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Reverse stock splits, institutional holdings, and share value.

We show that both the number of institutional investors and the percentage of shares that are held by institutional investors increase significantly after reverse splits with a presplit price lower than $5 and a target price higher than $5. This effect is larger than for other comparable reverse splits. These results suggest institutional holdings are affected by the prudent-person rule and reverse splits are used by firms to alleviate this constraint. We also show that an increase in institutional holdings that results from reverse splits is associated with an increase in share price.

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Despite its frequent occurrence, the reverse stock split has been the subject of relatively few studies. In this paper, we shed further light on the causes and consequences of the reverse stock split by analyzing its effects on institutional holdings and shareholder wealth using data from 1980 through 2010 for a large sample of reverse stock splits in the US markets.

The level of institutional ownership in US companies has risen significantly in recent decades and corporate managers are paying increasingly greater attention to institutional preference to attract more institutional investments in their stocks. (1) Prior research shows that institutional investors are more likely to hold stocks of companies with higher share prices and larger market capitalizations (Faulkenstein, 1996; Gompers and Metrick, 2001), higher quality ratings (Del Guercio, 1996), better governance structures (McCahery, Sautner, and Starks, 2010; Chung and Zhang, 2011), stable payout policies (Grinstein and Michaely, 2005), better managerial performances (Parrino, Sias, and Starks, 2003), and higher pay-for-performance sensitivity (Hartzell and Starks, 2003). The present study offers new insight into institutional preference by analyzing the effect of the reverse stock split on institutional holdings.

Anecdotal evidence suggests that companies use reverse splits as a means to expand and broaden their investor base by attracting more institutional investors and financial analysts. For example, Martin Brauns, chairman and chief executive officer (CEO) of Interwoven Inc., stated that, "We believe that the reverse stock split will position our stock in a price range more attractive to a broader range of institutional investors ... Realigning our share base is one more step in our process of delivering long-term shareholder value." (2) More recently, Vikram Pandit, CEO of Citigroup, told shareholders that its recent announcement of a 1-for-10 reverse stock split will "open doors for more potential investors to buy in." (3) Others disagree. For instance, Krantz (2011) and McDonald (2011) argue that the reverse split would not bring any real benefits to investors because it is just an accounting maneuver.

Despite the conflicting views on the effects of reverse stock splits on institutional investment and share value, there is no hard empirical evidence. (4) We provide such evidence in this study. In particular, we examine whether the number of institutional investors and the percentage of shares that are held by institutional investors increase after reverse splits. We also examine whether changes in institutional holdings that result from reverse splits have any effect on shareholder wealth.

Reverse splits help remove the penny stock image for low-priced stocks, making them more acceptable to institutional investors. (5) Penny stocks are notorious for being vulnerable to fraudulent schemes. (6) The Securities and Exchange Commission (SEC) warns investors in penny stocks that they "should be prepared for the possibility that they may lose their whole investment" and requires enhanced suitability and disclosure obligation of broker-dealers when selling penny stocks to customers. (7) In addition, reverse splits may also make low-priced stocks more acceptable to institutional investors by reducing the perceived risk of potential delisting (e.g., all things being equal, institutional investors are likely to believe that a stock selling at $6 has a lower probability of eventual delisting than a stock selling at $3).

The prudent-person rule mandates that institutional investors have fiduciary responsibility to clients and that they must invest with caution. For example, they should avoid investing in risky, speculative, or low quality stocks. They should also avoid stocks with a high probability of delisting. Badrinath, Gay, and Kale (1989) find evidence that institutional investors maintain prudence of their investments by including stocks with a safety-net potential. Del Guercio (1996) provides evidence that institutional investors, especially banks, are sensitive to the prudent-person rule and that their portfolios are tilted toward high quality stocks. Because low-priced stocks are typically perceived to be speculative, institutional investors are likely to avoid holding them. Institutional investors that hold penny stocks may find themselves in an indefensible position when being sued by clients for violating the prudent-person rule.

According to the SEC definition, penny stocks generally refer to stocks priced under $5. (8) The SEC definition of penny stocks has certainly influenced institutional investors' stock selection because they frequently filter out stocks under $5 from their portfolio. (9,10) For instance, when the Bank of America share price closed at $4.99 on December 19, 2011, Eric Teal, Chief Investment Officer at First Citizens Bancshares, told Bloomberg that, "As active managers, we have screens that usually prohibit us from buying stocks under $5 ... If we own it, we would not kick it out automatically, but generally we tend to avoid stocks like that." (11)

Therefore, if a firm disappears from institutional investors' "radar screen" because its share price drops below $5, a reverse split that raises the share price above $5 (albeit artificially) could help the firm to reappear on the radar screen. A mean-variance institutional investor who seeks to diversify her portfolio would now be able to invest in the stock that she was prohibited from investing in before the reverse split. In the present study, we provide evidence on whether reverse splits that remove the fiduciary concern by raising the share price above the $5 low price hurdle help attract additional institutional holdings.

In the incomplete information market as described by Merton (1987), investors consider only those stocks that they "know about" in the construction of optimal portfolios. As the number of investors who know about a company increases, its investor base expands and, as a result, its share price may increase also. Although in Merton's model the reduction in investors' opportunity sets arises from informational issues, he emphasizes that other factors, such as market segmentation and institutional limitation, could have similar effects. In the context of our study, a firm's investor base may be restricted if its share price is too low to meet the fiduciary responsibility of institutional investors. If the firm could expand its investor base by attracting more institutional investors through reverse splits, we may expect to find an increase in share price after reverse splits.

We measure institutional holdings by both the number of institutional investors (NII: Number of Institutional Investors) and the percentage of shares that are held by institutional investors (PIH: Percentage Institutional Holding). We employ an empirical methodology that combines the difference-in-difference approach and the propensity score matching technique to measure the effect of reverse splits on institutional holdings using a control sample of non-reverse-split firms. Our empirical findings can be summarized as follows.

First, we find that reverse splits with the presplit price lower than $5 and the target price higher than $5 (we call them L5H5 reverse splits) are followed by a significant increase in NII and PIH over the two-year postsplit period, and that such an increase cannot be explained by the reduction in risk and the improvement in liquidity after the reverse splits. We do not find similar increases in NII and PIH for other reverse splits. Decomposing the aggregate holdings into the holdings of each type of institution, we find that the postsplit increase in NII and PIH is largely due to L5H5 reverse splits that result in increased ownership by bank trusts, investment companies, pension funds and university endowments, and independent investment advisors. We interpret these results as evidence that reverse splits that reduce fiduciary concern about potential litigation (due to investment in penny stocks) entice greater institutional holdings.

Second, the results of a Factiva search for reasons provided by firms for reverse splits indicate that reverse splits are frequently prompted by the firm's desire to expand and broaden its investor base (about 40% of the sample). However, we find that the stated motives for a reverse split matter less than the reverse split per se to institutional investors. Third, we find that the postsplit increase in the number of analysts is concentrated on L5H5 reverse splits. This result lends further support to our conjecture that the removal of fiduciary concern is the channel through which reverse splits help entice institutional investors and financial analysts.

Finally, the postsplit increase in NII and PIH is associated with the postsplit increase in share price, which is consistent with Merton's incomplete market theory. However, the increase in share value due to the expansion of investor base is not large enough to offset the negative and unconditional share price change after reverse splits. Our results are thus consistent with the finding of prior research that reverse stock splits are associated with negative returns. (12)

The rest of the paper is organized as follows. Section I explains the data and study sample. Sections II and III analyze the effect of reverse splits on institutional holdings using figures and regressions. Section IV analyzes whether the effect of reverse splits on institutional holdings varies across different types of institutional investors. Section V examines whether the effect of reverse splits on institutional holdings depends on the firms' stated reasons for the reverse splits. Section VI examines the effect of reverse splits on analyst following. Section VII analyzes the relation between stock returns and changes in institutional holdings induced by reverse splits. Section VIII concludes the paper.

I. Data and Study Sample

A. Data Sources, Variable Measurement, and Descriptive Statistics

We identify all the reverse splits of common stocks listed on the NYSE, AMEX, or NASDAQ between 1982 and 2008 from data provided by the Center for Research in Security Prices (CRSP). (13) We include in the study sample only those reverse splits with a split ratio higher than 1-for-2 and those reverse split firms that are listed on the NYSE, AMEX, or NASDAQ from eight quarters before the reverse split quarter to eight quarters after the reverse split quarter. We include firms that are listed for at least eight quarters prior to the reverse split because our tests use the control group of non-reverse-split firms that are similar to the reverse-split sample in their presplit characteristics. We require that reverse split firms have available data to calculate their presplit characteristics.

We use only those firms that survived as least eight quarters after the reverse split quarter in order to examine changes in their institutional holdings and share prices after the reverse split. Although this sample selection method reduces our sample size significantly, it enables us to accurately analyze the relation between changes in share price and changes in institutional holdings triggered by the reverse split using a relatively homogenous group of firms (i.e., firms that are not delisted). Note that our main research question is not whether certain firms have greater institutional holdings than others, but whether changes in institutional holdings that result from the reverse split differ across firms with different types of the reverse split (i.e., across L5L5, L5H5, and H5H5 reverse splits). For this reason, it is imperative that we use the sample of survived firms that will enable us to test the reverse-split-induced price effect, not the delisting effect, on institutional holdings. After deleting those reverse splits that have other confounding events on the ex date, we are left with a sample of 847 reverse splits. (14)

We obtain quarterly 13F institutional holdings data and the type of 13F institutions from Thomson Financial. To assign a type to 13F institutions after 1998, we use Brian Bushee's classification. (15) We merge the 13F data with the reverse split data and calculate quarterly NII and PIH for each reverse split firm from eight quarters before the split to eight quarters after the split. We calculate operating performance, leverage, profitability, and growth opportunity (Tobin's Q) for each of our reverse split firms using data from Compustat. We use the data from CRSP to measure liquidity variables, such as price impact (the Amihud (2002) illiquidity measure), turnover ratio, and the percentage bid-ask spread (Chung and Zhang, 2014). We obtain the number of analysts following each firm from the Institutional Brokers' Estimate System (I/B/E/S) database. Finally, for each firm in our reverse split sample, we use Factiva to search for reasons for a reverse stock split that are either reported in news articles or stated explicitly by the firms' managers or boards of directors.

Table I shows the presplit characteristics of our study sample of 847 reverse splits. We provide details regarding the construction of each presplit characteristic in Appendix A. The mean presplit price is $0.80 and the mean target price is $5.73. (16) Thus, reverse split firms on average choose a split ratio that raises share price above the $5 threshold. The mean reverse split factor is between 1-for-8 and 1-for-9. The number of institutional investors, the percentage institutional holding, and the number of analysts tend to decrease prior to the reverse split. (17) Reverse split firms generally have poor stock returns and poor operating performance: the 12-month buy-and-hold return prior to the reverse split quarter less the 12-month buy-and-hold value-weighted market return is -25.47% and the industry-adjusted return on assets (ROA) (earnings before extraordinary items divided by total asset of the previous fiscal year) is -15.51%.

Presplit change in Risk, ILLIQ, Turnover, and Spread is the difference in the variable between year t-1 and t-2, where year t-1 is a year before the ex date and year t-2 is a year before year t-1. The last four rows in Table I show that reverse split firms experience an increase in risk, price impact, and the bid-ask spread, and a decrease in turnover ratio before reverse stock splits. Specifically, the standard deviation of daily stock returns increased by 0.53%, the Amihud illiquidity measure increased by 2.86, and the percentage bid-ask spread increased by 0.63%, while the daily share turnover ratio decreased by 0.32 between the two presplit periods. These results suggest that these firms experienced an increase in information asymmetries and adverse selection risks (which led to larger spreads and lower trading volumes) prior to their reverse splits.

B. Construction of the Control Sample Using the Propensity Score Matching Method

We measure the effect of reverse splits on the firm's institutional holdings by the difference in the pre- and postsplit change in institutional holdings between firms that split their shares (i.e., the test/treatment sample) and otherwise similar firms that did not split their shares (i.e., the control sample). Our initial non-reverse-split sample includes all non-reverse-split common stocks that are included in both the CRSP and Compustat databases during each reverse split quarter; that are listed on the NYSE, AMEX, or NASDAQ from eight quarters before the reverse split quarter to eight quarters after the reverse split quarter; and that have available data to calculate presplit stock characteristics.

We employ the propensity score matching method (Rosenbaum and Rubin, 1983) to identify the control group of non-reverse-split firms that are similar to the test/treatment sample in their presplit characteristics. (18) These presplit characteristics include share price, market capitalization, book-to-market ratio, stock return, operating performance, leverage, profitability, growth opportunity, risk, price impact, turnover, the bid-ask spread, and analyst coverage. (19) We also include the presplit number of institutional investors and the presplit percentage institutional holding as well as the presplit change in the number of institutional investors and the presplit change in the percentage institutional holding to ensure that the non-reverse-split firms have the same level and trend in these variables prior to the reverse split.

We partition 847 reverse splits into the following three groups according to their presplit and target prices: L5L5 group includes reverse splits with the presplit price and the target price both below $5; L5H5 group includes reverse splits with the presplit price below $5 and the target price above $5; and H5H5 group includes reverse splits with the presplit price and the target price both above $5. We obtain the propensity score of each reverse split type using the multinomial logistic regression, where the dependent variable is a categorical variable with four categories (i.e., L5L5, L5H5, H5H5, and the non-reverse-split sample described above) and the independent variables are the set of presplit firm characteristics explained above. Our matching estimator is a variant of nearest-neighbor matching and caliper matching (see Smith and Todd, 2005).

For each reverse split, we match (with replacement) five non-reverse-split firms that have the most similar (nearest distance) propensity score, where the propensity score is the predicted probability of issuing the same type of reverse split during the same reverse split quarter and that also belong to the same presplit price group as the price group of the reverse split firm. (20) To ensure the quality of the match, we impose a maximum tolerable distance between the propensity score of the non-reverse-split matched firm and the propensity score of the reverse split firm by removing "bad" matches, or those that have distances of more than 0.04 (or 4%). (21)

Finally, we impose the common support condition by removing reverse split firms if their propensity scores are larger (smaller) than the maximum (minimum) propensity score of nonreverse-split firms. The common support condition reduces the reverse split sample from 847 to 781 reverse splits. Thus, our final (postmatch) study sample consists of 781 reverse splits and 3,823 non-reverse-split matched firms. Among the 781 reverse splits, 489 reverse splits belong to the L5L5 group, 271 reverse splits belong to the L5H5 group, and 21 reverse splits belong to the H5H5 group. Among the 3,823 non-reverse-split matched firms, 2,376 are matches for L5L5 reverse splits, 1,342 are matches for L5H5 reverse splits, and 105 are matches for H5H5 reverse splits.

To assess the quality of match, we follow a diagnostic approach similar to the one used in Lemmon and Roberts (2010). Appendix B Panel A reports both the prematch multinomial logistic regression results and the postmatch binary logistic regression results. The multinomial logistic regression result shows that the presplit price, presplit change in NII and PIH, presplit firm size and book-to-market ratio, and presplit profitability are all significant predictors of reverse split events. However, when the sample is based on the postmatch sample, the binary logistic regression results show that none of the predictors are significant. While the pseudo [R.sup.2] of the prematch multinomial logistic regression is 0.348, the pseudo [R.sup.2] of the postmatch binary logistic regression is only 0.004.

Appendix B Panel B shows the balancing test results both before and after the match. While the prematch sample shows that reverse split firms and non-reverse-split firms differ in most presplit characteristics (except book-to-market ratio), the postmatch sample shows that none of the differences are significant. The results in both panels suggest that our reverse split sample and non-reverse-split matched sample have similar presplit characteristics. Finally, Panel C reports the size of the non-reverse-split matched sample before we remove "bad matches" and after we remove "bad matches." The results show that even before we remove "bad matches," best matches (i.e., matches with the nearest distance) have distances smaller than 0.04. For the 5th best matches (i.e., 5th nearest matches), the matched firm in the 95th percentile still has a distance smaller than 0.04. Thus, caliper matching does not significantly reduce the size of the matched sample.

In summary, these results suggest that the reverse split sample and the non-reverse-split matched sample share similar presplit characteristics and that any postsplit difference in institutional holdings between these two samples should not be attributable to the differences in their presplit characteristics.

II. Reverse Stock Splits and Institutional Holdings

Figures 1 and 2 show quarterly mean values of NII and PIH, respectively, for the three reverse split groups (i.e., L5L5, L5H5, and H5H5) and their control groups of non-reverse-split firms from eight quarters before the reverse split quarter to eight quarters after the reverse split quarter (event quarter from -8 to 8, where event quarter 0 is the reverse split quarter).

A. Institutional Holdings before Reverse Splits

Figure la and b (Figure 2a and b) show that before the reverse split quarter, reverse split firms in the L5L5 and L5H5 groups experience a decrease in NII (PIH). In contrast, Figure 1c shows that reverse split firms in the H5H5 group exhibit a general increase in NII before the reverse split quarter, except for quarter -1. Figure 2c shows that reverse split firms in the H5H5 group exhibit a sharp increase in PIH between quarter -1 and the reverse-split quarter. Note that the time-series variation in NII and PIH for the control sample of non-reverse-split firms is generally similar to that for each reverse split group before the reverse split quarter, indicating a high degree of match between the treatment (i.e., reverse-split) and control (i.e., non-reverse-split) samples.

B. Institutional Holdings after Reverse Splits

After the reverse split quarter, we find (see Figures 1b and 2b) that reverse split firms in the L5H5 group exhibit larger increases in NII and PIH than the control sample of non-reverse-split firms, indicating that firms in the L5H5 group entice more institutional investors and greater institutional ownership than otherwise similar non-reverse-split firms.

Figure 1a and c show that reverse split firms in the L5L5 and H5H5 groups do not incrementally attract more institutional investors (NII) than their respective control group after the reverse split (i.e., slope is similar between L5L5 and its control group and between H5H5 and its control group). Similarly, Figure 2c shows that reverse split firms in the H5H5 group do not exhibit an increase in institutional ownership (PIH) relative to the control sample after the reverse split quarter. We do find that reverse split firms in the L5L5 group (see Figure 2a) experience a small increase in PIH beyond that of the control group after the reverse split.

Figure 1d shows the difference in NII between reverse split firms and the control sample of non-reverse-split firms for the L5L5 and L5H5 group, respectively. The results show that the difference in NII between reverse split firms and the control sample for the L5H5 group increases after reverse splits, which is consistent with the result in Figure 1b that reverse split firms in the L5H5 group entice more institutional investors than otherwise similar non-reverse-split firms. In contrast, we find that the difference in NII between reverse split firms and the control sample for the L5L5 group does not increase after reverse splits, which is consistent with the result in Figure la that reverse split firms in the L5L5 group do not entice more institutional investors than otherwise similar non-reverse-split firms.

Figure 2d shows the difference in PIH between reverse split firms and the control sample of non-reverse-split firms for the L5L5 and L5H5 groups. The difference in PIH between reverse split firms and the control sample for the L5H5 group increases after reverse splits, which is consistent with the result in Figure 2b that reverse split firms in the L5H5 group entice greater institutional ownership than non-reverse-split firms. The difference in PIH between reverse split firms and the control sample for the L5L5 group also slightly increases after reverse splits, which is in line with the result in Figure 2a.

C. Effect of Reverse Splits on Minority Institutional Investors

We find that during the reverse split quarter (event quarter 0), reverse split firms in the L5L5 and L5H5 groups (see Figure la and b) experience a decrease in NII This decrease is mainly attributable to the decrease in the number of minority institutional investors that hold less than 1% of the firm's shares. Figure 3a (3b) shows the quarterly mean number of minority institutional investors for reverse split firms in the L5L5 (L5H5) group, together with the corresponding figure for the control sample. Similarly, Figure 3c (3d) shows the quarterly mean number of institutional investors that hold more than 1% of reverse split firms' shares in the L5L5 (L5H5) group, together with the corresponding figure for the control sample. Figure 3a and b show that the mean number of minority institutional investors for reverse split firms decreases more than the corresponding value for the control sample in the reverse split quarter. In contrast, Figure 3c and d show that the mean number of institutional investors that hold more than 1% of shares for reverse split firms does not decrease more than the corresponding value for the control sample in the reverse split quarter.

The decrease in the number of minority institutional investors may be an artifact of the reverse split. Reverse splits may reduce the number of minority shareholders because small shareholders may end up with less than one share (fractional share) after the reverse split. (22) Because firms typically do not issue fractional shares, fractional shareholders instead receive a cash payment that is equal to the value of the fractional shares that they otherwise would have received. Although institutional investors usually hold a larger number of shares than individual investors and are less likely to become fractional shareholders after reverse splits, some institutional investors may sell shares simply because they lose interest in holding a small number of shares.

Figure 3c and d also show that the mean number of institutional investors that hold more than 1 % of shares for reverse split firms increases more than the corresponding figure for the control sample after the reverse split quarter. However, Figure 3a and b show that the mean number of minority institutional investors for reverse split firms increases more than the corresponding figure for the control sample (i.e., steeper slope) after the reverse split quarter only for the L5H5 group (the L5L5 group and its control sample have almost identical slopes). We interpret these results as evidence that reverse splits have similar effects on NII for both the L5L5 and L5H5 groups in reducing minority institutional investors, but have stronger positive effects on NII for the L5H5 group than for the L5L5 group because only the former group enjoys the benefit of shedding the binding constraint of the $5 threshold.

D. Summary

Our results show that L5H5 reverse splits are the only type of reverse splits that are followed by an increase in both NII and PIH. We find that L5L5 reverse splits are followed by a small increase in PIH. In a later section, we show that such an increase in PIH is mainly attributable to independent investment advisors who are less subject to the prudent-person rule.

III. Regression Results

We use the difference-in-difference regression to formally examine the effects of reverse stock splits on NII and PIH. We calculate the difference-in-difference estimates of the change in NII and PIH (i.e., DD_NII and DD_PIH) from the one-year period before the reverse split quarter to the second one-year period after the reverse split quarter for each of 781 reverse split firms. (23) Although our difference-in-difference estimates take into account differences in presplit characteristics between reverse split firms and non-reverse-split matched firms, reverse splits may affect institutional holdings indirectly through their postsplit impact on liquidity, risk, or other firm fundamentals.

Prior research shows that institutional investors prefer to trade in liquid markets and therefore avoid low-priced stocks because they are associated with low liquidity (e.g., Faulkenstein, 1996; Gompers and Metrick, 2001; Bennett, Sias, and Starks, 2003; Brandt et al., 2010). Han (1995), Lamoureux and Poon (1987), Angel (1997), and Kim, Klein, and Rosenfeld (2008) show that reverse splits can improve the liquidity of stocks. These considerations suggest that the postsplit increase in institutional holdings could be driven by improved liquidity. Badrinath, Gay, and Kale (1989) and Del Guercio (1996) show that institutional investors prefer stocks with low risk. Dravid (1987) finds that volatility decreases after reverse splits. Thus, reduced volatility could be the mechanism through which reverse splits increase institutional holdings.

Del Guercio (1996) finds that bank trusts prefer stocks with positive earnings. McConnell and Servaes (1990) find a positive association between institutional ownership and Tobin's Q. Badrinath, Gay, and Kale (1989) suggest that institutional investors may avoid holding stocks of highly leveraged firms. Marchman (2007) shows that reverse split firms with lower leverage and better operating performance are associated with better long-run stock performance. Kim, Klein, and Rosenfeld (2008) find that reverse splits are followed by poor operating performance. Brennan and Hughes (1991) argue that firms may occasionally reverse split stocks to signal bad information. To the extent that institutional investors may react to such information, the postsplit change in institutional holdings may be related to the split ratio. Based on these considerations, we estimate the following regression model that includes these other potential determinants of institutional holdings (see Appendix A for a detailed description of each variable):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (1)

The first two columns in Table II show the regression results for DD_NII and the third and fourth columns show the regression results for DDJ'IH. The first and third columns show the regression results without the control variables and the second and fourth columns show the regression results with the control variables included. In all four columns, we find that the regression coefficients on L5H5 are all positive and significant, indicating that reverse stock splits in the L5H5 group result in an increase in both the number of institutional investors and the percentage of shares that are held by institutional investors. This result is consistent with our earlier observation from Figures Id and 2d.

The results show that the coefficients on L5L5 are negative and significant in the regression model for DD_NII and positive and significant in the regression model for DD_PIH. The negative coefficients on L5L5 in the DD_NII regression model are consistent with the result in Figure Id that the control-firm-adjusted NII after the reverse split is smaller than the corresponding value before the reverse split. The positive coefficients on L5L5 in the DD_PIH regression model are consistent with the result in Figure 2d that the control-firm-adjusted PIH after the reverse split is greater than the corresponding value before the reverse split.

The coefficients on H5H5 are not significantly different from zero in any regressions. This result is consistent with our earlier observation in Figures 1c and 2c that reverse split firms in the H5H5 group do not incrementally attract more institutional investors (both NII and PIH) than their respective control group after the reverse split (i.e., slope is similar between H5H5 and its control group).

We find that the coefficients on DD_Tobin's Q are positive and significant while the coefficients on DD_Risk are negative and significant, supporting our conjecture that institutional holdings increase with growth opportunity and decrease with risk. While the coefficients on DD_Turnover are positive and significant, the coefficients on DD_ILLIQ are positive and significant and the coefficients on DD_Spread are insignificant. Thus, the notion that reverse splits attract institutional holdings through improved liquidity receives limited support in our regression results. (24)

Prior research (e.g., Baker and Gallagher, 1980; Lakonishok and Lev, 1987; Conroy and Harris, 1999) suggests that firms split stocks to move share price toward the optimal level. If institutional holdings increase as firms reverse split stocks to move share price toward the optimal level, then even without any threshold at $5, the optimal price range could still explain the higher postsplit institutional holdings for L5H5 reverse splits than for L5L5 reverse splits, for the highest possible target price for L5L5 reverse splits is only $4.99, which is well below the optimal range. (25) However, the optimal price range cannot explain why L5H5 reverse splits also attract larger institutional holdings (PIH) than H5H5 reverse splits and why H5H5 reverse splits are not followed by a significant increase in institutional holdings.

IV. Does the Effect of Reverse Splits Vary across Different Types of Institutional Investors?

Prior research suggests that the applicability of the prudent-person rule varies across different types of institutions. Del Guercio (1996) argues that bank trusts are the only institutions directly affected by the prudent-person rule. Badrinath, Kale, and Ryan (1996) find that insurance companies tend to hold stocks with "safe" characteristics. Private pension funds are governed by the Employees Retirement Income Security Act of 1974 (ERISA). Cummins et al. (1980) and Cummins and Westerfield (1981) argue that ERISA gives private pension funds greater latitude to select stocks and diversify. Del Guercio (1996) argues that public pension funds are as legally constrained as bank trusts. Del Guercio (1996) also argues that mutual funds are regulated by SEC and are not affected by the prudent-person rule. Falkenstein (1996) finds that mutual funds have a strong aversion toward low-priced stocks (stocks under $5). Griffin and Xu (2009) and Jiao (2013) both show that hedge funds hold relatively less prudent securities. Stocks held by hedge funds tend to have lower share prices than stocks held by other types of institutional investors.

We decompose institutional holdings into the holdings of each type of institution, and examine the effect of reverse splits on the holdings of each type of institution separately. Specifically, we calculate DD_NII and DD_PIH and estimate Equation (1) for each type of institution. Table III shows that the coefficient on L5H5 is positive and significant for investment companies, independent investment advisors, and pension funds/university endowments in the regression model for both DD_NII and DD_PIH, indicating that reverse splits in the L5H5 group result in greater institutional ownership (both in number and size) for these institutional investors. For bank trusts, we find that the coefficient on L5H5 is positive and significant only in the regression model for DD_PIH, indicating that reverse splits that remove the low price hurdle result in greater percentage holdings but not in the number of bank trusts. We find that the coefficient on L5H5 is not significantly different from zero for insurance companies in either regression model. (26) Insurance companies assume risks from policyholders and have strong incentives to maintain a sound financial position. Badrinath, Kale, and Ryan (1996) argue that over 50% of their assets are in investment grade bonds and government agency bonds. Perhaps the reason that insurance companies are irresponsive to L5H5 reverse splits is that they simply are less interested in equity investment.

Table III shows that the coefficient on L5L5 in the DD_PIH regression model is positive and significant only for independent investment advisors. This result suggests that the significant and positive coefficients on L5L5 in the DD_PIH regression model reported in Table II are driven mainly by independent investment advisors. Since independent investment advisors have lower fiduciary standards and are more likely than other institutional investors to hold low-priced stocks, it may be not so surprising that L5L5 reverse splits can entice a small but significant increase in PIH.

Table III also shows that the coefficient on L5L5 is negative and significant for bank trusts, insurance companies, and independent investment advisors in the regression model for DD_NII, indicating that the negative coefficients on L5L5 in the DD_NII regression model reported in Table III are driven by these institutions. As discussed earlier, the smaller number of institutional investors after reverse splits may be attributed to the reduction in the number of minority institutional investors. Not surprisingly (given the results in Table II), we find that none of the coefficients on H5H5 are significantly different from zero for any type of institution.

V. Reasons for Reverse Stock Splits and Institutional Holdings

To examine whether the postsplit changes in NII and PIH differ across firms according to reasons for the reverse split, we search Factiva for news articles about reasons for each of the 781 reverse splits in our study sample and identify reasons for 362 reverse splits. Table IV Panel A shows five major reasons for reverse splits that are either reported in news articles or stated explicitly by firm managers or boards of directors. These reasons are not mutually exclusive; therefore, the total number of reason-firms (393) is greater than 362. (27)

The first category of reasons includes: to attract institutional investors, to improve the visibility and image of the firm, to initiate analyst coverage, to allow margin trading for retail investors, to improve liquidity, to enhance the eligibility of listing in other markets, and to move share price to an optimal range. The second category of reasons is to meet exchange listing requirements or to avoid delisting threats. The third reason is to squeeze out minority shareholders and reduce the cost of servicing shareholders. The fourth category of reasons for reverse splits is to enhance flexibility for future financing and to facilitate future mergers and acquisitions, especially when there are too many shares outstanding. Corporate charters typically stipulate the maximum number of shares permitted for issuance and having too many shares outstanding is likely to restrain future equity issuance. Reverse splits, which reduce the number of shares outstanding, therefore can increase firms' ability to issue additional shares. Finally, 14 reverse splits are associated with corporate reorganizations.

To examine whether the postsplit changes in NII and PIH vary with the reasons for reverse splits, we regress DD_NII and DD_PIH on five dummy variables for reverse split reasons and three dummy variables for reverse split types. The results (see Panel B in Table IV) show that reverse splits motivated by the third reason (i.e., to squeeze out minority shareholders and reduce the cost of servicing shareholders) result in the largest decrease in NII, followed by the second reason (to meet exchange listing requirements or to avoid delisting threats). However, we find that none of the reason dummy variables are significantly related to DD_PIH, suggesting that the stated motives for reverse splits matter less than the reverse split per se to institutional investors and that the reduction in the number of minority institutional investors and the corresponding decrease in their holdings are not sufficiently large enough to materially affect the total institutional holdings. Finally, we find that the regression coefficient on the L5H5 dummy variable is positive and significant in both regression models, confirming our earlier result that reverse splits in the L5H5 group exhibit the largest increase in NII and PIH.

VI. Reverse Stock Splits and Analyst Coverage

One might conjecture that analyst coverage increases after reverse splits because analysts have greater incentive to follow stocks with higher institutional holdings. (28) Chung (2000) argues that analysts serve as a marketing aid to brokers and therefore have greater incentives to follow high-quality stocks. To the extent that the SEC imposes strict restrictions on broker-dealers when they sell penny stocks to customers, reverse splits that move share price above the $5 hurdle should entice more analysts.

On the other hand, Brennan and Hughes (1991) suggest that analyst following and share price are negatively correlated because brokers have greater incentive to promote lower-priced stocks because they can generate greater brokerage commissions from these stocks. Hence, analyst coverage may actually decrease after reverse splits as they result in higher share prices. To examine the effect of reverse splits on analyst coverage, we estimate the following regression model:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (2)

where DD_NAF is the difference-in-difference estimate of the effect of reverse splits on the number of analysts. (29) Table V Column 1 shows that before including control variables, the regression coefficients on L5L5 and L5H5 are both positive and significant. Column 2 shows that after including control variables, only the coefficient on L5H5 remains positive and significant. Our results thus suggest that L5H5 is the only type of reverse split that is able to entice more analyst following. This result lends further support to our conjecture that the removal of fiduciary concern is the mechanism through which reverse splits help entice institutional investors and financial analysts.

VII. Effects of Reverse Splits on Share Price

Merton (1987) develops an incomplete information model of market equilibrium in which investors invest in only those stocks that they "know about." He shows that a firm's stock price increases with the number of investors who know about the stock in such a market. In this section, we analyze the effect of the reverse split on share price through its effect on institutional investment. To the extent that reverse splits remove the low price constraint on institutional investment and thereby increase the firm's investor base, we expect reverse splits to increase share prices, especially for those reverse splits that lead to large increases in institutional investment.

A. Measurement of Abnormal Returns

To measure the abnormal return to investors for firms that split their shares, we estimate the buy-and-hold abnormal return (BHAR) during the 24-month period after the reverse split using the method in Lyon, Barber, and Tsai (1999). We define BHAR as the difference in buy-and-hold returns between the reverse split firm and a reference portfolio, where the reference portfolio is composed of firms that are similar in size, book-to-market ratio, and past stock return to the reverse split firm. (30) That is,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

where [BHAR.sub.i], is the buy-and-hold abnormal return of reverse split firm i, ret is the monthly return, t = 0 is the reverse split month, and [N.sup.ref.sub.i] is the number of firms in the reference portfolio for reverse split firm i. The buy-and-hold return of the reference portfolio, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] measures the average buy-and-hold return of firms that are similar to the reverse split firm in terms of their sizes, book-to-market ratios, and past stock returns. Therefore, [BHAR.sub.i] measures the abnormal stock return of reverse split firm i that cannot be attributable to those factors (i.e., size, book-to-market ratio, and price momentum) that are believed to affect stock returns.

B. Empirical Methods

To the extent that BHAR is affected by unobserved factors that simultaneously determine both the reverse split and institutional holdings, BHAR may not accurately reflect the true effect of the reverse split on share prices. Because we test Merton's incomplete market theory by analyzing whether the reverse split affects share price through its effect on institutional holdings, the endogeneity problem may prevent us from making correct inferences. (31) To address this issue, we employ the two-stage least squares regression method using instrumental variables that are likely correlated with changes in institutional holdings but uncorrelated with abnormal stock returns.

We also calculate the difference-in-difference estimate of the effect of the reverse split on share prices (D_BHAR), and analyze how DJ3HAR varies with the difference-in-difference estimate of the effect of the reverse split on institutional holdings (DD_NII and DD_PIH). We define D_BHAR as the difference between the BHAR of the reverse split firm and the mean BHAR of the control group of otherwise similar firms that did not split their shares explained in Section I.B. (32) That is,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

where [BHAR.sub.i,j] is the buy-and-hold abnormal return of non-reverse-split control firm j for reverse split firm i, and [N.sup.C.sub.i] is the number of non-reverse-split control firms for reverse split firm i. (33)

The second term on the right-hand side of Equation (4), [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] could be considered the buy-and-hold abnormal return that would have been earned by investors in firm i had it not split its shares. Therefore, D_BHAR measures the portion of BHAR that is attributable to the reverse stock split and is a more accurate measure of the effect of reverse splits on share prices. Since DD_NII and DD_PIH are estimates of the change in institutional holdings that is also attributable to the reverse split, we test Merton's incomplete market theory by looking at whether D_BHAR is significantly related to DD_NII and DD_PIH.

C. Descriptive Statistics

Table VI shows the mean values of changes in institutional holdings ([DELTA]NII, [DELTA]PIH, DD_NII, and DD_PIH) and abnormal stock returns (BHAR and D_BHAR), where [DELTA]NII ([DELTA]PIH) is the change in the number (percentage holding) of institutional investors between the pre- and postsplit period for reverse split firms, and DD_NI1 (DD_PIH) is the same as previously defined (i.e., the control-firm-adjusted change in the number [percentage holding] of institutional investors between the pre- and postsplit period). (34)

Panel A shows the results for each of the three reverse split groups (L5L5, L5H5, and H5H5). The mean [DELTA]NII for each group is 0.14, 4.78, and 17.21, while the mean [DELTA]PIH for each group is 3.61%, 11.85%, and 11.92%, respectively. The mean DDJSIII for each group is -0.17, 0.17, and 0.1, while the mean DD_PIH for each group is 3.32%, 10.01%, and 2.27%, respectively, which is consistent with the result in Table II, Table III, and Table IV that the L5H5 group has the largest increase in DDJSHI and DD_PIH. In terms of the effect on share value, we find that the mean D_BHAR for L5L5, L5H5, and H5H5 reverse split firms is -58.74%, -49.65%, and -6.55%, respectively, indicating that investors in reverse split firms earn lower abnormal returns than investors in the control group of otherwise similar firms that did not split their shares. (35) This result is consistent with the finding of prior research that reverse stock splits are generally associated with negative returns in the post-reverse-stock-split period (e.g., Desai and Jain, 1997; Kim, Klein, and Rosenfeld, 2008).

To shed some light on the effect of institutional holdings on share value, we divide the sample into tercile groups according to [DELTA]NII, [DELTA]PIH, DD_NII, or DDJPIH. Panel B in Table VI shows that for the whole sample, BHAR increases with both [DELTA]NII and [DELTA]PIH, and D_BHAR increases with both DD_NII and DD_PIH. For example, when the tercile groups are formed by [DELTA]NII, we find that BHAR increases from -24.04% to 54.46% as [DELTA]NII increases from -9.07 to 15.41. Similarly, when the tercile groups are formed by DD_PIH, D_BHAR increases from -107.27% to -7.34% as DDPIH increases from -7.17% to 21.95%.

We find the similar positive association between changes in institutional holdings and abnormal stock returns when we replicate the analysis using the reverse splits that belong to each of the three reverse split groups separately. For example, for the L5H5 group, we find that BHAR increases from -47.35% to 42.19% as [DELTA]NII increases from -14.18 to 27.19 when the tercile groups are formed by [DELTA]NIL Similarly, D_BHAR increases from -99.05% to 9.73% as DD_PIH increases from -9.33% to 32.85% when the tercile groups are formed by DD_PIH. On the whole, these results provide preliminary evidence that changes in share price are positively associated with changes in institutional holdings.

D. Regression Results

1. Base-Line Ordinary Least Squares (OLS) Regression Results

To find out whether the positive relation between changes in institutional holdings and abnormal stock returns remains intact after controlling for the effects of firm characteristics, we estimate the following regression model:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

where [DELTA]LNII is the pre- and postsplit change in Log (1 + Nil) and all other variables are the same as previously defined. Column 1 in Table VII Panel A shows the results when we include only L5L5, L5H5, H5H5, [DELTA]LNII, and [DELTA]PIH in the regression. Column 2 shows the results when we also include other firm attributes in the regression. Consistent with the result in Table VI Panel A, reverse splits in the L5H5 group have lower abnormal returns {BHAR) than those in the L5L5 or H5H5 group. More important, both columns show that the coefficients on [DELTA]LNII and [DELTA]PIH are positive and significant, indicating that firms with larger increases in institutional holdings after the reverse split exhibit higher abnormal stock returns. We find that BHAR is not significantly related to other firm attributes.

2. Two-Stage Least Squares Regression Results

The positive association between changes in institutional holdings and abnormal stock returns could be driven by institutional investors' superior skills in predicting future returns. That is, institutional investors may increase their holdings because they expect higher stock returns. To address this issue, we employ the two-stage least squares (2SLS) method and estimate the following regression models:

First-stage regression:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

Second-stage regression:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

The first-stage regression model includes three instrumental variables--[DELTA]LNIIQIX, [DELTA]PIHQIX, and [DELTA]NAF--that are likely to vary with [DELTA]LN1I and [DELTA]PIH (i.e., relevance condition) but are not directly related to BHAR (i.e., exclusion condition). [DELTA]LNIIQIX is the pre- and postsplit change in Log (1 + NIIQIX), where NIIQIX is the number of institutional investors that are classified as quasi-indexers (see Bushee, 2004). Similarly, [DELTA]PIHQIX is the pre- and postsplit change in the percentage of shares held by quasi-indexers. We use [DELTA]LNIIQIX and IS PI HQ IX as instrumental variables because 1) quasi-indexers tend to follow passive investment strategies and thus their trading is unlikely to be driven by their prediction on future returns; and 2) [DELTA]LNIIQIX and [DELTA]PIHQIX increase with [DELTA]LNII and [DELTA]PIH because [DELTA]LNIIQIX is a constituent of [DELTA]LNII and [DELTA]PIHQIX is a constituent of [DELTA]PIH. (36) Prior research finds a strong and positive correlation between analyst following and institutional holding (e.g., O'Brien and Bushnan, 1990), but no robust evidence of a significant relation between analyst following and abnormal stock returns. (37) Hence, we use [DELTA]NAF as another instrumental variable.

Column 3 in Table VII Panel A shows that [DELTA]LNII is positively and significantly related to [DELTA]NAF and [DELTA]LNIIQIX. Similarly, Column 4 shows that [DELTA]PIH is positively and significantly related to [DELTA]NAF, [DELTA]LNIIQIX, and [DELTA]PIHQIX. We reject the joint hypothesis that coefficients on the three instrumental variables are all equal to zero at the 1% significance level. (38) The Cragg and Donald C-statistic (see Stock and Yogo, 2005) is 214.15, which is much larger than the critical values for the weak instrument test based on bias and size. Columns 3 and 4 also show that [R.sup.2] values (0.837 and 0.635) are relatively large. These results suggest that [DELTA]NAF, [DELTA]LNIIQIX, and [DELTA]PIHQIX are not weak instruments. Column 5 shows the results of the second-stage regression. The results show that the coefficients on [DELTA]LNII and [DELTA]PIH are both positive and significant, confirming the OLS results after controlling for a potential endogeneity problem. Finally, the Sargan test fails to reject the null hypothesis that the over-identifying restrictions are valid.

3. Difference-in-Difference Regression Results

To further assess the robustness of the relation between changes in institutional holdings and BHAR, we also employ the difference-in-difference regression using the control sample of non-reverse-split firms. Specifically, we examine whether the control-firm-adjusted BHAR (i.e., D_BHAR) could be explained by the control-firm-adjusted changes in Nil and PIH (i.e., DD_NII and DD_PIH) using the following regression model:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)

where all variables are the same as previously defined.

Table VII Panel B shows the regression results. The results show that regardless of control variables, the coefficients on DD_NI and DD_PIH are positive and significant at the 1% level, indicating that the control-firm-adjusted abnormal changes in share price are positively related to the control-firm-adjusted changes in Nil and PIH, (39) It is important to note that these results are unlikely to be driven by a survival bias. Our study sample is likely to be subject to the survival bias in the level of postsplit stock returns because it includes only firms that survived at least two years after the reverse split. However, there is no reason to believe that this bias also exerts an impact on how changes in share price are related to changes in institutional holdings for the survived firms.

We find that part of the return resulting from the postsplit increase in institutional holdings is not large enough to offset the unconditional negative return associated with reverse splits. For example, Column 2 in Table VII Panel B shows that the coefficients ([[beta].sub.1] and [[beta].sub.2]) on L5L5 and L5H5 are -0.34 and -0.61, suggesting that the unconditional effect of L5L5 reverse splits on abnormal returns is -34 percentage points and the unconditional effect of L5H5 reverse splits is -61 percentage points. Also, we showed earlier that the mean D_BHAR for the L5H5 group is -49.65 percentage points (see Table VI Panel A). As pointed out above, our study sample includes only those firms that survived at least two years after the reverse split. Hence, the actual postsplit return is likely to be lower than the level suggested by these figures. The negative return in the post-reverse-stock-split period is consistent with the finding of previous studies (e.g., Desai and Jain, 1997; Kim, Klein, and Rosenfeld, 2008). (40)

VIII. Summary and Concluding Remarks

In this study, we show that the reverse stock split affects institutional investment through the prudent-person rule. We show that reverse split firms in general experience a decrease in institutional ownership during the two-year period before reverse splits. We find that share price, firm value, and analyst coverage also decline during the presplit period. After the reverse split, however, these firms are able to reverse the downward trend in institutional ownership and analyst coverage. Specifically, we find that reverse split firms with a presplit share price below $5 and a target postsplit price above $5 attract significantly more institutional investment than the control group of non-reverse-split firms. We do not find a similar increase in institutional investment for reverse split firms with a presplit and target share price both below $5 and reverse split firms with a presplit price already above $5. Overall, these results are consistent with our conjecture that firms use the reverse stock split to attract institutional investors by removing their fiduciary concern regarding investment in low-priced stocks.

Our study also conducts empirical tests of the managerial belief that the increase in institutional investment that results from reverse stock splits helps raise share price and firm value, which is in line with the prediction of Merton's theory of incomplete markets. Consistent with both managerial belief and Merton's prediction, we find that the postsplit change in share value is positively related to the postsplit change in the number of institutional investors and/or in the percentage of institutional holdings, after controlling for other factors that might affect stock returns. These results support our conjecture that reverse splits remove the low price constraint on institutional investment due to fiduciary responsibility, increase the firm's investor base, and thereby increase the firm's market value. However, we find that the return resulting from the postsplit increase in institutional holdings is not large enough to offset the unconditional negative effect associated with reverse splits.

Appendix A

Variable Definitions

(a) L5L5 is equal to 1 if both the presplit and target price are below $5 and 0 otherwise.

(b) L5H5 is equal to 1 if the presplit (target) price is below (above) $5 and 0 otherwise.

(c) H5H5 is equal to 1 if both the presplit and target price are above $5 and 0 otherwise.

(d) Nil is the number of institutional investors that hold the firm's shares.

(e) PIH is the percentage of shares that are held by institutional investors (i.e., the number of shares held by institutional investors divided by the number of shares outstanding).

(f) NAF is the number of different analysts producing earnings forecasts during a year.

(g) MVE is the product of closing price and the number of shares outstanding at the beginning the reverse split quarter.

(h) BEME is the ratio of the book value of equity to the market value of equity. The book value of equity is at least five months earlier than the beginning of the reverse split quarter. We follow Fama and French (2001, p. 41) to measure the book value of equity.

(i) Mkt_Adj_Return is the 12-month buy-and-hold return prior to the reverse split quarter less the 12-month buy-and-hold value-weighted market return.

(j) Ind_Adj_ROA is the ROA (earnings before extraordinary items divided by total asset of the previous fiscal year) less the industry median ROA. We use the Fama-French 48 industry classification to define the industry median ROA.

(k) Ind_Adj_Leverage is the leverage ratio (the current and long-term debt divided by total asset) less the industry median leverage ratio. We use the Fama-French 48 industry classification to define the industry median leverage ratio.

(l) Profitability is the earnings before extraordinary items less preferred dividend plus income statement deferred taxes if available, divided by the book value of equity.

(m) Tobin's Q is the sum of market value of equity, preferred stock liquidation value, and current and long-term debt divided by total asset (see Chung and Pruitt, 1994).

(n) Risk is the standard deviation of daily stock returns during a year.

(o) ILLIQ is the Amihud illiquidity measure defined as the absolute value of daily return divided by daily dollar volume, averaged over a year. We calculate ILLIQ using the following formula:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

where [D.sub.y] is the number of days over a year before or after reverse split ex date, [R.sub.d] is the return on day d, and [VOLD.sub.d] the trading volume in dollars on day d.

(p) Turnover is the daily share volume divided by total shares outstanding, averaged over a year. We calculate Turnover using the following formula:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [D.sub.y] is the number of days over a year before or after reverse split ex date, [VOL.sub.d] is the share volume on day d, and [SHROUT.sub.d] is the number of shares outstanding on day d.

(q) Spread is the difference between the daily closing bid and ask prices divided by the midpoint of bid and ask, averaged over a year (see Chung and Zhang, 2014).

(r) [DELTA]NII is the pre- and postsplit change in NIL We calculate [DELTA]NII using the following formula:

[DELTA]NII = [[summation].sup.8.sub.q=5] [NII.sub.q]/4 - [[summation].sup.-1.sub.q=-4] [NII.sub.q]/4,

where [NII.sub.q] is the number of institutional investors for reverse split firm in quarter q.

(s) [DELTA]PIH is the pre- and postsplit change in PIH. We calculate [DELTA]PIH using the following formula:

[DELTA]PIH = [[summation].sup.8.sub.q=5] [NII.sub.q]/4 - [[summation].sup.-1.sub.q=-4] [PIH.sub.q]/4,

where [PIH.sub.q] is the percentage of shares held by institutional investors for reverse split firm in quarter q.

(t) [DELTA]LNII is the pre- and postsplit change in Log (1 + Nil). We calculate ALNII using the following formula:

[DELTA]LNII = Log (1 + [[summation].sup.8.sub.q=5] [NII.sub.q]/4) - Log (1 [[summation].sup.-1.sub.q=-4] [NII.sub.q]/4),

where [NII.sub.q] is the number of institutional investors for reverse split firm in quarter q.

(u) [DELTA]Ind_Adj_ROA, [DELTA]Ind_Adj_Leverage, [DELTA]Profitability, and [DELTA]Tobin's Q are the pre- and postsplit changes in firm characteristics. The presplit and postsplit periods are defined as the fiscal year before and after reverse split ex date.

(v) [DELTA]Risk, [DELTA]ILLIQ, [DELTA]Turnover, and [DELTA]Spread are the pre- and postsplit changes in firm characteristics. The presplit and postsplit periods are defined as the one-year period before and one-year period after reverse split ex date.

(w) The reference portfolio is composed of firms that are similar in size, book-to-market ratio, and past stock return to the reverse split firm. We form reference portfolio using the following method: in each reverse split month we divide all NYSE, AMEX, and NASDAQ stocks into ten groups according to the market value of equity using NYSE breakpoint. For each decile group, we further divide stocks into five groups evenly according to the book-to-market equity. For each of the 50 (10 x 5) groups, we further divide stocks into three groups evenly according to the 11-month compounded return (starting from the 12th month before the reverse split month to the 2nd month before the reverse split month). Finally, we remove stocks in the reference portfolio that were not continuously listed throughout the 4-year period around the reverse split ex date. We then find the matching reference portfolio from the 150 reference portfolios for each of reverse split firms according to market value of equity, book-to-market equity, and past returns.

(x) [DELTA]LNIIQIX is the pre- and postsplit change in Log (1 + NIIQIX). NIIQIX is the number of institutional investors that are classified as quasi-indexers (see Bushee, 2004). We calculate [DELTA]LNIIQIX using the following formula:

[DELTA]LNIIQIX = Log (1 + [[summation].sup.8.sub.q=5] [NIIQIX.sub.q] / 4) - Log (1 [[summation].sup.-1.sub.q=- 4][NIIQIX.sub.q] / 4),

where [NIIQIX.sub.q] is the number of quasi-indexers for the reverse split firm in quarter q.

(y) [DELTA]PIHQIX is the pre- and postsplit change in PIHQIX. PIHQIX is the percentage of shares held by institutional investors that are classified as quasi-indexers according to their trading behaviors. We calculate [DELTA]PIHQIX using the following formula:

[DELTA]PIHQIX = [[summation].sup.8.sub.q=5] [PIHQIX.sub.q]/4 - [[summation].sup.-1.sub.q=-1] [PIHQIX.sub.q]/4,

where [PIHQIX.sub.q] is the percentage of shares held by quasi-indexers for the reverse split firm in quarter q.

(z) [DELTA]NAF is the pre- and postsplit change in Log (1 + NAF). We calculate [DELTA]NAF using the following formula:

[DELTA]LNAF = Log(1 + [NAF.sub.post-spli],) - Log(1 + [NAF.sub.pre-split]),

where presplit and postsplit periods are defined as the one-year period before and after reverse split ex date.

(aa) DD_NII is the difference in the pre- and postsplit change in Log (1 + NII) between reverse split (treatment) firms and non-reverse-split (control) firms. We calculate DD_NII using the following formula:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [NII.sup.treatment.sub.q] is the number of institutional investors for reverse split (treatment) firm in quarter q and [[bar.NII].sup.control.sub.q] is the mean number of institutional investors for non-reverse-split (control) firms in quarter q.

(bb) DD_PIH is the difference in the pre- and postchange in PIH between reverse split (treatment) firms and non-reverse-split (control) firms. We calculate DD_PIH using the following formula:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [PIH.sup.treatment.sub.q] is the percentage institutional holding of reverse split (treatment) firm in quarter q and [[bar.PIH].sup.control.sub.q] is the mean percentage institutional holding of non-reverse-split (control) firms in quarter q.

(cc) DD_NAF is the difference in the pre- and postchange in Log (1 + NAF) between reverse split (treatment) firms and non-reverse-split (control) firms. We calculate DD_NAF using the following formula:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where the presplit and postsplit periods are defined as the one-year period before and after reverse split ex date.

(dd) DD_Ind_Adj_ROA, DD_Ind_Adj_Leverage, DD_Profitability, and DD_Tobin's Q are differences in the pre- and postsplit change in firm characteristics between reverse split (treatment) firms and non-reverse-split (control) firms. The presplit and postsplit periods are defined as the fiscal year before and after reverse split.

(ee) DD_Risk, DD_ILLIQ, DD_Turnover, DD_Spread are differences in the pre- and postsplit change in firm characteristics between reverse split (treatment) firms and non-reverse-split (control) firms. The presplit and postsplit periods are defined as the one-year period before and one-year period after reverse split ex date.

(ff) D_BHAR is the difference in the buy-and-hold abnormal return (BHAR) between reverse split firms and the control sample of non-reverse-split firms.

Appendix B

Propensity Score Matching

Panel A shows prematch multinomial logistic regression results and
postmatch binary logistic regression results. Panel B shows
balancing test results. Panel C shows the distance in propensity
score between treatment and control firms both before and after
imposing a tolerance on the maximum distance of 0.04. Numbers in
brackets are p-values. See Appendix A and Table I for a detailed
description of each variable. Numbers in parenthesis are
t-statistics.

Panel A. Regression Analysis

                                    Prematch Multinomial
                                    Logistic Regression

                                    L5L5     L5H5     H5H5

Presplit price                      -6.55    -0.98    -0.16
                                    [0.00]   [0.00]   [0.00]
Presplit change in Log (1 + NII)    0.00     0.01     0.01
                                    [0.01]   [0.00]   [0.01]
Presplit change in PIH              0.01     -0.18    0.03
                                    [0.93]   [0.34]   [0.97]
Presplit Log (1 + NII)              -1.69    -1.08    -1.99
                                    [0.10]   [0.36]   [0.59]
Presplit PIH                        -0.26    0.34     0.60
                                    [0.00]   [0.00]   [0.30]
Presplit Log (1 + NAF)              0.47     -0.78    -1.02
                                    [0.51]   [0.27]   [0.69]
MVE                                 -0.04    0.27     1.24
                                    [0.72]   [0.04]   [0.00]
BEME                                -0.30    -0.48    -0.46
                                    [0.00]   [0.00]   [0.33]
Mkt_Adj_Return                      -0.34    0.13     0.60
                                    [0.17]   [0.68]   [0.55]
Ind_Adj_ROA                         -9.26    -11.79   -30.61
                                    [0.07]   [0.10]   [0.51]
Ind_Adj_Leverage                    -32.44   50.11    102.40
                                    [0.28]   [0.16]   [0.35]
Profitability                       0.41     0.30     0.58
                                    [0.00]   [0.02]   [0.32]
Tobin's Q                           -0.48    -0.07    -2.24
                                    [0.19]   [0.89]   [0.16]
Presplit change in Risk             -0.01    -0.10    -0.30
                                    [0.77]   [0.15]   [0.25]
Presplit change in ILLIQ            0.03     0.13     0.53
                                    [0.79]   [0.49]   [0.42]
Presplit change in Turnover         5.37     -2.01    -19.91
                                    [0.08]   [0.66]   [0.24]
Industry dummy                      Yes                Yes
Year dummy                          Yes                Yes
Pseudo [R.sup.2]                   0.348              0.004
Number of observations             136,084            4,604

                                     Postmatch Binary
                                   Logistic Regression

Presplit price                            -0.03
                                          [0.31]
Presplit change in Log (1 + NII)           0.03
                                          [0.78]
Presplit change in PIH                    -0.33
                                          [0.69]
Presplit Log (1 + NII)                     0.03
                                          [0.64]
Presplit PIH                              -0.26
                                          [0.63]
Presplit Log (1 + NAF)                    -0.02
                                          [0.83]
MVE                                        0.00
                                          [0.10]
BEME                                       0.08
                                          [0.26]
Mkt_Adj_Return                             0.02
                                          [0.81]
Ind_Adj_ROA                                0.12
                                          [0.70]
Ind_Adj_Leverage                           0.05
                                          [0.82]
Profitability                             -0.05
                                          [0.69]
Tobin's Q                                  0.01
                                          [0.91]
Presplit change in Risk                   -1.48
                                          [0.59]
Presplit change in ILLIQ                  -0.63
                                          [0.90]
Presplit change in Turnover               -15.73
                                          [0.53]
Industry dummy
Year dummy
Pseudo [R.sup.2]
Number of observations

Panel B. Balancing Test

                             Prematch

                          Treatment   Control   Difference

Presplit price              0.80       8.03      -7.23 **
                                                 (-25.50)
Presplit change in Log      -0.02      0.13      -0.15 **
  (1 + NII)                                      (-9.54)
Presplit change in P1H      -0.01      0.02      -0.03 **
                                                 (-10.46)
Presplit Log (1 + NII)      1.82       2.38      -0.56 **
                                                 (-13.89)
Presplit PIH                0.09       0.20      -0.11 **
                                                 (-16.47)
Presplit Log (1 +           0.39       0.69      -0.30 **
  NAF)                                           (-10.83)
MVE                         46.94      85.27    -38.33 **
                                                 (-9.03)
BEME                        0.83       0.85       -0.02
                                                 (-0.77)
Mkt_Adj_Return              -0.25      -0.07     -0.18 **
                                                 (-10.91)
Ind_Adj_ROA                 -0.16      -0.04     -0.12 **
                                                 (-22.81)
Ind_Adj_Leverage            0.06       0.03      0.03 **
                                                  (5.76)
Profitability               -0.28      -0.06     -0.22 **
                                                 (-18.69)
Tobin's Q                   1.64       1.34      0.30 **
                                                  (7.80)
Presplit change in Risk     0.53       0.08      0.45 **
                                                  (9.56)
Presplit change in          2.86       0.71      2.15 **
  ILLIQ                                          (10.01)
Presplit change in          -0.32      -0.11     -0.21 **
Turnover                                         (-3.01)
Number of                 847         135,237
observations
                             Postmatch

                          Treatment   Control   Difference

Presplit price              1.33       1.42       -0.09
                                                 (-1.28)
Presplit change in Log      -0.01      -0.01      -0.00
  (1 + NII)                                      (-0.08)
Presplit change in P1H      -0.01      -0.01      -0.00
                                                  (-0.6)
Presplit Log (1 + NII)      1.79       1.75        0.03
                                                  (0.75)
Presplit PIH                0.08       0.08        0.00
                                                  (0.12)
Presplit Log (1 +           0.35       0.34        0.01
  NAF)                                            (0.50)
MVE                         40.68      37.21       3.47
                                                  (1.04)
BEME                        0.86       0.82        0.04
                                                  (1.16)
Mkt_Adj_Return              -0.25      -0.24      -0.01
                                                 (-0.25)
Ind_Adj_ROA                 -0.15      -0.15       0.00
                                                  (0.27)
Ind_Adj_Leverage            0.06       0.06       -0.00
                                                 (-0.17)
Profitability               -0.28      -0.27      -0.01
                                                 (-0.33)
Tobin's Q                   1.60       1.61       -0.01
                                                 (-0.30)
Presplit change in Risk     0.51       0.56       -0.04
                                                 (-0.61)
Presplit change in          3.02       3.14       -0.12
  ILLIQ                                          (-0.31)
Presplit change in          -0.31      -0.23      -0.08
Turnover                                         (-0.95)
Number of                 781         3,823
observations

Panel C of Propensity Score between Treatment and Each of the Five
Control Firms

Control firm                    N     Mean    Median

Before removing "bad" matches

Nearest distance                781   0.002    0.002
2nd nearest distance            781   0.003    0.003
3 rd nearest distance           781   0.005    0.005
4th nearest distance            781   0.006    0.006
5th nearest distance            781   0.008    0.008

After removing "bad" matches

Nearest distance                781   0.002    0.000
2nd nearest distance            774   0.003    0.000
3rd nearest distance            765   0.004    0.001
4th nearest distance            755   0.005    0.001
5th nearest distance            748   0.005    0.001

Control firm                    95th    99th    Maximum

Before removing "bad" matches

Nearest distance                0.009   0.022    0.033
2nd nearest distance            0.017   0.034    0.071
3 rd nearest distance           0.025   0.045    0.112
4th nearest distance            0.032   0.054    0.122
5th nearest distance            0.038   0.068    0.127

After removing "bad" matches

Nearest distance                0.009   0.022    0.033
2nd nearest distance            0.015   0.028    0.034
3rd nearest distance            0.021   0.034    0.040
4th nearest distance            0.025   0.037    0.040
5th nearest distance            0.028   0.038    0.040


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We are grateful to an anonymous referee, Marc Lipson (Editor), and Laura Starks for their valuable comments and suggestions. We also thank Maria Kasch, Kenneth Kim, session participants at the FMA annual conference, and seminar participants at the State University of New York at Buffalo for useful comments and discussions. We are solely responsible for the content of the paper.

(1) For instance, the Conference Board reports that institutional ownership in the largest 1,000 US corporations increased from 46.6% in 1987, to 61.4% in 2000, and then to 73% by the end of 2009.

(2) http://phx.corporate-ir.net/phoenix.zhtml?c= 115270&p=irol-newsArticle_pf&ID=443657&highlight=.

(3) See Dash (2011). For another example, Mikel D. Faulkner, chairman of Harken Energy Corporation, stated the following in conjunction with his company's decision to have a 1-for-10 reverse split on November 8, 2000: "We are recommending this action [reverse stock split] that our board believes may increase long-term shareholder value ... as our stock price has fallen below one dollar, it presents a number of difficulties in returning to acceptable levels. Many brokerage firms do not allow their brokers to recommend low-priced stocks or let clients purchase low-priced stocks on margin. Additionally, many equity research analysts are prevented from initiating coverage on low-priced stocks. Finally, many institutional investors that are capable of buying large blocks of stock, and therefore creating significant demand, are prevented from investing in low-priced stocks by internal policies. While the parameters of each firm vary, the combined effect of these problems is that the market for the common stock is severely limited, which we feel negatively affects Harken's stock price." http://www.theffeelibrary.com/Harken+Board+Announces+Stock+Repurchase+Program+and+One-forTen...- a065465486.

(4) Although Hwang, Dimkpah, and Ogwu (2012) report that the mean institutional holding of large capitalization stocks increases after the reverse stock split, they neither analyze a mechanism through which the reverse stock split changes institutional investment nor show whether their results are statistically significant.

(5) Although Han (1995) alluded to this idea, he did not provide pertinent empirical evidence.

(6) See http://www.sec.gov/news/press/2009/2009-l 17.htm.

(7) See http://www.sec.gov/investor/schedulel5g.htm.

(8) According to the SEC's Penny Stock Rule, penny stocks refer to stocks that are selling under $5 in the over-the counter market. Although this technical definition excludes stocks traded on major exchanges, the SEC explains that the term "penny stocks" extends to any stocks under $5. See http://www.sec.gov/divisions/marketreg/bdguide.htm and http://www.sec.gov/answers/penny.htm.

(9) Although we argue that fiduciary concern is the main reason for institutional avoidance of stocks priced under $5, other reasons such as margin trading limitation may also contribute to the formation of $5 as a threshold. Most brokerage firms require that investors put up a high initial and maintenance margin when they purchase stocks under $5 on margin. In addition, stocks under $5 are typically not allowed for short sale, suggesting that financial intermediaries view such stocks as poor collateral. However, since most of institutional investors do not trade on margin, perhaps except independent investment advisors, we expect that margin trading limitation only affects independent investment advisors.

(10) The existence of $5 threshold frequently appears in the reverse split news. For example, Penn Treaty American Corporation had a reverse stock split on July 11, 2005. One of the reasons the company stated for moving forward with the proposed reverse stock split, as quoted from reverse split news report, is that "Many sell-side firms will only recommend and many institutional investors and investment funds will only purchase shares of a company's common stock if its market price exceeds $5.00 per share." Another example is Citigroup. See http://money.cnn.com/2009/03/19/news/companies/citigroup/index.htm.

(11) See Gustin (2011).

(12) For example, Woolridge and Chambers (1983) find negative abnormal returns around the reverse split proposal date, approval date, and effective date. Peterson and Peterson (1992) find negative abnormal returns around the reverse split announcement date. Marchman (2007) finds that the market reacts more negatively to the reverse split for regulatory reason. Desai and Jain (1997) find negative abnormal return over the one- and three-year period following the reverse split announcement. Kim, Klein, and Rosenfeld (2008) find significant negative abnormal returns over the three-year period following the month of the reverse split. They argue that the short sale constraint prevents arbitrageurs from exploiting the negative information after the reverse split.

(13) More than 80% of our reverse split firms are listed on NASDAQ. The number of reverse splits peaks in 1992 (8.9% of the whole sample) and in 1998 (7.5% of the whole sample).

(14) There are 2,201 reverse splits between 1982 and 2008 with a split ratio larger than 1-for-2 in the CRSP database. Removing reverse splits that have other corporate events on the same date (using the CRSP distribution code to identify other events) reduces the sample size to 2,153. Requiring that stocks be listed on the NYSE, AMEX, or NASDAQ from 8 quarters before to 8 quarters after the reverse split reduces the sample size to 946. Of these, we find that 20 stocks do not have monthly return data or the presplit price. Removing these 20 stocks reduces the sample to 926 stocks. Requiring that firms have presplit characteristics in the Compustat database further reduces the sample size to 847.

(15) Thomson Financial explains that TYPECODE variable is not reliable after 1998. We use Brian Bushee's classification, which is more accurate. We thank him for providing us with the classification.

(16) The presplit price is the closing price on the last trading day before the ex date. The target price is the product of the presplit price and the split ratio. The split ratio is the ratio of the number of a firm's outstanding shares before and after the reverse split.

(17) Presplit change in NII and PIH is the difference in the variable between quarter -1 and quarter -8, where quarter 0 is the reverse split quarter.

(18) A matching estimator is valid if the outcome and the likelihood of receiving the treatment are independent, conditional on a set of characteristics that are observable. We choose a set of presplit characteristics that are related to institutional holdings and the likelihood of reverse split. Gompers and Metrick (2001) show that institutional investors prefer to invest in large, liquid stocks that have low past returns. Del Guercio (1996) shows that bank trust investment is tilted toward large capitalization stocks with low book-to-market ratios. Badrinath, Gay, and Kale (1990) find that institutional investors prefer stocks with "safe" characteristics such as large size, low volatility, or high liquidity. O'Brien and Bhushan (1990) find a positive relation between institutional ownership and the number of analysts.

(19) Although dividend is an important dimension to balance between reverse split and non-reverse-split firms, we note that more than 95% of the reverse split sample and more than 95% of the non-reverse-split sample are non-dividend paying firms. We find that even without including dividend as a covariate, our postmatch samples are still balanced in this dimension.

(20) For example, for a L5H5 reverse split firm, we identify five non-reverse-split firms that have the most similar propensity scores of issuing a L5H5 reverse split during the reverse split quarter and that also have a presplit price below $5.

(21) Our results are similar when we use different threshold distances.

(22) For example, Stratus Property Inc. had a 1-for-50 reverse split on May 29, 2001, which was immediately followed by a 25-for-1 forward split on the same day. Although the net effect of both splits would be 1-for-2 reverse stock split, all presplit shareholders holding less than 50 shares received cash in lieu of fractional shares after the reverse split. This seems to be a very effective way to reduce the number of minority shareholders without a large net split ratio. However, because the CRSP database reports only the net split ratio (i.e., 1-for-2 in this case), the reduction in the number of minority shareholders is not necessarily associated with the split ratio reported in the CRSP data.

(23) See Appendix A for the computational details of these variables.

(24) As a robustness check, we also investigate whether our results vary across different tick size regimes. If the higher transaction cost associated with a larger tick size were the reason behind the increase in institutional holdings for the L5H5 group, we would expect the benefit from the L5H5 reverse split to decrease from the $1/8 regime (before 1997) to the $1/16 regime (between 1997 and 2001) and also from the $1/16 regime to the decimal regime (after 2001). We find that our main results do not vary significantly across difference tick size regimes, rejecting the alternative explanation.

(25) Prior research suggests the optimal range is somewhere between $20 and $40.

(26) The results on insurance companies are somewhat sensitive to our matching approach. In other settings, we do find some evidence that reverse split firms in L5H5 group attract a small and significant increase in both NII and PIH.

(27) For example, although TeamStaffInc. reverse-split its shares on June 2,2000 to meet the NASDAQ listing requirement, Donald W. Kappauf, its president and CEO, also stated that "... we have been advised by various institutional investors and our financial consultants that at the current share price of the company's stock there are a significant number of funds and brokers that are prohibited from trading in our stock even though they have expressed an interest in the Company. Additionally with a higher stock price we hope to attract institutional buyers along with being better able to conclude acquisitions using our stock."

(28) Prior research (see, e.g., O'Brien and Bushan, 1990) shows that institutional ownership and analyst following are positively related.

(29) See Appendix A for the computational details of DD_NAF.

(30) The main purpose of using the reference portfolio is not to measure the effect of the reverse split per se on stock returns. Instead, it is to assess whether investors in firms that split their shares earn higher or lower returns than investors in other firms, after controlling for firm attributes that are believed to affect stock returns. Hence, the reference portfolio includes both reverse split firms and non-reverse-split firms that are similar to each reverse split firm. Appendix A (w) provides the detailed explanation of the reference portfolio. We use the same method to form the reference portfolio for each non-reverse-split firm when we conduct the difference-in-difference test discussed below.

(31) For example, if skillful institutional investors possess private information that a low-priced firm is undervalued, they may urge firm managers for a L5H5 reverse split to remove their investment restriction. In this case, we may observe an increase in both share price and institutional holdings after the L5H5 reverse split even if the simultaneous increase in share price and institutional holdings has nothing to do with Merton's incomplete market theory.

(32) We call D_BHAR the difference-in-difference estimate of the effect of reverse splits on share prices because it is the difference in BHAR between the reverse split firm and non-reverse-split control firms and BHAR itself measures the difference in buy-and-hold returns between the reverse split firm and the reference portfolio. Alternatively, we also call D_BHAR the control-firm-adjusted buy-and-hold abnormal return. We use the reference portfolio to control for the effect of size, book-to-market ratio, and price momentum on stock returns. In contrast, we use the non-reverse-split control firms to measure the effect of the reverse split on stock returns.

(33) We form a reference portfolio for each non-reverse-split firm and use Equation (3) to calculate [BHAR.sub.i,j].

(34) Appendix A provides the computational detail of these variables. An accurate comparison of the change in Nil across different types of reverse split should be based on DD_NII rather than A Nil because DD_NII measures the control- sample-adjusted change in Nil while AW/measures the absolute change in NIL The presplit mean Nil for H5H5 is 55.38 while the presplit mean Nil is only 7.10 and 20.86 for L5L5 and L5H5. Therefore, it is not surprising that H5H5 has the largest absolute increase in the number of institutional investors (AW/) but not the largest relative increase in the number of institutional investors (DD_NII).

(35) The mean BHAR for each group is 21.47%, -15%, and -12.15%, respectively. Hence, the average buy-and-hold return of L5L5 reverse split firms is higher than the average buy-and-hold return of firms with similar sizes, book-to-market ratios, and past stock returns (i.e., the reference portfolio). In contrast, the average buy-and-hold returns of L5H5 and H5H5 reverse split firms are lower than the average buy-and-hold return of the reference portfolio.

(36) To further confirm that the exclusion condition holds, we use the entire 13F database to analyze the relation between the change in holdings of quasi-indexers between quarter q and q-1 and the market-adjusted return in quarter q+1. We find that the relation is negative but insignificant. The relation is, however, positive and significant for both dedicated and transient institutional investors.

(37) Although prior research (see, e.g., Barber et al., 2003) provides evidence on the relation between the strength of analysts' recommendations and stock returns, the relation between the number of analysts and BHAR has not been clearly established in the literature. We find no statistically significant relation between [DELTA]NAF and BHAR (unreported) or between DD_NAF and D_BHAR (see Column 2 in Table VII Panel B) for our study sample of stocks.

(38) T-statistics are 902.7 and 283.34 and p-values are both below 0.001.

(39) To assess the economic significance of the postsplit abnormal return (D_BHAR) that is attributable to the postsplit increase in institutional holdings, we note from Table VI Panel A that the mean DD_NII is 0.17 and the mean DD_PIH is 10.01% ([approximately equal to] 0.1) for the L5H5 group. We also note that the coefficients on DD_NII and DD_PIH are 0.49 and 2.05 from Table VII Panel B (see Column 2). Thus, the abnormal return of L5H5 firms that is attributable to the postsplit increase in institutional holdings is 0.17 x 0.49 + 0.1 x 2.05 = 0.2883, or 28.83 percentage points.

(40) Understanding why reverse splits are associated with negative stock returns is beyond the scope of our study. However, two possible conjectures are: 1) firms that reverse split their shares are generally those that are on a downward trajectory (e.g., declining profits and market share) and reverse splits do not reverse the trajectory; 2) the reverse split itself may trigger a decline in share price because the reverse split may result in an increase in short sales by removing the short sale restriction imposed on stocks trading below $5.

Kee H. Chung and Sean Yang *

* Kee H. Chung is the Louis M. Jacobs Professor in the Department of Finance and Managerial Economics at State University of New York at Buffalo in Buffalo, NY and a Visiting Professor in the School of Business Administration at Chung-Ang University in Seoul, Korea. Sean Yang is a doctoral student in the Department of Finance and Managerial Economics at State University of New York at Buffalo in Buffalo, NY.

Table I. Presplit Firm Characteristics

This table shows the presplit characteristics of our study sample
of 847 reverse splits. Presplit price is the closing price on the
last trading day before the ex date. Target price is the product of
the presplit price and split ratio. Split Ratio is the ratio of the
number of a firm's outstanding shares before and after the reverse
split. Nil is the number of institutional investors that hold the
firm's shares in the quarter before the reverse split quarter. PIH
is the percentage of shares that are held by institutional
investors (i.e., the number of shares held by institutional
investors divided by the number of shares outstanding) in the
quarter before the reverse split quarter. NAF is the number of
different analysts producing earnings forecasts during a year
before the ex date. MVE is the product of closing price and the
number of shares outstanding at the beginning of the reverse split
quarter. BEME is the ratio of the book value of equity to the
market value of equity. Mkt_Adj_Return is the 12-month buy-and-hold
return prior to the reverse split quarter less the 12-month
buy-and-hold value-weighted market return. Ind_Adj_ROA is the ROA
(earnings before extraordinary items divided by total asset of the
previous fiscal year) less the industry median ROA.
Ind_Adj_Leverage is the leverage ratio (the current and long-term
debt divided by total asset) less the industry median leverage
ratio. Profitability is the earnings before extraordinary items
less preferred dividend plus income statement deferred taxes if
available, divided by the book value of equity. Tobin's Q is the
sum of market value of equity, preferred stock liquidation value,
and current and long-term debt divided by total asset. Risk is the
standard deviation of daily stock returns during a year. ILLIQ is
the absolute value of daily return divided by daily dollar volume,
averaged over a year. Turnover is the daily share volume divided by
total shares outstanding, averaged over a year. Spread is the
difference between the daily closing bid and ask prices divided by
the midpoint of bid and ask, averaged over a year. Presplit change
in Nil and PIH is the difference in the variable between quarter -1
and quarter -8, where quarter 0 is the reverse split quarter.
Presplit change in Risk, ILLIQ, Turnover, and Spread is the
difference in the variable between year t-1 and t-2, where year t-
1 is a year before the ex date and year t-2 is a year before year
t-1.

Variable                           Mean     Standard
                                           Deviation

Presplit price (dollars)           0.80        1.73
Target price (dollars)             5.73        5.71
Split ratio                        8.86       10.18
Number of institutional           11.69       18.08
  investors (MI)
Percentage institutional           8.72       13.97
  holding (PIH) (in%)
Number of analysts (NAF)           1.04        2.25
Market value of equity x          46.94       95.19
  holding (PIH) (in%) (MVE)
Book-to-market equity (BEME)       0.83        0.83
Market adjusted return           -25.47       53.55
  (Mkt_Adj_Return) (in%)
Industry adjusted ROA            -15.51       18.85
  (Ind_Adj_ROA) (in%)
Industry adjusted leverage         0.06        0.20
  (Ind_Adj_Leverage)
Profitability (in%)              -27.76       48.16
Tobin's Q                          1.64        1.24
Presplit change in the number     -1.26        6.50
  of institutional investors
  (NIT)
Presplit change in the            -1.33        7.19
  percentage institutional
  holding (PIH) (in%)
Presplit change in the number     -0.42        1.83
  of analysts (NAF)
Presplit change in risk            0.53        1.89
  (Risk) (in%)
Presplit change in Amihud          2.86        8.99
  illiquidity measure (ILLIQ)
Presplit change in turnover       -0.32        2.45
  ratio (Turnover)
Presplit change in bid-ask         0.63        2.60
  spread (Spread) (in%)

Variable                           25th      50th      75th

Presplit price (dollars)           0.13      0.48      1.00
Target price (dollars)             2.25      3.75      7.25
Split ratio                        4.00      5.00     10.00
Number of institutional            1.00      5.00     13.00
  investors (MI)
Percentage institutional           0.20      2.71     11.01
  holding (PIH) (in%)
Number of analysts (NAF)           0.00      0.00      1.00
Market value of equity x           5.09     13.36     35.48
  holding (PIH) (in%) (MVE)
Book-to-market equity (BEME)       0.17      0.52      1.29
Market adjusted return           -68.85    -41.75     -1.69
  (Mkt_Adj_Return) (in%)
Industry adjusted ROA            -32.80    -11.35     -0.31
  (Ind_Adj_ROA) (in%)
Industry adjusted leverage        -0.08      0.03      0.20
  (Ind_Adj_Leverage)
Profitability (in%)              -67.93    -11.01      8.58
Tobin's Q                          0.77      1.15      2.15
Presplit change in the number     -3.00      0.00      1.00
  of institutional investors
  (NIT)
Presplit change in the            -4.07     -0.07      0.44
  percentage institutional
  holding (PIH) (in%)
Presplit change in the number      0.00      0.00      0.00
  of analysts (NAF)
Presplit change in risk           -0.98      0.58      2.42
  (Risk) (in%)
Presplit change in Amihud         -0.22      0.38      6.80
  illiquidity measure (ILLIQ)
Presplit change in turnover       -1.46     -0.14      0.84
  ratio (Turnover)
Presplit change in bid-ask        -0.66      0.60      2.68
  spread (Spread) (in%)

Table II. Reverse Split and Institutional Holding

We use the difference-in-difference regression to examine the effects
of reverse stock splits on NII and PIH. We calculate the difference-
in-difference estimates of the change in Nil and PIH (i.e., DD_NII and
DD_PIH) from the one-year period before the reverse split quarter to
the second one-year period after the reverse split quarter for each
of 781 reverse split firms. We estimate the following regression model
that includes other potential determinants of institutional holdings
(see Appendix A for a detailed description of each variable):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

All regression coefficient estimates are multiplied by 100. Standard
errors are adjusted for heteroscedasticity. Numbers in parenthesis are
t-statistics.

                          (1)         (2)        (3)        (4)
                         DD_NII      DD_NII     DD_PIH     DD_PIH

L5L5                     -16.93 **   -8.73 *    3.32 **    3.41 **
                         (-5.36)     (-1.98)    (6.53)     (3.17)
L5H5                     17.40 **    19.85 **   10.01 **   8.77 **
                         (3.18)      (3.07)     (7.92)     (5.44)
H5H5                     9.67        9.83       2.27       0.92
                         (0.68)      (0.67)     (0.56)     (0.24)
DD_Ind_Adj_ROA                       -0.47                 0.54
                                     (-0.11)               (0.54)
DD_Ind_Adj_Leverage                  3.53                  -0.80
                                     (0.25)                (-0.24)
DD-Profitability                     -0.08                 0.05
                                     (-0.25)               (0.73)
DD-Tobins Q                          3.34 **               0.87 **
                                     (2.97)                (3.17)
DD_Risk                              -3.28 **              -0.60 **
                                     (-3.89)               (-2.88)
DD_ILLIQ                             42.00 **              13.59 **
                                     (2.63)                (3.09)
DD-Turnover                          1.74 **               0.25 **
                                     (4.60)                (2.63)
DD_Spread                            -36.21                1.64
                                     (-0.86)               (0.22)
Split Ratio                          -1.96 **              0.05
                                     (-4.97)               (0.41)
[R.sup.2]                0.046       0.151      0.149      0.197
Number of observations   781         581        781        581

** Significant at the 0.01 level.

* Significant at the 0.05 level.

Table III. Reverse Split and Institutional Holding across Different
Types of Institutional Investors

We decompose institutional holdings into holdings of each type of
institution, and examine the effect of reverse splits on the holdings
of each type of institution separately. Specifically, we calculate
DD_NII and DD_PIH and estimate the regression model in Table II for
each type of institution. See Appendix A for a detailed description
of each variable. All regression coefficient estimates are multiplied
by 100. Standard errors are adjusted for heteroscedasticity. Numbers
in parenthesis are t-statistics.

                    Bank                   Insurance
                    Trust                  Company

                 (1)        (2)       (3)         (4)
                 DD_NII     DD_PIH    DD Nil      DD_PIH

L5L5             -10.04 *   0.32      -12.63 **   0.16
                 (-2.46)    (1.40)    (-3.00)     (0.98)
L5H5             4.79       1.11 **     7.33        0.24
                 (0.95)     (3.93)    (1.41)      (1.21)
H5H5             4.13       0.36      -4.59       -0.32
                 (0.31)     (0.47)    (-0.33)     (-0.60)
Controls         Yes        Yes       Yes         Yes
[R.sup.2]        0.149      0.087     0.082       0.058
Number of        581        581       581         581
  observations

                    Investment             Independent
                    Company                Investment
                                           Advisor

                 (5)        (6)       (7)        (8)
                 DD_NII     DD PIH    DD_NII     DD_PIH

L5L5             1.49       0.40      -9.57 *    2.28 **
                 (0.41)     (1-26)    (-1.97)    (2.79)
L5H5             16.36 **   1.31 **   19.21 **   5.67 **
                 (3.61)     (3.40)    (3.21)     (5.63)
H5H5             6.93       -0.53     14.48      0.70
                 (0.57)     (-0.51)   (0.90)     (0.26)
Controls         Yes        Yes       Yes        Yes
[R.sup.2]        0.074      0.089     0.133      0.157
Number of        581        581       581        581
  observations

                 Pension Fund,
                 University Endowment,
                 Miscellaneous

                 (9)          (10)
                 DD_NII       DD_PIH

L5L5             -4.40        0.26
                 (-1.20)      (1.20)
L5H5             12.35 **     0.56 *
                 (2.73)       (2.05)
H5H5             11.40        0.74
                 (0.94)       (1.01)
Controls         Yes          Yes
[R.sup.2]        0.065        0.022
Number of        581          581
  observations

** Significant at the 0.01 level.

* Significant at the 0.05 level.

Table IV. Reverse Split Reasons and Institutional Holding

To shed some light on possible motives for reverse splits, we search
Factiva for news articles about reverse splits and identify reasons for
362 reverse splits. Panel A shows five major reasons for reverse splits
that are either reported in news articles or stated explicitly by firm
managers or boards of directors. These reasons are not mutually
exclusive; therefore, the total number of reason-firms (393) is greater
than 362. To examine whether the postsplit changes in NII and PIH
differ across firms according to the reasons for reverse splits, we
regress DD_NII and DD_PIH on five dummy variables for reverse split
reasons and three dummy variables for reverse split types. Panel B
shows the regression results. See Appendix A for a detailed description
of each variable. All regression coefficient estimates are multiplied
by 100. Standard errors are adjusted for heteroscedasticity. Numbers in
parenthesis are t-statistics.

Panel A. Reasons for the Reverse Stock Split
                                                 Frequency   Percentage

Reason 1: To attract institutional investors,       147        40.61%
  to improve visibility and image of the firm,
  to initiate analyst coverage, to allow
  margin trading for retail investors, to
  improve liquidity, to enhance the
  eligibility of listing in other markets, to
  move share price to the range of firms in
  "similar size" or "same industry"
Reason 2: To avoid delisting from exchange          176        48.62%
  (mainly from NASDAQ)
Reason 3: To squeeze out minority shareholders      14         3.87%
  and reduce the cost of servicing
  shareholders
Reason 4: To enhance the flexibility for            42         11.60%
  future financing and facilitate merger and
  acquisition
Reason 5: Reorganization                            14         3.87%
Total number of firms whose reasons for             362         100%
  reverse split can be found
Total number of reason-firms                        393         N/A

Panel B. Regression Results

                          (1)          (2)
                         DD_NII       DD_PIH

Reason 1                 -29.07 *      -0.70
                         (-2.10)     (-0.22)
Reason 2                 -39.09 **   0.56
                         (-2.70)     (0.16)
Reason 3                 -77.93 **   -9.38
                         (-3.53)     (-1.81)
Reason 4                 14.68       1.56
                         (0.91)      (0.41)
Reason 5                 -32.17      0.31
                         (-1.39)     (0.06)
L5L5                     18.80       4.66
                         (1.23)      (1.30)
L5H5                     45.85 **    12.28 **
                         (2.98)      (3.41)
H5H5                     40.18       6.43
                         (1.69)      (1.15)
[R.sup.2]                0.116       0.193
Number of observations   362         362

** Significant at the 0.01 level.

* Significant at the 0.05 level.

Table V. Reverse Split and Analyst Following

To examine the effect of reverse splits on analyst coverage, we
estimate the following regression model:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where DD_NAF is the difference-in-difference estimate of the effect of
reverse split on the number of analysts. See Appendix A for a detailed
description of each variable. All regression coefficient estimates are
multiplied by 100. Standard errors are adjusted for heteroscedasticity.
Numbers in parenthesis are t-statistics.

                         (1)        (2)
                         DD_NAF     DD_NAF

L5L5                     3.89 *     3.66
                         (2.50)     (1.40)
L5H5                     19.92 **   18.59 **
                         (5.63)     (4.02)
H5H5                     14.31      15.59
                         (1.19)     (1.26)
DD_Ind_Adj_ROA                      1.31
                                    (0.30)
DD_Ind_Adj_Leverage                 6.35
                                    (0.60)
DD_Profitability                    0.07
                                    (0.32)
DDJTobin s Q                        1.49
                                    (1.81)
DD_Risk                             -1.31 **
                                    (-2.78)
DD_ILLIQ                            29.39 **
                                    (2.81)
DD_Turnover                         0.54 *
                                    (2.53)
DD_Spread                           -25.40
                                    (-1.18)
Split Ratio                         -0.01
                                    (-0.03)
[R.sup.2]                0.071      0.104
Number of observations   781        583

** Significant at the 0.01 level.

* Significant at the 0.05 level.

Table VI. Reverse Split, Institutional Holdings, and Abnormal Stock
Returns

This table shows the mean values of changes in institutional
holdings ([DELTA]NII, [DELTA]PIH, DD_NII, and DD_PIH) and abnormal
stock returns (BHAR and D_BHAR), where [DELTA]NII ([DELTA]PIH) is
the change in the number (percentage holding) of institutional
investors between the pre- and postsplit period for reverse split
firms, BHAR is the buy-and-hold abnormal return of reverse split
firms, DJBHAR is the control-firm- adjusted buy-and-hold abnormal
return of reverse split firms, and DD_NII (DD_PIH) is the
control-firm-adjusted change in the number (percentage holding) of
institutional investors between the pre- and postsplit period for
reverse split firms. Panel A presents the results for each of the
three reverse split groups (L5L5, L5H5, and H5H5). To shed further
light on the effect of institutional holdings on share value, we
divide the sample into tercile groups according to [DELTA]NII,
[DELTA]PIH, DD_NII, or DD_PIH. Panel B shows the results for the
whole sample and each subsample of the three reverse split groups.
See Appendix A for a detailed description of each variable.

Panel A. Results for Each Reverse Split Group

       N     [DELTA]NII   [DELTA]PIH   BHAR

L5L5   525   0.14         3.61%         21.47%
L5H5   283   4.78         11.85%       -15.00%
H5H5   26    17.21        11.92%       -12.15%

       N     DD_NII   DD_PIH   D_BHAR

L5L5   489   -0.17    3.32%    -58.74%
L5H5   271   0.17     10.01%   -49.65%
H5H5   21    0.1      2.27%    -6.55%

Panel B. Results for the Whole Sample and Each Reverse Split Group
When Terciles Are Formed by [DELTA]NII, [DELTA]PIH, DD_NII, or DD_PIH

Tercile           Terciles Formed           Terciles Formed
Group             by [DELTA]NII             by [DELTA]PIH

                  N     [DELTA]   BHAR      N     [DELTA]   BHAR
                        NII                       PIH

Whole Sample
  Low             274   -9.07     -24.04%   278   -5.15%    -25.70%
  Medium          278    0.05     -7.40%    278    1.68%     4.18%
  High            282    15.41     54.46%   278    23.46%    45.67%
Subsample: L5L5
  Low             170   -5.95     -9.79%    175   -3.80%    -10.25%
  Medium          183   -0.22      0.51%    175    0.55%      6.38%
  High            172    6.55      74.70%   175    14.08%    68.30%
Subsample: L5H5
  Low             94    -14.18    -47.35%   94    -7.18%    -59.75%
  Medium          95     1.54     -39.58%   95     7.09%    -26.00%
  High            94     27.01     42.19%   94     35.70%    40.87%
Subsample: H5H5
  Low             8      -17.19   -55.59%   8     -10.53%   -70.46%
  Medium          9       4.83    -56.64%   9      9.30%    -8.09%
  High            9       60.17    70.95%   9      34.50%    35.63%

Tercile           Terciles Formed                 Terciles Formed
Group             by DD_NII                       by DD_PIH

                  N     DD_NII   D_BHAR     N     DD_PIH    D_BHAR

Whole Sample
  Low             260   -0.84    -112.73%   260   -7.17%    -107.27%
  Medium          261   -0.11    -48.96%    261    2.08%    -47.95%
  High            260   -0.01    -0.87%     260    21.95%   -7.34%
Subsample: L5L5
  Low             163   -0.91    -118.80%   163   -5.45%    -115.20%
  Medium          163   -0.2     -57.77%    163    1.04%    -55.27%
  High            163    0.6      0.35%     163    14.37%   -5.76%
Subsample: L5H5
  Low             90    -0.72    -87.39%    90    -9.33%    -99.05%
  Medium          91     0.06    -59.81%    91     6.56%    -59.51%
  High            90     1.18    -1.62%     90     32.85%     9.73%
Subsample: H5H5
  Low             7     -0.59    -75.24%   7     -16.53%    -68.44%
  Medium          7      0.07     7.80%    7      0.23%     -15.92%
  High            7      0.82     47.80%   7      23.11%     64.72%

Table VII. Reverse Split, Institutional Holdings, and Abnormal Stock
Returns: Regression Results

Panel A shows the OLS and 2SLS regression results. The OLS regression
model is as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

To address the endogeneity problem, we also estimate the following 2SLS
regression:

First-Stage Regression:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Second-stage regression:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

To further assess the robustness of the relation between changes in
institutional investment and BHAR, we also employ a difference-in-
difference regression using the control sample of non-reverse-split
firms. Specifically, we examine whether the control-firm-adjusted
BHAR (i.e., D_BHAR) could be explained by the control-firm-adjusted
changes in NII and PIH (i.e., DD_NII and DD_PIH) using the following
regression model and show the results in Panel B:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

See Appendix A for a detailed description of each variable. Standard
errors are adjusted for heteroscedasticity. Numbers in parenthesis
are t-statistics. Numbers in bracket are p- values.

Panel A. OLS and 2SLS Regression Results

                             OLS Results
                          (1)             (2)
                          BHAR           BHAR

L5L5                      0.14           0.25 *
                          (1.95)         -2.13
L5H5                      -0.49 **       -0.41 **
                          (-4.56)        (-2.61)
H5H5                      -0.48          -0.40
                          (-1.46)        (-1.07)
[DELTA]LNII               0.41 **        0.35 **
                          (4.44)         (2.87)
[DELTA]PIH                1.88 **        2.12 **
                          (4.43)         (4.19)
[DELTA]Ind_Adj_ROA                       0.02
                                         (0.55)
[DELTA]Ind_Adj_Leverage                  -0.12
                                         (-0.48)
[DELTA]Profitability                     0.00
                                         (0.15)
[DELTA]Tobin's Q                         -0.00
                                         (-0.15)
[DELTA]Risk                              0.04
                                         (1.73)
[DELTA]ILLIQ                             -0.28
                                         (-1.05)
[DELTA]Turnover                          0.00
                                         (0.30)
[DELTA]Spread                            -1.78
                                         (-1.42)
Split Ratio                              -0.02
                                         (-1.51)
[DELTA]NAF

[DELTA]LNIIQIX

[DELTA]PIHQIX

[R.sup.2]                 0.097          0.101
F-statistics

Sargan test

Number of observations    834            637

                          2SLS Results
                          First Stage                 Second Stage
                          (3)            (4)          (5)
                          [DELTA]LNII    [DELTA]PIH   BHAR

L5L5                      2.91           0.86         0.26 *
                          (1.51)         (1.21)       (2.23)
L5H5                      7.66 **        3.73 **      -0.37 *
                          (3.06)         (4.06)       (-2.32)
H5H5                      3.67           5.61 *       -0.37
                          (0.60)         (2.48)       (-0.97)
[DELTA]LNII                                           0.42 **
                                                      (2.90)
[DELTA]PIH                                            1.61 *
                                                      (2.26)
[DELTA]Ind_Adj_ROA        -0.83          0.05         0.02
                          (-1.32)        (0.22)       (0.55)
[DELTA]Ind_Adj_Leverage   -2.82          -1.11        -0.12
                          (-0.70)        (-0.75)      (-0.47)
[DELTA]Profitability      0.00           0.05 **       0.00
                          (0.03)         (2.80)       (0.24)
[DELTA]Tobin's Q          0.62           0.27         -0.00
                          (1.65)         (1.97)       (-0.13)
[DELTA]Risk               -0.04          0.12         0.03
                          (-0.13)        (0.94)       (1.68)
[DELTA]ILLIQ              5.34           0.62         -0.29
                          (1.21)         (0.38)       (-1.07)
[DELTA]Turnover           0.25"          0.00         0.00
                          (3.68)         (0.19)       (0.27)
[DELTA]Spread             -10.37         -0.30        -1.67
                          (-0.51)        (-0.04)      (-1.32)
Split Ratio               -0.29          0.15*        -0.01
                          (-1.60)        (2.34)       (-1.34)
[DELTA]NAF                13.46 **        4.11 **
                          (5.65)         (4.70)
[DELTA]LNIIQIX            92.38 **        3.15 **
                          (44.07)        (4.10)
[DELTA]PIHQIX             -22.65         109.81 **
                          (-1.70)        (22.43)
[R.sup.2]                 0.837          0.675        0.0767
F-statistics              902.70         283.34
                          [0.000]        [0.000]
Sargan test                                           1.85
                                                      [0.175]
Number of observations    637            637          637

Panel B. Difference-in-Difference Regression Results

                      (1)        (2)
                      D_BHAR     D_BHAR

L5L5                  -0.55 **   -0.34 *
                      (-5.75)    (-2.23)
L5H5                  -0.77 **   -0.61 **
                      (-8.06)    (-4.33)
H5H5                  -0.16      -0.09
                      (-0.67)    (-0.33)
DD_NI1                0.49 **    0.49 **
                      (4.43)     (3.32)
DD_PIH                1.89 **    2.05 **
                      (2.80)     (2.82)
DD_NAF                           -0.27
                                 (-1.33)
DD_Ind_Adj_ROA                   0.16
                                 (1.56)
DD_Ind_Adj_Leverage              0.03
                                 (0.10)
DD_Profitability                 0.01
                                 (0.55)
DD_Tobin's Q                     0.05
                                 (1.60)
DD_Risk                          0.03
                                 (1.17)
DD_ILLIQ                         0.16
                                 (-0.26)
DD_Turnover                      0.03 **
                                 (3.10)
DD_Spread                        0.48
                                 (0.67)
Split Ratio                      -0.02
                                 (-1.49)
[R.sup.2]             0.155      0.196
Number of observations781        581

** Significant at the 0.01 level.

* Significant at the 0.05 level.
COPYRIGHT 2015 Financial Management Association
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Publication:Financial Management
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Date:Mar 22, 2015
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