Journal of Financial Economics 61 (2001) 77–106
`
`Short-sellers, fundamental analysis,
`and stock returns$
`
`Patricia M. Dechowa,*, Amy P. Huttonb, Lisa Meulbroekb,
`Richard G. Sloana
`a University of Michigan Business School, Ann Arbor, MI 48109, USA
`b Harvard Business School, Harvard University, Boston, MA 02163, USA
`
`Received 19 August 1998; received in revised form 26 June 2000
`
`Abstract
`
`Firms with low ratios of fundamentals (such as earning and book values) to market
`values are known to have systematically lower future stock returns. We document that
`short-sellers position themselves in the stock of such firms, and then cover their
`positions as the ratios mean-revert. We also show that short-sellers refine their trading
`strategies to minimize transactions costs and maximize their investment returns. Our
`evidence is consistent with short-sellers using information in these ratios to take
`positions in stocks with lower expected future returns. # 2001 Elsevier Science S.A. All
`rights reserved.
`
`JEL classification : G12; G14; M41
`
`Keywords: Short-sellers; Fundamental analysis; Trading strategies
`
`$This paper has benefited from the comments of seminar participants at the Australian
`Graduate School of Management, the American Accounting Association 1999 Annual Meetings,
`Cornell University, Louisiana State University, Harvard Business School, University of North
`Carolina, University of Southern California, University of Texas at Austin, and Northwestern
`University. We are also grateful for the comments from the editor, Bill Schwert, and the referee
`(Ken French).
`
`*Corresponding author. Tel.: +1-734-764-3191; fax: +1-734-936-8716.
`
`E-mail address: dechow@umich.edu (P.M. Dechow).
`
`0304-405X/01/$ - see front matter # 2001 Elsevier Science S.A. All rights reserved.
`PII: S 0 3 0 4 - 4 0 5 X ( 0 1 ) 0 0 0 5 6 - 3
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`1. Introduction
`
`Conventional wisdom characterizes short-sellers as sophisticated investors
`who incur relatively large transactions costs attempting to short-sell and
`subsequently repurchase temporarily overpriced securities.1 Asquith and
`Meulbroek (1996) provide evidence that short-sellers, as a group, successfully
`identify securities that subsequently underperform the market. In this paper,
`we identify the characteristics of the securities targeted by short-sellers.
`Specifically, we examine whether short-sellers target stocks of firms that are
`priced high relative to fundamentals such as earnings and book values.
`A large body of evidence demonstrates that ratios of measures of
`fundamental value to market value systematically predict future stock returns.
`These ratios compare estimates of ‘‘intrinsic’’ values based on accounting data
`to observed market prices. They range from simple ratios such as earnings-to-
`price and book-to-market (e.g., Fama and French, 1995; Lakonishok et al.,
`1994) to ratios based on more sophisticated valuation models such as Ohlson
`(1995) (e.g., Frankel and Lee, 1998; Dechow et al., 1999). Given the well-
`documented predictive ability of these ratios with respect to future stock
`returns, they provide a natural starting point for investigating the trading
`strategies of short-sellers.
`We document a strong relation between the trading strategies of short-sellers
`and ratios of fundamentals to market prices. Our tests indicate that short-
`sellers target securities that have low fundamental-to-price ratios and then they
`unwind their positions as these ratios revert to normal levels. We also show
`that short-sellers refine their trading strategies in three ways in order to
`maximize their investment returns. First, short-sellers avoid securities for
`which the transactions costs of short-selling are high. Second, short-sellers
`supplement their trading strategies by using information beyond that in
`fundamental-to-price ratios that has predictive ability with respect to future
`returns. Third, we show that short-sellers avoid shorting securities with low
`fundamental-to-price ratios when the low ratios are attributable to temporarily
`low fundamentals. In other words, short-sellers act as if they are able to
`discriminate between low ratios that are due to temporarily low fundamentals
`and low ratios that are attributable to temporarily high prices.
`A straightforward interpretation of our results is that low fundamental-to-
`price ratios are associated with temporary overpricing that is actively exploited
`by short-sellers. This interpretation is consistent with the Lakonishok et al.
`(1994) hypothesis that ‘‘na.ıve’’ investors tend to be overoptimistic about the
`future prospects of stocks with low fundamental-to-price ratios. Under this
`interpretation, our evidence suggests that short-sellers are sophisticated
`
`1 See, for example, Business Week, August 5, 1996, pp. 63–68, Fortune, November 9, 1998 p. 272,
`and Forbes, December 28, 1998, pp. 101–103.
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`79
`
`investors who play an important role in keeping the price of stocks in line with
`fundamentals. An alternative interpretation of our results is that
`low
`fundamental-to-price ratios are associated with unique risk characteristics.
`This interpretation is consistent with the Fama and French (1992) hypothesis
`that stocks with low fundamental-to-price ratios have low sensitivity to the
`‘‘book-to-market’’ risk factor. Under this interpretation, short-sellers achieve
`superior returns by short-selling low-risk stocks. These superior returns are
`compensation for the increased exposure to the book-to-market risk factor. In
`an attempt to discriminate between these competing interpretations, we
`conducted a telephone survey of major global short-selling hedge funds. The
`fund managers all endorsed the first interpretation provided above, i.e., they
`short-sell stocks they perceive to be overpriced. However, it is also possible that
`short-sellers inadvertently load up on the risk factor conjectured by the second
`interpretation above.
`The paper proceeds in four sections. The next section develops our
`predictions. Section 3 describes our research design, Section 4 presents the
`results, and Section 5 concludes.
`
`2. Empirical predictions
`
`We begin in Section 2.1 by describing the institutional features of short-
`selling and identifying the objectives, risks, and costs of short-selling. Section
`2.2 then describes several established techniques for predicting future stock
`returns by comparing ratios of fundamental measures of value to market
`prices. These sections provide the underpinnings for our empirical predictions,
`which are presented in Section 2.3. In Section 2.4 we discuss the possible
`confounding effects of any unidentified risk factors on the interpretation of our
`results.
`
`2.1. Institutional details on short-selling
`
`A short sale is a sale of a stock that one does not already own, but has
`borrowed from a brokerage house, a large institutional investor, or another
`broker-dealer. The short-seller establishes the position by selling the borrowed
`stock, and closes the position by buying the stock back at a later time, using the
`purchased shares to extinguish the initial loan of the stock. By selling short, an
`investor can profit from a decrease in the stock price. The risk-return profile for
`a short position is very different from that of a long position. A short-seller’s
`maximum gain is the sale price of the stock (if the stock price falls to zero),
`while the loss is potentially unlimited (if the stock price rises). Because of the
`high risk associated with short-selling, and because of its putative potential for
`manipulating stock prices, short-selling is heavily regulated in U.S. stock
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`markets and is not allowed in many foreign stock markets. Many institutional
`investors are prohibited from short-selling, or restricted in the size of their
`short positions relative to the overall size of their portfolios. Asquith and
`Meulbroek (1996) provide an extensive review of the institutional aspects of
`short-selling. Here we provide only a brief summary of the process in the
`United States.
`Regulation in the United States has developed from beliefs that short-sellers
`can cause stock prices to spiral downward. The ensuing regulations act to
`increase the cost of
`short-selling. The U.S. Securities and Exchange
`Commission requires short-sellers to sell only on a ‘‘plus tick’’ or a ‘‘zero
`plus tick,’’ that is, when the stock price has increased. The proceeds from a
`short sale are not available to the short-seller. Instead, the proceeds are
`escrowed as collateral for the owner of the borrowed shares. Typically, the
`short-seller receives interest on the proceeds, but the rate received (the
`‘‘rebate’’) is below the market rate. The difference is the compensation to the
`lender of the stock. Thus, short-sellers cannot directly use the proceeds from
`short sales to reinvest or to hedge their short position. Regulation T, set by the
`Federal Reserve, requires short-sellers of stocks to deposit additional collateral
`of 50% of the market value of the shorted shares. The short-seller can use
`either long positions in other securities or interest-bearing Treasury securities
`to meet this additional margin requirement, mitigating the cost of maintaining
`this additional collateral (any dividends or interest earned on securities in the
`collateral margin account accrue to the short-seller). If the price of the shorted
`stock rises, increasing the liability of the short-seller, additional collateral funds
`are generally required. The tax treatment of short positions contributes to the
`high cost of short-selling. All profits from a short sale are taxed at the short-
`term capital gains rate, no matter how long the short position is open. Finally,
`the short-seller is required to reimburse the stock lender for any dividends or
`other distributions paid to the shareholders of the shorted stock while the short
`position is open. Because the ex-dividend stock price of the shorted stock is
`generally higher than the pre-dividend stock price less the amount of the
`dividend (e.g., Frank and Jagannathan, 1998), dividend reimbursement
`represents a real cost to the short-seller (in addition to inconvenience and
`transactions costs).
`The standard stock-lending practice is that the loan must be repaid on
`demand. This practice exposes short-sellers to the risk of being ‘‘squeezed.’’ A
`short squeeze occurs when the lender of the borrowed shares wants to sell the
`stock. If the short-seller is unable to find an alternative lender, the short-seller
`must repurchase the shares in the open market to repay the loan and close the
`position. To avoid this risk, a short-seller can borrow on a term basis for an
`additional fee, but most short-sellers seem to prefer the risk of a squeeze to the
`cost of a term loan, and term loans are rare. To help short-sellers assess the
`probability of a squeeze, the broker will sometimes reveal the identity of the
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`lender of the shorted stock. Generally, a short squeeze is less likely for more
`liquid securities,
`such as
`large market-capitalization stocks with high
`institutional ownership, since it is easier for brokers to find alternative lenders
`of such stocks in the event that the original lender demands the return of the
`borrowed shares.2
`Short-selling is therefore riskier and more expensive than establishing a long
`position. Because short sales are more costly than long transactions, Diamond
`and Verrechia (1987) suggest that short-sellers will not trade unless they expect
`the price to fall enough to compensate them for the additional costs and risks
`of shorting. Short-sellers, they propose, are therefore more likely to be better
`informed than are investors with long positions. A short sale is the most direct
`way for an investor to bet that a stock’s price will decrease.3 Of course, short
`sales occur for a myriad of reasons, only one of which is a belief by the short-
`seller that the stock is overvalued relative to its fundamentals. In a merger
`situation, investors often simultaneously go long in the target firm’s stock and
`short
`in the acquiring firm’s stock. In ‘‘pairs trading’’
`investors hedge
`themselves by shorting a security whose return is highly correlated with the
`return of another security they have purchased (e.g., selling Dell short and
`purchasing Gateway). Another reason for short-selling is to arbitrage a price
`differential between the stock and debt convertible into the stock. These other
`reasons for short-selling are not motivated by the expectation of a price decline.
`Thus, to the extent that short-selling is attributable to these other activities,
`they add noise to our empirical tests.
`Early research on short interests by Figlewski (1981), Woolridge and
`Dickinson (1994), Brent, Morse, and Stice (1990), and Figlewski and Webb
`(1993) fails to document a strong relation between short interest and excess
`returns. However, Asquith and Meulbroek point out that the power of the tests
`in these studies is weak, since their sample selections are not based on the
`magnitude of the short interests. As documented by Asquith and Meulbroek,
`many firms have very small short positions (less than 0.5%). These small short
`positions are likely to represent hedge positions, rather than a systematic
`attempt to exploit perceived overpricing. By focusing on a sample of firm-years
`with large short interests (e.g., firm-years with short positions greater than
`2.5% of shares outstanding), Asquith and Meulbroek document a strong and
`
`2 An extreme example of a short squeeze is the case of Amazon.com. In June 1998, the number of
`shorted Amazon shares neared its entire float. The firm then announced a stock split, and the stock
`price rose significantly, with demand coming from both long investors and short-sellers who were
`squeezed due to the lack of shares to borrow. Fears of a short squeeze have been cited as an
`important reason why many short-sellers avoid heavily shorting ‘‘overpriced’’ Internet stocks (see
`St. Louis Post-Dispatch, July 19, 1998, p. E3).
`3 Asquith and Meulbroek (1996) point out that although the option market may seem a less
`costly way to achieve the same goal, many hedge-fund managers and other practitioners state that
`the option market is even more expensive, particularly for hard-to-borrow stocks.
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`consistent relation between short interests and excess returns. They document
`that stocks with high levels of short interest perform significantly more poorly
`than comparable stocks without short positions.
`
`2.2. Ratios of fundamentals to market prices
`
`Basu (1983), Lakonishok et al. (1994), and Sloan (1996) show that various
`measures of cash flows scaled by price are positively related to future stock
`returns. Basu (1983) and Fama and French (1992) show that earnings-to-price
`ratios are positively related to future returns. Stattman (1980), Rosenberg et al.
`(1985), and Fama and French (1992) show that book-to-market ratios are
`positively related to future returns. Considerable prior research has investi-
`gated each of these ratios, and their predictive ability with respect to future
`returns is well documented, so we do not describe them in detail. However,
`research on the more sophisticated value-to-market measure is less well known
`and is discussed below.
`In a dividend-discounting framework, firm value can be expressed as the sum
`of the book value of common equity plus the present value of future abnormal
`earnings (see Edwards and Bell, 1961; Ohlson, 1995):
`
`Et½xatþtŠ
`ð1 þ rÞt;
`
`Pt ¼ bt þ
`
`X1
`
`t¼1
`
`where
`
`bt
`= book value of common equity at time t
`tþt; = Earningstþt rbtþt1
`xa
`r
`= cost of equity capital.
`
`Following Ohlson (1995), Dechow et al. (1999) model abnormal earnings as
`a simple autoregressive process:
`tþ1 ¼ o xat þ etþ1:
`
`xa
`Intrinsic value can then be expressed as
`Pt ¼ bt þ axa
`t
`
`with
`
`a ¼
`
`o
`;
`1 þ r o
`where o measures the persistence of abnormal earnings. This valuation model
`combines information in both earnings and book value. A persistence
`parameter of o ¼ 1 implies a pure earnings model, while a persistence
`parameter of o ¼ 0 implies a pure book value model. Empirically, Dechow
`et al. (1999) show that the average persistence parameter is around 0.6. They
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`83
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`demonstrate that the ratio of intrinsic value to market value computed using
`o ¼ 0:6 is more highly associated with future returns than the earnings-to-price
`and book-to-market ratios. We employ their procedure in computing our
`value-to-market ratio.
`
`2.3. Empirical predictions
`
`The focus of this paper is on determining whether short-sellers exploit the
`predictable returns associated with the valuation ratios identified above. Prior
`research has shown that high cash-flow-to-price, earnings-to-price, book-to-
`market, and value-to-market firms earn higher one-year-ahead returns than do
`firms with low values for these ratios. So long as sophisticated investors do not
`perceive stocks with relatively high fundamentals to be riskier, we expect them
`to take advantage of these predictable returns. That is, we expect sophisticated
`investors to buy stocks for which the predictable returns are the highest (where
`cash-flow-to-price, earnings-to-price, book-to-market and value-to-market are
`high) and (short) sell stocks for which the predictable returns are the lowest
`(where cash-flow-to-price, earnings-to-price, book-to-market, and value-to-
`market are low). It is difficult to identify which long-positioned investors are
`sophisticated. However, as argued above, short-sellers represent sophisticated
`investors who claim to specialize in selling overpriced stocks.
`Our primary empirical prediction is that short interests will be relatively high
`in firm-years with relatively low values of cash-flow-to-price, earnings-to-price,
`book-to-market, and value-to-market ratios. We also predict that short-sellers
`will subsequently cover their positions as the predictable returns are realized
`and stock prices fall back in line with fundamentals. Finally, we investigate
`whether the magnitudes of short positions are influenced by differences in the
`relative transactions costs associated with shorting different securities. Such
`evidence would suggest that the effectiveness of short-selling as a mechanism
`for enhancing market efficiency is limited by the high transactions costs
`associated with short-selling.
`
`2.4. Risk and fundamental-to-price ratios
`
`Our results and their interpretation will be confounded if fundamental-to-
`price ratios capture risk factors unknown to us, that are responsible for the
`lower returns of low fundamental-to-price stocks (Fama and French, 1992). If
`these ratios do indeed capture risk factors, then there are two additional
`interpretations of our results:
`
`1. Short-sellers have unique preferences for the risk factors, which motivates
`their trading behavior with respect to low fundamental-to-price stocks; and
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`2. Short-sellers think that they are profiting from short-selling overpriced
`securities, but they are inadvertently loading up on the unidentified risk
`factors.
`
`In an attempt to discriminate between these alternative interpretations, we
`surveyed the world’s ten largest short-selling hedge funds. (The rankings are
`from Managed Accounts Report, Inc. as of February 1999). One of the ten
`funds chose not to participate, but the nine respondents confirmed the
`conventional wisdom that their primary objective is to profit from short-selling
`temporarily overpriced stocks (survey results available upon request). They
`argued against the first risk factor interpretation described above. Of course, it
`is still possible that they inadvertently load up on risk in line with the second
`interpretation described above. Nevertheless, it is informative that sophisti-
`cated investors reject the risk factor interpretation. The fact that these
`sophisticated investors ‘‘vote with their feet’’ by shorting millions of dollars
`based on their belief that low fundamental-to-value ratios are associated
`with temporary mispricing provides additional credence to the mispricing
`interpretation.
`
`3. Sample formation and variable measurement
`
`In Section 3.1 we discuss the data sources and sample selection. In Section
`3.2 we discuss our variable measurement.
`
`3.1. Data sources and sample selection
`
`We require the following information to test our predictions: financial
`statement data, stock returns, institutional holdings data, and short interest
`data. Annual financial statement data are obtained from COMPUSTAT.
`Monthly stock returns are obtained from the Center for Research in Security
`Prices (CRSP). We obtain institutional data from Spectrum’s quarterly tapes.
`Short interest data are extracted from Asquith and Meulbroek’s database of
`monthly short interests. This database includes all New York Stock Exchange
`(NYSE) and American Stock Exchange (AMEX) firms and covers the time
`period 1976–1993. The original data sources for the Asquith and Meulbroek
`database are the Standard and Poor’s Daily Stock Price Record and Quarterly
`History Tape for the years 1976–1990 and the exchanges (NYSE and AMEX)
`for the years 1990–1993.
`Given the limits of the short interest database, our analysis is restricted to
`NYSE and AMEX firms in the years 1976–1993. Use of financial statement
`and stock return data eliminates firm-years not appearing on COMPUSTAT
`or CRSP. Tests using the Spectrum data are restricted to the years 1983–1993.
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`3.2. Variable measurement
`
`The short interest variable used in our analysis is the percent of outstanding
`shares shorted. This is equal to the number of common shares shorted divided
`by the total number of common shares outstanding. We measure short
`positions three months after the end of the fiscal year from which we extract the
`financial data to compute our fundamental-to-price ratios. This provides us
`with reasonable assurance that the financial data would have been available to
`short-sellers. The return cumulation period also begins three months after the
`fiscal year-end. We use buy-and-hold one-year-ahead stock returns (including
`dividends). We measure abnormal returns by adjusting each firm’s return by
`the equal-weighted return for all NYSE and AMEX stocks over the same time
`period. Note that this measure of abnormal returns makes no adjustment for
`differences in risk across firms, and so potentially biases our results in favor of
`mispricing. However, previous research has established that the predictable
`returns associated with the fundamental-to-price ratios are robust with respect
`to a variety of techniques for adjusting returns, and so we employ this relatively
`straightforward adjustment method. Asquith and Meulbroek (1996) also
`establish that the negative relation between excess returns and short positions is
`robust to a variety of techniques for calculating excess returns.
`We examine two measures of institutional holdings at the fiscal year-end: the
`percent of outstanding shares held by institutions and the number of
`institutions investing in the common stock of the firm. We also calculate
`dividend yields as cash dividends paid per share (Compustat item 21) divided
`by stock price. Finally, we construct the four fundamental-to-price ratios
`described in Section 2.2. Similar to prior research, we exclude observations
`when the numerator is negative and winsorize the most extreme 1% of our
`observations. We measure the earnings-to-price ratio as operating income after
`depreciation generated from year t 1 to t (Compustat item 178) divided by
`the product of common shares outstanding (Compustat item 25) and the firm’s
`fiscal year-end price (Compustat item 199). We measure the cash-flow-to-price
`ratio as cash flow generated from year t 1 to t divided by the product of
`common shares outstanding and the fiscal year-end price. Following Sloan
`(1996), cash flows are measured as earnings minus accruals, with earnings
`measured as described above and accruals measured as follows:
`Accrualst ¼ ðDCAt DCashtÞ ðDCLt DSTDt DTPÞt Dept;
`
`where
`DCAt=change in current assets (Compustat item 4)
`DCLt=change in current liabilities (Compustat item 5)
`DCasht=change in cash and cash equivalents (Compustat item 1)
`DSTDt=change in debt included in current liabilities (Compustat item 34)
`DTPt=change in income tax payable (Compustat item 71) and
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`Dept=depreciation and amortization expense (Compustat item 14).
`
`We measure the book-to-market ratio as the book value of common equity
`(Compustat item 60) divided by the product of common shares outstanding
`and the fiscal year-end price. We measure the value-to-market ratio at t as
`Book value of common equityt þ a1 ½Abnormal earningstŠ
`Common shares outstandingtPricet
`
`;
`
`a1 ¼
`
`and
`Abnormal earningst=Earningst (Compustat item 18) (Book value of
`common equityt1  r), and
`o
`1 þ r o
`where o is the persistence factor of abnormal earnings and r, the discount rate,
`is set equal to the long-run average return on equity of 12%. Following
`Dechow et al. (1999), we measure the persistence factor o for firm i in year t by
`performing the following pooled cross-sectional/time-series regression using all
`firm-years with available data in all prior years up to year t:
`Abnormal earningsi;t1 ¼ a0 þ o (Abnormal earningsi;t2)+ei;t1.
`
`In 1983, we use all firm-years prior to 1983, and in 1984 we use all firm-years
`prior to 1984, etc. We do not use information about abnormal earnings in year
`t since firms have different financial year-ends, and so not all information
`would necessarily be available for calculating o. For more details on this model
`see Ohlson (1995) and Dechow et al. (1999).
`
`4. Results
`
`Section 4.1 provides the results of our basic analysis of the relation between
`short interests, fundamental-to-price ratios, and future stock returns. Section
`4.2 presents additional
`results
`that provide further
`insights
`into the
`determinants of short interest.
`
`4.1. Short positions and the fundamental-to-price ratios
`
`Asquith and Meulbroek (1996) report that while most firms have less than
`0.5% of their outstanding shares shorted, a few firms have very large short
`positions (more than 5% of outstanding shares are shorted). The distribution
`of short positions is very similar for our sample of 34,037 firm-years. No short
`positions are observed for 12,445 firm-years, or 36.6% of the observations.
`Approximately 46% of our firm-year observations have very small short
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`positions (more than zero but no more than 0.5%). However, the distribution
`is highly skewed, with fewer than 2% of firm-years having over 5% of their
`outstanding shares shorted. Fig. 1 provides a calendar time plot of short
`positions. The average short interest has increased over time. Part of this
`increase is likely to be due to the deregulation of the capital market and the
`growth in hedge funds. Similar time trends are also observed in our
`fundamental-to-price ratios. Our empirical tests take into account the effect
`of this serial correlation on coefficient estimates.
`Panel A of Table 1 provides evidence on the relation between short positions
`and future returns. We sort firm-years into six categories based on the
`magnitude of the short position in the stock. Note that the number of
`observations varies across the categories, ranging from 12,445 in the category
`with no short positions to 564 in the category with over 5% of the outstanding
`shares shorted. For each category, we sort firm-years by calendar year and
`calculate the mean one-year-ahead abnormal return for each calendar year.
`The average of the 18 calendar-year mean abnormal returns are reported in
`Panel A. Consistent with Asquith and Meulbroek (1996) we document a
`negative relation between the level of short interest and future stock returns.
`Future abnormal returns decline monotonically with the level of short interest.
`For firms with no short positions, the average one-year-ahead abnormal return
`is 2.3%, while for firms with over 5% shorted, the average abnormal return
`falls to 18.1%.4 For each of the categories with short positions, the average
`abnormal return is significantly lower than the average abnormal return for the
`firm-years with no short positions.5
`In the tests that follow, we classify firms with over 0.5% of outstanding
`shares shorted as firms with ‘‘high short’’ positions, while the remaining firms
`are classified as ‘‘low short’’ positions. We focus on ‘‘high shorts’’ (as opposed
`to nonzero shorts) to increase the power of our tests. Large short positions are
`more likely to represent a consensus among short-sellers that a stock is
`
`4 The time-series mean abnormal return for all firms with over 0.5% shorted is 3.5% with a
`standard error of 0.009 (significant at the 0.001 level using a two-tailed test). The time-series mean
`abnormal return for firms with over 0.5% shorted but less than 5% shorted is 2.4% with a
`standard error of 0.012 (significant at the 0.06 level using a two-tailed test). Thus, firms that we
`classify as having ‘‘high short’’ positions have significantly negative abnormal returns.
`5 For each of the short interest portfolios, for each calendar year, we subtract the mean abnormal
`return on the no-short portfolio from the mean abnormal return on the short interest portfolio. We
`then determine whether the 18 resulting hedge portfolio returns are significant using the time-series
`standard errors of the hedge portfolio returns. The significance levels for each category are less than
`0.06 using a two-tailed test. We also investigate the robustness of these results by computing the
`standard errors of portfolio returns, weighting each observation by the square root of the reciprocal
`of the number of observations in the portfolio. This procedure controls for any heteroskedasticity
`introduced by changing numbers of portfolio observations over calendar time. However, because
`the number of observations is relatively constant over time, it has little discernible effect on the
`standard errors.
`
`Coalition for Affordable Drugs IV LLC - Exhibit 1042
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`

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`88
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`P.M. Dechow et al. / Journal of Financial Economics 61 (2001) 77–106
`
`Fig. 1. Average percent of outstanding shares shorted three months after the fiscal year-end.
`Sample consists of 34,037 firm-year observations over the sample period 1975–1993 with data
`available on both the number of shares shorted and the variables required to compute the
`fundamental-to-price ratios.
`
`overpriced (consistent with the return results in Panel A of Table 1). This 0.5%
`cutoff is arbitrary however, and so we test the sensitivity of our results to this
`cutoff. The tenor of our results is unchanged when we use 1% or 2.5% cutoffs.
`Panel B of Table 1 reports the relation between the four fundamental-to-
`price ratios and future abnormal stock returns. Firm-year observations are
`assigned to ten portfolios based on the relative magnitude of their ratios. The
`ranking procedure is carried out separately for each ratio and each calendar
`year. We then pool the observations across calendar years such that portfolio 1
`contains the lowest values of each of the ratios and portfolio 10 contains the
`highest values of each ratio across the sample period. Recall that prior research
`has documented a positive relation between one-year-ahead abnormal returns
`and each of the four ratios. Panel B indicates that we can replicate prior
`findings for our sample of firm-years. For cash-flow-to-price, the abnormal
`returns vary from 6.1% in portfolio 1 to 9.9% in portfolio 10. For earnings-
`to-price, the abnormal returns are slightly smaller, varying from 3.1% in
`portfolio 1 to 10.4% in portfolio 10. For book-to-market, the abnormal
`returns are 2.7% in portfolio 1 and 9.6% in portfolio 10. Finally, for our
`value-to-market ratio, the abnorma