An Examination of Initial Shareholdings in Tender Offer ... - Springer Link

Review of Quantitative Finance and Accounting, 12 (1999): 171–188 © 1999 Kluwer Academic Publishers, Boston. Manufactured in The Netherlands.

An Examination of Initial Shareholdings in Tender Offer Bids DANIEL ASQUITH Deloitte & Touche, 1000 Wilshire Blvd, Los Angeles, CA 90017, email: [email protected] ROBERT KIESCHNICK Federal Communications Commission, 2000 M Street N.W., Washington, D.C. 20554, email:[email protected], (Corresponding Author)

Abstract. We examine the initial shareholdings taken by bidders prior to making tender offer bids (“toeholds”) in order to test predictions of selected models of tender offers. Our data suggest a significantly negative relationship between first bidder premia and toeholds, which is consistent with the models of Shleifer and Vishny (1986) and Hirshleifer and Titman (1990), but inconsistent with the models of Harrington and Prokop (1993), Chowdhry and Jagadeesh (1994), and Burkart (1995). Key words: Toeholds, tender offers, beta regression analysis

1. Introduction The initial shareholding of a bidder in the target firm prior to bidding for the firm (the “toehold”) is a critical variable in a number of theoretical papers (e.g. Chowdhry and Jagadeesh (1994)). The bidder is likely able to acquire the toehold at a substantially lower price per share than necessary to acquire the remaining shares in a takeover. Therefore, absent other considerations, the failure to acquire a sizable toehold would appear to be forgoing a profitable opportunity. However, in practice, we observe a wide range of toeholds, with a substantial fraction of bidders acquiring no shares in the target prior to their bidding. The ability of bidders to acquire toeholds is limited by legal and market constraints. The primary legal constraint is the Williams Act. The Williams Act requires that anyone who purchases a beneficial interest of 5% or more of the shares of a company has to file a form 13d with the Securities and Exchange Commission (SEC) disclosing his holdings and intentions within 10 business days.1 Any substantial increase or decrease in these holdings, or change in intentions, require the prompt filing of an amended 13d. In practice, a 1% change in holdings is considered substantial. Under the Williams Act, the initiation of a tender offer requires the filing of a form 14d, which is the original source of toehold data used in this paper. Once the form 14d is filed, no additional shares may be purchased on the market. The Williams Act requires that tender offers remain open for at least 20 business days, during which time shareholders may reverse their decision to tender. Fur-

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DANIEL ASQUITH, ROBERT KIESCHNICK

ther, shares tendered in an over-subscribed offer are accepted on a pro-rata basis, and any increase in offer price is given to all lendering shareholders. Market constraints on a bidder’s acquisition of a toehold include the increase in price that large buying may cause and the ability to keep such buying secret before the threshold 5% is reached and disclosure under the Williams Act is required. Bagwell (1992), in work on Dutch auction repurchase tender offers, has estimated that on average, for a firm to purchase 15% of its own shares, the firm must offer a premium of 9.1%. Bagwell’s work is consistent with an upward sloping supply curve for shares. Under this presumption, purchases by a potential bidder might increase the firm’s share price and thereby reveal the firm to be a takeover target. If the firm is suspected to be a takeover target, any stock purchased would have to incorporate expectations about the potential takeover bid premium. On the other hand, Kyle and Vila (1991) have discussed how the presence of noise traders may enable a bidder to acquire an initial shareholding without fully revealing the intention to bid, strengthening the theoretical argument for large initial shareholdings. This paper examines whether or not selected theories of bidding strategy in tender offers are consistent with publicly available data by focusing on bidder toeholds in a sample of filed tender offers. Previous research has included the toehold acquired as an independent variable in studies of the success of a tender offer (Walkling (1985)), the premium paid in a tender offer (Walkling and Edmister (1985)), whether the offer was resisted by target management (Walkling and Long (1984)), and on the increase in target stock price prior to the offer being filed (Jarrell and Poulsen (1989)). However, unlike prior research, we examine influences on the distribution of first bidder toeholds and therefore treat first bidder toeholds as endogenously determined. Such a presumption is consistent with Chowdhry and Jegadeesh’s (1994) model of takeovers. To examine influences on the distribution of first bidder toeholds, we are confronted with an interesting statistical problem that is shared by a number of empirical studies in finance. Specifically, the toehold is a proportion of a total that by definition ranges over the interval [0,1].2 Prior regression analyses of such dependent variates have been conducted by either assuming that the conditional distribution is a normal distribution or by assuming that the conditional distribution is a censored normal distribution. Neither of these distributional assumptions are conceptually appropriate. A toehold, before scaling, is only defined over the interval [0,1]. Therefore a toehold is neither normally distributed, nor the result of censoring. At best, the results of applying regression strategies based upon these distributional assumptions to these data are that the estimators are inefficient. At worst, the estimators are biased and inconsistent.3 In either case, the results of applying these regression strategies to such data are potentially misleading. Consequently, in order to examine influences on first bidder toeholds, we must develop an appropriate statistical model for bidder toeholds. To accomplish this and address the research issues of interest, we organize the paper as follows. In Section 2, we set out salient features of the models to be tested. In Section 3, we describe our sample and the data. In Section 4, we present univariate statistical tests of key hypotheses. In Section 5, we develop a regression model for toehold data based upon the beta distribution and report the results from applying this model to our data. Finally, in Section 6, we provide a summary of our results and conclusions.


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Our study suggests two important results. First, we find a significantly negative unconditional and conditional correlation between first bidder premiums and first bidder toeholds, which is inconsistent with the implications of the models of Harrington and Prokop (1993), Chowdhry and Jagadeesh (1994), and Burkart (1995). Such results are, however, consistent with the models of Shleifer and Vishny (1986) and Hirshleifer and Titman (1990), and the results reported in Walking and Long (1984) and Betton and Eckbo (1994). Second, we find evidence that the relationship between first bidder toeholds and premia may be more complex than captured in the models of Shleifer and Vishny (1986) or Hirshleifer and Titman (1990). Specifically, we find that target firm size moderates the relationship between first bidder toeholds and premia. One explanation for this effect is the influence of firm size on bidder competition. However, we find evidence that bidder competition does not influence first bidder toeholds in a manner consistent with this explanation. Consquently, additional research is required to explain the influence of firm size on the relationship between first bidder toeholds and premia.

2. Theories related to toeholds Grossman and Hart (1980) formulated a free rider problem in tender offers by modeling a bidder who requires control of the firm to improve the value of the firm.4 To induce shareholders to tender their shares the bidder must offer a premium over the current market price. However, the shareholders know that in order for the bidder to profit, this offer price must be less than the value of the firm under the bidder’s control. The choice facing an individual shareholder is whether to tender his shares at a premium over the market price represented by the offer or to retain his shares. If the offer fails, the shareholder retains his shares, whether he tenders them or not. If the offer succeeds and he tenders, then he receives the offer price. If the offer succeeds and the shareholder retains his shares (does not tender), he will have shares worth more than the offer price. If the shareholder is small enough that his individual decision to tender does not affect the success of the offer, then not tendering is a weakly dominant strategy. However, if all shareholders individually follow the strategy of retaining their shares, then the offer will fail, despite the fact that all shareholders would be better off if the offer succeeds. Grossman and Hart suggested that to mitigate the free rider problem, shareholders of potential targets could allow a successful bidder to dilute the value of minority shareholders. This would enable bidders to induce shareholders to tender and resolve the free rider problem. Shleifer and Vishny (1986) modeled a means for the bidder to profit on a tender offer despite the free rider problem and without dilution. The bidder cannot expect to profit on the shares acquired in the tender offer because of the free rider problem. The bidder can, however, profit on the increase in value of the shares the bidder owns prior to making the offer (the toehold). Shleifer and Vishny assume that the value of the improvement the bidder can make to the firm is private knowledge of the bidder, but that other shareholders can infer the expected dollar value of this improvement from the size of the bidder’s


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toehold and the fact that a bid is made. Shleifer and Vishny assume all other shareholders will tender their shares if the bid is at least as great as the expected share value. In equilibrium, because of the assumption that indifferent shareholders always tender, the expected value is determined by the marginal bidder who will lose the same amount on the shares acquired in the bid as he gains on his toehold. The bidder always bids this expected value (which, conditional on a bid being made and the toehold, is a constant), so the expected profit on these shares is zero, the shareholders always tender, and all bids succeed. While the bidder toehold is an essential variable in Shleifer and Vishny’s model, it is not a strategic variable. In their model, a bidder with a smaller toehold requires a larger minimum dollar improvement to bid. Consequently, Shleifer and Vishny’s model implies that bidder toeholds should be negatively correlated with bidder premia in observed tender offers. Further, in Shleifer and Vishny’s model, a bidder with a zero toehold would have to bid the maximum premium to convince existing shareholders to tender. Thus, a bidder with zero toehold can not profit, and so will not bid. However, a large percentage of tender offers have a zero toehold: 62% in Bradley, Desai, and Kim (1988) and 28.82% for all first bidders in this study.5 These data suggest a problem with Shleifer and Vishny’s model. Hirshleifer and Titman (1990) do not assume that indifferent shareholders tender with probability one in their model. As a result, in their mixed strategy equilibrium, offers sometimes fail. A higher bid increases the probability of the offer succeeding; thus, the amount of the premium bid becomes a signal of the bidder’s valuation of the firm under new ownership. In equilibrium, the bidder bids the true dollar value of his expected improvement, conditional on a bid being made, and the amount bid is independent of the size of the toehold. As in Shleifer and Vishny’s model, the toehold is an essential, but not a strategic variable. Larger toeholds, nevertheless, allow bidders with smaller improvements to profit on their bid. Consequently one should expect larger toeholds to be correlated with smaller premia in observed tender offers. However, Hirshleifer and Titman’s model implies a smaller negative correlation than Shleifer and Vishny’s model does, because within their model, for a given offer, the premium is independent of the toehold. So one would expect a more dispersed pattern of premia relative to toeholds. In contrast to the above models, Chowdhry and Jegadeesh (1994) make the toehold a strategic variable of the bidder. They make the same basic assumptions as Hirshleifer and Titman, but assume that the bidder can secretly acquire a toehold. They argue that the acquisition of a toehold will change the price at which shareholders will tender their shares if the size of the toehold affects the shareholders’ beliefs about the value they will receive if they retain their shares. Chowdhry and Jegadeesh derive an equilibrium in which acquiring a smaller toehold credibly signals a smaller improvement, which induces shareholders to accept a lower offer price. Similarly, in equilibrium, bidders with a larger improvement will both acquire a larger toehold and bid higher. A bidder with a larger improvement does not try to acquire a smaller toehold and bid lower, because this increases the probability the offer will fail. A bidder with a smaller improvement does not acquire a larger toehold because this increases the necessary bid causing him to lose on the acquired shares. Therefore, their model predicts smaller toeholds are associated with smaller premia, a larger toeholds are associated with larger premia.


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The models of Harrington and Prokop (1993) and Burkart (1995) also predict a positive relationship between bidder toeholds and premia, but are structured quite differently than the above models and do not focus on first bidder strategies. Rather, Burkart (1995) focuses upon the bidding strategies of two bidders competing for a target. Burkart shows that the greater a bidder’s toehold, the greater a bidder’s tendency to “overbid” for the firm and thereby dissipate gains on the toehold. In contrast, Harrington and Prokop (1993) model a multistage bidding process, whereby a bidder revises his or her bid after failing to buy enough shares to acquire the firm. Thus a bidder’s toehold alternatively influences and is influenced by a bidder’s premia.

3. Description of the data 3.1 Sample selection and data sources The sample for this study was based upon the 1980–1986 Tender Offer Statistics collected by Douglas Austin & Associates, Inc. This consists of 827 records of tender offers filed with the Securities and Exchange Commission on form 14d. A 14d filing contains details of the offer including the bidder’s shareholding in the target firm on the filing date. By using this source, we are only using those tender offers actually filed. The distinction between a bid and a filed tender offer is an important one. There is no formal definition of what constitutes a takeover bid. If a “raider” approaches a target and offers a specific dollar amount per share to target management for the firm, this would probably constitute a bid. If the management refused and the raider threatened to take his offer directly to the shareholders, this is still a bid. Such bids frequently appear in the Wall Street Journal as “proposed a tender offer” or “threatened a hostile tender offer.” Until the offer is actually made to the shareholders and filed with the SEC, it is not legally a tender offer and does not appear in this sample. There is a selection bias in measuring toeholds and other variables for only those tender offers filed. Tender offers that were considered but not actually filed are not represented. For example, many targets in this sample have only one tender offer filed, but have multiple bidders when a bid is defined as above. A possible way for correcting for this bias would be to start with 13d filings. However, since approximately 50% of the filed offers have less than a 5% toehold on the 14d filing date, no 13d would be filed on these offers. Additionally, the 10-day window for filing a 13d means that the 14d filing will sometimes precede the 13d filing. Consequently, while there are problems with using filed tender offers to identify bids, we do not know of a better alternative that would also allow us to measure bidder toeholds. Of the original 827 filed offers, 30 could not be used for the following reasons. Nineteen offers were removed because they were not independent offers, but simply the multiple filing of forms for the same contest or data errors. Three were defensive offers by the target firm or a party controlled by the target firm. Four were for a unit of the target


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firm only, and therefore more similar to buying a unit than a takeover. Four were recurring partial tender offers for a single firm, Life Investors, by a Dutch firm, that acquired control in a 1981 offer. The original offer is included but the follow-up offers are not. Additional filed offers were deleted from our sample due to a lack of data. Specifically, to calculate premia, prices are taken from the Center for Research in Security Prices (CRSP) tapes. 103 events were lost because a CUSIP could not be identified for the target firm; 31 were lost because, although a CUSIP was identified, no prices were found on the CRSP tapes for the relevant time period; 2 were lost because they began trading less than 60 trading days before the offer; and 52 of the remaining offers were removed because, as primarily cash offers, their premia could not be reliably computed. The above exclusions reduced our sample to 609 offers. Finally, for this sample of 609 tender offers, we excluded those filed tender offers that were by management (19) or represented a second or subsequent bidder (129).6 Our final sample represents 461 tender offers made by first bidders from 1980 through 1986. We exclude management buyout offers because the models we are testing focus on the bidding strategy of an outside bidder for a firm. Thus, management’s shareholdings in the target prior to the bid, would be determined by factors other than those considered in the models we are testing. Similarly, we exclude filed offers of second bidders from our sample because the models we are testing focus primarily upon first bidder strategies.7 Whether a filed offer was made by the first bidder or a subsequent bidder was determined by examination of the Wall Street Journal Index, and in some cases, the Wall Street Journal for stories about the target firms.

3.2 Classification of tender offers We define an “opposed” offer as an offer where, at any point in the process, the target management announced that the offer was not in the best interests of shareholders and/or took defensive steps against the offer. All other offers are classified as “not opposed.” A problem in the tender offer data is that while the typical discussion of tender offers is of hostile tender offers, the majority of offers are not opposed (289 out of 461 in our sample). Further, the opposed/not opposed dichotomy may be empirically misleading. Offers classified as “not opposed” range from a way of implementing an agreed merger to an offer where the target management announces they are taking no official position on the offer. Opposed offers range from the offer is inadequate (often changed to support for an increased offer) to definite action against the bidder, including lawsuits under securities and anti-trust laws, “poison pills” and “Pac-man” defenses, and searches for white knights. Furthermore, it is incorrect to assume that all negotiated tender offers are friendly. Negotiation may vary from an amicable exchange of information to bitter disagreements where the target acquiesces only because of pressure exercised by the bidder. Thus, negotiated and friendly may not be synonymous. Walkling and Long (1984) recognized the problems with this dichotomy and defined as “acquiescent” offers those that were originally opposed but later agreed to by management when a higher premium was offered. They found no major difference in their results when


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these offers were included as either opposed or not opposed. However, acquiescent offers also run the gamut of opposition. The wide range and often bidder-specific nature of defensive tactics, combined with difficulty of predicting the effectiveness of tactics as evidenced by the range of tactics used in acquiescent offers, makes improving on the opposed/not opposed dichotomy difficult. Further, relying on a finer distinction may also be subject to reporting biases.

3.3 Measurement of the tender offer premium We measure the tender offer premium as the initial offer price (PIOP) minus the stock price before the offer (PB-60) divided by the stock price before the offer (PB-60). We use as our measure of the target’s stock price before the offer, PB-60, the stock price of the target 60 trading days prior to a “base” date (defined below). We use the initial price proposed by the bidder as the offer price because we feel it to be more conceptually consistent with some of the models we are testing. However, we also computed premiums based upon the final offer price and found no change in the inferences drawn.8 The “base” date used in this paper to calculate premiums is the earlier of the trading day before news of a potential offer first appeared in the Wall Street Journal or the 14d filing date. A potential problem with adjusting this date for earlier news or rumors is that rumors may be false. While most of the market reaction will occur when the rumor arises, some may occur afterwards. Pound and Zeckhauser (1990) found that takeover rumors in the Wall Street Journal’s “Heard on the Street Column” often proved false and that buying rumored targets produced significantly positive returns in those firms subsequently taken over, but zero returns overall. Previous research has used a shorter window for calculating premia. Walkling (1985) and Walkling and Edmister (1985) used a premium based on the target stock price 14 days (10 trading days) before the offer was filed with the SEC. Both papers also corrected the date for prior announcements in Wall Street Journal, but again used a 14-day window. Walkling and Long (1985) use only the corrected 14 day premium. Walkling, Walkling and Edmister, and Walkling and Long are based on Austin Data from 1972–1977. Comment and Jarrell (1987) and Jarrell and Poulsen (1989) used 20 trading days, but Jarrell and Poulson used a special news-adjusted event date which was prior to the usual Wall Street Journal announcement date. We chose a combination of a news-adjusted “base” date and a long window to capture the full premium offered. Since we used a long period, we have adjusted the premium for changes in the market over this period. For NYSE and AMEX we have subtracted the S&P 500 index change over this period; for NASDAQ firms we used the NASDAQ composite index. All stock prices and stock indices were taken from the CRSP tapes, and so S&P 500 index and NASDAQ composite index returns do not include dividends. Since target returns reflect changes in target share prices, an adjustment for market wide price changes was deemed appropriate. For the total sample of 461 first bidder tender offers, the mean


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premium (in %) was 44.14 with a standard deviation of 35.57. For the subsample of first bidders opposed by management, the mean premium was 40.61% with a standard deviation of 28.46.

3.4 Measurement of target size We also used data from the CRSP tapes to calculate for each sample tender offer the target firm size, which we defined as total share value of common shares 60 days before the base date (PB-60 x common shares outstanding). One reason we consider this variable is that it proxies for a bidder’s cost of acquiring a toehold, which is why we measure firm size by the market value of its equity rather than by the market value of its debt and equity. For a given percent toehold, the larger the market value of the firm the greater the cost of acquiring that toehold. Thus, if the cost of acquiring a toehold influences the size of the first bidder’s toehold, then target size should be a determinant of first bidder toeholds. Because of skewness in the distribution of target sizes, we use the natural logarithm of firm size (LNSIZE) in subsequent statistical analysis. For the sample of 461 first bidders, the mean LNSIZE was 11.15 with a standard deviation of 1.77. For the subsample of first bidders opposed by management, the mean LNSIZE was 11.65 with a standard deviation of 1.89.

3.5 Measurement of bidder toeholds We measure a bidder’s toehold by the percentage of the target firm’s outstanding stock held by the bidder as of the 14d filing date. For reasons stated earlier, we used bidders’ 14d filings to obtain these data. Table 1 reports the frequency distribution of bidder toeholds

Table 1. Frequency distribution of sample toeholds.

Toehold (%) 0 0⬍tⱕ10 10⬍tⱕ20 20⬍tⱕ30 30⬍tⱕ40 40⬍tⱕ50 50⬍tⱕ60 60⬍tⱕ70 70⬍tⱕ80 80⬍tⱕ100 Total:

Sample of all first bidders

Sample of first bidders that are subsequently opposed by mgmt

Frequency 133 131 51 35 25 28 24 15 13 6 461

Frequency 37 86 28 10 3 4 0 2 2 0 172


Percent 28.85 28.42 11.06 7.59 5.42 6.07 5.21 3.25 2.82 1.30 100.0

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Percent 21.51 50.00 16.28 5.81 1.74 2.33 0 1.16 1.16 0 100.0



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for the sample of first bidder tender offers and for the subsample of opposed first bidder tender offers. Separate from the issues discussed earlier with the use of these data, we wish to draw the reader’s attention to three other aspects of these data revealed in Table 1. First, these frequency distributions are highly skewed and include a large number of zero toehold observations. Thus these data do not appear to be drawn from a normal distribution. A Shapiro-Wilk’s W test confirms this impression for both samples at the 1% level. Consequently we must recognize the non-normality of the distribution of toehold data in testing hypotheses about these data. Second, there are substantial number of zero toeholds in both the full first bidder tender offer sample and the opposed first bidder tender offer subsample. Consequently, even in opposed offers, some first bidders are choosing to forgo potential profit on a toehold in the target in exchange for some other benefit, presumably strategic. Third, there are a number of observations in both samples for which the first bidder possesses a toehold in excess of 40% on the 14d filing date. While some of these observations may not represent the kinds of transactions the models we are testing were designed to address, we can not say a priori which observations. Thus, we choose not to delete them for concern over introducing another source of sample selection bias into our tests. Further, these observations may simply reflect the point made earlier that a bidder can acquire a significant number of additional shares in the target within the 13d’s 10-day window, and end up filing a 14d before filing a 13d.

4. Univariate tests of hypotheses We first conduct two simple tests of the ideas set out above by examining the unconditional correlations between bidder toeholds and premia, and between bidder toeholds and target sizes.

4.1 The relationship between toeholds and tender offer premia Shelifer and Vishny (1986) and Hirshleifer and Titman (1990) predict that larger toeholds are associated with smaller premia. However, since the premium bid in Hirshleifer and Titman’s model is not directly linked to the toehold, the bid premia may vary more for a given toehold. On the other hand, larger toeholds are associated with larger premia in Harrington and Prokop (1993), Chowdhry and Jegadeesh (1994), and Burkart (1995). To test these conflicting predictions, we examine the Kendall’s Tau-b correlation coefficient between toeholds and tender offer premia. We use this nonparametric measure of correlation since we have shown that the assumption (i.e., bivariate normality) underlying tests using the Pearson correlation coefficient are violated by these data. For our full sample of 461 first bidder tender offers, the Kendall’s Tau-b coefficient between toeholds and tender offer premia is -0.056 which is significantly different for zero at the 7% level. For our opposed first bidder subsample, Kendall’s Tau-b coefficient between toeholds and tender offer premia is -0.057 which is significantly different from zero at a level less than


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7%.9 Consequently, the unconditional correlations between first bidder toeholds and premia are more consistent with the models of Shleifer and Vishny (1986) and Hirshleifer and Titman (1990) than with Harrington and Prokop (1993), Chowdhry and Jagadeesh (1994), and Burkart (1995). Further, the low correlations may suggest that the data are more consistent with Hirshleifer and Titman’s model than with Shleifer and Vishny’s model.

4.2 The relationship between toeholds and firm size As mentioned earlier, the cost of acquiring a given percent toehold will go up with firm size. Further, firm size can also influence bidder competition by limiting the set of firms that could reasonably get financing and make a bid. For these reasons we expect that the larger the firm size the smaller the toehold. To test for such a relationship, we examine Kendall’s Tau-b coefficient between toeholds and firm size (where firm size is proxied by LNSIZE) for our two samples. For the sample of first bidders, this coefficient is -0.063 and for the subsample of opposed first bidders this coefficient is -0.091, both of which differ significantly from zero with p-values less than 4%.10 Thus, as expected, we infer that first bidder toeholds are negatively correlated with target size.

5. Multivariate tests of hypotheses One obvious criticism of the above tests is that they fail to account for other influences on the relationships in question, and particularly the joint variation of variables. Consequently we turn to multivariate tests of the conditional relationship between first bidder premia and toeholds.

5.1 Regression model We showed earlier that the data reject the hypothesis that first bidder toeholds, the dependent variable in our analysis, are normally distributed. Thus a normal regression model, whether linear or nonlinear, is inappropriate for studying influences on first bidder toeholds.11 Further, since first bidder toeholds are only defined over the interval [0,1] rather than being observationally censored to range over this interval, the two limit Tobit regression model, which has been applied to regression analysis of other proportional variables in finance, is inappropriate for the analysis of these data.12 One of the standard models assumed for random variables on the interval [0,1] is the beta distribution. Johnson, Kotz, and Balakrishnan (1995) provide over dozen examples from different social and physical sciences in which the beta distribution was found to be a better fitting distribution for the continuously measured proportional data under study than considered alternatives. Consequently, there is precedent in the literature for using the beta distribution as a distributional model for continuously measured proportional data.


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To develop a regression model based upon a distributional assumption that bidder toeholds are distributed as beta random variates we use concepts from the generalized linear model literature.13 A generalized linear model typically comprises three components: (1) Independent response variables y1, y2, …, yn which share the same form of parametric distribution from the exponential family. (2) A qx1 vector of parameters ␤ and an nxq model matrix X. (3) A monotone and differentiable link function g(.) that defines the relationship between E(yi) ⫽ µi and xi • ␤, i.e. g(µi) ⫽ xi • ␤. Most generalized linear models presume that y is distributed as: ƒ(y i ; ␪ i, ␾) ⫽ exp

冋

(y i ␪ i ⫺ b(␪ i)) a i (␾)

⫹ c(y i, ␾)

册

(1)

When ␾ is known, then equation (1) is an instance of the class of linear exponential models. When is ␾ unknown, then equation (1) is an instance of the class of exponential dispersion models. While the beta distribution is a member of the exponential family of distributions, it is not a member of either of the above exponential classes and so does not fit the typical generalized linear model assumptions. Rather, the beta distribution is an instance of the class of exponential models that fit the following form: ƒ(y i; ␪) ⫽ exp 关␣(␪)b(y i) ⫹ c(y i) ⫹ d(␪)兴

(2)

More specifically, the two parameter beta distribution expressed in exponential form is:

冋

ƒ(y i ; ␪) ⫽ exp (␤ ⫺ 1) 1n (y i) ⫹ 1n

冉冊冉 y i␣ ⫺ 1 ⌫ (␣)

⫹ ln

⌫ (␣ ⫹␤) ⌫(␤)

冊册

(3)

Thus we must turn to extensions of the generalized linear model framework profiled in Gay and Welsch (1988) to develop an estimable regression model based upon the assumption that bidder toeholds are conditionally distributed as two parameter beta random variates. We begin by assuming that the yi are i.i.d. for i ⫽ 1, …, n and that the conditional expectation of yi can be expressed as: E (y i ⱍ X i) ⫽ µ i.


(4)

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Since the model matrix, X, and the parameter vector, ␤, are determined by the specific application under consideration we defer specification of these elements of a beta regression model to section 5.2 below. The next elements we need to specify are: µ i ⫽ h(␩i) ⫽ h(x i • ␤) where ␩i ⫽ xi • ␤ , and

(5)

␩i ⫽ g(µi).

(6)

The response function, h (.), is a one-to-one and sufficiently smooth function, and the link function, g(.), its inverse. One possibility is to follow a traditional linear regression specification and use the identity response and link functions. Unfortunately, such an approach is inappropriate because of the implied conditional mean can take values over ⺢, rather than over [0,1], the proper range for these data. This is the same kind of problem faced by applying the linear probability model to the analysis of binary data.14 Consequently we need to specify a nonlinear response function and a nonlinear link function. We use the logit link specification because it is consistent with prior research practice and because it provides a flexible functional relationship that we can exploit in specifying the estimated model.15 Specifically, we use the following re-expression for equation (5): µ i ⫽ h(␩i) ⫽

1 1 ⫽ . 1 ⫹ exp(⫺␩i) 1 ⫹ exp(⫺xi • ␤)

(7)

This equation then implies the following re-expression of equation (6) as : ␩i ⫽ g(µi) ⫽ 1n

冉冊 µi

1 ⫺ µi

.

(8)

Note that this specification restricts the conditional mean of a beta distributed regressand to the interval (0,1), which is appropriate. In order to derive an estimable regression model using the maximum likelihood principle, we must now relate the above relationships to the parameters of the beta distribution. Specifically, for the beta distribution defined in (6), we have: E(yi) ⫽

p . p⫹q

(9)

We now must map ␩´ i to either p or q, i.e. we must treat one or the other parameter as a function of xi, in order to develop a log-likelihood function for the beta regression model. We will map xi • ␤ into q for two important reasons. First, q is the shape parameter for the beta distribution. Second, a priori considerations may force the researcher to specify a particular value for p. For example, if one is to allow zero proportions for finite valued regressors, then one will need to assume that p ⫽ 1.


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Given this assumed mapping, we develop the following expression for q that is consistent with equation (9) above: q(xi) ⫽ p exp (⫺xi • ␤ ).

(10)

We then substitute this expression for q into the following expression of the conditional distribution of beta distributed random variate: ƒ(yi ⱍ Xi) ⫽

冋

⌫ (p ⫹ q(Xi)) ⌫ (p) ⌫ (q(Xi))

册

y ip⫺1 (1 ⫺ yi) q(Xi) ⫺ 1.

(11)

To estimate the effect of the different conditioning variables (x1, …, xr) we use the maximum likelihood estimation principle to derive estimates of the vector ␤ by maximizing the above log-likelihood function with respect to the parameters ␤ and p. Again, for problems which must allow for zero valued proportions, p must equal 1, and we need only estimate ␤ in these cases. Thus the appropriate log-likelihood function will depend upon any a priori restrictions we place on p. For the general case, we have (ignoring constant terms): 1n ƒ(y i ⱍ x i) ⫽ 1n ⌫ (p ⫹ p e ⫺xi • ␤) ⫺1n ⌫ (p) ⫺ 1n ⌫ (p e ⫺xi • ␤ ) ⫹ (p ⫺ 1) 1n (y i) ⫹ (pe ⫺xi •␤ ⫺ 1) 1n (1 ⫺ y i).

(12)

We will use the above log-likelihood expression to estimate a beta regression model for our first bidder toehold data. Because the beta distribution is a member of the exponential class of distributions, these maximum likelihood estimators have all the mathematical and statistical properties established for maximum likelihood estimators for this class of distributions.16

5.2 Regression results Using the above statistical model (equations 10 and 11), we test the influence of first bidder premia (PREM) and target firm size (LNSIZE) on bidder toeholds in tender offers using the following specification: x i • ␤ ⫽ ␤ 1 (Premium) ⫹ ␤ 2 (Firm Size) ⫹ ␤ 3 (Premium 多 Firm Size).

(13)

We have already pointed out reasons why first bidder premia and target firm size may conceptually influence bidder toeholds, and we have presented evidence of significant unconditional correlations between these variables and first bidder toeholds. We include an interaction term between first bidder premia and target firm size for two reasons.


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184 Table 2. Beta regression analysis of first bidder toeholds.

CONSTANT PREM LNSIZE PREM*LNSIZE

All first bidders

First Bidders that are subsequently opposed by management

0.492 (1.080) -1.845 (-2.774)** -0.172 (-4.293)** 0.174 (2.975)**

-0.427 (-0.627) -4.112 (-3.199)** -0.142 (-2.379)** 0.337 (2.917)**

Notes: PREM represents the premium and is defined as the offer price minus the stock price before the offer divided by the stock price before the offer. LNSIZE proxies for firm size and is defined as the natural logarithm of the market value of the firm prior to the tender offer. Asymptotic t tests reported in parentheses. ** represents significance at the 5% level.

First, the gains from restructuring a poorly performing target may increase in target size (e.g. diseconomies of scale) and so first bidder premia will be influenced by target firm size. Thus we must adjust the influence of first bidder premia on first bidder toeholds for the indirect effect of target size on first bidder premia. Second, the product of the first bidder’s premium times the target firm size captures the opportunity cost of the first bidder failing to take a toehold. For example, if one was to bid 10% over the base price then 10% x the market value of the target (evaluated at the base price) equals the total incremental value of the target, and the opportunity cost of one not taking a t% toehold is simply t% x 10% x market value of target. We report separately in Table 2 the estimates of ␤ for the full sample of first bidder tender offers and for the subsample of first bidder tender offers opposed by management. We report separate ␤ estimates because, while we think that bidders form rational expectations of likely management opposition, these expectations are not well proxied by ex post identifications of managerial opposition impounded in some dummy variable and are likely to influence all the determinants of initial toeholds. Of the two estimations, we expect the estimation of the subsample of first bidder tender offers opposed by management to be the more relevant to the models we are testing because these models are implicitly, if not explicitly, concerned with bidding strategies in the context of potentially hostile takeovers. Both sets of estimates, however, suggest similar relationships between first bidder toeholds and target size and first bidder premiums. To get a better understanding of these estimated relationships, we will use the estimated equation for expected toeholds for the opposed first bidders reported in Table 2 for different target firm sizes. For LNSIZE ⫽ 2, the expected toehold is given by {1 / (1 ⫹ exp (0.711 ⫹ 3.438 * PREM))}, while for LNSIZE ⫽ 12, the expected toehold is given by {1 / (1 ⫹ exp (2.131 ⫹ 0.068 * PREM))}. Thus our results suggest that for a given target size, the higher the first bidder premia, the lower the first bidder’s toehold. This pattern is consistent with our earlier univariate results and with the models of Shleifer and Vishny (1986) and Hirshleifer and Titman (1990) of tender offers. Once again, we do not find the data to be consistent with the models of Harrington and Prokop (1993), Chowdhry and Jagadeesh (1994), and Burkart (1995). The estimated equations


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also suggest, however, that this relationship diminishes as the target firm size grows. In essence, the larger the target firm size the smaller the toehold a first bidder can be expected to take for all expected premia. One reasonable explanation for this pattern is that target firm size influences bidder competition, and thereby the relationship between first bidder toeholds and premia. If the observed pattern is due to the effect of target firm size on bidder competition, then our results are inconsistent with Hirshleifer and Titman’s model of tender offers, because typically, the larger the firm the less competition there is for it. Further, in Hirshleifer and Titman’s model, if a first bidder expects competition, then the first bidder should take a zero toehold. To test this implication of their model, we examine the incidence of zero and positive toeholds across cases where there was or was not bidder competition. We present in Table 3 the results of this analysis both for the first bidder sample and the opposed first bidder subsample. While these results provide no support for the Hirshleifer and Titman model’s implication that a first bidder will take a zero toehold if they expect bidder competition, these results also provide no support for the notion that a reduction in expected bidder competition is associated with a zero toehold. Consequently alternative explanations of the influence of target firm on the relationship between first bidder toeholds and premia will need to be developed and tested in future research.

6. Summary This study examines the initial shareholdings of tender offer bidders (“toeholds”) in a comprehensive sample of tender offers filed with the SEC between 1980 and 1986 in order to test different models of the takeover process. We find a significantly negative unconditional correlation between first bidder toeholds and premia, and a significantly negative conditional correlation between first bidder toeholds and premia that is mediated by target size, both directly and indirectly. Table 3. Contingency table analysis of first bidder toeholds and bidder competition. Panel A: Full sample of First Bidders No subsequent bidder competition Subsequent bidder competition Zero first bidder toeholds 111 (29.60) 22 (25.58) Positive first bidder toeholds 264 (70.40) 64 (74.42) Total first bidders 375 86 Note: Percentage of column total reported within parentheses. Likelihood Ratio ChiSquare ⫽ 0.561 (p ⫽ 0.454) Panel B: Subsample of Opposed First Bidders No subsequent bidder competition Subsequent bidder competition Zero first bidder toeholds 25 (25.00) 12 (16.67) Positive first bidder toeholds 75 (75.00) 60 (83.33) Total first bidders 100 72 Note: Percentage of column total reported within parentheses. Likelihood Ratio ChiSquare ⫽ 1.758 (p ⫽ 0.184).

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These findings have several important implications. First, the significantly negative unconditional and conditional correlations between first bidder premiums and first bidder toeholds are consistent with the models of Shleifer and Vishny (1986) and Hirshleifer and Titman (1990) and inconsistent with the models of Harrington and Prokop (1993), Chowdhry and Jagadeesh (1994), and Burkart (1995). Further, our evidence is consistent with findings in Walking and Long (1984) and Betton and Eckbo (1994). This consistency of evidence is especially interesting because these alternative studies model the statistical relationship between bidder premiums and bidder toeholds differently than we do. Walking and Long (1984) model first bidder toeholds as exogenous and first bidder premiums as endogenous. Betton and Eckbo (1994) model first bidder toeholds and premia as exogenous to event transition probabilities and state-contingent payoffs. Second, while our results are generally consistent with the models of Shleifer and Vishny (1986) and Hirshleifer and Titman (1990), we find evidence that the relationship between first bidder toeholds and premia is more complex than captured in these models. Specifically, we find that target firm size significantly influences this relationship. One explanation for this complexity is the influence of target firm size on bidder competition. The data we examine, however, do not provide support for this explanation. Consequently, future research is required to explain this complexity and better understand the choice of toehold taken in a target.

Acknowledgments We would like to thank Jim Brandon, David Hirshleifer, Andrew Dick, William Klein, Bruce McCullough, Tim Opler, Ivan Png, Maggie Queen, Eric Rasmussen, Sheridan Titman, J. Fred Weston, and the anonymous reviewers for helpful comments. Haleh Naimi, Jessica Iversen, Kee Foong, Scott Newman, and Vicky Tang provided excellent research assistance. Financial support from the Research Program in Competition and Business Policy at UCLA and General Motors and ALCOA Foundation Doctoral Fellowships is gratefully acknowledged. The views expressed in this paper are neither those of Deloitte & Touche LLP nor those of the Federal Communications Commission.

Notes 1. It is important to recognize that a potential bidder can continue to purchase stock during the 10 day period before they file the 13d and thus they are not limited to a 5% holding. Further, they can accumulate a rather large shareholding before filing a 14D statement simply by continuing to file amended 13d statements. 2. Or the interval [0,100], depending upon scaling. This same attribute is shared by a number of studies of a firm’s capital structure (e.g. Bradley, Jarrell, and Kim (1984) or Titman and Wessels (1988)), the firm’s mix of private versus public debt (e.g. Easterwood and Kadapakkam (1991)), and the firm’s dividend policy (e.g. Dempsey and Laber (1992)). 3. See Amemiya (1985) for further discussion of these issues. 4. For much more detailed discussions of the free rider problem and various “solutions”, see Weston, Chung and Hoag (1990) (Appendix A & B) or Hirshleifer (1992).


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5. Bradley, Desai, and Kim’s data is for the period 1963–1984 and only includes successful bids. 6. Of the 609 filed offers, 475 were made by the first bidder. Of the 134 filed offers not made by the first bidder, 5 were made by management and 35 were opposed. 7. Including filed offers of second or subsequent bidders does not change any inferences drawn in this paper. Interestingly, the conditional and unconditional negative correlations reported between bidder premia and toeholds are larger for both opposed and unopposed offers when we include filed offers of second bidders in the sample. 8. In fact, our empirical inferences are strengthened, especially the negative correlation between bidder toeholds and premia, when we use this second measure of premiums. This second premium measure is similar to the premium measure in Schwert (1996), which focused upon premiums paid. 9. Using our second premium measure, the Kendall Tau-b between toeholds and premia is -0.11 for the full sample and -0.12 for the opposed first bidder subsample. Each of these correlations is significantly different from zero at the 1% level. 10. The correlation between bidder toeholds and target firm sizes for the sample of all bidders (first and subsequent) less management buyouts (590 filed offers) is -0.082 which is significantly different from zero at the 1% level. 11. The estimators of a normal, linear or nonlinear, regression model when applied to the present data can be biased and inefficient. See Ameniya (1985), Chapter 2, for a discussion of the effects of applying the normal regression model to non-normally distributed dependent variables. 12. See Rajan and Zingales (1995) for an example of the application of the two limit Tobit regression model to the analysis of a proportional random variate. See Maddala (1991) for a discussion of the inapplicability of the two limit Tobit regression model for proportional data. 13. See McCullagh and Nelder (1989) or Fahrmeir and Tutz (1994) for surveys of this literature. 14. See Greene (1997), page 873 for further discussion of this and other problems with the linear probability model. 15. Ramanathan (1993) presents the logit model for regression analysis of proportional data. This model, which is a nonlinear normal regression model, is roughly consistent with a logistic response function and a logit link function. However, as shown earlier, the distributional assumption underlying this model is inappropriate for the bidder toehold data. This conclusion is reinforced by the number of zero toeholds in the samples under study. 16. See Fahrmeir and Tutz (1994) for further discussion of these issues.

References Amemiya, T., Advanced Econometrics. Cambridge: Havard University Press, (1985). Douglas Austin & Associates, Inc., 1980–86 Tender Offer Statistics, (1988). Bagwell, Laurie Simon, “Dutch Auction Repurchases: An Analysis of Shareholder Heterogeneity.” Journal of Finance 47, 71–106, (1992). Betton, Sandra and B. Espen Eckbo, “Toeholds, Competition, and State-Contingent Payoffs in Tender Offers.” unpublished working paper presented at the 1995 AFA meetings, (1994). Bradley, Michael, G. Jarrell, and E. Han Kim, “On the Existence of an Optimal Capital Structure: Theory and Evidence.” Journal of Finance 39, 857–880, (1984). Bradley, Michael, A. Desai, and E. Han Kim, “Synergistic gains from corporate acquisition and their division between the stockholders of target and acquiring firms.” Journal of Financial Economics 21, 3–40, (1988). Burkart, Mike, “Initial Shareholdings and Overbidding in Takeover Contests.” Journal of Finance 50, 1491–1515, (1995). Center for Research in Security Prices. Stock Files. 1990. Chowdhry, B. and N. Jagadeesh, “Pre-Tender Offer Share Acquisition Strategy in Takeovers.” Journal of Financial and Quantitative Analysis 29, 117–129, (1994).


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Comment, Robert and Gregg A. Jarrell, “Two Tier and Negotiated Tender Offers: The Imprisonment of FreeRiding Shareholders.” Journal of Financial Economics 19, 283–310, (1987). Dempsey, S.J. and G. Laber, “Effects of Agency and Transaction Costs on Dividend Payout Ratios: Further Evidence of the Agency-Transaction Cost Hypothesis.” Journal of Financial Research 40, 317–321, (1992). Easterwood, J.C. and P. Kadapakkam, “The Role of Private and Public Debt in Corporate Capital Structures.” Financial Management 20, 49–57, (1991). Fahrmeir, L. and G. Tutz, Multivariate Statistical Modelling Based on Generalized Linear Models, New York: Springer-Verlag, (1994). Gay, David M. and Roy E. Welsch, “Maximum Likelihood and Quasi-Likelihood for Nonlinear Exponential Family Regression Models.” Journal of the American Statistical Association 83, 990–998, (1988). Grossman, Sanford J. and Oliver D. Hart, “Takeover Bids, the Free Rider Problem and the Theory of the Corporation.” Bell Journal of Economics 11, 42–64, (1980). Greene, William, Econometric Analysis, Upper Saddle River: Prentice-Hall, Inc., (1997). Harrington, Joseph E. (Jr) and Jacek Prokop, “The Dynamics of the Free-Rider Problem in Takeovers.” Review of Financial Studies 6, 851–882, (1993). Hirshleifer, David, “Mergers and Acquisitions: Strategic and Informational Issues.” Working Paper # 16–92, AGSM—UCLA, (1992). Hirshleifer, David and Sheridan Titman, “Share Tendering Strategies and the Success of Hostile Takeover Bids.” Journal of Political Economy 98, 295–324, (1990). Jarrell, Gregg A. and Annette B. Poulsen, “Stock Trading Before the Announcement of Tender Offers: Insider Trading or Market Anticipation?” Journal of Law, Economics and Organization 5, 225–248, (1989). Johnson, N.L., S. Kotz, N. Balakrishnan, 1995, Continuous Univariate Distributions, Volumes 1 and 2, NY: John Wiley & Sons, Inc. Kyle, Albert S. and Jean-Luc Vila, “Noise Trading and Takeovers.” Rand Journal of Economics 22, 54–71, (1991). Maddala, G.S., “A Perspective on the Use of Limited-Dependent and Qualitative Variables Models in Accounting Research.” The Accounting Review 66, 788–807, (1991). McCullagh, P. and J.A. Nelder, Generalized Linear Models, New York: Chapman & Hall, (1989). Pound, John and Richard Zeckhauser, “Clearly Heard on the Street: The Effect of Takeover Rumors on Stock Prices.” Journal of Business 63, 291–308, (1990). Rajan, Raghuram and Luigi Zingales, “What Do We Know about Capital Structure? Some Evidence from International Data.” Journal of Finance 50, 1421–1460, (1995). Ramanathan, Ramu, Statistical Methods in Econometrics, New York: Academic Press, Inc., 1993. Schwert, G. William, “Markup pricing in mergers and acquisitions.” Journal of Financial Economics 41, 153–192, (1996). Shleifer, Andrei and Robert W. Vishny, “Large Shareholders and Corporate Control.” Journal of Political Economy 94, 461–488, (1986). Titman, S. and R. Wessels, “The Determinants of Capital Structure Choice.” Journal of Finance 43, 1–19, (1988). Walkling, Ralph A., “Predicting Tender Offer Success: A Logistic Analysis.” Journal of Financial and Quantitative Analysis 20, 461–478, (1985). Walkling, Ralph A. and Robert O. Edmister, “Determinants of Tender Offer Premiums.” Financial Analysts Journal 15, 27–37, (1985). Walkling, Ralph A. and Michael S. Long, “Agency Theory, Managerial Welfare, and Takeover Bid Resistance.” Rand Journal of Economics 15, 54–68, (1984). Wall Street Journal Index, 1979–87, Princeton, N.J.: Dow Jones Books. Weston, J. Fred, Kwang S. Chung, and Susan E. Hoag, Mergers, Restructuring and Corporate Control, Englewood Cliffs, N.J.: Prentice-Hall, (1990).


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