 −2.67 (2.94) −2.04 (2.47) −2.11 (2.17)
Lawsuit 179 −3.07 (2.06) −1.95 (1.39) −2.93 (1.88)
All legal 241 −2.82 (3.32) −1.91 (2.48) −2.55 (2.89)

Exchange switch 53 0.58 (0.27) 1.32 (0.70) −0.83 (0.33)
Urge not lend 132 −4.52 (3.07) −4.55 (3.18) −4.00 (2.48)
Friendly owners 51 −4.69 (1.82) −3.15 (1.25) −6.95 (2.19)
Other technical 58 −8.81 (2.45) −7.26 (1.99) −9.93 (2.42)
All technical 180 −2.79 (2.36) −1.97 (1.87) −2.90 (2.33)

All events 257 −2.85 (4.32) −1.88 (3.41) −2.40 (3.81)

All events, value weighted 257 −1.31 (1.81) −1.23 (1.72) −1.95 (3.22)

Monthly returns in percents for the 12 months following an event, calculated using calendar time portfolios. Portfolios are equally weighted except for the last row, which is value weighted. Market-adjusted returns are returns minus the return on the CRSP value-weighted index. Characteristic adjusted are returns minus the returns on a value-weighted portfolio of all CRSP firms in the same size, market-to-book, and one-year momentum quintile. Four-factor alpha is the intercept from a regression of returns in excess of T-bills on the three factors of Fama and French (1993), size, value, and market, plus a fourth price, momentum factor, similar to Carhart (1997). “N months” is the number of calendar months available for market-adjusted returns (the number may be lower for the other columns). T-statistics are in parentheses.

As shown in Table 2, event firms tend to be growth firms, so it is important to test whether the return effect reflects only this fact. The next column of Table 4 shows characteristic-adjusted returns, which control for size, value, and momentum. Following Daniel et al. (1997), it subtracts from the event firm return the return on a portfolio of firms matched on market equity, market-to-book, and prior-one-year return quintiles (a total of 125 matching portfolios).3 As expected, this adjustment decreases the magnitude of the effect, but the remaining effect is still strikingly large and significant.

An alternate way to adjust for value, size, and momentum is to calculate alphas from a factor regression. The last column of Table 4 reports intercepts from a four-factor model where the factors are the market, size, and value as in Fama and French (1993), augmented with a prior-year return factor as in Carhart (1997).4 Again, after this risk adjustment, a large and significant effect remains.

The last row of Table 4 shows the value-weighted returns. Here, the returns are somewhat less dramatic, although the effect is still substantial and statistically significant (it is significant for the two-sided hypothesis for the factor regression, and for the one-sided hypothesis for the market-adjusted and characteristic-adjusted means). The fact that value weighting gives a smaller effect is consistent with the idea that smaller stocks are more difficult to short and thus can be more overpriced.

Table 5 shows the coefficients from the four factor regressions. Most notable are the coefficients on value and momentum factors. For the value factor, the coefficient is insignificantly different from zero, suggesting that these firms’ returns do not behave much like other growth firm returns. For the momentum factor, the coefficient is significant and negative, suggesting that these firms are behaving like firms with negative momentum. This finding is not surprising: these firms have falling prices during the 12-month post-event period in which these factor loadings are estimated, so one might expect their returns to be correlated with other firms with falling prices. Table 2 showed that, prior to the event, the firms had positive (not negative) momentum since their prior-year returns were above median. If one reestimates the regression for the one month after the event (rather than the 12 months), one gets a positive loading on the momentum factor. So, going into the event, the firms have positive momentum, while after the event they have negative momentum.

Table 5

Four factor regressions for one-year horizon returns

Description α  RMRF  HML  SMB  UMD  R2
Claims conspiracy −2.06 (1.32) 1.19 (3.07) −0.33 (0.60) 1.88 (3.93) −1.17 (2.89) 0.26
Alleges lies −1.76 (1.79) 0.89 (3.48) −0.56 (1.52) 1.36 (4.32) −0.47 (1.77) 0.25
Considering options −4.90 (2.91) 1.45 (3.95) 0.20 (0.31) 1.59 (2.91) −0.56 (1.07) 0.20
All belligerent −1.94 (2.31) 1.23 (6.16) −0.42 (1.35) 1.53 (5.54) −0.58 (2.54) 0.36

Requests investigation −2.11 (2.17) 1.31 (5.71) 0.00 (0.01) 0.75 (2.25) −0.79 (2.70) 0.23
Lawsuit −2.93 (1.88) 0.73 (1.97) −0.60 (1.10) 1.58 (3.19) −0.37 (0.94) 0.16
All legal −2.55 (2.89) 0.99 (4.73) −0.14 (0.42) 1.34 (4.63) −0.40 (1.69) 0.25

Exchange switch −0.83 (0.33) 1.59 (2.34) −0.07 (0.07) 1.95 (2.35) 0.79 (0.81) 0.22
Urge not lend −4.00 (2.48) 0.86 (2.45) 0.25 (0.38) 1.28 (2.29) −0.45 (1.11) 0.15
Friendly owners −6.95 (2.19) 2.73 (2.86) 1.51 (1.39) 1.79 (1.83) 0.43 (0.43) 0.19
Other technical −9.93 (2.42) 2.71 (1.96) −2.08 (1.14) 0.81 (0.48) −0.67 (0.41) 0.17
All technical −2.90 (2.33) 1.28 (4.40) 0.55 (1.10) 1.70 (4.05) −0.02 (0.05) 0.22

All events −2.40 (3.81) 1.06 (7.11) −0.34 (1.47) 1.50 (7.21) −0.55 (3.24) 0.44

All events, value weighted −1.95 (3.22) 1.45 (10.19) 0.02 (0.09) 0.74 (3.75) −0.47 (2.89) 0.43
Description α  RMRF  HML  SMB  UMD  R2
Claims conspiracy −2.06 (1.32) 1.19 (3.07) −0.33 (0.60) 1.88 (3.93) −1.17 (2.89) 0.26
Alleges lies −1.76 (1.79) 0.89 (3.48) −0.56 (1.52) 1.36 (4.32) −0.47 (1.77) 0.25
Considering options −4.90 (2.91) 1.45 (3.95) 0.20 (0.31) 1.59 (2.91) −0.56 (1.07) 0.20
All belligerent −1.94 (2.31) 1.23 (6.16) −0.42 (1.35) 1.53 (5.54) −0.58 (2.54) 0.36

Requests investigation −2.11 (2.17) 1.31 (5.71) 0.00 (0.01) 0.75 (2.25) −0.79 (2.70) 0.23
Lawsuit −2.93 (1.88) 0.73 (1.97) −0.60 (1.10) 1.58 (3.19) −0.37 (0.94) 0.16
All legal −2.55 (2.89) 0.99 (4.73) −0.14 (0.42) 1.34 (4.63) −0.40 (1.69) 0.25

Exchange switch −0.83 (0.33) 1.59 (2.34) −0.07 (0.07) 1.95 (2.35) 0.79 (0.81) 0.22
Urge not lend −4.00 (2.48) 0.86 (2.45) 0.25 (0.38) 1.28 (2.29) −0.45 (1.11) 0.15
Friendly owners −6.95 (2.19) 2.73 (2.86) 1.51 (1.39) 1.79 (1.83) 0.43 (0.43) 0.19
Other technical −9.93 (2.42) 2.71 (1.96) −2.08 (1.14) 0.81 (0.48) −0.67 (0.41) 0.17
All technical −2.90 (2.33) 1.28 (4.40) 0.55 (1.10) 1.70 (4.05) −0.02 (0.05) 0.22

All events −2.40 (3.81) 1.06 (7.11) −0.34 (1.47) 1.50 (7.21) −0.55 (3.24) 0.44

All events, value weighted −1.95 (3.22) 1.45 (10.19) 0.02 (0.09) 0.74 (3.75) −0.47 (2.89) 0.43

Regression results using calendar time monthly returns in percents for the twelve months following an event. Portfolios are equally weighted except for the last row, which is value weighted.

RMRF is returns on the CRSP value-weighted portfolio minus T-bill returns. HML is the value factor (the return of low M/B stocks high M/B stocks), SMB is the size factor (the return on small stocks minus big stocks), and UMD is the momentum factor (the return of stocks with high prior-year returns minus stocks with low prior-year returns). T-statistics are in parentheses.

In summary, event firms have extremely low subsequent returns that are not explained by value, size, or momentum, using either characteristic adjustment or factor models. Event firms have returns that are 2% to 3% lower than non-event firms.

## 5. Effect on Shorting Costs and Short Interest

This section examines direct evidence on the ability to short the event firms. One measure of the cost and difficulty of shorting comes from the stock lending market. While I do not have access to data on rebate rates in the stock lending market for the sample firms (these data are proprietary and generally go back only a few years), I can compare the sample with a list of high-cost stocks provided in D’Avolio (2002). He lists 35 firms with very high shorting costs in his sample of April 2000–September 2001 (the annual shorting costs range from 10% to 79%). In April 2000, there are 6,647 valid firms in the CRSP database, so about 0.5% of the universe has very high shorting costs. I compare his list to the firms in my sample with initial events from April 1999 (one year before his sample starts) to September 2001 (when his sample ends). There are 36 firms in my sample during this period. The overlap of the two groups consists of six firms; thus, 16% of the event firms have very high shorting costs, a much higher rate than the 0.5% in the general population of stocks. It is clear that the probability of such a high degree of overlap is miniscule. Thus, the sample is much more expensive to borrow than a random sample of firms, consistent with the hypothesis that the sample firms are subject to short sale constraints.

Other evidence comes from reported short interest for each stock. Here, one lacks a natural null hypothesis to test. Unlike the case of returns, where the natural null hypothesis is that post-event returns are unpredictable, it is difficult to tell simply by looking at the quantity of shorting whether the anti-shorting events have any effect.

Figure 1 shows the average ratio of short interest to shares outstanding in event time.5 Six months prior to the event, the ratio is already elevated at around 5.5% (a level that is the 78th percentile relative to the universe of all stocks). It rises steadily over time, peaking two months after the event at 10.7% (the 92nd percentile), and remains roughly constant thereafter. One interpretation is that the rising level of short interest causes the firms to take the anti-shorting actions.

Figure 1

Short interest ratio for all events

The figure shows the monthly ratio of short interest to shares outstanding, in event time. Month zero is the first month that any anti-shorting event takes place for the firm.

Figure 1

Short interest ratio for all events

The figure shows the monthly ratio of short interest to shares outstanding, in event time. Month zero is the first month that any anti-shorting event takes place for the firm.

While it is difficult to interpret these results in the absence of a null hypothesis, it seems clear that something is happening around the event date, since the rapid rise in short interest halts. In that sense, it could be that the anti-shorting actions are effective at stopping the growth of short interest. On the other hand, the actions certainly do not cause the level of short interest to substantially and rapidly decrease. Since one does not know what short interest would have been in the absence of an anti-shorting event, it is impossible to draw solid inferences from this evidence.

In summary, the anti-shorting firms are expensive to short, and there is a large increase in short interest prior to the event itself.

## 6. Short Squeezes

This section examines in more detail the events where firms attempt to coordinate a short squeeze by asking their shareholders to withdraw shares from the stock loan market. I focus on this event since it is the most common of the technical events designed to create a squeeze.

Journalists and market participants often cite short squeezes as explanations for movements in stock, bond, and commodity markets. One common definition is that a short squeeze occurs when the price of a security rises, causing the short sellers to experience a decline in net wealth. Either because of lower wealth, increased risk aversion, fear of further price rises, or margin calls, the short seller then covers his position, increasing the demand for the security and driving the stock price further up. In contrast, the definition of a short squeeze used here is when a short seller is involuntarily forced to cover his short position because he is no longer able to borrow the security. Most of the literature on short squeezes focuses on either theoretical issues or empirical findings in the bond, commodity, and derivative markets (e.g., Jarrow 1992, 1994; Kumar and Seppi 1992; Jegadeesh 1993; Pirrong 1993, 2001; Nyborg and Sundaresan 1996; Merrick, Naik, and Yadav 2002). D’Avolio (2002), using data from the stock lending market, finds little evidence for short squeezes in his 18-month sample.

Wall Street wisdom suggests that high short interest stocks are good to own because they may rise due to a short squeeze. According to this view, one should be willing to buy overpriced stocks in anticipation of a short squeeze that will drive prices still higher. An example of this idea is given in the case of GenesisIntermedia, which also illustrates direct manipulation in an attempt to enrich specific individuals. On April 25, 2001, Chief Executive Ramy El-Batrawi sent a letter to shareholders asking them to contact their brokers and have shares put into cash accounts, making the shares unavailable for lending to short sellers. Between April 25 and May 25, the stock rose 39%.

GenesisIntermedia was 92% owned by a group of four insiders, including 45% ownership by its chairman, Saudi financier and arms merchant Adnan Khashoggi (a central figure in the Iran-Contra affair). According to Hirsch (2001):

“I think that after our chairman sent out his letter, our shareholders started to take possession of some of their shares, forcing the shorts to cover their positions,” said Douglas Jacobson, the company's chief financial officer. “There also may be upward pressure on the stock from people seeing the letter and then buying in anticipation that the short squeeze will get more dramatic.” Indeed, Jacobson conceded that Khashoggi might be among those investors and might eventually sell shares to bring his holding closer to the third of the company he owned previously. According to documents filed with the Securities and Exchange Commission, Khashoggi purchased more than 60,000 shares at about \$11.30 each since El-Batrawi's letter. “It could end up being very good for him to have the shorts buy back shares from him,” Jacobson said.

There are 29 cases in the sample where firms attempt a coordinated loan withdrawal. For the purposes of this section, five of these are discarded. Two had event dates that were identified only by month (these events are reflected in the long-term returns shown in Section 4). Three have no clear event date, since media reports simply mentioned that discouraging lending was a continuing policy of the firm (these events are reflected in the long-term returns shown in Section 4, with the event date set equal to observation date). Of the remaining 24 cases, 22 were clearly public information that was available in real time, and in two cases the event was semi-private, and only appeared in the media subsequent to the event (these two cases are reflected in the long-term returns shown in Section 4, with the event date set equal to the observation date).

Before reviewing the evidence on these actions, it is instructive to consider how these events differ from other events typically studied in financial economics. First, these events are not clean and exogenous. Unlike, for example, earnings announcements, which come at pre-announced and regular intervals, these events are entirely endogenous and occur partly in response to the level of stock prices. Other news (including about other anti-shorting activities) may also be occurring in the same window. Second, these events are not only information events, but also technical events reflecting the operations of the stock loan market. In a world with frictions (as opposed to the standard assumption of frictionless and informationally efficient markets), it is not clear whether one would expect prices to immediately reflect the short squeeze, or to slowly respond as the squeeze is put into effect. It presumably takes some time for investors, after receiving the suggestion, to contact their brokers to withdraw their shares from the loan market, and short sellers who have their loans withdrawn have several days to deliver the shares. Finally, the evidence will necessarily have a limited ability to measure the efficacy of anti-shorting actions. It is hard to tell whether an anti-shorting action has any effect because one does not know how much shorting there would be in the absence of action. It could be that prices would have fallen faster if the action had not been taken. All that can be said is that one can be fairly confident that the anti-shorting actions did not make life easier for short sellers.

Figure 2 shows trading volume around event days (days are trading days, not calendar days). The volume is expressed as the percentile of exchange-adjusted turnover relative to the CRSP universe. As shown in Table 2, event firms tend to be high-volume firms in general, and before the event the firms tend to be in the top quartile of turnover. Volume spikes up on the event date, suggesting that something is indeed happening. Even with only 24 firms, this spike in volume on the event day is statistically significant. D’Avolio (2002) reports that high-recall days have extremely high trading volume, consistent with the event causing recall of stock loans. Of course, this spike does not prove that the anti-shorting action is causing volume to increase; it could be that the action is taken in response to higher volume or to some other unobserved event.

Figure 2

Volume for urge events

The figure shows trading volume in event time. Trading volume is measured as share turnover, and is expressed as percentile turnover relative to other stocks on the same day and in the same exchange. Day zero is the trading day on which the first urge event occurs, where the firm urges shareholders not to lend shares to shorter sellers.

Figure 2

Volume for urge events

The figure shows trading volume in event time. Trading volume is measured as share turnover, and is expressed as percentile turnover relative to other stocks on the same day and in the same exchange. Day zero is the trading day on which the first urge event occurs, where the firm urges shareholders not to lend shares to shorter sellers.

Figure 3 shows cumulative average market-adjusted returns around event days. Since returns are so volatile and there are only 24 firms, standard errors are large, and one would need incredibly large mean returns in order to get statistical significance. Figure 3 shows that cumulative returns are not incredibly large, and thus there is generally nothing in Figure 3 that is statistically significant. Looking at the point estimates, there is some evidence that the actions do succeed in slightly raising prices temporarily. Cumulative returns are 4.6% from day t-5 to day t + 5. By day t + 20, a month after the event, however, nothing much has changed. The most notable feature of Figure 3 is the pre-event increase in returns, reflecting perhaps insider buying in anticipation of the squeeze, or perhaps other events. Figure 3 also shows cumulated alphas from the Fama-French three-factor model estimated on daily data, which are about the same as cumulated average market-adjusted returns.

Figure 3

Cumulative returns for urge events

The figure shows cumulative returns in event time. Market-adjusted returns are returns minus the return on the CRSP value-weighted index. Three-factor alpha is the intercept from a regression of returns in excess of Treasury bills on the three factors of Fama and French (1993): size, value, and market. Day zero is the trading day on which the first urge event occurs, where the firm urges shareholders not to lend shares to shorter sellers.

Figure 3

Cumulative returns for urge events

The figure shows cumulative returns in event time. Market-adjusted returns are returns minus the return on the CRSP value-weighted index. Three-factor alpha is the intercept from a regression of returns in excess of Treasury bills on the three factors of Fama and French (1993): size, value, and market. Day zero is the trading day on which the first urge event occurs, where the firm urges shareholders not to lend shares to shorter sellers.

Summarizing, these actions do not seem to have much ability to raise prices, although it could be that absent these events prices would have fallen more. What is clear is that this ability, if it exists, is only temporary, and that long-term returns on these stocks are abysmal.

## 7. Conclusion

The evidence shows that when firms take anti-shorting actions, their stock returns are extraordinarily low over the subsequent months and years. The evidence confirms the hypothesis that short sale constraints allow stocks to become overpriced. While the underperformance of −2% per month is very large, it is similar in magnitude to the −1%-to-−10% range found in other studies of stocks with very high short sale constraints.

The 25 years of evidence studied here is valuable because of the difficulty of finding direct data on short sale constraints. Jones and Lamont (2002) find data for six years (1926–1933), while Lamont and Thaler (2003), Ofek, Richardson, and Whitelaw (2004), and Cohen, Diether, and Malloy (2007) studied data for a few years around the year 2000. Each one of these five data sets has unique characteristics, and it is conceivable that any one result reflects chance or an unusual sample period. But, taken together, the evidence shows that in extreme cases where short sellers want to short a stock but find it difficult to do so, overpricing can be very large.

Much has happened since this article first circulated in 2002 and its results were described in Lamont (2006). Academic work on this topic has continued. For example, Karpoff and Lou (2010) explore the role of short sellers in uncovering fraud. Their article also contains references to related articles that have been written since 2002. More dramatically, the chaotic events of September 2008 have highlighted the roles of both short sellers and regulators.

In September 2008, the SEC banned short selling of certain financial stocks in the United States, with other countries initiating similar bans. This ban, which ultimately proved to be temporary, had predictably deleterious effects on market liquidity (Boehmer, Jones, and Zhang 2009). This event highlights the uncertain and hostile regulatory environment faced by short sellers, and the ever-present possibility of the ultimate short sale constraint: prohibition by law.

Leading up to September 2008, several Wall Street firms made what this article would categorize as “belligerent statements” blaming short sellers for undermining confidence. One prominent critic of short sellers was Richard Fuld, Lehman Brothers CEO, a particularly interesting development because Lehman, as a prime broker, derived a substantial portion of its income by facilitating stock lending. For example, in April 2008, Fuld denied that his firm had liquidity problems (Horowitz 2008): Mr. Fuld and other Lehman executives have accused investors who short the firm's stock—making money by betting the price will fall—of spreading false rumors about the firm's ability to finance its businesses … “I will hurt the shorts, and that is my goal.”

Readers of this article will not be surprised to learn that Lehman subsequently collapsed amid allegations of fraudulent accounting and that returns on its stock from April 2008 to September 2008 were approximately −100%. Thus, there is dramatic out-of-sample evidence that is consistent with the central finding of this article.

I have identified stocks that are grotesquely overpriced. It is important to note that these cases are not typical. Most firms do not attack short sellers, and most large-cap stocks are not difficult to sell short. Thus, one cannot conclude from the evidence that short sale constraints are a pervasive phenomena in the stock market. What we know is that for most stocks, very little short selling occurs (relative to other trading activity) and most investors never go short. Thus, something is constraining short selling, perhaps lack of knowledge about shorting, institutional constraints, risk, or cultural issues. Generalizing from the narrow (but dramatic) evidence presented, one can speculate that these more general short sale constraints also affect stock prices.

If you observe a firm taking an anti-shorting action, should you immediately short it? The evidence here cannot answer that question. Although on paper such a position can make large gross returns on average, maintaining the short position might be difficult or expensive. Even if there are no problems borrowing the stock, a short seller may need to spend time and money dealing with lawsuits and investigations. It is unclear how these costs and benefits net out. It is clear, however, that it is a bad idea in general to own stock in a firm that is taking these actions. Investors seeking high returns should look elsewhere.

The fact that firms take anti-shorting actions tells us that they must believe these actions are worth doing. A substantial body of research studies whether firms opportunistically take advantage of mispricing by issuing equity when it is overpriced and buying it back when it is underpriced (e.g., Loughran and Ritter 1995). Corporate managers certainly say they are trying to time the market (Graham and Harvey 2001). However, it is usually difficult to discriminate between the hypothesis that firms are responding to rational changes in discount rates as opposed to over or under pricing (e.g., Polk and Sapienza 2009). The anti-shorting actions studied here show that firms are not just passively responding to market signals, but are in fact actively trying to prop up their stock prices. In this respect, the phenomenon is similar to the evidence on earnings accruals, which can be interpreted as firms actively manipulating accounting numbers to cause overpricing. Similarly, firms encourage analysts to issue optimistic forecasts, and reward optimistic analysts with investment banking business (e.g., Michaely and Womack 1999).

In addition to the overpricing hypothesis, there are two alternative explanations of the results. The first is that anti-shorting actions are a signal that insiders know that the firm is overvalued, so that the low returns reflect inside information instead of short sale constraints. While it is certainly true that anti-shorting actions may reveal negative inside information, this does not explain why it takes so long for the information to be reflected in stock prices. With no frictions, the information should be immediately incorporated. In contrast, short sale constraints provide an explanation for the slow reaction of prices to information. Since the effect persists for years, the low returns are not primarily a short-term under reaction to bad news. Rather, the low returns reflect persistent overpricing.

A second alternative explanation, favored by the firms used in the sample, is that short sellers are actually manipulating prices, driving prices down over long periods of time. The problem with this explanation is that many of the sample firms are subsequently revealed to be fraudulent. Thus, the short sellers are identifying firms having bad fundamental value. In public battles between short sellers and firms, short sellers usually are vindicated by subsequent events. The evidence suggests that short sellers play an important role in detecting not just overpricing, but also fraud. Policymakers might want to consider making the institutional and legal environment less hostile to short sellers.

For example, in 1989, Congress held hearings about the evils of short selling, featuring testimony from supposedly victimized firms. One Congressman described short selling as “blatant thuggery.” But who was the victim and who was the thug? During the hearings, an SEC official testified that “many of the complaints we receive about alleged illegal short selling come from companies and corporate officers who are themselves under investigation by the Commission or others for possible violations of the securities or other laws” (U.S. House of Representatives 1991, pp. 434–35). Officials from three firms testified. Subsequent to this testimony, the presidents of two of these three firms were prosecuted for fraud, while for the third, the SEC determined that the company had made materially false and misleading statements.6 More systematic evidence comes from Dechow, Sloan, and Sweeney (1996), who study SEC enforcement actions for earnings manipulation, and Griffin (2003), who studies earnings restatements leading to shareholder lawsuits. Both find that short interest starts to rise several months prior to the public announcement of bad news. This evidence indicates that short sellers are able to anticipate bad news about earnings and identify fraud.

I thank Nicholas Barberis, Douglas Diamond, Karl Diether, Toby Moskowitz, Rob Stambaugh, Will Goetzmann, two referees, and seminar participants at Berkeley, Boston College, Carnegie Mellon, the Chicago Quantitative Alliance, the London School of Economics, the NASD, the NBER, the Q Group, and Stanford for helpful comments. I also thank Karl Diether and Yan Zhang for research assistance. I also thank the NYSE and Toby Moskowitz for data. I gratefully acknowledge support from the Alfred P. Sloan Foundation, the Center for Research in Securities Prices at the University of Chicago Graduate School of Business, the National Science Foundation, and the Q Group. I am particularly grateful to John Cochrane, Wayne Ferson, and Jeff Pontiff for their encouragement. Send correspondence to Owen A. Lamont, Department of Economics, Harvard University, Cambridge MA, 02138; telephone: (617) 495–3442. E-mail: olamont@fas.harvard.edu.

1 There are a small number of firms for which the event date is clear and occurs in a month prior to the observation date (the first time the event is mentioned in the media). These firms are included in the long-term returns after the observation date, but the “first 12 months” is in reference to event date. So, if the event occurs in January and I observe it in March, it gets into long-term return portfolio in March but stays for only 10 months, not 12. The same holds true for firms that are not in CRSP in the event month but are subsequently added. In cases where there is no well-defined event date, I use the observation date for the event date. To eliminate double counting, a firm is only reflected in a given average once in any given month. For example, a firm is included in the all-event calculation in month t if any event occurred in months t-12 to t-1.
2 I plugged the delisting return from CRSP into the monthly return sequence in the month after the last available regular return. So, if a firm delists in February, has the last monthly return in January, and CRSP records a delisting return in April, I plug that delisting return in for February. Following Shumway (1997), in the very few cases where no delisting return is available, I plug in -30%.
3 These 125 portfolios are reformed every month based on the market equity, M/B ratio, and prior-year return from the previous month. However, following Fama and French (1993), the M/B ratio is only updated annually in July, based on the value as of the previous December.
4 I am grateful to Ken French for these data. All four factors come from his web site. They are RMRF, the excess market return, SMB (the return on small stocks minus big stocks), and HML (the return of high book-to-market stocks minus low book-to-market stocks), a price momentum factor, and UMD (the return of stocks with high prior-year returns minus stocks with low prior-year returns).
5 The data on short interest are limited (from 1992 to 2001 for the NYSE, and from 1995 to 2001 for NASDAQ), and data availability cuts the sample by more than half.
6 The three firms, with citations to the subsequent SEC charges, were American City Business Journals (Wall Street Journal 1991), Carrington Laboratories (U.S. House of Representatives 1991, p. 513), and IGI, Inc. (Wall Street Journal 2002). As mentioned in Section 2, there are a total of eight firms involved in the Congressional hearings, but these were the only three in which company officials actually testified.

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text:
# Integral square error computation

1. Oct 23, 2007

Hi,
I am struggling computing the integral square error between two square waves. one is ideal and the other is assymetric.
the equation for the assymetric is:
x(t)=
A for |t|<=To/4+ε/2
and
-A for (To/4)+(ε/2)<|t|<=To/2

we were asked to plot the ideal( without the ε) and actual (or assymetric) waveforms and compute the integral square error between the two waveforms.

I only have the final solution which is 4εA^2. I cannot find it

format: plain


text:
# Vectors – Proof that four given points form parallelogram – Exercise 4493

Exercise

Prove that the points

$$A(2,1,-4),B(1,3,5),C(7,2,3),D(8,0,-6)$$

Form a parallelogram ABCD.

Proof

Coming soon…

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