A New Informativeness Principle: Managerial Incentives Decline in Stock Price Informativness * Version: May 24, 2012 Brandon Chen. Peter L.

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1 A New Informativeness Principle: Managerial Incentives Decline in Stock Price Informativness * Version: May 4, 01 Brandon Chen Peter L. Swan Abstract Holmstrom (1979) established the informativeness principle when he showed that even very imperfect information can be used to improve the welfare of the principal and agent. Holmstrom and Tirole (1993) appears to show that use of price-based incentives should increase when stock prices become more informative about managerial action such as when firm scale is greater. To the contrary, we show that the sum of price and non-price incentives must always fall with increased informativeness, explaining why larger firms are less reliant on incentives. Moreover, the price sensitivity always falls if the precision of the price signal of performance exceeds that of the accounting signal. We empirically confirm our model s prediction to show that the use of equity-based incentives actually falls when institutional traders impound more information in stock prices. In other words, monitoring and incentives are substitutes. Despite the lower use of equity-based incentives and the even lower still use of bonus incentives, the CEO works harder and her total compensation increases. Our paper not only redresses previous confusion about managerial incentives and price efficiency due to informed trading, but also utilizes a new way to infer price informativeness from the number of institutional informed traders as well as the magnitude of their trades from a swing measure of informed trading. In its first application to the United States, we show that the swing measure can be inferred from SEC 13f filings and is robust to a number of tests. JEL Classification: D8, G14, G3, G3 Keywords: Informativeness, Incentives, Substitutes, CEO pay, Institutional monitoring, Governance through Trading. * We thank Renée Adams, Rajesh K. Aggarwal, Anat Admati, Riccardo Calcagno, especially Alex Edmans, David Feldman, Daniel Ferreira, Florian Heider, Bengt Holmstrom to whom we owe special thanks, Albert (Pete) Kyle, Pedro Matos, Paul Pfleiderer, Jaeyoung Sung, Jean Tirole, Terry Walter, and seminar participants at University of New South Wales, La Trobe University, 010 Giblin Workshop, 010 FIRS Conference, 010 China International Conference in Finance, 010 ISB CAF Summer Research Conference in Finance, 010 Econometric Society World Congress and 01 American Finance Association participants for comments on earlier versions and the Australian Research Council (ARC) for financial support. We also thank Kai Li, our discussant at the 01 AFA Conference in Chicago for comments. School of Economics and Finance, Victoria University of Wellington, New Zealand. brandon.chen@vuw.ac.nz. School of Banking and Finance, Australian School of Business, University of New South Wales, Sydney, NSW 05 Australia. peter.swan@unsw.edu.au.

2 In his famous paper, Holmstom (1979) formulated the informativeness principle as to how sharing relationships such as agency can be improved. In a world with moral hazard, even imperfect additional information about the agent s unobservable actions makes both the principal and agent better off. Holmstrom reprises his seminal contribution in Holmstrom and Tirole (1993) (hereafter, HT) where they conclude (pp ) that manager stock price incentives increase absolutely (i.e. incentives are more high-powered) as stock price becomes more informative. They argue that larger stocks (i.e. increased firm scale) trading in more liquid markets will have more informative stock prices since informed traders (i.e. speculators ) can hide more effectively in the crowd as in Kyle (1984, 1985), giving rise to more high-powered incentives. Conversely, if control considerations give rise to some form of vertical integration with weaker performance information in the stock price then lowerpowered incentives will be used (HT p.698). These model findings seem peculiar as practically every study of pay for performance sensitivity shows that sensitivity falls rather than rises with increases in firm size and that high-powered contract (e.g. MacDonald s franchise contracts) usage occurs in vertical relationships when there is less informative stock price information. Sensitivity is typically high in start-ups with highly uncertain stock market valuations. We show that these counterintuitive predictions are not due to technical error in the HS model itself but rather are simply a consequence of their redefinition of price incentives from the proportion of shares allocated to the manager into a measure of equity performance by multiplying by informativeness itself. They do this to help simplify and sign their comparative-static findings but forget to translate back again into their original units when interpreting results. 4 Once this problem is 4 HT (p. 695) state that their transformed equity incentive term, i.e., ' b' ˆ p ˆ, where ˆ p ˆ is the equity share allocated to the manager that they (incorrectly) interpret as their price-based incentive, will fall with increases in their observational error term, i.e., ' ', that worsens the informational content of price (HT, p. 69). In their framework, after retransforming units, a fall in the observational error that improves the informational content of price will generally (but not always) result in a fall in the equity incentive, not a rise. In

3 corrected we find that pay for performance sensitivity falls absolutely with a more informative stock price on the reasonable supposition that the price signal has greater precision for many firms than the non-price signal utilizing accounting numbers. Thus, from the perspective of our findings, young firms with high inside ownership and low liquidity have low precision of the price signal and thus relatively high precision of the accounting signal. The ineffectiveness of market monitoring means that management needs high share ownership and pay for performance sensitivity to create alignment of interests in order to compensate for the weakness of stock price informativeness. HT point out that, relative to its benefits, the costs of informed traders earning large profits comes ultimately as an expense borne by insiders is it depresses stock price. Such relatively illiquid stocks may be more valuable as part of a conglomerate with no trading of divisional shares and almost complete reliance on accounting numbers. The large fall in managerial shareholdings following acquisition and conversion to a conglomerate division need not indicate any sizeable change in market monitoring. The discontinuous fall in managerial share ownership with acquisition may be largely irrelevant with negligible change in the already low level of market monitoring. This theory also explains why most small businesses and a number of large businesses remain unlisted. If these companies were to list creating relatively illiquid stocks and thus the need for high-powered incentives, the gains in terms of better motivating the manager relative to just accounting performance may not outweigh the losses incurred by noise traders. Empirically, we find that sensitivity always declines with respect to both informativeness and firm scale, the latter being a proxy for informativeness. In the limiting theoretical case in which non-price incentives are irrelevant, we show that it is always the case that incentives correspondence with us, Bengt Holmstrom has acknowledged the problem and hence the misleading nature of their results. 3

4 are less high-powered the more informative is stock price. By following the Wall Street Rule or taking the Wall Street walk, dubbed Governance through Trading (GTT) by Gallagher, Gardner, and Swan (011) (hereafter, GGS), informed traders can considerably remove extraneous information that disguises managerial actions in stock prices. They accomplish this by driving price toward fundamental value determined by managerial action. The resulting greater sensitivity of stock price to managerial action stock price informativeness makes a non-performing manager more vulnerable to the decline in stock prices and thus ensures that the manager exerts appropriate costly effort ex ante. Edmans and Manso (011) (hereafter, EM) establish this as a theoretical proposition with the manager s equity allocation taken as given exogenously since their concern is not with the manager s contract. 5 GGS show empirically that informed trades, particularly those taking an aggressive form dubbed swing trades akin to stock turnover but with three legs such as buy-sell-buy or sell-buy-sell, results in subsequent firm outperformance consistent with higher managerial effort. They show using the daily trades of investment managers that swing trades are profitable after transaction costs, indicating that they are informed. Profitability is also improving at a diminishing rate in initial portfolio holdings up to an optimal holdings level. This indicates that long-only institutional investors invest more in acquiring information in a stock the higher are their holdings, as predicted by Edmans (009). Diminishing liquidity with increased information about future stock value predicates an optimal holdings level for trading purposes. Profitability is also declining in the number of fund managers swing trading simultaneously, indicating that fund managers observe correlated signals of future value. 5 Their assumption rules out endogenous sale of the firm to the manager, a corner solution that could arise in the context of a risk-neutral manager. 4

5 In this paper, we empirically implement GTT s swing trades using quarterly 13f filing data. Since GTT boosts the efficiency of the equity performance incentive, a smaller level of CEO equity incentives does the same or better job. Despite reduced use of incentives, the CEO works harder and, empirically, her total compensation increases. In our setting, stock price based incentives (equity allocation) is neither exogenous nor increasing in stock price informativeness. Rather, it is a substitute for institutional monitoring based on GTT and thus diminishes the more effective is GTT. We take a simple analogy based on the idea that, since incentives are expensive to create, a more efficient incentive due to GTT should result in a smaller outlay on the incentive: 6 the introduction of an automobile with a diesel engine that is more fuel-efficient (institutional informed trading, or GTT, introduced) than an equivalent automobile with a gasoline engine (no GTT). To keep it simple, the price of a gallon of diesel and gasoline are identical and do not vary. One might expect that the diesel automobile would use less fuel each week (equity allocation lower) because of its greater fuel efficiency even if driven further each week due to its greater fuel economy (the agent works harder). That is, the technological fuel efficiency improvement (GTT) and the number of gallons of fuel purchased each week (equity allocation) are likely to be substitutable, not complementary, but we cannot rule out complementarity on theoretical grounds alone. 7 Our new informativeness theory is on stronger ground when it comes to the more general question of monitoring versus incentives. Incentives are always substitutable for informed 6 We thank Gerald Garvey for this analogy. 7 That is, a priori we cannot rule out the possibility that the automobile uses more gallons of diesel each week (equity allocation increases) if the driving mileage response to the lower effective cost of fuel is sufficiently elastic with respect to the diesel innovation. This complementary relationship is more likely, the fewer are the initial gasoline-miles with the owner preferring to use more efficient public transport running on gasoline (analogous to the use of accounting-based bonus incentives within a conglomerate with negligible divisional equity) when private gasoline costs are too high (since equity is highly inefficient prior to GTT, accounting incentives dominate). If the productivity gain with diesel is sufficiently high, private diesel mileage replaces both private gasoline mileage and gasoline-based public transport such that diesel usage is now higher (under GTT, the equity allocation increases as a conglomerate s division is separately floated). 5

6 trader monitoring. We establish a new and quite general result: the sum of equity and nonprice (bonus) incentives unambiguously fall in response to better monitoring. This represents our surprising informativeness principle: the more effective is a mechanism such as stock price in disciplining management because it contains more performance information, the less its use in optimal agency contracts. The substitutability-complementarity issue cannot be resolved empirically under the HT framework, as the (single) informed trader s effort to increase price informativeness by investing in a better signal is unobservable unless proxied by an increased firm scale. By extending our corrected version of HT s model to multiple informed traders, however, we are able to construct proxies for institutional informed trading and empirically investigate its relation with the use of managerial incentives. In our extended set up, price informativeness is proportional to the number of informed traders as well as their trade aggressiveness as measured by the magnitude of swing trades and informed trader informational advantage: the price is least informative when there is merely one informed trader (pure monopoly, as in HT), and it becomes more informative as the number of informed traders increases (as in Cournot competition and EM). 8 By analyzing institutional investors actual trading data recorded in the Thomson Reuter s 13f filing database, we are able to infer from their trading patterns the magnitude of informed trading via the size of swings and the number of informed traders, both of which make stock prices more informative. Our regression results show that the use of equity-based incentives actually falls as stock price informativeness increases. In other words, these two governance mechanisms are substitutes. While our (and reinterpreted HT) model is consistent with substitutability in a weak form; empirically, the substitutes relation exists in a strong form. We also demonstrate, 8 To keep things simple, we abstract from the multi-period nature of the HT model. This simplified HT model is a special case of ours with the number of informed traders set equal to one, but only after HT s equity incentive is measured correctly (see below). 6

7 based on a sample consisting of 77% of S&P 1500 stocks, , that increased informativeness not only reduces equity-based incentives and the sum of equity and bonus incentives (as it must do), but also raises the level of total CEO pay because empirically higher managerial productivity outweighs the fall in the use of incentives. To put our model and findings into context, traditional theories argue that concentrated ownership helps alleviate the agency problem embedded in the manager-shareholder relationship in a firm, because only large shareholders have incentives to monitor the manager through direct intervention, or voice, as termed by Hirshman (1970). Recent research shows the possibility of an alternative channel through which multiple blockholders may still exert effective governance despite the power of using voice being reduced. In terms of theory, both Admati and Pfleiderer (009) and Edmans (009) focus on a single blockholder that exerts governance through trading. In addition, many empirical works note this alternative monitoring mechanism of institutional trading. For example, Parrino, Sias and Starks (003) show that some institutional investors engage in the biggest sell-off in a firm four quarters immediately before CEO firing occurs. Sias, Starks and Titman (006) provide evidence that institutional investors possess information that affects prices permanently. With a different focus but in a similar vein, Chen, Harford and Li (007) show that some institutional investors will sell their stakes in a firm when they anticipate a large enough value reduction. Gopalan (008) finds evidence that institutional selling is a predictor of subsequent poor performance and firm takeover. A survey conducted by McCahery, Saunter and Starks (011) finds that a high proportion (80%) of responding institutional investors is willing to use GTT as a governance mechanism. 9 9 In addition, Yan and Zhang (009) find that short-term trading by institutional investors forecast future returns. Ferreira, Ferreira and Raposa (011) find that stock price informativeness is associated with board structure. Boehmer and Kelley (009) show that institutional trading is associated with greater pricing efficiency. Ferreira, Laux and Markarian (009) find that managerial equity-based incentives are a substitute for institutional trading. 7

8 The organization of the paper is as follows. Section I presents the theoretical framework that forms the basis of our empirical analysis. Section II discusses our data source and the construction of several institutional investor- and manager-related variables. Section III provides the rationale of using the buy-sell-buy and sell-buy-sell trade sequence as the proxy for the institutional informed trading, or Governance through Trading. We present our empirical tests in Section IV. Section V concludes. I. Optimal Contracting with Informed Traders A. Incentives and Price-(and Non-price-) based Signals As in EM s model, we view a blockholder simply as a shareholder who has greater information than the market and do not require her to hold a certain proportion (e.g., 5%) of a firm. Our model refers to informed investors or traders, not blockholders per se. We introduce an optimal managerial contract for a risk-averse manager whose reward depends on both stock price and non-price performance measures. The model is a two-stage game. In the first stage the manager is hired by firm owners (inside shareholders) and takes actions a[0, ) that affect firm (terminal) value, v : v a ( 1) Nature determines a (terminal) value v for the firm s equity from a normally distributed value v Ɲ a,. The higher the variance, the more valuable is the receipt of this signal to informed traders 10 but the harder it is to infer managerial actions from stock price movements. Random shocks represented by not only garble the managerial actions but also raise the risk borne by the risk-averse manager. Thus, it is desirable to eliminate the impact of these shocks from a contracting perspective. 10 This is what EM refer to as the trader s informational advantage parameter since if there were no variance in the signal there would be no point in trading. 8

9 The manager s total income, I, consists of three parts: a fixed salary, 0, plus the cash equivalent of an equity allocation of shares granted by insiders to the manager that is evaluated at the equilibrium market clearing price 11 at the rate, p, and an allocation, y, in the form of a cash payment based on the residual terminal value, paid by inside stockholders to the manager at the time of termination. CEO total pay has the following representation: I p y ( ) 0 p y, where denotes the cash reward based on the (observable) stock price, p, and y y can be p p viewed as the CEO s terminating bonus, based on a non-price (e.g., accounting) performance measure of the firm s terminal value, y, that is imperfectly related to the actual terminal value, v. Specifically, yv, with ~ Ɲ(0, ) that is normally distributed denoting the independent non-price observational error term (accounting valuation term). Here we follow Calcagno and Heider (009) by adopting a more general specification of the non-price signal than HT who by contrast adopt a more complicated three-period model with short- and longterm bonus and incentive effects. Our manager can depart at any time (so long as there is a non-price signal) whereas the HT manager must depart at a pre-specified date. The manager is paid an amount in cash that is directly related to stock price performance, 0 p p, plus an amount in expectation of yy E v 0 pp y, p in the form of the net cash equivalent of shares at the terminal date. We view the term ( v0 p p) as the net liquidation value of the firm and y y as the projection (i.e., linear regression) of the terminal bonus jointly on the accounting signal y and stock price p. 11 This is what HT call stock appreciation rights in their formulation of the problem in a three period setting. 9

10 The risk-averse manager s exponential CARA utility function depends on the manager s U I, a exp I 1 a income less her cost of effort,, where is the manager s coefficient of constant absolute risk aversion (CARA) and 1 a is the manager s quadratic cost of effort function. The total number of shares in the firm is normalized to 1, made up of shares retained by insiders with the residual number sold to liquidity traders. There are N symmetric risk-neutral informed traders and each trade 1 shares. Free float is fixed and N plays no role, as in EM. B. Trading Demand of Informed Investors and Price Informativeness The equilibrium price is determined in the second stage of the game. We adopt Kyle s (1984, 1985) model and extend Admati and Pfleiderer (1988), EM, HT, and Calcagno and Heider (Appendix A, 009) in modeling N separate individual signals received by informed traders in our analysis of trading demands. Each informed trader submits a market order, x s, after observing an imperfect heterogeneous signal of the true (common) value of the firm, si v i, where i is an independent and normally distributed observational error term with i i N 1 1 s s v N N i i Ɲ a, i1 N i1 and 1 N i1 i Ɲ 0, representing the N individual trader mean signal and error terms, respectively. 1 The trading strategy of each informed trader is a linear function of the imperfect signal: x s, where denotes Kyle s (1985) trade aggressiveness, and some constant. Uninformed risk-neutral (noise) traders as a group submit market orders u ~ Ɲ (0, u ) i i with mean zero and variance, u. The 1 Our assumption here differs from the model in the body of Calcagno and Heider (009) since in their model there is no collective error in the signals when summed up over all traders. We believe that this is the first time our problem with multiple investors and independent observational errors has been posed and solved. 10

11 market-clearing price that is not fully revealing of the actions of informed traders is then set by a competitive market maker who observes only the total order flow, N z x u, made i1 i up of both the informed trader and uninformed trader demands. Note that in our study we normalize the price and incentive contract to place it on a gross (i.e., pre-managerial compensation) basis as in HT and Calcagno and Heider (008). 13 This normalization procedure results in the definition of the gross (normalized) share price as pˆ 0 1 p p; the corresponding normalized manager income becomes: I ˆ ˆ pˆ ˆ y. ( 3) 0 pˆ y We solve this two-stage game by backward induction. We start from the second stage, taking the efforts of the manager as given to solve for the equilibrium (normalized) price. We then move back to the first stage and solve for the optimal managerial effort as well as firm owners contracting parameters. Proposition 1: The equilibrium normalized price is: * 1 ˆ N p 1 a a, i 1 i u ( 4) N where Kyle s lambda, N ( 1) u N, ( 5) which simplifies to the HT (equation (11) expression u, 1 when N=1. 13 In the context of different models, both HT and Calcagno and Heider (009) recognize the need to normalize by grossing up to remove the direct effects of pay from the stock price. The relation between the observed price, p, (which is measured net of managerial cash outlays) and the gross price undistorted by incentive payments, pˆ, is as follows: p pˆ 0 p p. 11

12 and the informativeness coefficient is N N, N 1 ( 6) N where. N 1 Informativeness is increasing in the number of informed traders, 0, N N N 1 and as the magnitude of the observational error term is reduced, 0, as in the original HT model. These relationships mean that we need only consider the impact of a change in informativeness,, on incentive allocations and performance rather than its various components. Since informed traders are likely to know more about larger stocks trading in more liquid markets, one expects this observational error term to diminish in firm size, as HT originally proposed. Informativeness is also increasing in trader informational advantage,, conditional on the reasonable supposition that there is observational error term. Note that N and N N 1 when each informed trader s signal is perfect and 1, HT s, exactly as in equation (11) of HT when trade aggressiveness summed over all informed participants is:. Aggregate informed N N u, ( 7) HT ' s u which corresponds to HT s trade aggressiveness parameter with only one informed investor. 1

13 Proof : See Appendix A. Hence, systematically profitable trade sequences that by definition are informed are indicative of a strong trader informational advantage. The second effort term in the normalized price (equation ( 4)) represents out-of-equilibrium effort, a. In equilibrium, a * a and thus the terms in equation ( 4), a * and a, cancel out, leaving the equilibrium price dependent on equilibrium effort, a *, plus informative effects. Aggregate trade aggressiveness given by N in equation ( 7) provides an additional rationale for our proxy for institutional trader monitoring based on actual trading data (introduced in section III). It is increasing in the number of informed traders. It is also higher the smaller is the magnitude of the variance of the informed trader observational error,, as in HT. Moreover, it is increasing in the volatility of noise trading, u, and diminishing in the magnitude of the trader informational advantage,. C. The Manager s Actions and Incentives We now explore the manager s effort level and her incentives in the first stage of the game. Since the utility function of the risk-averse CEO takes the negative exponential form, her optimizing problem can be expressed as: 1 a * arg max EI Var I a ( 8) a The first-order condition yields the optimal managerial effort level: ˆ ˆ. ( 9) * a pˆ y Before we solve the firm owners optimization problem for the absolute weights of equitybased pay allocation, ˆ p, and non-equity-based pay allocation, ˆ y, to determine the value of 13

14 the manager s optimal effort, we first consider the relative weight placed on equity-based pay allocation. In our structure with both CARA preferences and normally distributed returns, the optimal contract must minimize the total income risk faced by the risk-averse manager. Therefore, the firm owners (i.e. inside shareholders ) objective is to choose the best combination of ˆ p ˆ and ˆ y that minimize the variance of managerial income Var I subject to effort level being optimal for the manager (equation( 9)). We state the following result: Proposition : The ratio of equity-based to non-equity-based compensation becomes ˆ. pˆ ˆ y 1 ( 10) Substituting the ratios from ( 10) into the optimal effort expression, ( 9) above, we obtain: * 1 * ˆ ˆ pˆ a and y a, ( 11) 1 1 where and The manager s normalized equity allocation increases relative to the bonus share allocation the greater is the measurement error of the non-price (accounting) signal,, and the larger the number of informed traders ( ). Also, it increases the smaller is the informational advantage of informed traders,, and the smaller the observational error term, In the special case corresponding to HT s assumption of an informational monopolist, we obtain ˆ pˆ 1 ; ; and ˆ y u 14 which is equivalent to eqs. (30)-(3) of HT (1993, p. 695). In comparing our results with HT it is important to note that HT do not utilize the ratio of equity ˆ pˆ and bonus incentives,, in their comparative-statics following their eq.(4) (1993, p. 693) but, as an ˆ y (unintended) consequence of variable transformation, use what they refer to as the incentive ratio ˆ pˆ 1, where in HT s terminology, HT ' s ' v' and ˆ pˆ HT ' s ' b', implicitly holding ˆ y

15 Proof: See Appendix A. Having examined the relative weight on equity and bonus-based pay allocation, we now solve the firm owners optimization problem for the absolute weights of the share and bonus ˆ p ˆ allocations, and ˆ y. The risk-neutral firm owners choose the parameters of the manager s incentive contract to maximize the expected value of the firm net of the manager s income, max E ˆ p, ˆ y v I, ( 1) subject to the manager s incentive compatibility and participation constraints. The first order conditions yields the following proposition: Proposition 3: The respective optimal incentives are: ˆ 1 * * pˆ a * * ˆ y a. and ( 13) Substituting these optimal solutions into the expression for the optimal effort level (equation ( 9)) and simplifying yields: a * ( 14) Proof: See Appendix A. constant the terms and that go to make up stock price informativeness,, when the same terms are varied on the other side of the equation. Thus HT s sign condition for an increase in the informed trader s measurement error in observing terminal value to reduce the relative use of equity incentive is ˆ p Sign ˆ Sign ˆ pˆ 4, whereas it should read Sign ˆ Sign. Fortunately, both y ˆ y sign conditions are negative so that the comparative-static results based on sign here are similar for HT s transformed incentive ratio and the actual ratio but, in principle, they differ. 15

16 The terms involving the CARA coefficient, 0, in the optimal incentive values given by equation ( 13) and optimal effort (equation ( 14)) reflect second-best contracting considerations with a risk-averse manager such that all incentives are less high-powered and effort lower the more risk-averse the agent. Conversely, having the agent s preferences approach risk-neutrality (i.e. 0) achieves full efficiency but can make informed investor monitoring less relevant if high-powered incentives can be used in franchise contracts (i.e. sell the firm to the manager). Nonetheless, if there are constraints on the ability to eliminate agency problems by selling the firm to the manager, then there is still a role for informed trading to improve manager monitoring. We now get to the core of the paper by examining the effect of higher price informativeness on ˆ p ˆ and ˆ y due to increasing the number of informed traders, N, or smaller observational error volatility,, perhaps due to increased firm scale, although larger more liquid stocks benefit with respect to both elements. We examine the comparative-statics of the equity allocation, equation ( 13) with respect to informativeness,, as this represents either more informed traders or a smaller error volatility term: Proposition 4: A sufficient condition for the equity allocation (i.e pay-performance sensitivity) to fall with increased stock price informativeness is that the precision of the stock price signal exceed that of the non-price (i.e. accounting signal). Proof: See Appendix A. Intuitively, this finding makes a great deal of sense: the more accurate is the information in the stock price relative to alternative signals such as accounting information, the more productive is equity (i.e. pay-performance sensitivity) as an incentive device. Hence, the less of their own equity (i.e. wealth) insiders have to give away to the manager. 16

17 Nonetheless, HT prove the following proposition that, on the face of it, contradicts Proposition 4: Proposition 4 (HT Version): The (transformed) equity allocation is always rising in stock price informativeness and thus incentives must become more high-powered as liquidity and informativeness rise with firm scale. In fact, HT state explicitly that their transformed equity allocation ˆ p ˆ falls in response to an increase in the error volatility term, ( in HT s notation). 15 In fact, there is no contradiction due to HT s transformation of the equity incentive into a measure of equity s effectiveness and their only lapse is in failing to transform it back prior to analysis. Thus, as Proposition 4 shows, in general it is not possible to sign the impact of more informed traders on the equity allocation unequivocally on theoretical grounds alone because the relative magnitudes of parameters of interest are latent when both equity and bonus payment incentives are utilized. Hence, we need to rely on the empirical evidence as presented in Section IV. This empirical evidence in turn provides information about the relevant latent variables. A potentially empirically relevant case arises when non-price incentives are weak, i.e. stock price precision is high relative to (say) accounting precision. One easily shows in this case that a corner solution pertains with no non-price incentives: 1 ˆ, pˆ ( 15) 15 Note that as Bengt Holmstrom points out in correspondence, there are no technical errors in the proofs in HT as all the comparative-static results are reported for the transformed equity share incentive variable that is in reality the incentive due to equity and bears little relationship to the equity allocation itself. It is only in their verbal interpretation of the model that he refers to as misleading as this transformed equity share incentive is treated as being the actual equity allocation whereas it is not. 17

18 with a * ˆ p ˆ and, obviously, the equity allocation is always falling in stock price informativeness,. Note that in this case, HT mistake ˆ p ˆ. * a for their original equity allocation Proposition 5: The impact of higher stock price informativeness on the non-price incentive allocation is always negative. With more efficient informed trader monitoring due to greater price informativeness, the requirement to provide non-price incentives (i.e. accounting-based bonus payments) always reduces. Proof: See Appendix A. Proposition 6: The risk-averse manager s effort and thus firm performance is always increasing in stock price informativeness. Proof: See Appendix A. Hence, the effort of the risk-averse manager, and therefore firm performance, is always increasing in the number of informed traders and reductions in the observational error term. Increased stock price informativeness due to more traders or a smaller observational error term must always increase managerial effort except in the limiting case in which effort is already at first best. Combined with the results in Proposition, multiple informed traders lead to higher trading volume and more intense trade aggressiveness, causing greater price informativeness and an increase in firm value accordingly. 16 Hence, in more informationally rich markets with more aggressive informed traders we should observe both higher asset values and lower stock returns. We now obtain a general result on the substitutability of equity and bonus incentives for informed trader monitoring. 16 In our setting, as in the EM and HT framework, firm value and managerial effort has no bearing on informed traders trading profits. 18

19 Proposition 7: The sum of price (equity) and non-price (i.e. accounting bonus) incentives is always diminishing in stock price informativeness. Proof: See Appendix A. It is important to recognize that this striking result holds regardless of whether the equitybased incentive is increasing in informativeness. Hence, we obtain an exceedingly strong result in terms of the general substitutability of managerial incentives for informed trader monitoring. It makes intuitive sense, as it is expensive for shareholders to incentivize riskaverse managers. The more effectively stock price informativeness reveals the manager s own actions and thus the more she is self-motivated to perform, the lower the cost burden placed on shareholders. We now examine the impact of increased informativeness on the manager s expected ˆ ˆ ˆ a since the expected values of ˆp and y are given by income, * E I equilibrium managerial productivity, 0 pˆ y * a. Proposition 8: In general, expected managerial income cannot be signed unambiguously with respect to stock price informativeness induced by either a larger number of informed traders or more informed traders as incentives are reduced while both performance and performance pay rises, depending on how risk-averse is the manager. It is thus an empirical issue. Proof: See Appendix A. To recover the weights placed on equity-based and non-equity-based pay in the original managerial incentive contract, equation ( ) from the normalized ones in equation ( 3), we present the following proposition: 19

20 Proposition 9: Following the general approach of Calcagno and Heider (009) but with a quite different specification, the transformed components of the manager s contract can be expressed in terms of its original components: 1 1p 1 ˆ ˆ ˆ 0 0, pˆ,, and. y y 1 p 1 p 1 1 ( 16) Proof: See Appendix A. II. Data and Descriptive Statistics We merge CRSP/Compustat database with Standard & Poor s (S&P) ExecuComp database (from 199 to 007) to calculate CEO incentives. The institutional trading and shareholdings data are sourced from Thomson Reuter s 13f filing database. 17 All the firm-level accounting and stock price data are from Compustat and CRSP, respectively. A. CEO Incentives Data The ExecuComp database covers about 1,500 firms in the S&P It contains valuable compensation-related information for the top five (sometimes more) executives of each firm including total amounts of salary, bonus, long-term incentive plan, restricted stock grants and stock option grants. In this study, we focus only on CEO compensation because we expect the CEO alone to have the greatest power in a firm s decision-making process and to be the focus of institutional investor monitoring. We compute the pay-for-performance sensitivity (PPS) of CEO s total equity-based compensation as our proxy for equity-based pay allocation in the text. PPS as a proper proxy can be easily motivated since higher PPS indicates a closer alignment of interests between the CEO and the shareholders as posited by Jensen and Murphy (1990) and Hall and Liebman 17 Institutions with more than $100 million of securities under management are required to report to the SEC. The Thomson Reuter s 13f filing database contains the aggregate shareholdings for each institution on the quarterly basis. Disclosure is required for all positions greater than 10,000 shares or $00,000. 0

21 (1998). Our PPS measure consists of two parts: PPS_Cum_Option and PPS_CEO_Shares. The former is calculated as per Yermack (1995) and Core and Guay (00) 18 and is used to measure the dollar change in value of CEO option holdings for every $1,000 change in the value of the firm (shareholders value). The latter is used to measure the dollar change in CEO shareholdings (including restricted stock) for every $1,000 change in the firm value. The combined PPS measure is termed PPS_Total. It is worth noting that PPS_Cum_Option comprises the value of all outstanding options, as we believe the value of unexercised stock options granted in previous years also provides incentives that will influence CEOs actions (e.g. Jensen and Murphy (1990)). We also include CEO total compensation and other pay components (salary, bonus, and equity-based incentives) in our sample. Total compensation is the total direct compensation data derived from ExecuComp, defined as the sum of salary, bonus, total value of restricted stock granted, total (Black-Scholes) value of stock options granted, long-term incentive pay, and other annual payouts (including pension and health benefits, perquisites, etc). In Panel A of Table I we can see that on average, PPS_Total is about $35 per $1,000 change in shareholder value. Around 67% of PPS_Total can be attributed to CEO shareholdings (including restricted shares), and the remaining part to CEO option grants. The average CEO s total compensation is $4.9 million in 006 dollars. Of this amount, salary averages $760,000 and bonus $784,000. We also aggregate all equity-based components 19 and the sum averages $.97 million. All the CEO pay measures are right-skewed. <<Insert Table I>> 18 In particular, we compute PPS_Cum_Option by dividing the share equivalent of CEO cumulative option holdings by the total number of shares outstanding at the beginning of the fiscal year. Whereas the share equivalent of CEO option holdings is the product of the delta (i.e. the hedge ratio, based on the Black-Scholes formula adjusted for dividends) and the number of options granted in current and previous years. We apply the same method to compute PPS_CEO_Shares (note that hedge ratio of shares is 1). We then multiply PPS by 1000 to reflect the dollar change in CEO option grants for every $1,000 change in the firm value. 19 Equity-based components include CEO s restricted stock grants, stock option grants, and long-term incentive pay (LTIP). LTIP is included because it is mostly equity-based in public listed firms. 1

22 B. Institutional Trading and Ownership Measures We identify informed institutional investors by verifying whether they engage in a specific trading pattern. We make necessary adjustments suggested by the database provider (WRDS) before constructing variables related to institutional holdings. 0 B.1. Institutional Ownership Measures For each stock, we aggregate shares held across all institutions and divide it by the total number of shares outstanding at the end of each quarter to construct the institutional ownership measure (IO). We also construct the Top5_shrout measure by summing up the holdings of the five largest institutional investors for each firm and scale it by the total number of shares outstanding at the end of each quarter. These ownership concentration measures, as per Chen, Harford, and Li (007), are proxies for voice of institutional investors but differ from the concentration measure used by Hartzell and Starks (003) that ignores share ownership. Smith and Swan (01) shows that their findings are either insignificant or reversed when one uses a more reasonable size proxy based on the logarithm of market capitalization. B.. Institutional Trading Pattern and Turnover We analyze all institutional trades in a year (four quarters). We split up all trades in a year into several trading patterns based on the sign of change in the quarterly holdings of a particular stock. Hence, a trading pattern represents how an institution investor trades a particular stock within a year. Since Thomson Reuter s data fix the report date for a year at every March, June, September and December, we take every December of the previous year as the starting point and calculate the quarterly change of shareholdings of an institutional 0 To make sure that all shares in the 13f reports are adjusted for splits and special distributions we merge the 13f reports with CRSP monthly stock file dataset and use FDATE (file date in Thomson 13f dataset) and CRSP cumulative adjustment factors to make the adjustment. We also make similar adjustments for total number of shares outstanding and price sourced from CRSP.

23 investor for a particular stock for the next four quarters. We identify the following eight mutually exclusive trading patterns: (i) Buy-Sell-Buy (BSB), (ii) Sell-Buy-Sell (SBS), (iii) Sell-Buy (SB), (iv) Buy-Sell (BS), 1 (v) Hold-Hold-Hold (HHH), (vi) Buy-Buy-Buy (BBB), (vii) Sell-Sell-Sell (SSS), and finally (viii) Others (one occurrence of either Sell or Buy in the sequence). We require an institutional investor to hold the stock for four consecutive quarters for her trade sequence to be valid. For each stock, we calculate turnover ratio of each trading pattern identified in a year. The details are as follows: we firstly compute the annual trading volume of an institutional investor by summing the absolute value of the quarterly change in holding within a year (i.e., four quarters). Then for each stock, we aggregate the trading volume across all institutional investors engaging in a particular trading pattern, scaling it by the total number of shares outstanding at the end of each September (because we start with each December of the previous year, the ending quarter is September of each year). We repeat the same process for all the trading patterns and finally arrive at a dataset containing the turnover rate of each of the seven trading patterns for each stock, totaling 4,679 firm-years (covering 16 years from 199 to 007). We also construct a measure called InstTrade that represents the total institutional turnover by aggregating all the trading volume annually (regardless of the trading patterns) across all institutions, scaling it by its total number of shares outstanding. Panel B of Table I shows the average institutional ownership of the 13f institutions is about 60% in the year range, which is seven percentage point higher than a decade ago reported in Hartzel and Starks (003), using data. The ownership concentration of the top five institutions averages 4%, which is only slightly higher than a decade ago. The mean of total institutional turnover is about 3.5% with a standard deviation 1 Pattern (3) also includes both Sell-Buy-Hold and Hold-Sell-Buy sequences; pattern (4) also includes Buy- Sell-Hold and Hold-Buy-Sell sequences. We exclude the trading pattern, HHH, because there is no change in holdings, hence no turnover rate. 3

24 of 13% and the mean turnover of all the trading patterns is 3.5%, varying from 0.17% (the Sell-Buy pattern) to 11.7% (the Others pattern). B.3. Other Control Variables We include control variables widely used in the literature on managerial compensation. Ln_MktCap is the natural log of market value of equity, measured as the product of the number of shares outstanding and share price, both of which we source from CRSP. Firm size measured in this way is highly negatively associated with pay-performance sensitivity. While not surprising, it is actually support for the major prediction of the original HT model after correcting for HT s confusion between pay-performance sensitivity and performance due to equity (i.e. the difference between Proposition 4 and Proposition 4 (HT Version) above). The difference of MktCap between year t and year t-1, ΔMktCap, and the lagged value of ΔMktCap are included as per Hartzell and Starks (003) to control for change in shareholder value. We also include Debt_Ratio, computed as the ratio of total liabilities to total assets, for debt has been widely viewed as an alternative monitoring mechanism in principal-agent theory, and therefore can affect CEO incentives. Tobin_Q, defined as the ratio of the market value of assets 3 to the book value of total assets, is included as a popular proxy for the firm s growth opportunities in the literature. We compute the above two firm-level controls based on the Compustat dataset. We also include both the yearly buy-and-hold cumulative returns (CumRet) and standard deviation of market capitalization (Dol_Volat) because the former deals with the potential association between the firm s performance and CEO pay whereas the latter is highly related to the talent of CEO as per Sung and Swan (009). We compute both of them from CRSP. All the price level-related variables are CPI deflated (006 = 100). In all of our analyses, we also control for year and industry effects. Year dummy variables allow both PPS and other CEO pay component to vary year by year. They also control for 3 See Sung and Swan (009) for more details on the calculation of the market values of assets. 4

25 exogenous factors that may influence PPS and other CEO pay component, such as the overall market condition. Industry dummy variables act as fixed effects at the industry level. Our final unified dataset covers more than 77% of the firms in ExecuComp from 199 to 007, totaling 17,946 firm-years. We winsorize all the continuous variables at the 1% and 99% levels to mitigate the effect of extreme observations. 4 As can be seen from Panel C of Table I, the average annual stock return (buy-and-hold) is 17.7% with a standard deviation of nearly 49%. The standard deviation of market capitalization averages $,10 million. The debt ratio of all the firms in our sample is about one quarter and Tobin s Q is 1.8 on average. Finally, the mean (median) firm size is about $7.4 billion ($1.8 billion). III. Following Governance through Trading BSB and SBS as Swing Trades We follow GGS to identify institutional investors aiming to make trading profits rather than to extract private benefits from acquiring control of the firm or to gain from better governance of the firm. Of all the eight trading patterns, the sequence of a Buy, followed by a Sell, then a Buy ( BSB sequence) or a Sell, followed by a Buy, then a Sell ( SBS sequence) in a stock fits the characteristics of institutional investor monitoring best. Indeed, GGS show that these are profitable sequences even after transaction costs. These two sequences involve large swings (defined as the distance from the peak to trough in the holdings), suggesting institutional investors engaging in such trading are either constantly monitoring the CEO or are receiving strong signals regarding future firm value for other reasons. Either way, they are likely to have a strong trader informational advantage. Greater swing also implies higher trade aggressiveness as shown in equation ( 6) above, which in turn 4 There is a potential overlapping issue in merging CEO incentives-related data with institutional trading/ownership data and firm-level control variables, since ExcuComp is fiscal-year-based annual dataset (same as Compustat) and the Thomson 13f reports are a calendar-year-based quarterly dataset. We avoid this by selecting firms with fiscal year-end month in September, October, November, and December only. See Appendix B for further details. 5