Delisting returns and their effect on accounting-based market anomalies $

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1 Journal of Accounting and Economics 43 (2007) Delisting returns and their effect on accounting-based market anomalies $ William Beaver a, Maureen McNichols a,, Richard Price b a Graduate School of Business, Stanford University, USA b Jones Graduate School of Management, Rice University, USA Received 18 June 2005; received in revised form 28 November 2006; accepted 14 December 2006 Available online 5 January 2007 Abstract We show that tests of market efficiency are sensitive to the inclusion of delisting firm-years. When included, trading strategy returns based on anomaly variables can increase (for strategies based on earnings, cash flows and the book-to-market ratio) or decrease (for a strategy based on accruals). This is due to the disproportionate number of delisting firm-years in the lowest decile of these variables. Delisting firm-years are most often excluded because the researcher does not correctly incorporate delisting returns, because delisting return data are missing or because other research design choices implicitly exclude them. r 2007 Elsevier B.V. All rights reserved. JEL: G14; M41; G33; G34 Keywords: Accounting; Anomalies; Delisting returns; Accruals 1. Introduction The treatment of delisting returns has received relatively little attention in the accounting literature. A delisting return is the return on a security after it has been $ We thank an anonymous referee and Doug Skinner (the editor) for helpful comments. We also gratefully acknowledge financial support from the Stanford University Graduate School of Business and the Rice University Jones Graduate School of Management. Corresponding author. Tel.: ; fax: addresses: beaver_william@gsb.stanford.edu (W. Beaver), mcnichols_maureen@gsb.stanford.edu (M. McNichols), richardp@rice.edu (R. Price) /$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi: /j.jacceco

2 342 W. Beaver et al. / Journal of Accounting and Economics 43 (2007) removed from an exchange, and is calculated by comparing the security s value after delisting with the price on the last trading day. Delistings occur most frequently due to mergers and acquisitions or poor performance (e.g., bankruptcy). The omission of delisting returns is likely to affect estimates of portfolio returns because the expected return conditional on the reason for delisting is not generally zero. In addition, if the market return measure does not include delisting returns, market and market-adjusted returns will be affected. To demonstrate the potential impact of excluding delisting returns, we revisit anomalies based on earnings, accruals, cash flows and the book-to-market ratio (Sloan, 1996; Lakonishok et al., 1994; Bernard and Thomas, 1989, 1990). These studies compare the future returns of firm-years in high vs. low deciles of different accounting variables. These anomalies lead to questions of market efficiency with respect to fundamental accounting variables. In this paper, we demonstrate that portfolio returns, as conventionally measured in prior research, are sensitive to the treatment of delisting returns. We do not take a position on whether our findings provide evidence in favor of or against market efficiency because our analysis does not consider transaction costs, among other costs of implementing a trading strategy. As pointed out by Sloan (1996), findings of market inefficiency in historical data do not necessarily imply that strategies based on the findings are exploitable. Because firms that delist are on average highly risky and potentially illiquid, the exploitability of their returns is an open question. We find that the exclusion of firms that are delisted in the return accumulation period, hereafter delisting firm-years, does not uniformly increase or decrease portfolio returns. The effect on inferences about market efficiency depends on the partitioning variable or trading strategy. For portfolios partitioned on earnings, cash flows, and the book-tomarket ratio, the difference between average returns in extreme deciles increases when delisting firm-years are included. In contrast, for portfolios partitioned on accruals, average returns in the lowest accruals decile decrease significantly when delisting firm-years are included, but there is no significant change in the highest accruals decile. These results are due to the disproportionate concentration of delisting firm-years with very negative returns in the lowest decile of these variables. We examine the implications of using size-decile returns (or in general, market returns) that do not include delisting returns. In general, CRSP market return measures, including the commonly used Stock File Capitalization Decile Indices, do not include delisting returns. If researchers include delisting returns in the sample, but do not adjust the corresponding market return, portfolio returns will be affected. Three research design choices can result in the inadvertent exclusion of delisting firmyears. First, requiring future earnings excludes two-thirds of delisting firm-years. Second, nearly half of all delistings occur outside the date range provided by the CRSP/Compustat merged database, so valid delisting firm-years are excluded if one does not include matches outside the CRSP-specified date range. Third, when using monthly delisting returns, researchers unfamiliar with the details of CRSP data who use replacement values for firms with missing delisting returns will not identify all missing delisting returns because monthly delisting returns generally contain a partial month return even when the delisting return is missing. 1 Treating partial month returns as valid delisting returns implicitly assumes a delisting return of zero, which can affect estimated portfolio returns. 1 CRSP provides daily delisting returns, which are the returns attributable to the delisting and monthly delisting returns, which generally include the return from the beginning of the month to the date of the delisting, defined by CRSP as the partial month return, and the daily delisting return.

3 Researchers conducting tests of market efficiency should assess the sensitivity of their findings to the inclusion of delisting firm-years in their sample. Our findings indicate that inferences concerning market efficiency are sensitive to the treatment of delisting returns. The magnitude of the effects we document suggests that researchers should carefully consider whether the exclusion or inclusion of delisting firm-years affects inferences in tests of market efficiency and in other settings. Section 2 discusses the background and related research. Section 3 discusses the computation of delisting returns. Section 4 contains descriptive statistics. Section 5 contains the results of empirical analysis. Section 6 concludes. 2. Background discussion We focus on delisting returns for two reasons. First, we are unaware of any prior study that examines the treatment of delisting returns in the accounting literature and its implications for research design. The treatment of delisting firm-years varies substantially across studies. Many papers follow Sloan (1996) and include a description such as the following: the delisting return is compounded with the buy-and-hold return and 100% is used as the delisting return when it is missing and the firm was forced to delist. 2 Xie (2001) does not describe what is done with missing delisting returns. Hribar and Collins (2002) specifically state that firms with missing delisting returns are deleted. Mohanram (2004) uses 30% when delisting returns are missing for reasons related to poor performance. Piotroski (2000) assumes that all delisting returns are zero. Other papers are silent about how delisting firm-years are treated (Desai et al., 2004; Zach, 2003; Thomas and Zhang, 2002; Collins and Hribar, 2000; Zhang, 2005; Khan, 2005; Mashruwala et al., 2006). Second, delisting firm-years are not uniformly distributed across portfolios commonly formed on deciles of earnings, accruals, cash flows and the book-to-market ratio, variables of great interest to accounting researchers. As a result, the treatment of delisting returns can have a significant impact on estimated returns associated with trading strategies based on these variables Related research W. Beaver et al. / Journal of Accounting and Economics 43 (2007) The accounting and finance literatures document several puzzling patterns in return behavior, including the accrual anomaly (Sloan, 1996), post-earnings announcement drift (Ball and Brown, 1968; Bernard and Thomas, 1989, 1990), the value-glamour anomaly (Lakonishok et al., 1994), and the momentum anomaly (Jegadeesh and Titman, 1993). The literature finds that returns from portfolios partitioned on fundamental variables such as earnings, accruals, cash flows, the book-to-market ratio and past returns are unexpectedly high or low. A number of recent papers examine potential research design problems of tests of market efficiency. Kothari et al. (2005) show that passive deletion (exclusion of observations that do not survive the horizon studied) can lead to findings of systematic mispricing. Kraft et al. (2006) show that portfolio returns to an accruals-based strategy are sensitive to robustness tests such as trimming. Khan (2005) finds that accounting for 2 The following papers provide brief explanations of the treatment of delisting returns that are very similar to Sloan (1996): Sun (2003), Kraft et al. (2006) and Dopuch et al. (2005).

4 344 W. Beaver et al. / Journal of Accounting and Economics 43 (2007) additional risk factors causes the difference in returns between extreme accruals decile portfolios to become insignificant. Two studies in the finance literature address research design issues associated with delisting returns. Shumway (1997) documents that CRSP data were generally missing delisting returns for firms with poor performance (this has since been corrected by CRSP). Shumway and Warther (1999) find that when delistings for performance-related reasons are included, the size effect that small firms outperform large firms disappears for NASDAQ stocks. Both Shumway (1997) and Shumway and Warther (1999) suggest that researchers be explicit about how they handle delisting returns and alert researchers to potential problems with these data. Our paper follows the tradition of these two papers in documenting the effect of delisting returns on anomalies. Our study differs from these studies in three respects. First, our study addresses several issues relevant to the proper calculation of delisting returns from the CRSP database. Specifically, researchers who are unaware that monthly delisting returns contain a partial month return even when the delisting return is missing will fail to correct for the missing return. We find that nearly half of all delistings occur outside the date range provided by CRSP in the merged CRSP/Compustat database. In addition, if future earnings are required, nearly two thirds of all delistings are excluded due to lack of earnings data. Second, we do not find a uniform effect of delisting exclusions on inferences about market efficiency. Unlike Shumway (1997) and Shumway and Warther (1999), who document generally decreased returns to trading strategies when delistings are included, most notably with the size effect, our findings indicate that inclusion of delistings can increase or decrease the returns to different trading strategies. Third, the exclusion of delisting returns can affect estimates of market returns. If researchers include delistings in the sample, but do not adjust the market return measure, market-adjusted returns will be affected. Besides the inadvertent exclusion of delistings from the sample, subtle research design choices can also lead to the over-weighting of delistings in the sample. For example, if all available observations that meet minimum data requirements are used in conducting analysis, delistings will be over-represented in the most recent fiscal year. The most recent fiscal year of Compustat data typically will not have the required CRSP data to compute future returns. However, if the firm delists before the end of the return accumulation period, the firm will be included in the sample because fewer months of return data are required for delisting; the latest fiscal year will be composed primarily of delisting firmyears if care is not taken. Another example of a research design choice that can result in delistings being over-weighted in analysis is the use of 100% as a replacement value for missing delisting returns. Replacement values are discussed in the following section. 3. Delisting returns A delisting return is the return on a security after it has been removed from a stock exchange. CRSP provides a three-digit delisting code that explains the nature of the delisting. Most delistings are classified as mergers (51% of the delistings in our sample, delisting codes ) or dropped delistings 3 (44% of the delistings in our sample, delisting codes ). Delisting returns are computed from liquidation payments or 3 Examples of dropped delistings include bankruptcy, stock price below acceptable level, and insufficient assets, equity, or capital. Also within this range of delisting codes is the more recent phenomenon of firms who go

5 from other information about the value of the security after delisting. CRSP allows up to 10 years after the delisting to learn the delisting return and updates the records as needed. Most delisting returns are realized soon after the delisting. Untabulated descriptive statistics show that of the 4,142 dropped delistings in our sample that have nonmissing monthly delisting returns, 79% of delisting distribution payments are made in the month of the delisting and 16% are made after the month of the delisting, but within three months of the delisting. The remaining 5% of delisting payments occur more than three months after the delisting month. Researchers generally assume that delisting returns are realized immediately. These statistics suggest that the assumption is usually, although not always, reasonable Compounding delisting returns with standard returns If the researcher requires monthly returns for every month in the range 4 ½t; t þ kš then firms that delist in this range will be excluded from the sample. In the case of mergers, these returns are typically significantly positive. In the case of dropped delistings, these returns are typically significantly negative. To avoid excluding delisting firm-years, the delisting return can be used as a proxy for the return on the day of the delisting and can be compounded with standard returns. 5 The Appendix shows how to do this in detail. When a security delists, CRSP creates a record for the delisted security that indicates the delisting date, the reason for the delisting, and the delisting return. CRSP provides daily delisting returns and monthly delisting returns. Daily delisting returns are straightforward they contain only the delisting return, or the return given by using the last available price before delisting and the payment ultimately received by shareholders for the delisted security. The monthly delisting return generally contains the daily delisting return as well as the return from the beginning of the month to the date of the delisting. CRSP defines the return from the beginning of the month to the delisting date as the partial month return, and the return attributable to the delisting itself as the delisting return. Usually, the delisting occurs before the last trading day of the month. 6 In this case, the monthly delisting return contains the partial month return and the delisting return. However, if the delisting occurs on the last trading day of the month, the monthly delisting return contains only the delisting return because the standard monthly return is not missing Missing delisting returns W. Beaver et al. / Journal of Accounting and Economics 43 (2007) In some cases, the delisting return is unknown or under investigation by CRSP. Shumway (1997) and Shumway and Warther (1999) show that the exclusion of firms with missing delisting returns can significantly affect estimated portfolio returns. Untabulated descriptive statistics show that 9.4% of monthly delistings in CRSP have missing delisting (footnote continued) dark, or the choice by firms to delist from the NYSE, AMEX or NASDAQ to avoid filing with the SEC, as discussed in Leuz et al. (2006). 4 The range ½t; t þ kš is the range specified by researchers such as annual returns. 5 In order to compound delisting returns with standard returns, researchers must separately merge delisting returns (found in the WRDS mse file) with monthly returns (found in the WRDS msf file). 6 According to CRSP, the last trading day of the month is the last weekday of the month that the market was open for exchange.

6 346 W. Beaver et al. / Journal of Accounting and Economics 43 (2007) returns. Missing delisting returns are overwhelmingly dropped delistings: 94% of missing delisting returns are dropped delistings, while only 3% of missing delisting returns are merger-related. When the delisting return is unknown, the daily delisting return is missing. The monthly delisting return is missing (i.e., has no numeric value) only when the delisting occurs on the last trading day of the month. Otherwise, the monthly delisting return contains the partial month return. 7 Untabulated descriptive statistics show that in our sample of NYSE, AMEX and NASDAQ firms from 1962 to 2002, 702 delisting returns are missing in the monthly file. Of these, 645 of the corresponding monthly delisting returns are not literally missing, but contain partial month returns. Because many monthly delisting returns contain only partial month returns, they should be treated as missing. Shumway (1997) and Shumway and Warther (1999) suggest using a replacement value to avoid excluding firm-years with missing delisting returns. The median delisting return for firms delisted for poor performance reported in both papers is 30%, which can be used as a replacement value. Shumway and Warther (1999) suggest 55% can be used for NASDAQ firms. Rather than using a single replacement value for missing delisting returns, we use multiple replacement values depending on the nature of the delisting. For our replacement values, we use the average daily delisting return for the corresponding three-digit delisting code. We do this because average delisting returns vary significantly for different delisting codes. Using the information provided by CRSP about the delisting allows us to treat delisting categories differently. For example, our estimate of the delisting returns for bankrupt firms with missing delisting returns is different from the estimate for firms that voluntarily delist (go dark ). Specifically, we compute the average daily delisting return for every three-digit delisting code for all available delistings with nonmissing daily delisting returns, and use this as the replacement value for the missing delisting returns. The replacement value is compounded with the return from the beginning of the return accumulation period to the delisting date, as described in the Appendix. Sloan (1996) and the subsequent literature that describe how delistings are treated often use 100% as a replacement value. Since average delisting returns for the various categories of dropped delistings are generally not this low, this is probably too extreme an adjustment and likely results in a lower estimate of the return. When we use 100% as a replacement value, following Sloan (1996), our inferences are largely unchanged, but returns in the lowest decile of all anomaly variables decrease by up to 1%. Although our use of multiple replacement values is arguably better than the use of a single replacement value, the use of any replacement value is an estimate of an unknown return. Researchers should exercise caution and judgment in interpreting results, especially if results are sensitive to the choice of replacement values Computing market-adjusted returns An important aspect of the research design for market efficiency studies is the computation of risk-adjusted returns. 8 Much of the literature uses size-adjusted returns, 7 Refer to the Appendix for a detailed discussion. 8 We thank the reviewer for suggesting an examination of this issue.

7 W. Beaver et al. / Journal of Accounting and Economics 43 (2007) following Sloan (1996). The sample mean market-adjusted return should equal zero but will not if researchers apply market-return measures in a manner that weights observations differently from the weighting of returns in the market index. We discuss four reasons that market-adjusted returns can be nonzero. 9 First, nonzero average market-adjusted returns can result from the treatment of delisting returns. If delisting firm-years are included in the sample but excluded from the market-return measure, the average sample market-adjusted return can be nonzero. Second, Barber and Lyon (1997) show that long-run market-adjusted buy-and-hold returns can be significantly negative. They discuss that this is attributable in large part to the skewness of the returns distribution. Third, the sample average market-adjusted return can be nonzero due to differences in the population of firms that is used to create the market-return measure compared to the sample of firms for which enough data are available to conduct the analysis. If the sample of firms is used as a benchmark for itself, the problem of nonzero marketadjusted returns is eliminated by construction. However, the average risk-adjusted returns that would be realized on a sample can be nonzero. Finally, differences in how observations are weighted or grouped in the construction of market index returns vs. how they are weighted or grouped in research designs can result in nonzero average market-adjusted returns. Addressing all of these issues is beyond the scope of this paper, but we address the first because it relates to an important effect of the exclusion of delistings. Many market return measures provided by CRSP do not include delisting returns. In particular, the commonly used CRSP Stock File Capitalization Decile Indices 10 exclude delisting returns. The only CRSP-supplied return measures that include delisting returns are the CRSP Cap-Based Portfolio Indices and the CRSP Indices for the S&P 500 Universe. 11 In order to avoid excluding delisting returns from decile returns, we adjust the CRSP Stock File Capitalization Decile Indices to include delisting returns. We use the CRSP decile assignments and compute decile returns with the CRSP methodology after merging standard monthly returns, nonmissing delisting returns, and replacement values for missing delisting returns. The decile return is measured as the average return for decile firms, weighted by the lagged market value of equity. In addition to providing results using size-adjusted returns, we present results of portfolio tests with raw returns as a robustness check. The results with raw returns show directly what happens to average portfolio raw returns without the market adjustment. The extent to which the risk related to delistings is incorporated in the market-return measure is also important, but is not the primary focus of this paper Using the CRSP/Compustat merged database Many studies merge Compustat and CRSP using the CRSP/Compustat merged database (CCM). This file provides a direct link between the Compustat primary firm identifier, GVKEY, and the CRSP primary security identifier, PERMNO, and provides date ranges over which this link is effective. In cases where a GVKEY links to different 9 For our sample of firms, the average size-adjusted return is significantly negative over , 0:0063 ðt ¼ 2:051Þ, but is insignificant for , 0:0015 ðt ¼ 0:803Þ. 10 Wharton Research Data Services (WRDS) provides SAS data sets based on these Stock File Capitalization Decile Indices. They are the commonly used ermport and mport files. 11 The exclusion of delisting returns from indices is not clearly identified in CRSP documentation, but was communicated to us by CRSP technical support.

8 348 W. Beaver et al. / Journal of Accounting and Economics 43 (2007) securities (PERMNOs) over its history, CCM provides the link information so that returns can be merged. A significant number of delisting firm-years are excluded if CCM date ranges are interpreted literally. If return data outside the interval are not merged with Compustat, up to half of all delistings are excluded. The CCM manual states that If the CRSP data extends before or after the Compustat data for a company, the last known PERMNO can be used to identify the issue. Thus, the range in CCM should be appropriately extended to ensure that valid delistings are merged with Compustat. If Compustat and CRSP are merged using the CUSIP identifier, roughly 6% to 10% of total observations, including a similar percentage of the population of delistings, will be lost compared to using CCM, depending on how the merge is done Sample data 4.1. Sample period and variable definitions We use two sample periods: (1) , for which we use the balance sheet method to compute cash flows and accruals, and (2) , for which we use the statement of cash flows for cash flows and accruals measures. We effectively use data from 1961 to 2004 because we require lagged assets and 12-month returns beginning four months after fiscal year-end. The sample includes all non-adr NYSE, AMEX and NASDAQ firms that meet data requirements, excluding banks, insurance and real estate companies (SIC codes between 6000 and 6999). 13 We include NASDAQ firms because the incidence of delistings is significantly greater among NASDAQ firms, and because they are increasingly included in studies in the anomalies literature. 14 We measure earnings, E t, as operating income, DATA178 from Compustat, and income before extraordinary items, DATA Cash flows, CF t, are measured using the balance sheet method (Sloan, 1996) and using the statement of cash flows, excluding cash flows from extraordinary items and discontinued operations (Hribar and Collins, 2002), DATA308 DATA124. We compute accruals, AC t,ase t CF t. When using the balance sheet method to compute cash flows, we compute accruals with operating income. When using the statement of cash flows, we compute accruals using income before extraordinary items. Following Sloan (1996) and most subsequent papers, we deflate all accounting variables by the average of total assets, DATA When merging on CUSIP, we use the CNUM and CIC from Compustat and the NCUSIP from CRSP, ensuring that all current and historical CUSIPs are used. Fewer observations are lost with a merge based on the six-digit CUSIP: the sample size is only 6% smaller than when CCM is used. When using the eight-digit CUSIP, the sample size is roughly 10% smaller. This could be improved depending on what other steps are taken. 13 The exclusion of these companies does not significantly affect inferences. Sloan (1996) also excludes banking and insurance firms due to lack of data availability to compute accruals. The use of historical SIC codes (DATA324, which is only available after 1987) vs. the most recent SIC code (DNUM, which we use), does not change inferences either. 14 Inferences also hold when NASDAQ firms are excluded. Although Sloan (1996) includes only NYSE and AMEX firms, other papers include NASDAQ firms (Xie, 2001; Desai et al., 2004). 15 Inferences are unchanged whether DATA18 (earnings measure from income statement) or DATA123 (earnings measure from the cash flow statement) is used. 16 The literature following Sloan (1996) generally deflates by average assets, but papers examining other anomalies typically deflate by price.

9 W. Beaver et al. / Journal of Accounting and Economics 43 (2007) We measure market-adjusted returns in year t þ 1, UR tþ1, as 12-month, size-adjusted, buy-and-hold returns beginning four months after fiscal year-end. We compute size-decile returns as described earlier. To avoid excluding delisting firm-years, we use the return from the beginning of the accumulation period through the delisting date, including the delisting return, as the proxy for year t þ 1 returns, DR tþ1. We assume that when a firm is delisted, the proceeds are reinvested in the same size decile equally among all remaining stocks at the end of the delisting month. To show the sensitivity of results to delisting firm-years, the analysis is conducted including and excluding delisting firm-years. As defined earlier, a delisting firm-year is an observation that delists in the return accumulation period. Fiscal year t is a delisting firm-year if the firm delists in year t þ 1. We form deciles by fiscal year using all observations that meet the specified data requirements. Generally, we require the accounting variable in year t (E t ; AC t ; CF t or BM t ) and the return measure in year t þ Descriptive statistics Table 1 reports the number of delistings in CRSP that merge with Compustat. Panel A shows that after 1950 there are 18,388 monthly delisting returns in the 2004 CRSP file, of which 3,571 do not merge with Compustat because the security (PERMNO) is not in CCM, leaving 14,817 potential delistings to merge with Compustat. If the date of the fiscal year-end is required to be within the CCM date range, only 58.7% of delistings merge (of the 14,817 delistings that could merge with Compustat, only 8,701 are within the date range specified by CCM). 17 If the date range of CCM is extended where appropriate (if the PERMNO does not link to another GVKEY), many more delistings can be merged. An additional 32% (4,769 of 14,817) of these delistings occur within six months of the end date in the range specified by CCM. If the date range is extended as far as possible, 98.6% of all delistings successfully merge (14,613 of 14,817). Care must be taken to ensure that all valid delistings merge. Table 1 shows the frequency of delistings by decade in our sample of firms over the period in Panel B. The left column shows that the average yearly sample size (including delisting and nondelisting firm-years) increases steadily from the 1960s (average 1,492 firms per year) to the 1990s (average 5,403 firms per year). The frequency of delistings increases monotonically over time, from 0.7% in the 1960s, to 10.8% after The frequency of merger-related delistings also increases over time, from 0.5% of the sample in the 1960s to 4.4% after Similarly, the frequency of dropped delistings increases from 0.2% in the 1960s to 6.2% after The final two columns of panel B show the percentage of dropped delistings that have missing delisting returns. In the 1960s, 28% (72%) of dropped delistings have missing monthly (daily) delisting returns. This generally decreases over time to 2.5% (14.8%) after 2000 for monthly (daily) delisting returns. A significant number of dropped delistings have missing delisting returns, most notably prior to Researchers who use daily delisting returns should be aware that there are more missing daily than monthly delisting returns; if the date of the delisting payment is greater than 10 trading days after the delisting date, it can be missing in the daily file, but not in the monthly file. Delistings with missing daily but 17 Sample code provided by WRDS requires the date of the fiscal year-end to be within the date range provided by CCM.

10 350 W. Beaver et al. / Journal of Accounting and Economics 43 (2007) Table 1 Number and frequency of occurrence of delistings Panel A: number of delistings that merge with Compustat Total delistings in CRSP 18,388 PERMNO is not in CCM 3,571 Potential delistings to merge with Compustat 14,817 Delistings within CCM date range 8,701 Delistings p6 months after CCM date range 4,769 Delistings merge after extending date range 14,613 Delistings do not merge after extending date range 258 Panel B: frequency of delistings by decade Time period Average sample size Average percentage of sample delisted All (%) Mergers (%) Dropped (%) Average percentage of dropped delistings with missing delisting returns Monthly dr (%) Daily dr (%) , , , , , Panel A shows the number of monthly delisting returns post 1950 in the CRSP database, the number that merges with Compustat and explains why all delisting returns do not merge using the CRSP/Compustat merged database (CCM). Extending the date range means extending the CCM link end date as far as appropriate to allow delistings outside the range provided by CCM to be included in the sample. Panel B shows the frequency of delistings over the sample period, Merger-related delistings include delisting codes Dropped delistings include delisting codes Average sample size over each decade is shown as well as the average percentage of delistings in that decade. The final columns show the percentage of dropped delistings with missing delisting returns (dr) in both the daily and monthly files. not monthly delisting returns do not have unknown delisting returns, but they are reported as missing in the CRSP daily file because the delisting payment is delayed. Rather than using a replacement value for these delistings, the monthly delisting return can be used with daily return data to determine the daily delisting return. Table 2 shows the total number of firm-year observations in the sample over The minimum data requirements for our study are current earnings and future returns. Panel A shows that 153,969 observations meet these requirements. Most of these observations, 143,049, are nondelisting firm-years. Most of the nondelisting firm-year observations have nonmissing future earnings (142,313 firm-years with nonmissing E tþ1 vs. 736 firm-years with missing E tþ1 ). There is a total of 5,577 merger-related delisting firmyears. Most of these have missing future earnings (774 firm-years with nonmissing E tþ1 vs. 4,803 firm-years with missing E tþ1 ), so requiring future earnings excludes 86% of all mergers. There is a total of 4,819 dropped delisting firm-years. Many of these firm-years have nonmissing future earnings (2,849 firm-years with nonmissing E tþ1 vs. 1,970 firmyears with missing E tþ1 ), so requiring future earnings excludes about half of all dropped delistings. Panel B shows that the sample size decreases by 16,155 ð153; ; 814Þ when the additional financial statement variables are required to compute accruals.

11 W. Beaver et al. / Journal of Accounting and Economics 43 (2007) Table 2 Sample size with and without delistings Firm-years Nonmissing E tþ1 Missing E tþ1 Total Missing/total Panel A: sample size with earnings Nondelisting 142, , Delisting Merger-related ( ) 774 4,803 5, Dropped ( ) 2,849 1,970 4, Other Delisting subtotal 3,769 7,151 10, Total firm-years 146,082 7, , Panel B: sample size with cash flows and accruals Nondelisting 126, , Delisting Merger-related ( ) 723 4,587 5, Dropped ( ) 2,685 1,852 4, Other Delisting subtotal 3,542 6,791 10, Total firm-years 130,365 7, , This table shows the number of observations in the sample including NYSE, AMEX and NASDAQ firms over Current operating Income, E t, and either year t þ 1 size-adjusted returns ður tþ1 Þ or year t þ 1 delisting returns are required; the return accumulation period begins four months after the fiscal year-end and continues for 12 months. Panel A shows the total number firm-years in the sample, grouped by nondelisting and delisting firm-years (observations that are delisted in the return accumulation period). The number of each group with nonmissing and missing future earnings ðe tþ1 Þ is also presented. Panel B in addition requires current cash flows ðcf t Þ and accruals ðac t ¼ E t CF t Þ. Cash flows are computed using balance sheet data as in Sloan (1996). The last column of the table shows the percentage of each group that has missing E tþ1. In sum, requiring E tþ1 results in the exclusion of nearly two-thirds of all delistings. In a merger, the stock of the acquired firm generally ceases to trade and the acquired firm will likely stop filing financial reports with the SEC. As a result, there are very few mergerrelated delistings that have future earnings. With dropped delistings, a firm often continues to exist and files its financial reports with the SEC even though it is no longer listed on the NYSE, AMEX or NASDAQ. Table 3 shows average delisting returns for the major categories of delistings and the decile locations of these delistings. Panel A shows that over the sample period, there are 5,577 merger-related delistings, 392 exchange delistings, 132 liquidation delistings and 4,819 dropped delistings. The average size-adjusted return including delisting returns beginning four months after fiscal year-end through the delisting for mergers is 28%, of which 2% is the daily delisting return. In contrast, for dropped delistings the size-adjusted return is 51%, of which 14% is the daily delisting return. Table 3 shows the number of merger-related and dropped delisting firm-years in the deciles of the anomaly variables examined in this paper in Panel B. For delistings due to mergers in book-to-market ðbm t Þ and earnings ðe t Þ deciles, the number of delisting firmyears is the lowest in decile 1 (385 in decile 1 of E t, 407 in decile 1 of BM t ), but the number of observations in the remaining deciles fluctuates between 420 and 650. There is an increasing trend across cash flows ðcf t Þ deciles (335 in decile 1 and 570 in decile 10), and a

12 352 W. Beaver et al. / Journal of Accounting and Economics 43 (2007) Table 3 Average delisting returns and decile concentrations of delistings Category n URþ dr dr Panel A: delistings by category , , Decile E t AC t CF t BM t Panel B: decile concentrations of delistings Mergers: delisting codes Dropped securities: delisting codes ,913 1,480 1,415 1, , Panel A shows the number of delistings in the sample over for NYSE, AMEX and NASDAQ firms. Average size-adjusted returns are also shown including monthly returns prior to delisting with the delisting in year t þ 1 ður þ drþ and the (daily) delisting return (dr) by itself. Panel B shows the distribution of delistings across deciles. Deciles are formed by fiscal year with the following variables: operating income ðe t Þ; accruals ðac t Þ and cash flows ðcf t Þ computed using the balance sheet method; and the book-to-market ratio ðbm t Þ. CRSP groups delistings as follows: is mergers; is exchanges; is liquidations; is dropped securities. decreasing trend across accruals ðac t Þ deciles (558 in decile 1 and 399 in decile 10); firms with low accruals and high cash flows are more likely to be acquired. Dropped delistings are concentrated in extreme deciles. There is a large difference in the number of observations in the lowest vs. all other deciles for all of the anomaly variables: for earnings ðe t Þ, there are 1,913 in decile 1 vs. 66 in decile 10; for accruals ðac t Þ there are 1,480 in decile 1 vs. 510 in decile 10; for cash flows ðcf t Þ, there are 1,415 in decile 1 vs. 241 in decile 10. With the book-to-market ðbm t Þ ratio, there are significantly more delistings in the extreme low and high deciles (1,464 in decile 1 and 861 in decile 10 compared to 227 in decile 5).

13 W. Beaver et al. / Journal of Accounting and Economics 43 (2007) This pattern is consistent with Piotroski (2000), who finds that firms with weak current signals are more likely to delist for adverse reasons and with Mohanram (2004), who finds that firms with strong fundamentals are less likely to be delisted for adverse reasons. In sum, merger-related delistings are comparatively more evenly distributed over the various anomaly deciles and dropped delistings exhibit substantial concentration in the lowest decile. Thus, excluding dropped delistings is likely to significantly affect results because of the uneven distribution across deciles, i.e., the returns in the lowest deciles will generally be significantly higher if delistings are excluded. Table 4 shows additional descriptive statistics for delisting firm-years by accruals decile. These statistics show that dropped delistings in the lowest accruals decile exhibit a very high risk of bankruptcy, have consistently negative earnings, have extremely negative special and extraordinary items and are very highly levered. The reported statistics include: the Z-Score 18 (Altman, 1968); the average percentage of earnings in the past 5 years with negative net income, estimated for each firm as the number of firm-years with negative earnings divided by the number of firm-years with nonmissing earnings in the past 5 years; the average sum of special items and extraordinary items deflated by average assets; and the average leverage as measured by total liabilities divided by total assets. All variables except for the percentage of negative earnings in the past 5 years are winsorized at the top and bottom 1% to reduce the influence of outliers. Table 4 Panel A shows descriptive statistics for mergers. The Z-Score is positive for all deciles (2.52 for decile 1, which generally increases to 28.3 for decile 10). The Z-Scores in Panel A suggest that the average firm that is acquired in a merger is not in immediate danger of bankruptcy. Firms in the lowest accruals decile have a higher fraction of past earnings that are negative (0.47 for decile 1 vs in decile 10). The average special and extraordinary items are increasing across deciles ( 0:04 in decile 1 vs. 0 in decile 10). Finally, leverage does not vary significantly across deciles (0.54 in decile 1, 0.52 in decile 5 and 0.47 in decile 10). Table 4 Panel B shows descriptive statistics for dropped delistings. The Z-Score is significantly negative for the lowest decile, but fluctuates for the remaining deciles ( 5:08 for decile 1, 3.40 for decile 5 and 2.06 for decile 10). The Z-score for dropped delistings in the lowest accruals decile is very different than the Z-score for mergers in Panel A. This is not surprising since bankruptcies are included in the set of dropped delistings. Dropped delistings have a much higher fraction of past earnings that are negative (0.77 for decile 1 and 0.67 for decile 10). Special and extraordinary items are significantly negative for all deciles, but are the most negative for the lowest decile ( 0:09 for decile 1 vs. 0:03 for decile 10). Finally, leverage is higher for dropped delistings than for mergers, and is highest for the lowest decile (1.04 for decile 1 vs for decile 10). Table 5 shows the average anomaly decile firm size and the impact of delistings on sizedecile returns. Panel A shows the average firm size, as measured by the market value of equity at the beginning of the year t þ 1 return accumulation period, across the deciles of the anomaly variables examined in this paper. With earnings and cash flows, there is a strictly monotonic increase in average firm size across deciles: for earnings ðe t Þ, average 18 We use the original coefficients reported by Altman (1968) as follows: Z-Score ¼ 1:2 working capital=assets þ 1:4 retained earnings=assets þ 3:3 EBIT=assets þ 0:6 market value of equity/total liabilities þ 0:999 revenue=assets. Altman (1968) finds that firms with a Z-Score below exhibit greater risk of bankruptcy.

14 354 W. Beaver et al. / Journal of Accounting and Economics 43 (2007) Table 4 Descriptive statistics by accruals decile for delisting firm-years Decile Z-Score NIo0 SI þ EI Leverage n Panel A: mergers (codes ) Panel B: dropped delistings (codes ) , This table shows additional descriptive statistics by accruals decile for delisting firm-years (observations that are delisted in the return accumulation period). The averages of the following variables are presented: Altman s Z- Score; the average percentage of earnings in the past 5 years with negative net income ðnio0þ; the average sum of special items and extraordinary items deflated by average assets ðsi þ EIÞ; and the average leverage as measured by total liabilities divided by total assets. All variables except for the percentage of negative earnings in the past 5 years ðnio0þ are winsorized at the top and bottom 1% to reduce the influence of outliers. Panel A shows descriptive statistics for mergers (delisting codes ). Panel B shows descriptive statistics for dropped delistings (delisting codes ). The sample is pooled over and includes NYSE, AMEX and NASDAQ firms. Accruals deciles are assigned by fiscal year. firm size increases from $64 million in decile 1 to $1,974 million in decile 10; for cash flows ðcf t Þ, it increases from $71 million to $1,923 million. With accruals ðac t Þ, extreme deciles consist of smaller firms ($272 million and $226 million in deciles 1 and 10, respectively) with larger firms in middle deciles ($1,372 million in decile 5). With the book-to-market ratio ðbm t Þ, larger firms are generally in low deciles ($1,329 and $1,958 million in deciles 1 and 2, respectively) with small firms in the high deciles ($82 million in decile 10). Table 5 Panel B compares CRSP size-decile (Stock File Capitalization Decile) returns to the size-decile returns we compute that include delisting returns. We compound returns over calendar years after 1990 because the number of delistings is greater in this period, although the pattern is observable over the entire time period. CRSP decile returns and the adjusted decile returns are both monotonically decreasing across size deciles: CRSP sizedecile returns are 31% in the lowest size decile and 12.2% in the highest whereas the sizedecile returns that are adjusted to include delisting returns are 27.3% in the lowest size decile and 12.2% in the highest. The most significant differences between CRSP size-decile

15 W. Beaver et al. / Journal of Accounting and Economics 43 (2007) Table 5 Decile firm size and the impact of delistings on size-decile returns Decile E t AC t CF t BM t Panel A: average decile firm size , , , , , , , , , , , , , , , , Size decile CRSP decile return Adjusted decile return Difference Panel B: Comparing CRSP decile returns to decile returns that include delistings Panel A shows the average market value of equity of firms in the deciles examined in this paper: earnings ðe t Þ, accruals ðac t Þ, cash flows ðcf t Þ and the book-to-market ratio ðbm t Þ. The sample is pooled over and includes NYSE, AMEX and NASDAQ firms. Deciles are assigned by fiscal year. The average market value of equity is reported for each decile of the corresponding variable. Panel B shows the difference between CRSP sizedecile (stock file capitalization decile) index returns and size-decile index returns that are adjusted to include delisting returns, as discussed in the paper. Returns are compounded over calendar years. We report the average index returns from for size-deciles of NYSE, AMEX and NASDAQ firms. returns and the adjusted size-decile returns are in the lowest deciles (CRSP returns are 3.7% and 1.2% higher in size deciles 1 and 2, respectively). These results are consistent with the descriptive statistics in Panel B of Table 3 and Panel A of Table 5. Since dropped delistings are concentrated in the lowest deciles of earnings, cash flows and accruals, and the firms in the lowest deciles of these variables are generally smaller, the exclusion of missing delisting returns from the size-decile returns has the most significant impact in the lowest size deciles. 5. Empirical analysis We conduct two types of tests to demonstrate the impact of delisting returns on empirical analysis of anomalies. First, we estimate regressions of future size-adjusted returns on earnings, accruals and cash flows following Beaver and McNichols (2001). Second, we conduct an analysis of future returns with portfolios formed on the level of

16 356 W. Beaver et al. / Journal of Accounting and Economics 43 (2007) earnings, accruals, and cash flows, all deflated by average assets, following Sloan (1996), and on the book-to-market ratio, following Lakonishok et al. (1994) Empirical methods We employ the following regression models which regress year t þ 1 size-adjusted returns on year t accounting variables: UR tþ1 ¼ a þ be t þ e tþ1, (1) UR tþ1 ¼ a þ gcf t þ dac t þ e tþ1. (2) Market efficiency implies that b ¼ 0 and that g ¼ d ¼ 0, i.e., future risk-adjusted returns should not be predictably related to current publicly available information. We do not trim the variables in these regressions to provide consistency between regression results and portfolio tests, which also use untrimmed data. Inferences are not significantly affected if the data are trimmed or if models are estimated in ranks. Sloan (1996) does not trim. Our portfolio tests are based on decile portfolios formed using the following variables at time t: earnings ðe t Þ, accruals ðac t Þ, cash flows ðcf t Þ and the book-to-market ratio ðbm t Þ. Average returns are computed for each decile. Market efficiency implies that risk-adjusted returns should be insignificant for each decile. The Mishkin (1983) model is also used in the literature, following Sloan (1996). Wedo not tabulate findings using the Mishkin framework because it requires future earnings and consequently, two-thirds of delisting firm-years would be excluded. Regressing future returns directly on current accounting variables avoids excluding delisting firm-years, which is the focus of our study Results Return regressions Table 6 presents the estimation results for Eq. (1). Panel A shows that when delisting firm-years are excluded, the estimated coefficient on income before extraordinary items over is marginally significant, 0:019 ðt ¼ 1:94Þ, and the estimated coefficient on operating income over is significant, 0:045 ðt ¼ 5:57Þ. Panel B shows that when delisting firm-years are included, the coefficient on income before extraordinary items over increases in magnitude and significance to 0:089 ðt ¼ 10:6Þ and the coefficient on operating income over increases to 0:117 ðt ¼ 16:61Þ. These findings suggest that stock prices do not completely reflect the future implications of current earnings. This is inconsistent with Sloan (1996), who finds that the market correctly estimates earnings persistence. The difference in results can be attributed to differences in research design. We regress future size-adjusted returns directly on current earnings while Sloan (1996) uses the Mishkin framework, which requires future earnings and therefore excludes a significant number of observations, including delisting firm-years. We also include firms traded on the NASDAQ, which are excluded from Sloan (1996). Finally, our sample time period extends beyond the time period of Sloan (1996) and, consequently, includes many more delistings. Our results are consistent with Bernard and Thomas (1989, 1990), Abarbanell and Bernard (1992) and Collins and Hribar (2000), who find mispricing of earnings.

17 W. Beaver et al. / Journal of Accounting and Economics 43 (2007) Table 6 Return regressions with earnings UR tþ1 ¼ a þ be t þ t (1) income before extraordinary items operating income Estimate t-value Estimate t-value Panel A: excluding delisting firm-years a b n 74, , R 2 a Panel B: including delisting firm-years a b n 82, ,969 R 2 a This table shows the results of the regression of future size-adjusted returns ður tþ1 Þ on current earnings ðe t Þ. The earnings measure used is income before extraordinary items over the time period and operating income over The measure of returns is the 12-month, size-adjusted return beginning four months after the fiscal year-end. Delisting firm-years (observations that are delisted in the return accumulation period) are excluded in Panel A and included in Panel B. Variables are not trimmed for this analysis, but inferences are essentially unchanged when the top and bottom 1% of all variables are trimmed. Table 7 contains the estimation results for Eq. (2). This analysis controls for the incremental effect of cash flows ðcf t Þ and accruals ðac t Þ for each other. This is important because the two components of earnings are significantly negatively correlated. In Panel A, when delisting firm-years are excluded, the estimated coefficients are significant for both sample periods. For the sample period using cash flow statement data, the estimates are 0:092 ðt ¼ 6:58Þ for CF t and 0:066 ðt ¼ 4:61Þ for AC t. For the sample period, using the balance sheet method, the estimated coefficients are 0:075 ðt ¼ 8:72Þ for CF t and 0:206 ðt ¼ 12:15Þ for AC t. Panel B shows that when delisting firmyears are included, cash flow coefficient magnitudes increase and become more significant while accrual coefficient magnitudes become insignificant or less significant. For the sample period, the coefficients are 0:168 ðt ¼ 13:62Þ for CF t and 0:005 ðt ¼ 0:39Þ for AC t. Over , the coefficients are 0:147 ðt ¼ 19:19Þ for CF t and 0:07 ðt ¼ 4:79Þ for AC t. These results show that the cash flow effect gets stronger, while the accrual effect becomes weaker when delistings are included. The insignificance of accruals in the regression for is consistent with Desai et al. (2004), who find that in the presence of other fundamental variables, cash flows is highly significant, while accruals is insignificant. 19 Our results suggest that the insignificance of accruals in the multivariate 19 Although not discussed in their paper, we confirmed by correspondence that Desai et al. (2004) do include delisting returns. Also, Desai et al. (2004) do not require future earnings as Sloan (1996) does.

18 358 W. Beaver et al. / Journal of Accounting and Economics 43 (2007) Table 7 Return regressions with cash flows and accruals UR tþ1 ¼ a 0 þ gcf t þ dac t þ e t CF and AC from cash flow statement (2) CF and AC from balance sheet method Estimate t-value Estimate t-value Panel A: excluding delisting firm-years a g d n 69, , R 2 a Panel B: including delisting firm-years a g d n 76, , R 2 a This table shows the results of the regression of future size-adjusted returns ður tþ1 Þ on current cash flows ðcf t Þ and accruals ðac t Þ. Cash flows and accruals are computed with the balance sheet method over and with cash flow statement data over The measure of returns is the 12 month, size-adjusted return beginning four months after the fiscal year-end. Delisting firm-years (observations that are delisted in the return accumulation period) are excluded in Panel A and included in Panel B. Variables are not trimmed for this analysis, but inferences are essentially unchanged when the top and bottom 1% of all variables are trimmed. regression is due, in large part, to delisting firm-years. Our results provide an explanation for why the different designs of Desai et al. (2004) and Sloan (1996) lead to different conclusions about investors ability to process accruals Portfolio tests of earnings deciles Results of portfolio tests of all anomaly variables are presented with size-adjusted returns and raw returns. Inferences are consistent with both measures of returns, demonstrating the robustness of the results. The results with raw returns show the effect of excluding delisting firm-years on portfolio returns without an adjustment for expected returns. We use size-adjusted returns as our measure of market-adjusted returns because it is commonly used in the literature. Since all raw decile returns are significantly positive, we do not report the associated t-statistics in the tables. Table 8 shows the results of portfolio tests of earnings deciles. Panel A shows that when delisting firm-years are excluded, the difference between extreme deciles is insignificant over (using income before extraordinary items) and significant over (using operating income). Over , both extreme deciles, and the difference between them, 0:01 ðt ¼ 0:52Þ, are insignificant. Over the difference is 0:043 ðt ¼ 4:02Þ: decile 1 is 0:028 ðt ¼ 2:93Þ and decile 10 is 0:015 ðt ¼ 3:04Þ.

19 W. Beaver et al. / Journal of Accounting and Economics 43 (2007) Table 8 Returns of earnings deciles E t decile income before EI operating income Mean R tþ1 Mean UR tþ1 t-value Mean R tþ1 Mean UR tþ1 t-value Panel A: excluding delisting firm-years n 74,542 74, , ,049 Panel B: including delisting firm-years n 82,208 82, , ,969 This table shows returns by earnings decile. Data are ranked by fiscal year earnings ðe t Þ deflated by average assets. Average returns are computed for each decile. Income before extraordinary items (EI) is used over and operating income is used over The return measures used are raw returns ðr tþ1 Þ and size-adjusted returns ður tþ1 Þ starting four months after the fiscal year-end compounded for 12 months. Delisting firm-years (observations that are delisted in the return accumulation period) are excluded in Panel A and included in Panel B. Panel B shows that when delisting firm-years are included, the difference between extreme deciles increases in magnitude and significance. Over , the difference is 0:107 ðt ¼ 6:11Þ: decile 1 is 0:083 ðt ¼ 5:44Þ and decile 10 is 0:024 ðt ¼ 2:79Þ. Over the difference is 0:108 ðt ¼ 10:92Þ: decile 1 is 0:085 ðt ¼ 9:83Þ and decile 10 is 0:023 ðt ¼ 4:79Þ. The same effect is observable in raw returns. Over both time periods there is a significant decrease in the returns of the lowest decile. Returns in decile 1 decrease from in Panel A to in Panel B over and from 0.15 in Panel A to in Panel B over Also, over both time periods, the largest return of any decile in Panel B is decile 10: 0.16 over and over The difference between extreme deciles of raw returns is positive and significant: over and over

20 360 W. Beaver et al. / Journal of Accounting and Economics 43 (2007) The regression results presented in Table 6 are consistent with the results presented in Table 8. Both analyses show a significant earnings effect whether delisting firm-years are included or excluded, and that the effect becomes stronger in magnitude and significance when delisting firm-years are included, over both time periods Portfolio tests of accruals deciles Table 9 shows the results of portfolio tests of accruals deciles. Panel A shows that when delisting firm-years are excluded, the difference between extreme deciles is significant over both time periods. Over , using accruals computed with cash flow statement data, the difference is 0:139 ðt ¼ 6:94Þ and decile returns are generally decreasing across deciles (decile 1 is and decile 10 is 0:073). Over , the difference is 0:135 ðt ¼ 11:04Þ and, again, decile returns are generally decreasing across deciles (decile 1 is and decile 10 is 0:080). Panel B shows that when delisting firm-years are included, the difference between extreme deciles decreases in magnitude and significance. Over , the difference between extreme deciles decreases to 0:063 ðt ¼ 3:44Þ. The lowest AC t decile return is now insignificantly negative, 0:024 ðt ¼ 1:62Þ. The difference between extreme deciles remains significant because of the large negative returns in decile 10, 0:087 ðt ¼ 8:46Þ. Over , the difference is 9.7% ðt ¼ 8:43Þ. Again, the most significant change across deciles is in the lowest decile: returns in decile 1, 0:007 ðt ¼ 0:77Þ, are insignificant while returns in the highest decile increase in absolute magnitude and significance, 0:09 ðt ¼ 12:84Þ. The same effect is observable in raw returns. Over both time periods there is a significant decrease in the returns of the lowest decile. Returns in decile 1 decrease from in Panel A to in Panel B over and from in Panel A to in Panel B over The difference between extreme deciles of raw returns decreases from to over and from to over The regression results in Table 7 are largely consistent with the results presented in Table 9. Both tests suggest that the accrual effect is sensitive to the inclusion of delisting firmyears in the sample. Both tests show that the accrual effect is significant when delisting firm-years are excluded, and that the effect weakens as delisting firm-years are added, due to the disproportionate number of dropped delistings in the lowest accruals decile Portfolio tests of cash flow deciles Table 10 shows the results of portfolio tests of cash flow deciles. Panel A shows that when delisting firm-years are excluded, the difference between extreme deciles is significant over both time periods. Over , using cash flows from the cash flow statement, the difference is 0:10 ðt ¼ 5:47Þ and decile returns are generally increasing across deciles (decile 1is 0:04 and decile 10 is 0.059). Over , the difference is 0:113 ðt ¼ 9:98Þ and, again, the decile returns are generally increasing across deciles (decile 1 is 0:064 and decile 10 is 0.049). Panel B shows that when delisting firm-years are included, the difference between extreme deciles increases in magnitude and significance. Over , the difference between extreme deciles is 0:165 ðt ¼ 9:78Þ. The main difference is that returns in the lowest decile fall to 0:103 ðt ¼ 7:22Þ. Over , the difference between extreme deciles is 0:159 ðt ¼ 15:06Þ, which is attributable to returns in the lowest decile falling to 0:109 ðt ¼ 12:13Þ.