An Evaluation of Shareholder Activism

Transcription

1 An Evaluation of Shareholer Activism Barbara G. Katz Stern School of Business, New York University 44 W. 4th St., New York, NY tel: ; fax: corresponing author Joel Owen Stern School of Business, New York University 44 W. 4th St., New York, NY tel: ; fax: March 2014 JEL classifications: G30, G34, G11, G14 Key wors: shareholer activism, activism, evaluation of activism, hege funs, corporate governance, iversifie portfolios 1

2 Abstract We evelop a metho to evaluate shareholer activism when an activist targets firms whose shareholers are iversifie portfolio holers of possibly correlate firms. Our metho of evaluation takes the portfolios of all of the shareholers, incluing the activist, as its basis of analysis. We moel the activist from the time of the acquisition of a foothol in the target firm through the moment when the activist ivests the newly acquire shares. We assume that uring this perio, all exchanges of securities, an their corresponing prices, are achieve in Walrasian markets in which all participants, incluing the activist, are risk-averse price-takers. Using the erive series of price changes of all the firms in the market, as well as the erive series of changes in all the portfolio holings over this perio, we evaluate the impact of activism on the activist, on the group of other shareholers, an on the combine group. We show that when activism is beneficial to the activist, the group of other investors may not benefit; furthermore, even when the activist benefits from activism, the value of the market may ecrease. When the activist benefits from activism, an increase in the value of the market is a necessary but not suffi cient conition for the group of other investors to benefit also from activism. In aition, we show that the combine group, the activist plus the group of other investors, benefits if an only if the value of the market increases an, uner this conition, either the activist or the group of other investors, but not necessarily both, benefits. 2

3 1 Introuction We evelop a metho to evaluate shareholer activism when an activist targets firms whose shareholers are iversifie portfolio holers of possibly correlate firms. Our metho of evaluation takes the portfolios of all of the shareholers, incluing the activist, as its basis of analysis. We moel the activist from the time of the acquisition of a foothol in the target firm through the moment when the activist ivests the newly acquire shares. We assume that, uring this perio, all exchanges of securities, an their corresponing prices, are achieve in Walrasian markets in which all participants, incluing the activist, are risk-averse price-takers. Using the erive series of price changes of all the firms in the market, as well as the erive series of changes in all the portfolio holings over this perio, we evaluate the impact of activism on the activist, on the group of other shareholers, an on the combine group. Our evaluation provies answers to the following questions: Who benefits from activism? If the activist benefits, is it at the expense of the other investors? Do the benefits of activism, when they occur, imply an increase in the value of the market over the perio of activism? 1 Our contribution to the literature is the proposal of a metho of evaluation of activism which is applicable not only to the activist but also to other market participants, an which takes into account the iversification of shareholers portfolios. 2 Using our metho, we show that when activism is beneficial to the activist, the group of other investors may not benefit; furthermore, even when the activist benefits from activism, the value of the market may ecrease. When the activist benefits from 1 Variants of these questions have been raise elsewhere, for example, in Kahan an Rock (2007), Bebchuk an Weisbach (2010), an Emans (2013). 2 See Hansen an Lott (1996) who emphasize that, in the presence of externalities, the appropriate objective of analysis is the portfolio, in which spillovers can be incorporate, rather than the iniviual stock prices an their responses to announcements. 3

4 activism, an increase in the value of the market is a necessary but not suffi cient conition for the group of other investors to benefit also from activism. In aition, we show that the combine group, the activist plus the group of other investors, benefits if an only if the value of the market increases an, uner this conition, either the activist or the group of other investors, but not necessarily both, benefits. Our approach to activism iffers from others not only in its ealing with iversifie portfolio holers 3 an in its metho of evaluation, but also in escribing the process by which the activist acquires an ultimately ivests of new shares in the target firm. 4 In other moels, one or more of the following, which we assume, are not assume: Owners of the target firm are iverse portfolio holers, owners of the target firm are risk-averse investors, all market participants are involve as price-takers in a Walrasian market, an the focus is on the entire perio of involvement of the activist. Furthermore, other moels generally o not focus on evaluating activism from the perspective of the activist as istinct from the group of other shareholers. 5 Elsewhere when evaluation is iscusse, evaluation epens on the impact on the target firm alone. 6 For example, in the empirical literature activism is juge as 3 An exception to the general lack of consieration of iversifie shareholers portfolios is Amati et al. (1994) where iversifie portfolios are consiere but, unlike in our approach, the activist is given extraorinary power in first choosing the size of the foothol an only following that oes the market come into play. Though obviously in this approach the activist benefits, attention in the paper is irecte to equilibrium in the securities market (where small passive investors benefit in a free-rier sense), but not to an explicit evaluation of the impact of activism on the other shareholers as istinct from the activist or on the value of the market. 4 See, for example, Emans (2013) for a thorough review of theoretical an empirical literature on blockholers an shareholer activism. 5 There are exceptions, as in, for example, Cliffor (2008), Becht et al. (2009) an Boyson an Mooraian (2011). 6 For example, Bebchuk et al. (2013) argue that activism oes not prouce long term eleterious effects on target firms. Exceptions to the focus on the evaluation of activism on a single target firm inclue Lee an Park (2009) an Gantchev et al. (2013) who fin spillover effects from a target firm 4

5 being beneficial base on the increase in the price of shares of the target firm at the time the activist announces acquiring those shares via a Scheule 13D filing. 7 As our results show, neglecting the iversification of shareholers in the metho of evaluation may lea to incorrect conclusions regaring the benefits of activism. Other issues of interpretation arise when statements concerning the benefits to shareholers o not istinguish between those pertaining to the activist, those pertaining to the group of other investors in the target firm, or those pertaining to the combine group. In Section 2 we moel the sequence of equilibria prices an holings of iversifie shareholers over the course of activism. In Section 3 we evelop the conitions on which the initial ecision of activism is base. We propose a metho of evaluation of activism in Section 4, an use the results erive in Sections 2 an 3 to implement this proposal an investigate its ramifications. In Section 5 we raise issues for iscussion an suggest possible extensions to our moel. 2 The Impact of Activism on Prices an Portfolio Rebalancing The moel that we consier specifies four moments in time at which investors gather together to compete for shares in firms for their portfolios. These moments are to others. 7 See, for example, Brav et al. (2009) an Klein an Zur (2009). Both stuies highlight the increase in average excess return aroun the time of Scheule 13D filing, an its persistence. Primarily on that basis, both stuies posit activism benefits target firm shareholers. Boyson an Mooraian (2011) an Cliffor (2008), for example, fin that both activist hege funs an shareholers benefit from activism when consiering a single firm. Becht et al. (2009) in a stuy of a single U.K. fun, fin activism benefits that fun an also its shareholers. Becht et al. (2014), stuying activism in Asia, Europe an North America, fin activism is associate with abnormal returns to the target firm in the three regions. 5

6 istinguishe by the information sets available to investors at each of these points in time. At time t = 0, all participants hol the same view regaring the future values of the firms, an come together to buy shares in these firms base on that commonly hel information. We refer to the set of portfolios etermine in this manner as the benchmark portfolios. We assume that the benchmark portfolios remain the same until one of those investors, calle the activist, comes to believe that his involvement can alter the performance of a firm. Since his belief in the future value of the firm is ifferent from that of all other market participants at this point, the acquisition of new ownership woul be iffi cult if this information were share with other investors. Thus, we assume that the activist must surreptitiously acquire these new shares, keeping his belief in the future value of the target firm to himself. Given this belief, the activist must first ecie whether it woul be avantageous for him to act on the basis of this belief. If not, activism obviously oes not occur. Shoul the ecision to act be taken, then the activist moves at time t = 1 to acquire shares to facilitate his objective. This move at time t = 1 precipitates a new competitive market equilibrium with asymmetric information: The activist acts on his private information while the views of all other investors concerning the future values of the set of firms remain unchange. If the activist acquires a suffi cient number of shares, then, at time t = 2, the activist announces this publicly by filing Scheule 13D. 8 At the time of the filing, the other investors become informe of the activist s intent to improve the performance of the firm. Note, time t = 2 might follow quite closely after time t = 1. Having gaine knowlege of the activist s intent, the remaining investors enter into a new competitive equilibrium for shares. Here, the activist refrains from entering into traing since he nees the shares he has alreay acquire to carry out 8 When an owner acquires 5% or more of the voting power of a registere security, an has the intent to attempt to alter the policies of the current management, SEC rules require that Scheule 13D (the so-calle beneficial ownership report), be file within 10 ays. 6

7 his activist program. Subsequently, at time t = 3, it becomes known to all market participants whether or not the activist has been successful in his plans to improve the firm. 9 This new information acquire by all market participants inuces a new competitive equilibrium with all investors participating. Shoul the activist s holings fall suffi ciently, he announces this by filing an amene Scheule 13D (Scheule 13D/A). The time between t = 2 an t = 3 can be lengthy. Finally, at time T, all uncertainty concerning the firms is resolve an all the firms are liquiate. In each competitive market equilibrium we assume that there exists the same set of N risky assets an a riskless one. Each of the M risk-averse investors is a price-taker an a von Neumann-Morgenstern expecte utility of en-of-perio wealth maximizer. We now introuce some notation. Let x it be the N x 1 vector of shares hel by investor i, i = 1,..., M, at time t, t = 0, 1, 2, 3, in the N firms. Let y it be the amount investor i borrows (lens) at time t to facilitate purchases. Let p it be an N x 1 vector of ranom prices per share of the N firms that woul prevail at time T as perceive by investor i at time t, an let p 0 be the price of the riskless asset. Let u i be the utility function of investor i, w it be the wealth with which the i th investor comes to the market at time t an, for convenience, let p 0 = 1. At time t, t = 0, 1, 2, 3, the equilibrium process is efine as follows. Taking the N x 1 vector p t as given, investor i etermines x it which satisfies arg max xit E it u i (y it + x it p it) s.t. y it + x itp t = w it where E it is the expectation of investor i at time t with respect to the istribution of p it an a prime enotes a transpose operation. The equilibrium price vector at time t, P t, yiels the emans x it so that all shares are M sol, i.e., = Q where Q is the N x 1 vector whose elements are the total x it i=1 number of shares in each of the N risky firms. For convenience, we normalize Q 9 In our moel we o not allow the leakage of information as to the success of the activist between time t = 2 an time t = 3; however, we mention the aitional complications such leakage might engener in Section 5 below. 7

8 an represent it by 1, an N x 1 vector whose elements are 1, so that x it represents the vector of proportional ownership of investor i at time t in the N risky firms. We assume that each investor has an exponential utility function with Pratt-Arrow coeffi cient of absolute risk aversion a i. We further assume that the ranom vector p it is normally istribute with mean vector µ it an positive efinite covariance matrix Ω it. With these assumptions, the equilibrium solution at each time t is the solution to a specific nonhomogeneous (homogeneous) portfolio problem base on the changing information. Solutions to each of these problems are erive by applying the results from Rabinovitch an Owen (1978). Maximizing the expecte utility for each of the participants at each moment of time results in the maximum expecte utility over the time perio t = 0 to t = 3. This follows because, since borrowing an lening are allowe, the only carryover when optimizing at time t is the resulting wealth from the optimization at time t 1. However, as shown in Rabinovitch an Owen (1978), the optimum solutions, x it an P t, at time t o not epen on this preceing wealth. Therefore, each local optimization is separate from any other. Furthermore, our choice of four traing moments is base on the assumption that traing only takes place at those times when a change of information occurs, an we assume these changes are inepenent of one another. In our moel, we have chosen to abstract from the usual activities of the activist, for example, from attempting to acquire representation on the boar, changing ivien policy, changing CEO salary, an/or selling parts of the firm, etc. Instea, we have chosen to characterize activities into ways in which they alter the future istribution of prices. Specifically, some activities will affect the mean, others the variance an still others the covariance of the target firm with other firms. Inee, some activities will affect these three features in various combinations. This abstraction permits us to eal with the issue of iversifie ownership. 8

9 We now introuce the specifics of our moel. At time t = 0, all investors agree on their assessments of the istribution of prices that will occur at time T. Thus, in this case, µ i0 = µ 0 an Ω i0 = Ω 0. We state this well-known equilibrium solution result without proof in the next proposition. Proposition 1. At time t = 0, µ i0 = µ 0 an Ω i0 = Ω 0, i = 1,..., M. Then the equilibrium solution yieling the benchmark is x i0 = i 1, i = 1,..., M, an P 0 = µ 0 1 Ω 01 where i = 1 a i an = i. Following this market exchange, one of the investors comes to believe that, with suffi cient shares in a particular firm, he can improve its performance an thereby benefit from his activism. 10 We esignate this activist as investor 1, an refer to the activist as A. The single firm that is the target of A s interest is firm Since we have assume that all investors can borrow, len, as well as sell short, A must have these capabilities as well. Thus, our moel necessarily exclues mutual funs as activists, but inclues both hege fun activists an other entrepreneurial activists such as iniviual investors an private equity funs. 12 If A procees with his plan to acquire aitional shares, it is one surreptitiously, an it forces a new roun of traing. A comes to this roun of traing with preictions as to how his involvement in the target firm woul alter the future istribution of 10 Although we o not explore the case in which the activist might benefit even if his activities are etrimental to the target firm, our moel coul be use to examine this situation. See comments in Section 5, below. 11 The activist has only one target firm in our moel. This assumption is mae for convenience of exposition. 12 Mutual funs are subject to the Investment Company Act of 1940 which, among other things, prevents them from selling short, borrowing, an holing concentrate positions. Hege funs, by having a small number of high net worth investors, are not subject to this Act, an, accoringly, are not governe by the regulation of fees specifie in the Act. See, for example, Brav et al. (2008, pp ) for a iscussion of ifferences between mutual funs an hege funs. 9

10 prices of all securities. In particular, we assume this involvement woul change the mean an the covariance matrix of A s istribution by the amounts µ an Ω, respectively. We note that both these changes epen on the change that woul occur shoul A be successful with his plans, the change that woul occur shoul A be unsuccessful with his plans, an the probability of each. For convenience, we assume that shoul A be unsuccessful, the parameters revert to those at time t = 0, i.e., µ = Ω = This framework leas to a heterogeneous information equilibrium whose solution is given in Proposition 2. The proof of this proposition, an all following propositions an the lemma, can be foun in the Appenix. Proposition 2. Let the istributional parameters for A be µ 11 = µ 0 + µ an Ω 11 = Ω 0 + Ω an let those for investor i, i = 2,..., M, be µ i1 = µ 0 an Ω i1 = Ω 0. Then, at t = 1, the equilibrium solution is given by [I + ( 1 ) ΩΩ 1 0 ](P 1 P 0 ) = 1 ( µ Ω1/) x 11 x 10 = ( 1 )Ω 1 0 (P 1 P 0 ) an x i1 x i0 = i Ω 1 0 (P 1 P 0 ) for i = 2,..., M. Proposition 2 establishes the relationship between the changes in prices an the changes in the portfolios hel by all investors ue to activism. These changes are base on the changes in the mean an covariance matrices, µ an Ω, respectively. Since µ an Ω are arbitrary in this proposition, we now restrict them, in keeping with our moelling of A. We assume at time t = 1 that A is active only in firm 1, an believes that the expecte price per share of firm 1 will increase by m > 0 if he succees, an remain the same otherwise. 14 The expecte values of the remaining firms are unchange. The variance of the price of firm 1, as well as the covariances of 13 Not making this assumption woul introuce aitional free parameters complicating, but not changing, our results. 14 The issue of whether the activist coul benefit if m < 0 is iscusse later. 10

11 the price of firm 1 with the other firms, might, however, change. 15 The covariances between two prices, neither of which involves firm 1, are unchange. Thus, we assume that the covariance matrix of prices might change in the first row an first column if the activist succees an woul remain the same otherwise. We next make these changes explicit. We introuce the following notation. The subscript 1 is use for a vector or matrix to enote that vector or matrix without its first element or first row, respectively, e.g., the N x 1 vector v, with first element v 1, is written as v = (v 1, v 1). We let Ω 1 0 = (ω 1,..., ω N ) = ω1 1 ω 1 1 where R is a positive efinite N 1 x R ω 1 1 N 1 symmetric matrix. The omission of the first row of the matrix Ω 1 0 will be written as Ω 1 1,0. If we efine the N x N matrix V = v 1 an π as the v 1 0 probability that A will succee in his plans, A approaches the market at t = 1 with parameters µ 11 = µ 0 +πme 1 an Ω 11 = Ω 0 +πv where e 1 is an N x 1 vector with 1 in the first position an zeros elsewhere. The other investors remain with their previous information, i.e., µ i1 = µ 0 an Ω i1 = Ω 0, i = 2,..., M. We next present a lemma that permits us to solve explicitly for the inverse neee to etermine the equilibrium price changes in Proposition 2. In what follows, we let (P 1 P 0 ) = ((P 1 P 0 ) 1,..., (P 1 P 0 ) N ), where (P 1 P 0 ) j is the j th component of (P 1 P 0 ). Scalar components for other vectors are inicate in a similar manner. Lemma. The N x 1 vectors x = (x 1, x 1) an z = (z 1, z 1) an the matrix M = [I α ( x v 1 z ) ] satisfy M[I+αVΩ 1 0 ] = I where 15 See, for example, Lee an Park (2009) an Gantchev et al. (2013) who fin evience of the impact of activism in the target firm affecting other firms. v 1 11

12 x 1 = 1 c [v ω 1 αω 1 1(v 1Ω 1 1,0v)/(1 + αv 1ω 1 1)] x 1 = 1 c [Ω 1 1,0v α (v 1Ω 1 1,0v) (1 + αv 1ω 1 1) ω1 1] z 1 = z 1 = ω 1 1 c(1 + αv 1ω 1 1) 1 c(1 + αv 1ω 1 1) [(1 + αv ω 1 )ω 1 1 αω 1 1Ω 1 1,0v] c = 1 + αv ω 1 α 2 ω 1 1(v 1Ω 1 1,0v)/(1 + αv 1ω 1 1) an 0 < α 1. Since M[I+αVΩ 1 0 ] = I, it follows that Ω 1 0 M is the inverse of [Ω 0 +αv]. Because this latter matrix is assume to be positive efinite, its inverse must have positive iagonal elements. It follows that the upper left iagonal element of Ω 1 0 M must be positive an this can only happen if c(1 + αv 1ω 1 1) > 0. For the remainer of the paper we assume that the parameters satisfy c > 0 an 1 + αv 1ω 1 1 > 0. This lemma allows us to present the equilibrium prices at t = 1 explicitly. We o this in the next proposition. Proposition 3. At time t = 1, µ 11 = µ 0 +πme 1 an Ω 11 = Ω 0 +πv, an µ i1 = µ 0 an Ω i1 = Ω 0, i = 2,..., M. Then the equilibrium prices can be written as where [ ] g 1 (P 1 P 0 ) = g 2 v 1 g 1 = 1π c [m v 1/ + α 1 (v 1Ω 1 1,0v)/(1 + αv 1ω 1 1)] g 2 = 1π c [ αω 1 1 (m v 1/) αv 1ω 1 1 (1 + αv ω 1 )] an α = 1 π. 12

13 Propositions 2 an 3 emonstrate the result of the surreptitious acquisition of shares by A. A s preictions of the changes that his activism woul prouce cause him to seek to alter his portfolio holings consistent with his preictions. Because he ha to acquire shares in the market 16, an because his view of future prices was ifferent from that of other investors, the market exchange was characterize by a heterogeneous information equilibrium. Uner these conitions, Propositions 2 an 3 establish the relationship between A s preictions an their impact on prices an holings of all market participants at time t = 1. In particular, Proposition 3 shows how changes in the variance or covariances affect the price change of firm 1, an all prices connecte to firm 1. Furthermore, Proposition 2 extens this observation to the holings themselves. Shoul A believe that the result of his activism woul have no aitional effect on the covariances between firm 1 an the remaining firms, i.e., v 1 = 0, then from Proposition 3, it follows immeiately that prices other than the price of shares of the first firm woul not change. However, using Proposition 2 uner the conition that v 1 = 0, we note that holings for all investors change nevertheless. That is, a rebalancing of portfolios occurs for all investors even though only the price of the shares of the target firm changes. Since these rebalancings involve a money exchange, this emonstrates that a change in the price of the target firm, by itself, is not enough to evaluate the impact of activism on shareholers of this firm. This observation leas us to propose, in Section 4 below, a metho of evaluation that avois this criticism. Examining the change in the price of the shares of firm 1 exhibite in Proposition 3, it is not clear, in general, that this price increases without imposing some further conitions. These conitions on g 1 will be clarifie when, after iscussing the remain- 16 See, for example, Kahan an Rock (2007, p. 1069) where they state "... it is noteworthy that activist hege funs usually accumulate stakes in portfolio companies in orer to engage in activism." Italics in original. 13

14 ing two equilibria, we aress the preliminary ecision that A woul have ha to have mae to become an activist in the first place. 17 Assuming A has acquire suffi cient shares at time t = 1, then at t = 2, he announces this by filing Scheule 13D. With the release of information containe in his filing of Scheule 13D, all investors, except for A, institute a traing roun base on this new information. A is not be involve in this traing roun since we assume his acquisition of aitional shares was preicate on the fact that he woul continue to hol shares long enough to execute his plan. 18 Thus, the traing roun at time t = 2 is again one of homogeneous information, but with the number of shares hel by A exclue from the competition. More precisely, at time t = 2, A oes not trae an each of the other investors learns of the information hel by A. Thus, at this time we have M 1 investors sharing the same information µ i2 = µ 0 +πme 1 an Ω i2 = Ω 0 +πv, i = 2,..., M. The result of this competition is containe in the next proposition. Proposition 4. At time t = 2, A oes not trae, an µ i2 = µ 0 + πme 1 an Ω i2 = Ω 0 + πv, i = 2,..., M. Then the equilibrium solution yiels P 2 = µ 0 + πme (Ω 0 +πv)(1 x 11 ) an x i2 = x i1 for i = 2,..., M. Proposition 4 establishes the fact that the new information acquire by the remaining investors when A abstains from the traing roun has no impact on their 17 We nee to elay the iscussion for the following reason. Uner the assumptions that A will have acquire aitional shares, he will be able to begin his efforts to alter the irection of the firm. This, however, has come at a cost of acquiring these aitional shares that can be written as P 1(x 11 x 01). In the initial ecision as to whether to become an activist, A must consier this cost against the expecte revenue he will subsequently receive when he has finishe his activist activities an sells his extra shares on the market. 18 See Cliffor (2008) who fins that hege funs o not seem to buy or sell aitional shares when they change from a passive status to an active one, although that change in status necessitates a filing of Scheule 13D. 14

15 holings. The intuition for this result is as follows. A woul not wish to sell his recently acquire shares in firm 1 since this woul unermine his purpose as an activist. Given this point, he woul not wish to trae his shares in other firms either, since he alreay optimize his holings in these firms in conjunction with his purchase of aitional shares in firm 1 when using his private information. (In fact, he woul be at a isavantage to trae in a market in which all investors ha the same information as he i.) On the other han, the other investors, having been alerte to the activism by the Scheule 13D filing, now may want more of the shares of firm 1, an can only get those shares from among themselves. In their attempt to get more shares, the prices will change. At these change prices, however, it becomes optimal for these other investors to en up with portfolios ientical to the ones they selecte at time t = Subsequently, at time t = 3, there is new information since it becomes known as to whether or not A was successful. The istributional parameters hel by all market participants, incluing A, then are either µ 0 +me 1 an Ω 0 +V if A were successful, or µ 0 an Ω 0 otherwise. Thus, all investors participate in a homogenous information equilibrium. Shoul this equilibrium result in the sale of suffi cient shares in firm 1 by A, then at this time A files Scheule 13D/A, acknowleging the change in his ownership. The next proposition provies the results. 19 In form, the result of Proposition 4 bears a resemblance to equation (3) in Amati et al. (1994). This resemblance is eceiving for two reasons. First, the shares acquire by the activist in Amati et al. were acquire strategically, that is, not as a price-taker, whereas our activist acquire his shares in a Walrasian market. Secon, though firms are consiere correlate in the Amati et al. paper, it is assume that activism can only affect the mean of the istribution of prices whereas we assume activism can affect both the mean of the istribution an its covariance matrix. Neglecting the impact on the covariance structure obscures the necessary portfolio rebalancing an the costs associate with it. 15

16 Proposition 5. At t = 3, if A is successful, µ i3 = µ 0 +me 1 an Ω i3 = Ω 0 +V, i = 1,..., M. At t = 3, if A is not successful, µ i3 = µ 0 an Ω i3 = Ω 0, i = 1,..., M. If A is successful, the equilibrium price P 3 = P U 3 = µ 0 +me 1 1(Ω 0 +V)1; if A is unsuccessful, the equilibrium price is P 3 = P L 3 = P 0. In either case, x i3 = x i0 = i 1. One interesting feature of Proposition 5 is that whether successful or not at time t = 3, A chooses to sell the aitional shares he acquire at time t = 1 in firm That is, there is no way for A, if successful, to take avantage of the improve istribution of prices once the result of his activism becomes known. In equilibrium, the combine eman of all the shareholers, incluing A, force this result. The erivations of the equilibria in our moel were preicate on an initial ecision mae by A: The ecision to become an activist or not. In the next Section we iscuss how this preliminary ecision was mae. 3 The Decision to Become an Activist In our moel, A approaches the ecision to become an activist with a presumption of how the future value of the target firm, as well as the future values of other firms, woul change as a result of his activism. This is summarize by the parameters of his subjective probability istribution of the future value of the target as well as other firms in the market. Uner what conitions oes this istribution warrant activism? In consiering this istribution, A is aware that he will have a significant impact on the equilibria that follow. A also knows that to acquire shares or to sell shares, he must involve himself in these competitive equilibria. Since A can anticipate the results of these equilibria in expectation, he can also anticipate the costs of all of the portfolio rebalancing involve as well as the portfolio he woul hol when he exits 20 See Brav et al. (2008), where it is note that the sheing of excess shares when activism is conclue is typically via sales in the market. 16

17 the target firm. Using these results, for A to procee, we assume that the parameters of this istribution must satisfy two conitions. First, the parameters must affor A the expectation of acquiring suffi cient aitional shares in the target firm at time t = 1 to enable his activism. Secon, the parameters must affor A the expectation of avoiing a loss over the course of his activism. We assume that activism will occur only when both of these conitions are satisfie. We next show that satisfying these conitions is equivalent to placing constraints on the parameters of A s subjective probability istribution. We enote by CA1 the conition that A expects to acquire more shares in the target firm. Using the notation establishe above, we write CA1 as (x 11 x 10) 1 > From Propositions 2 an 3, we have (x 11 x 10) 1 = ( 1 )ω 1 (P 1 P 0 ) = ( 1 )[g 1 ω 1 1 g 2 v 1ω 1 1]. Thus, the constraint CA1 is equivalent to g 1 ω 1 1 g 2 v 1ω 1 1 > 0 an is satisfie when the parameters of A s subjective probability istribution satisfy this inequality. The expectation of acquiring aitional shares oes not imply that the expectation of the change in price of the shares of the target firm at time t = 1, g 1, is positive. That is, CA1 can be satisfie with g 1 < 0, epening on whether v 1ω 1 1 is suffi ciently negative. We enote by CA2 the conition that A expects not to suffer a loss over the course of his activism. From Proposition 5, it follows that the money exchange in A s rebalancing resulting from the equilibrium at time t = 3 is P 3(x 11 x 13). Since x 13 = x 10, this amount can be written as P 3(x 11 x 10). Similarly, the money exchange by A at time t = 1 ue to rebalancing is P 1(x 10 x 11). Thus, the total money exchange by A from t = 1 to t = 3 is (P 3 P 1 ) (x 11 x 10). Starting with the 21 We coul have impose the requirement (x 11 x 10) 1 > τ > 0 but for convenience chose τ = 0. 17

18 portfolio value P 0x 10 an ening with the portfolio value P 3x 10, A s total change in portfolio value is (P 3 P 0 ) x 10. Thus, the change in value to A from his involvement in activism is given by (P 3 P 1 ) (x 11 x 10) + (P 3 P 0 ) x 10. Since at time t = 3, P 3 can take on one of two values (refer to Proposition 5), A s expecte change in value from activism is E π (P 3 P 1 ) (x 11 x 10)+E π (P 3 P 0 ) x 10 where E π is the expectation taken with respect to the binary istribution of P 3. Finally, we can write CA2 as the constraint E π (P 3 P 1 ) (x 11 x 10) + E π (P 3 P 0 ) x 10 > 0. As with CA1, we can write the inequality of CA2 in terms of the parameters of A s subjective istribution by using Propositions 2, 3 an 5. Together, we call the two conitions for activism, CA1 an CA2, CA an note that CA places constraints on the parameters that the potential activist brings to the problem. Only when CA is satisfie will A procee. The implie constraints formalize the iea that among all possible targets that A might choose, only some are eeme worthy of pursuing. For the remainer of the paper we assume that the constraints in CA hol. 4 Methoology to Evaluate Activism Having establishe the conition CA that permits an activist to procee, an having presente the results of the equilibria over the course of A s involvement with the target firm, we now use these results to construct a methoology to evaluate activism. Our metho of evaluating activism takes the sequence of erive equilibria as given an provies an answer to the question: How i the activist, A, an the group of investors excluing the activist, G, fare over the course of activism? Our metho of evaluation epens on the creation of a measure for A an for G, each of which involves two calculate values. The first calculate value is the sum of the money exchange for the rebalancing of the portfolios require at each of 18

19 the intervening equilibria (t = 1, 2 an 3) for A an G, respectively. We esignate these rebalancing amounts for A an G as R(A) an R(G), respectively. The secon calculate value is the ifference between the portfolio value hel at the en of activism (t = 3) an the portfolio value hel prior to activism (t = 0) for A an G, respectively. We esignate these ifferences for A an G as D(A) an D(G), respectively. We use these calculate values to efine the measure of evaluation for A as Ψ(A) = R(A) + D(A) an for the remaining investors, G, as Ψ(G) = R(G) + D(G). Since the function Ψ represents the net financial gain (loss) over the course of activism, we say that activism benefits A if, at time t = 3, Ψ(A) > 0 an activism benefits G if, at time t = 3, Ψ(G) > 0. We next use the equilibria results to evaluate the Ψ functions explicitly. We begin with A. As argue in Section 3 above, the sum of the money exchange by A in rebalancing over the perio of activism, R(A), is given by (P 3 P 1 ) (x 11 x 10). (At time t = 2, A is not involve in the equilibrium so there is no rebalancing on his part.) Also, from Section 3, the change in A s portfolio value, D(A), is given by (P 3 P 0 ) x 10. Thus, the evaluation of activism for A is Ψ(A) = (P 3 P 1 ) (x 11 x 10) + (P 3 P 0 ) x 10. Since this evaluation occurs at time t = 3, P 3 = P U 3 or P L 3 (see Proposition 5). Note, unlike the similar calculation one by A to satisfy CA2, this evaluation takes place at time t = 3, when the value of P 3 is known. Since, from Proposition 1, x 10 = 1 1, D(A) = 1 (P 3 P 0 ) 1. The quantity (P 3 P 0 ) 1 is the actual change in the market value ue to activism over its course, an we enote it by S. Thus, Ψ(A) = R(A) + 1 S, which epens on the change in market value cause by activism, S, an emonstrates that this change is neee in evaluating activism but in itself is not suffi cient to measure the total impact of activism on A. We now aress Ψ(G), the measure of gain or loss from activism for the group of other investors. We let x Gt = M x jt, t = 0, 1, 2, 3, be the group holings at the j=2 various equilibria. In line with the argument above, the money exchange at time 19

20 t = 1 for G is P 1 (x G0 x G1 ). At time t = 2, all money is exchange among members of G itself, an therefore there is no change for the group. Using the same argument as use at time t = 1, an recalling that x G3 = x G0, the money exchange at time t = 3 is P 3 (x G1 x G0 ). Thus the money exchange ue to portfolio rebalancing by G is given by R(G) = (P 3 P 1 ) (x G1 x G0 ). At time t = 3, G, having starte with a portfolio value P 0x G0, is left with a portfolio value P 3x G0 at time t = 3. Thus, D(G) = (P 3 P 0 ) x G0 an Ψ(G) = (P 3 P 1 ) (x G1 x G0 ) + (P 3 P 0 ) x G0. Since x G0 = (1 1 )1, Ψ(G) = R(G) + (1 1 )S. We note that although the equilibrium prices at time t = 1 play a role in our evaluation metho, by themselves they are only important in so far as they contribute to R(A) an R(G). We next establish the relationship between Ψ(A) an Ψ(G). Proposition 6. (a) R(A) + R(G) = 0. (b) Ψ(A) + Ψ(G) = S. Proposition 6(a) establishes the fact that whatever financial benefit (loss) A acquires in the rebalancing of portfolios, G loses (gains). However, achieving a benefit or a loss by itself provies no information as to whether activism is beneficial, i.e., whether Ψ > 0. Proposition 6(b) eals with this issue. Since S is the total change in the market value ue to activism, 6(b) shows that this change is split between A an G. Since neither Ψ(A) nor Ψ(G) nee be positive, this split may not imply a benefit for both. In fact, shoul S = 0, Proposition 6 shows that the result of activism is zero-sum. But is it reasonable to consier values of S 0? That is, if, as a consequence of A s consierations of becoming an activist, A etermines that the value of the market woul fall as a result of his activism, woul this imply that CA coul not be satisfie? We next show that there are circumstances in which this implie ecline in the value 20

21 of the market woul not eter the potential activist from proceeing. Proposition 7. There are instances of A s subjective probability istributions such that espite A being aware that the impact of his activism woul lower the value of the market, CA woul be satisfie an A woul procee with activism. Furthermore, if successful, A woul benefit but G woul not. The instance explore in the proof of Proposition 7 is where A expects that if he succees in his eneavors, the sole result, asie from m > 0, woul be to increase the correlation, namely v 2, between the target firm an one other firm, firm 2. The assumption that v 2 < m < 2v 2 where 0 < v 2 < 1, is enough to show that CA is α satisfie. It also follows that the price of the target firm increases at time t = 1 an at the same time the price of firm 2 ecreases. This ecrease causes a ecrease in the value of the market at this time. However, espite this, with CA satisfie, A procees with his activism which, in turn, leas to a ecrease in the value of the market over the entire perio of activism, i.e., S falls. Finally, we show that if A succees, A benefits an G oes not benefit. As a result of Proposition 7, in consiering the benefits to those involve in activism, we must consier situations where activism coul cause changes in the value of the market that are negative as well as positive. We next examine the relationship between Ψ(A) an Ψ(G), making this relationship explicitly epenent on R(A) an S. Proposition 8. (a) Ψ(A) > 0 an Ψ(G) > 0 iff 1 S < R(A) < (1 1 )S. (b) Ψ(A) > 0 an Ψ(G) < 0 iff R(A) > max[ 1 S, (1 1 )S]. (c) Ψ(A) < 0 an Ψ(G) > 0 iff R(A) < min[ 1 S, (1 1 )S]. () Ψ(A) < 0 an Ψ(G) < 0 iff (1 1 )S < R(A) < 1 S. The constraints in Proposition 8(a) can only be satisfie if S > 0. Thus, 8(a) 21

22 exhibits the fact that for both parties to benefit, S must be positive an A must be constraine in the terms of the gains mae in rebalancing his portfolio. Similarly, as exhibite in part (), when neither benefit, it is necessary that S be negative an A be severely restricte in the rebalancing amounts he can make. The intervening results constrain R(A) but S may or may not be positive. Our evaluation of activism is preicate on the knowlege of the outcome of the A s activities at time t = 3. The evaluations will change epening on whether or not A is successful. The next proposition examines the relationship between Ψ(A) an Ψ(G) when this istinction is mae. Proposition 9. (a) If A is successful, then (1) Ψ(A) > 0. (2) Ψ(G) > 0 iff R(A) < (1 1 )S. (3) Ψ(G) < 0 iff R(A) > (1 1 )S. (b) If A is not successful, then (1) Ψ(A) < 0. (2) Ψ(G) > 0. Significantly, Proposition 9(a) shows that A always gains when activism is successful, while the gains or losses of G epen on the magnitue of the gains by A. As the magnitue of the A s gains increase, a point is reache where G loses. Part (b) of the proposition shows that if A is not successful, A loses while G always gains. One can interpret Proposition 9 more generally. Given that A only procees having alreay etermine that CA is satisfie, A woul be assure that, if successful, he woul benefit by the amount Ψ(A). With this guarantee, A woul procee an, if successful, at time t = 3 woul receive Ψ(A). However, as a result of the activism, the value of the market changes over that perio by the amount S. Thus, A gets 22

23 Ψ(A) from the amount S, leaving the rest to G. Obviously, when Ψ(A) is too large compare to S, G must make up the ifference, possibly resulting in a loss for G. Our approach has the avantage that it separates A from G in evaluating activism. To be complete, we next consier what our metho of evaluation woul prouce if we use it to evaluate the totality of shareholers in the target firm, i.e., A an G together. The evaluation of this enlarge group is referre to as Ψ(A+G). In keeping with our metho of evaluation, we efine Ψ(A + G) = R(A + G) + D(A + G) where R(A + G) = R(A) + R(G) an D(A + G) = D(A) + D(G). Proposition 10. (a) Ψ(A + G) > 0 iff S > 0. (b) If Ψ(A + G) > 0, then at least one of A an G will benefit. (c) If Ψ(A + G) > 0, then activism will benefit only A or only G if R(A) oes not satisfy 1 S < R(A) < (1 1 )S. Proposition 10 states that the enlarge group A+G benefits over the course of activism if an only if activism leas to an increase in market value. But from Proposition 10(b) an 10(c), it follows that the benefit to the enlarge group oes not necessarily translate to benefits for both A an G. Thus, in claims for the benefits of activism, it is important to make clear the particular group that is being aresse. This raises an issue with an evaluation of the impact of activism appearing in some of the literature. 22 There, the claim is mae that activism benefits shareholers since the price of the target firm increases at the time of the Scheule 13D filing an persists. This claim leaves unspecifie or vague whether the group that benefits in the statement in the literature is A or G or A+G. If the shareholers referre to in the empirical literature are either A or G, then Propositions 8 an 9 show that, with iversifie portfolio holers, this conclusion cannot hol. If, as in Proposition 10, we 22 See, for examples, Brav et al. (2009) an Klein an Zur (2009). 23

24 focus on the combine group, A+G, it is only uner severely restrictive conitions that an increase in the target price at the time of the Scheule 13D filing yiels a benefit of activism over the course of activism, even when ealing with iversifie portfolio holers. 5 Discussion Our metho of evaluation of activism is applie separately to the activist an to the group of other investors, as well as to the combine group of all shareholers, when the activist an shareholers in the target firm are iversifie portfolio holers of possibly correlate firms. Our metho is istinguishe by several features. First, it epens on two values compute from the series of price changes an portfolio changes resulting from activism, namely from the funs exchange ue to portfolio rebalancing an the change in market value over the course of activism, R(A) an S, respectively. Secon, the evaluation epens on all of the activities that occur from the moment that the activist ecies to become an activist by acquiring aitional ownership in the target firm until the moment the activist ivests this aitional ownership. Thir, a preliminary jugement to procee with activism, the CA conition, is escribe an assume as a prerequisite to action. We fin that when the activist is successful in his eneavors, he always benefits. The fact that the activist benefits may be accompanie by a loss for the group of other investors an/or a ecline in the value of the market. If the activist is not successful in his eneavors, he suffers a loss from his activities, the group of other investors gains, an the value of the market oes not increase. We show, however, that the preliminary jugement to become an activist lessens the number of instances that will lea to the activist s failure to successfully complete his plans. Thus, we conclue that activism benefits the activist, possibly at the expense of the group of 24

25 other shareholers. In consiering the combine group of the activist an the other shareholers, we fin that this combine group benefits if an only if the value of the market increases as a result of activism; furthermore, the benefits may not be share by both the activist an the group of other investors. Our metho of evaluation enables us to raw istinctions which we think have been obscure in parts of the literature. Asie from being able to evaluate the activist separately from the group of other investors, our metho exposes the costs an benefits of the two, as well as the competition between them for any benefits. For example, the funs exchange by the activist in rebalancing his portfolio over time, R(A), equals R(G). So gains mae by the activist are at the expense of the group of other investors. This relationship is hien when the focus is on the totality of all the shareholers, the activist plus the group of other investors. Our moel relies heavily on the assumption that activism may alter the covariance structure between the target firm an other firms. In support of this assumption, we fin empirical evience that activism affects firms other than the target firm. In fact, there are instances in which the covariance structure becomes meaningful in the strategy of the activist. 23 See, for example, the escription of AXA s propose acquisition of MONY in Kahan an Rock (2007), an Lee an Park (2000) who emonstrate the impact of activist behavior on the prices of other firms. Also, Greenwoo an Schor (2009) show that targets for which a merger or sale of part of the assets earn more than targets without those prospects, Becht et al. (2014) confirms a similar fining internationally, an Gantchev et al. (2013) ocument spillover reactions of hege 23 One particular recent event provies a useful example of an activity of an activist attempting to alter the covariance between firms. In this case, the hege fun Eminence Capital owns stakes in both Men s Wearhouse an Jos. A. Bank, an has mae clear that it esires the takeover bi of the latter by Men s Wearhouse to be successful. See Michael J. e la Merce, "Jos. A. Bank in Talks to Buy Eie Bauer," New York Times, 2/3/14. (On 3/11/14, Men s Wearhouse agree to buy Jos. A Bank.) 25

26 fun activism. 24 When the activist is successful, why is it that the activist benefits while the group of other investors may not? The reason becomes clear when glancing at the sequence of equilibria over the course of activism. It is apparent at the outset at time t = 1 that the activist brings private information to the equilibrium (his plan to alter the future value of the target firm) giving him an avantage that carries through the rest of his involvement with the target firm. This avantage is similar to that of insie information, albeit future insie information. Furthermore, when this information leas to profitable rebalancing exchanges, R(A) > 0, the activist gains at the expense of the group of other investors. Turning to our assumptions, we have assume that there is a single activist in a single firm. This assumption can be generalize to many activist in many firms using the same approach we employe here. The further assumption that these multiple activists coul form coalitions as an aitional complexity not resolvable by our approach an nees further consieration. We have assume the activist s activities woul lea, in expectation, to an increase 24 Other strategies that may exploit the covariance structure inclue those that make use of hien ownership (that is, economic ownership hel without voting rights) an empty voting (that is, voting exceeing economic ownership); see Hu an Black (2007). However, the use of erivatives, an in particular, equity swaps, to mask the accumulation of shares that woul necessitiate a 13D filing, has been challenge in Feeral Court in connection with a case involving The Chilren s Investment Fun an CSX; see, for example, Stowell (2010). Accoring to Stowell (2010, p. 249), the 2008 ruling in the CSX vs. The Chilren s Investment Fun Management case "represents a strong challenge to hege funs who attempt to conceal their true economic position through the use of erivatives." We note that more recently, the 2n Circuit U.S. Court of Appeals, consiering the same case, left unsettle exactly uner what circumstances cash-settle total equity swap agreements provie beneficial ownership. In the context of the Do-Frank Act, since section 766(b) amens Sections 13() an 13(g) of the Exchange Act, this issue remains not fully settle. See Cuillerier an Hall (2011). 26