- Email: [email protected]

Insider trading and managerial incentives Jie Hu

a,1

, Thomas H. Noe

b,*

a

b

Asia Fixed Income, Bank Boston, Central, Hong Kong A.B. Freeman School of Business, A.B. Freeman Chair of Finance, Tulane University, New Orleans, LA 70118-5996, USA Received 24 February 1999; accepted 24 January 2000

Abstract We derive conditions under which permitting manager ``insiders'' to trade on personal account increases the equilibrium level of output and the welfare of shareholders. These increases are produced by two eects of insider trading. First, insider trading impounds information about hidden managerial actions into asset prices. This impounding of information allows shareholders to make better personal portfolio-allocation decisions. Second, allowing insider trading can induce managers to increase, on average, the correlation between their personal wealth and ®rm value beyond the level dictated by the employment relationship alone. This increased correlation increases managerial incentives. When these two eects are only weakly present, permitting insider trading harms shareholders, because insider trading reduces shareholder control over the performance±compensation relationship. In addition, when managerial eort incentives are high and corporate governance costs are low, managers may prefer insider-trading restrictions because such restrictions force shareholders to oer them a larger fraction of output through the employment relationship. Ó 2001 Elsevier Science B.V. All rights reserved. JEL classi®cation: D23; D82; G38 Keywords: Agency; Insider trading; Regulation; Market eciency

*

Tel.: +1-504-865-5425; fax: +1-504-865-6751. E-mail addresses: [email protected] (J. Hu), [email protected] (T.H. Noe). 1 Tel.: +852-2867-7651. 0378-4266/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 4 2 6 6 ( 0 0 ) 0 0 0 9 8 - 4

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1. Introduction Securities trading by corporate ocers has become one of the most heavily regulated capital market transactions. The securities and exchange (SEC) Act of 1933, as interpreted by the Supreme Court in cases such as Speed v. Transamerica Corporation, places broad prohibitions on trading by corporate insiders who use ®rm-speci®c private information. More recent legislative initiatives, such as the Insider Trading and Securities Fraud Enforcement Act of 1984, have forti®ed this prohibition. Not surprisingly, the rationale for this elaborate structure of regulation has received signi®cant attention from both ®nancial economists and legal scholars. Much of this attention has been provided by the ``law and economics'' scholars. For the most part, these scholars have viewed insider trading prohibitions unfavorably. This view ®nds its classic expression in the work of Manne (1966). One Manne's for allowing insider trading is that such trading allows the information possessed by insiders to be rapidly impounded in the prices of securities and thus increases the eciency of capital markets. The importance of this argument is evidenced by its profound impact on subsequent research into insider trading. Another aspect of Manne's discussion has received considerably less analytical attention: the eect of security market transactions on managerial incentives and agency problems within the corporation. According to Manne, and to other adherents of the law and economics school, security trading can improve the alignment of interests between outside claimants and management by allowing managers to pro®t from the appreciation in ®rm value engendered by their eorts. Much of the subsequent literature on insider trading has been devoted to examining the arguments of Manne in a rigorous analytical fashion. The results of these analyses have not, in general, been supportive of Manne's conclusions. For example, Fishman and Hagerty (1992) show that insider trading may discourage the production of information by outside analysts and thus reduce the net informational eciency of stock markets. It has also been demonstrated by Ausubel (1990) and Manove (1989) that, even in the absence of this eect, the adverse selection costs for outsiders engendered by insider trading make the raising of external ®nance more costly for outside investors. Manne's second argument in favor of insider trading also has been critiqued in Noe (1997) who demonstrates that, even if managerial short sales are prohibited, endogenous changes in the pattern of managerial compensation in response to a relaxation of insider trading restrictions may actually decrease the equilibrium level of managerial eort. This paper develops a model that links the moral hazard and informational transmission aspects of insider trading and shows that the bene®cial eects of insider trading, which are not entirely apparent when the informational and moral hazard arguments for insider trading are modeled separately, become

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apparent when the two problems are interlinked. More speci®cally, we show that when managers have private information about the scope of the private bene®ts they can earn from consuming perks and/or avoiding eort, permitting insider trading can both increase ®rm output and increase the welfare of shareholders. Shareholder welfare is improved through the following mechanism: permitting insider trading leads managers to take positions in the ®rm's stock. These positions are long when managerial compensation is a small fraction of ®rm value, and are short when compensation is a large fraction of ®rm value. The size of a manager's position is independent of her private information. To induce this uniform pattern of portfolio holdings across the range of private signals, share prices must vary with managers' information signal. Thus, managerial trading increases the informativeness of prices and the welfare of shareholders, and, when managers extract only a small fraction of ®rm value in explicit compensation, it also increases the fraction of the ®rm's value captured by managers. The above argument implies that, when projects have fairly low average eort costs and when forcing managers to pay out corporate cash ¯ows is not very costly, shareholders are able to grant managers only a small fraction of ®rm value in explicit compensation and rely on insider trading to induce large managerial shareholdings. These shareholdings, in turn, augment a manager's incentive to increase output. In this scenario, permitting insider trading increases shareholder welfare for two reasons: It both provides low-cost incentives for managerial eort and makes prices more informative. When forcing cash payouts is very costly and applying eort to the project is also costly, insider trading also improves owner welfare. In this case, owners recognize that, regardless of the insider trading regime, they will be able to extract only a small fraction of the ®rm's output for themselves. By permitting insider trading, owners can at least reduce their exposure to the risks associated with the manager's private information. Permitting insider trading is disadvantageous only when eort is fairly sensitive to the exact fraction of ®rm output captured by management. In this case, the short positions insiders may optimally take in their capital market transactions negate some of the incentive eects of the managerial compensation, adversely aecting eort. If this eect is substantial enough, it can more than compensate for the positive impact of insider trading on price informativeness. The eect of insider trading on managerial welfare is somewhat at odds with its eect on shareholder welfare. When governance costs are low and insider trading is permitted, shareholders will attempt to capture almost all ®rm value by oering managers little explicit compensation. In essence, shareholders will simply compensate managers by giving them insider trading rights. If insider trading is legally prohibited, then shareholders, deprived of this compensation option, are forced to oer more direct compensation to assure eort. Thus, the ability of shareholders to substitute insider

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trading opportunities for direct compensation may adversely aect managerial welfare and lead managers to prefer, ex ante, to be deprived of insider trading opportunities by the state. These results are related to, but do not overlap, the results of a number of recent papers on insider trading. Bebchuk and Fershtman (1994) also consider the consequences of insider trading for managerial behavior. They show that insider trading opportunities encourage managers to increase project risk. Our work diers from Bebchuk and Fershtman's in three important respects. First, we model a costly eort decision by the manager, rather than a costless choice of project variance. Second, we assume that shareholders as well as managers are risk averse, while Bebchuk and Fershtman assume that shareholders are risk neutral. Third, we model the process of price determination. Bebchuk and Fershtman, in contrast, assume that insiders capture an exogenously speci®ed fraction of the dierence between true and expected project value. These differences between our analysis and Bebchuk and Fershtman (1994) naturally lead to our, generally more favorable, assessment of insider trading. First, in our setting, insider trading can improve managerial motivation. In fact, the improvement of managerial incentives is one of the two important eects of insider trading that we identify. This is precisely the eort-increasing eect of insider trading originally identi®ed by Manne (1966). In contrast, Bebchuk and Fershtman do not model eort choices or eort-motivation problems. An equally important point of dierence between our model and Bebchuk and Fershtman's is that, in our model, the manager's information signal and eort are complementary inputs to the production process (i.e., they have positive cross derivatives). This complementarity between information and eort ensures that, in equilibrium, eort and the information are positively related. Because eort increases value, the positive relationship between eort and information implies a positive relationship between private information and ®rm value. This monotonicity, plus rational expectations, permits market prices to impound private information regarding ®rm value. Thus, when trade is permitted, market participants can infer the manager's private information from market prices and thus better infer ®rm value. Because we assume shareholders are risk averse, in our analysis, the increased informativeness of prices permits welfare increasing portfolio allocations. In contrast, in Bebchuk and Fershtman, shareholders are risk neutral and so are indierent across all portfolio allocations at equilibrium prices. Thus, the portfolio bene®t from insider trading is absent in their analysis. Our work is also related to Shin (1996) analysis in that it focuses on the optimal regulation of insider trading. However, the trade-os determining optimal regulatory policy in our analysis dier considerably from those in Shin. In our analysis, all gains and losses from insider trading are absorbed by insider managers and shareholders. In Shin's, an exogenous group of liquidity traders subsidize insider trading through their trading losses. Thus, Shin's

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objective function for determining optimal insider trading policies ± minimizing the losses of liquidity traders ± has no analog in our framework. In addition, he considers market structure variables, while we consider the sort of ®rm-speci®c variables typically utilized in corporate-®nance research. In summary, there are three key features in our modeling setup that together account for the dierence between our evaluation of insider trading and the results of earlier authors. First, managers' interests are not aligned with shareholders'. Second, private information is related to the degree of misalignment. Third, information about the degree of misalignment, per se (independent of potential use of the information to correct misalignment) has value to shareholders. Our speci®c model incorporates these three key features by postulating eort-averse managers, complementarity between eort aversion and the private signal, and risk averse shareholders. Our analysis can be generalized beyond these speci®c assumptions, but only to the extent that the three features are preserved. The paper is organized as follows. Section 2 develops our basic model of compensation and managerial eort in the absence of insider trading. This model is developed in a setting imposing only fairly general restrictions on preferences and production technologies. Section 3 develops a parametric rational expectations model of insider trading. Section 4 determines the optimal investment in governance both in the presence and absence of insider trading opportunities. Section 5 considers the eect of insider trading on the ex ante welfare of shareholders and identi®es those parameterizations of the model under which insider trading increases shareholder welfare. Section 6 provides a graphical welfare analysis of the eects of insider trading on managerial welfare, shareholder welfare, and economic eciency. Section 7 presents some concluding remarks. 2. Basic model First, we delineate a three-date model of manager-shareholder interaction. At date 1, the ®rm is owned by a single shareholder and managed by a manager. At this date, the shareholder makes a decision regarding an investment in a governance technology. The signi®cance of this decision will be explained later. At date 0, the manager makes an eort decision, e. Later, we shall incorporate an opportunity for the manager and the shareholder to trade securities at date 0 into the basic, no-trade scenario outlined here. The manager's decision will aect the date 1 value, V, of the ®rm. This value is then divided between the shareholder and the manager. We assume that the division of value between shareholder and manager is determined by the following reduced-form speci®cation: For the shareholder to capture a fraction 1 b of total ®rm value, the shareholder must make an

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investment of c b; c in corporate governance, where b is the fraction of value captured by the manager, and c is a parameter representing the cost of governance. We assume that the governance technology function is smooth and, in addition, impose the following restrictions on its functional form (see Fig. 1): G1

a 8c P 0; c b 1; c 0;

b

d 8b 2 0; 1; c b; c 0 0;

o c < 0; ob e

c

o c > 0; ob2

o c > 0; oc f

o c < 0: oboc

The assumptions imply that: (a) if the ®rm is willing to concede all value to the manager, i.e., set b equal to 1, then governance is free; (b) increasing the fraction of value conceded to the manager lowers the cost of governance; (c) increasing the governance cost parameter, c, increases the cost of governance; (d) if the governance cost parameter equals zero, the cost of governance is zero; (e) the marginal cost function is convex; (f) the marginal impact of increasing governance costs falls as the fraction of value conceded to the manager increases. A special case of our analysis is when c 0, in which case c b; 0 0 for all b 2 0; 1. Here, no investment need be made by the shareholder to capture ®rm value. This case represents a situation in which any fractional

Fig. 1. Optimal investment in the governance technology and the quality of governance technology. Note: In this diagram, the average managerial eort preference parameter, r, and variance of the managerial eort preference parameter, r2r , are both ®xed at 1. The parameter representing costs of governance, c, is plotted over its admissible range, 0; 4. As the graph illustrates, when the governance technology is very ecient or very inecient, the optimal dollar investment in governance is small.

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allocation of value between shareholders and managers can be costlessly implemented through contracts. Costless contracting is a special case of our analysis, but we also allow for costly contracting, i.e., for c > 0. Our costly contracting speci®cation is consistent with the incomplete contracts view of manager±shareholder relations (e.g., Aghion et al., 1994). There are a number of models of managerial compensation under incomplete contracting, whose exact results will depend on the speci®c way renegotiation is modeled. However, it is possible to generate incomplete contracting models consistent with our reduced form model of contracting costs. Consider the following incomplete contracting scenario: Suppose that the manager has the opportunity to renegotiate the terms of her contract after she has determined her eort level. The manager's negotiating position is based on the fact that she possesses ®rm-speci®c skills that render the value of the ®rm without the manager 1 bV , which is less than its value with the manager, V. Suppose that the manager makes a ®rst-and-®nal proposal to the shareholder for dividing output. This bargaining assumption ensures that the shareholder will receive nothing more than the value of the ®rm without the manager's ®rm-speci®c skills, 1 bV . Further assume that b is in¯uenced by the shareholder's up-front investment in a technology that increases the ``replaceability'' of the manager. This model yields the allocation produced by the reduced form costly contracting function, with the manager receiving the fraction b of total output and the shareholder paying c b; c at time 1 for the corporate governance technology. Another interpretation consistent with our formulation is that b represents the fraction of cash ¯ows that, although observed by both the manager and shareholder, cannot be veri®ed by third parties such as the legal system. These cash ¯ows can be expropriated by managers. Investment in the governance technology increases the fraction of cash ¯ows that are veri®able. 2 Firms invest in governance technologies in a number of ways, e.g., increasing the number of outside directors, improving cost accounting systems, and investing in extensive management development systems that make current top management easier to replace. Contrete examples can be found thorughout the history of industrial capitalism. One example of investment in governance technologies is provided by the choice of investment banker by American ®rms in the 1890s. Corporations choose between underwriters who performed no monitoring activities such as Kuhn and Loeb, on the one hand or J.P. Morgan on the other hand. J.P. Morgan, the most expensive underwriter, imposed extensive monitoring requirements on the ®rms (see Ramirez, 1995) through the appointment of ``Morgan Men'' to the board. Another interesting concrete

2 See Hart (1988) for a discussion of the importance of observable but unveri®able cash ¯ows in the structuring of corporate governance.

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example comes German ®rms in the 1990s. These German ®rms (e.g., Bayer, Daimler-Benz, Deutsche Bank and Hoechst) adopted the extensive reporting requirements of US Accounting Standards (GAAP) (Evans, 1996). These companies stated explicitly that the purpose of adopting GAAP was to increase transparency of ®rm cash ¯ow to outsiders. As we explained in the previous paragraph, increases in transparency increase veri®ability and thus reduce managerial perk consumption. In summary, if we adopt an incomplete, costly contracts view, the shareholder who invests neither in making the manager replaceable, nor in mechanisms to unseat the manager, nor in mechanisms to verify cash ¯ows, will not receive a signi®cant fraction of ®rm output. Our analysis will be consistent with this incomplete contracts perspective when we assume that c > 0. In contrast, our analysis will be consistent with the complete contracts view of the world when we assume c 0. Both complete, or ``costless contracting'' and incomplete, or ``costly contracting'' are thus consistent with the reduced-form cost function we employ. Not only do we allow for both perspectives, but we also demonstrate in subsequent sections that the contracting technology is an important variable in our comparative statics. Costly contracting is important because it sets up a trade-o between managerial private bene®ts and the shareholders' share of ®rm value. As the shareholders' share of ®rm value is increased through the imposition of costly governance technology, managers respond by increasing their consumption of the private bene®t of reduced effort. Thus, tightening governance has adverse consequences both directly through increased direct costs and indirectly through managers diverting their eorts away from corporate activities. However, although governance technology may shrink the overall corporate value through these two eects, it increases the fraction of value captured by shareholders. The timing of events is displayed below. Date

1

The shareholder makes an investment in governance technology, c.

Date 0

Date 1

Manager makes unobservable eort decision, e. If ®nancial markets are open, manager and shareholder also make trading decisions.

Value, V, is observed and divided.

The terminal value received by the manager is thus given by bV . We assume that, at date 0, when the manager makes her eort decision, V is a random variable that is positively dependent on managerial eort. More speci®cally, we assume that V V e e N~ , where N~ is a zero-mean, ®nite variance, random variable. The manager makes her eort decision based on utility maximization. We assume that the manager maximizes an expected utility function, u. The

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manager's payo depends on the sum of monetary payos, x, and private bene®ts from eort given by an eort-preference function, /. These bene®ts can be either positive or negative and depend on both the manager's eort level, e, and an eort preference parameter that we will term r. The manager's utility, for a given realization of uncertainty, is thus given by u / r; e x, r; e; x 2 R3 . We impose the following additional restrictions on the expectedutility function: G2

a u0 > 0;

b u00 6 0:

Assumption (G2) implies that the manager's expected utility function is (a) monotonically increasing and (b) weakly concave. The relationship between the eort preference parameter and eort is restricted by the following assumptions: G3

a

o/ > 0; oroe

b

o/ < 0; oe2

c

o/ P 0: oe3

Assumption (G3) ensures that (a) the marginal bene®t of providing eort increases as the eort parameter increases, i.e., eort, e, and r are complements; (b) the marginal bene®t of providing eort is falling in the level of eort; and (c) the marginal bene®t of eort is weakly convex in the eort level. Assumption (c) is a technical restriction that will be used in the subsequent analysis only to ensure uniqueness of the optimal shareholder governance policies. The variation in the marginal cost of providing eort implied by the variations in r can arise from a number of dierent sources. For example, managers may vary in the degree to which they have pro®table alternative activities. Those managers with more pro®table outside options will have a higher cost of applying eort to corporate projects. Dierences in ability can also generate variation with higher-ability managers ®nding it easier to apply a given level of eort. On the other hand, r can capture characteristics of the project itself, with some projects imposing lower eort costs than others. Regardless of the interpretation, at a technical level, complementarity between marginal eort costs and r is a sine qua non for producing the subsequent results. All of the factors noted above, eort preferences, non-pecuniary bene®ts, and the eort costs associate with speci®c projects, are likely to be only imperfectly understood by the shareholder. We capture shareholder uncertainty regarding these trade-os by assuming that r is random from the perspective of the shareholder. For simplicity, in the future, we will simply refer to r as the manager's eort preference parameter. Because the random end-of-period cash ¯ow received by the manager is given by bV~ b e N~ , we see that the manager's utility, U, as a function of her eort level (e), and the fraction of the total cash ¯ow she appropriates (b), and the managerial eort preference parameter (r), is given by

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G4

h i U r; e; b E ufb e N~ / r; eg :

2.1. The manager's eort decision The manager's eort problem is, thus, max U r; e; b: e2R

The ®rst-order condition for this problem is o U r; e ; b 0: oe

1

Substituting (G4) into (1) yields the following necessary condition for an optimal eort level: h i o / r; e b E u0 fb e N~ / r; eg 0: oe Because u0 > 0 by (G2(a)), the ®rst-order condition can be simpli®ed to o / r; e b 0: oe

2

Assumption (G3(b)) implies that any solution to (2) in fact maximizes managerial utility. This ®rst-order condition permits a complete characterization of managerial eort in a fairly general setting. This characterization is developed in the following lemma. Lemma 1. Managerial effort is increasing in r, the managerial effort preference parameter, and is increasing in b, the fraction of output captured by the manager. Proof. This result follows directly from the implicit function theorem, the ®rstorder condition, Eq. (2), and Assumptions (G2(a)) and (G2(b)). 2.2. Shareholder policies Next, note that our Assumption (G2(b)) ensures that the map e ! o=oe/ e; r is strictly increasing and thus invertible. Thus, a well-de®ned function, which we will call e ; , relates r and b to the level of managerial eort. By Lemma 1 this function is smooth and increasing in r and in b. The shareholder, recognizing the relationship between her choice of b and managerial eort, determines corporate policy. The shareholder maximizes ex ante (i.e., date 1) wealth over choices of b. Because the shareholder has incomplete information regarding the manager's eort preference parameter, r, from the shareholder's perspective, this parameter is a random variable.

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Further, we assume that shareholder preferences are consistent with expected utility maximization with an utility-of-wealth function, v, where v satis®es the following conditions: G5

a v0 > 0;

b v00 < 0:

(G5) implies that (a) shareholders have strictly increasing utility of wealth and are (b) strictly risk averse. The shareholder determines b at date 1. Thus, the utility of the shareholder at date 0 is given as follows: G6

WN b Evf 1

b e ~ r; b N~

c b; cg:

The shareholder's problem is given as follows: max WN b:

b20;1

We focus on interior solutions to this problem. Such solutions are characterized by the ®rst-order condition: o ~0 ~ 0 P v fP g 0; WN b E 3 ob r; b N~ c b ; c; 4 P~ 1 b e ~ o ~ o o c b ; c: P e ~ r; b N~ 1 b e ~ r; b 5 ob ob ob Dierentiating the objective function again yields " # 2 o ~ o ~0 ~ 00 00 ~ P v fP g E P v WN b E f P g ; ob ob2 o ~ P 1 ob2

b

o e ob2

o e ob

o c: ob2

6 7

Assumption (G5(b)) ensures that the ®rst term in (6) is negative. Assumption (G3(c)) ensures that 1 b o=ob2 be 6 0; Lemma 1 ensures that the other two terms in expression (7) are negative. Thus, o=ob2 bP~ < 0; Assumption (G5(a)) implies that v0 > 0. Thus, the second term on the right-hand side of (6) is also negative. Thus, WN00 b < 0. This implies that all solutions of the ®rst-order condition maximize WN and, moreover, any such solution is unique. 2.3. Comparative statics when insider trading is prohibited In contrast to the straightforward comparative statics of the manager's effort selection problem, the comparative statics of the shareholder's problem are subtle. It is not possible to obtain monotone comparative statics without imposing more structure on the shareholder's problem. Two of the problems

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hindering comparative static analysis are (a) the nonlinear transformation of eort-preference uncertainty induced by the optimal eort function, e , and (b) the eect of wealth shifts on the level of shareholder risk aversion. Because the map ~ r ! e ~ r; b is, in general, nonlinear, and because the degree of nonlinearity can be aected by b, shifts in b, as well as aecting expected eort levels, can also increase or decrease the variance of eort, which, through shareholder risk aversion, aects the shareholder's valuation of the project. To obtain monotone comparative statics, we must abstract from these eects. Thus, henceforth we impose the following quadratic functional form on the managerial eort function: QE

/ r; e re

e2 :

By expression (2), under (QE), the equilibrium eort level for the manager is given as follows: 1 e b r: 2

8

Without imposing a quadratic eort function, monotone comparative statics cannot be produced. The second obstacle to monotone comparative statics is the eect of wealth shifts on risk aversion levels. Such eects can produce highly counterintutive results. For example, suppose shareholder risk aversion is increasing in wealth. In this case, increased governance costs, by lowering shareholder wealth, increase the value of the risky ®rm cash ¯ows. This, in turn, increases the shareholder's desired fraction of ®rm output. Thus, increases in the cost of capturing rents can lead the shareholder to increase the fraction of rents she captures. This rather odd result is ruled out if we impose the following restriction on shareholder preferences: Shareholder risk aversion is nonincreasing, i.e., the shareholder's Arrow±Pratt risk aversion, DARA

a w

v00 w=v0 w; is nonincreasing in w:

Under these two assumptions, we can report the following comparative static. Theorem 1. Suppose the managerial effort cost function is quadratic and the shareholder exhibits nonincreasing absolute risk aversion, then (a) increases in the cost of governance parameter, c, increase the fraction of value conceded to the manager, b , and (b) an upward shift in mean effort preference, r E~r, decreases the fraction of value conceded to the manager. If, in addition, the shareholder exhibits constant absolute risk aversion, then (c) increasing uncertainty regarding managerial effort preferences increases the fraction of value the shareholder concedes to the manager. Proof. First consider (a). By the implicit function theorem, the sign of db =dc equals the sign of o=obocbcWN . Next note that

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o o o ~ 0 o ~ 00 WN P E v fP g P~E P v fP g ; oboc oboc oc ob o ~ P oboc o ~ P oc

o c; oboc o c: oc

693

9 10 11

Note that, by Assumption (G1(f)), o=obocbcP~ > 0; by Assumption (G5(a)), v0 > 0. Thus, Ev0 fP g > 0. These observations imply that o ~ 0 P Ev fP g > 0: oboc

12

By (G1(c)), o ~ P < 0: oc

13

From the de®nition of o=obocbcWN given in (9) and (13), we see that if we can show that E

o ~ 00 P v fP g < 0; ob

14

we will have established that o ~ o ~ 00 PE P v fP g > 0: oboc ob

15

If (15) holds, then (9) and (12) imply that o=obocbcWN > 0, and result (a) is established. Thus, to complete the proof we need only show that (14) holds. The proof that (14) holds is tedious. 3 However, it is straightforward. To initiate the proof that (14) holds, note that v00 v0 a, where a is the Arrow±Pratt risk aversion coecient de®ned in expression (DARA) above. Our assumption of quadratic eort costs (QE) implies that o=obbe 12. Thus, from expressions (4) and (5), we see that, under the quadratic functional form (14) can be reexpressed as follows:

3

The proof is similar structurally to the proof of Arrow (1965), Appendix, Section 4.

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h o ~ 00 P v fP g E X~ ob 1 X~ ~ r N~ ; 2 1 o b c; y 2 ob 1 z 1 b b c : 2 E

y v0 f 1

i b X~ zg ;

b X~ zgaf 1

16 17 18 19

By our Assumption (DARA) that risk aversion is nonincreasing, af 1 b X~ zg 6 af 1 b y zg whenever X~ P y. Thus, for X~ P y, we have, because X~ y P 0 and v0 > 0 by Assumption (G5(a)), that X~

yv0 f 1 b X~ zgaf 1 b X~ zg 6 X~ y v0 f 1 b X~ zgaf 1 b y zg;

X~ P y:

20

Again, by (DARA), af 1 b X~ zg > af 1 b y zg whenever X~ < y. Thus, for X~ > y, we have, because X~ y < 0 and v0 > 0, X~

yv0 f 1 b X~ zgaf 1 b X~ zg 6 X~ yv0 f 1 b X~ zgaf 1 b y zg;

X~ < y:

Next, note that (20) and (21) together imply that h i E X~ yv0 f 1 b X~ zgaf 1 b X~ zg h i 6 E X~ yv0 f 1 b X~ zg af 1 b y zg:

21

22

Note that, by the fact that the ®rst-order condition, expression (3), holds, h i E X~ yv0 f 1 b X~ zg 0: 23 Thus, by expressions (23) and (22), we can conclude that h i E X~ yv0 f 1 b X~ zgaf 1 b X~ zg 6 0:

24

Expressions (24) and (16) establish (14), which in turn establishes part (a) of Lemma 1. ~ where d~ is a zero mean random variNext, we establish (b). Let r~ r d, able. We aim to show that db =d r < 0. To establish this result, ®rst note that, by the implicit function theorem, the sign of db =dr equals the sign of o=obo rb rWN . Next note that

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o o ~ 0 o o ~ 00 WN P Ev fP g P~E P v fP g ; obo r obo r o r ob o ~ 1 P ; obo r 2 o ~ 1 P 1 b : o r 2

695

25 26 27

The result that db =d r < 0 thus follows from expressions (14), (G5(a)), (26) and (27). Next consider (c). The assumption of constant absolute risk aversion implies an exponential form for the shareholder's utility function. Using the exponential form of v0 , we can reexpress the ®rst-order condition as E y

X~ v0 f 1

b X~ g 0:

28

Consider the eect of increasing uncertainty regarding the managerial eort parameter by replacing the random variable representing uncertainty regarding managerial preferences, r~, with ~ r0 r~ g~, where g~ is independent of both the ~ noise in output term N and of the original managerial preference variable r~. Note that given the quadratic cost of eort speci®cation, managerial eort under ~ r0 will shift by 12 g~ from its level under ~r. For this proof only, de®ne the function f by 1 1 0 ~ ~ f b E y X g~ v 1 b X g~ : 29 2 2 Note that the optimal level of b under r~0 , which we represent by b0 , is implicitly determined by the equation f b0 0. Note also that our earlier result showing the uniqueness of an interior maxima for the shareholder's choice of b implies that f has at most one root and is greater than 0 for all values of beta less than the root. Thus, if we can show that f b > 0, we shall have shown that b0 > b . To establish that b0 > b , note that 1 1 f b E y X~ g~ v0 1 b X~ g~ 30 2 2 1 31 E y X~ v0 f 1 b X~ gv0 1 b g~ 2 1 0 1 gv f 1 b X~ gv0 1 b g~ : 32 E 2 2 Because g~ and X~ are independent and v0 is exponential, the term given by expression (31) can be expressed as h i ~ 1 0 0 ~ E y X v f 1 b X g E v 1 b g~ : 33 2

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By the ®rst-order condition, Eq. (28), the ®rst expectation vanishes. Thus from (33) we can conclude that 1 E y X~ v0 f 1 b X~ gv0 1 b g~ 0: 34 2 Next consider the second term, given by (32). Because the expectation of g~ 0, o 1 0n ~ 1 0 gv 1 b X v 1 b g~ E 2 2 1 1 Cov g; v0 1 b X~ g~ : 35 2 2 By independence, and by the fact that the ®rst term in the covariance expression is increasing in g and the second term is decreasing in g, Cov < 0, implying that 12 Cov > 0. Thus expression (35) is positive, which implies, when (35) is combined with (31), (32) and (34), that f b > 0. This establishes result (c). The intuition behind Theorem 1 is straightforward. An increase in the costs of monitoring has two eects on the shareholder ± (a) it lowers her wealth and it makes extracting value from the project more costly. Assuming that risk aversion is nonincreasing, the wealth eect (weakly) increases risk aversion and thus reduces the desirability of the risky cash ¯ows from the project. This eect, combined with the increased cost of extracting project cash ¯ows, leads the shareholder to cede a larger fraction of cash ¯ows to the manager. The intuition for (b) is very similar. Increasing the manager's average eort preference raises shareholder wealth and makes project investment more attractive. Thus, such increases lead the shareholder to adjust upward the fraction of project rents she attempts to capture. The comparative static relating to increased uncertainty regarding managerial eort is a bit more subtle. Increased uncertainty regarding the manager's eort preferences (a) spreads the distribution of shareholder wealth and thus the range of risk aversion levels at which investment in the project is evaluated; at the same time, increased uncertainty (b) lowers the value of the project. If we bracket out wealth eects on the level of risk aversion by assuming constant absolute risk aversion, then eect (b) leads the shareholder to increase the fraction of project value she concedes to the manager. However, without controlling for wealth eects, determinate comparative statics are not possible. 3. Insider trading in a rational expectations equilibrium In this section, we solve for the rational expectations equilibrium in ®nancial claims market when both the manager and the shareholder can trade claims on

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®rm output. In this market, claims on the ®rm's stock, along with a riskless bond, trade on an anonymous securities market. The price of the riskless bond and the ®rm's stock are observable at date 0. Moreover, agents can condition their asset demands and eort decisions on these prices. Rational expectations characterize equilibrium in the securities market at date 0. 4 We consider the trading/eort decision for a ®xed investment in the corporate governance technology. Speci®cally, we assume that the ®rm has one share outstanding and let hm hs be the net trade by manager (shareholder). The total date 1 payo to the manager is thus given by bV hm 1

bV

P :

The payo to the shareholder at date 1 is 1 hs 1

bV

hs P :

The date 0 market clearing price in the capital market is determined via a rational expectations equilibrium: agents take the price as given; the shareholder conjectures a relationship between P and the equilibrium managerial eort level, e ; the manager maximizes simultaneously over eort, e, and portfolio holdings, hm given her private information regarding the eortpreference parameter, r~. In equilibrium, the shareholder's conjectures are con®rmed and markets clear; that is, net trades in the stock sum to zero. Thus, a rational expectations equilibrium consists of trading strategies of the manager hm and the shareholder hs , and an eort strategy for the manager, e . These strategies are functions of the agent's private information and market prices. A rational expectations equilibrium is thus triple hm ; hs ; e ; P~, satisfying the following conditions: h SR hs P 2 argmaxh E vf 1 h 1 bV~ e ~r i hP c b; cgjP~ P 8P ; MR

MC

h n e r; P ; hs r; P 2 argmax e;h E u bV~ e o i h 1 bV~ e P / r; e jP~ P 0 hs P~ hm ~ r; P~;

8 r; P ;

w:p:1:

In a rational expectations equilibrium, market clearing requires that prices adjust to re¯ect the manager's portfolio demand. The shareholder's portfolio 4

By using a rational expectations CARA-Normal framework to analyze insider trading, we follow Leland (1992) and diverge from Shin (1996) and Noe (1997), who use a market microstructure model featuring uninformed liquidity traders with exogenous security demands.

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decision in turn depends on the manager's eort decision, because this decision aects the risk±return trade-o for stock ownership. The shareholder uses the relationship between price and managerial eort to infer the level of managerial eort. As can be seen from the above discussion, in order for the price-inference problem to be tractable, we need to ensure that (a) risky asset demand be related to prices and private information in straightforward fashion and (b) the value-to-price relationship be tractable. Virtually the entire rational expectations literature, including all such literature on insider trading, has accomplished these objectives by assuming that random payos are normally distributed and that all agents have constant absolute risk aversion utility functions. Therefore, from this point forward, we work with a parametric rational expectations model in which the following parametric restrictions are imposed in addition to the general model Assumptions (G1)±(G5), and the quadratic eort preference function Assumption (QE): P1 P2 P3

u w v w e w ; r~ is normally distributed with mean r and variance rr ; N~ is a unit normal random variable:

Assumption (P1) implies that both shareholder and manager have constant absolute risk aversion utility-of-wealth functions, with absolute risk aversion level of 1. Assumptions (P2) and (P3) ensure that all uncertainty arises from normally distributed random variables. The assumption of quadratic eort costs ensures that the eort-choice function transforms eort preferences into eort choices in a linear fashion and thus preserves normality. These assumptions ®t our analysis in the standard CARA-Normal rational expectations framework. Under (P1)±(P3), and assuming trade is permitted, the manager's utility is given by h n oi U T hm ; e; r; P ; b E exp re bV~ e hm 1 bV~ e P e2 : The manager's optimization problem (MR) thus becomes MTP

max UT e; hm ; r; b; P :

hm ;e2R2

Solving this simple optimization problem for an arbitrary choice of b 2 0; 1 yields the following optimal eort/trading decision: MET-e

e r; P r

MET-t

hm r; P

P 1

b

;

r 1

2P b

1

b

b 2

1

b

:

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699

Next let RP represent the risk premium on the stock, i.e., the dierence between the expected payout to shareholder and the market price of the stock. By our assumption that the total payo to the ®rm is V e N~ , and the fact that the manager extracts b fraction of the ®rm through the employment relationship, RP, the expected payo to the stock equals 1 be . Thus, the risk premium is given by e 1 b P . Substituting (MET-a) into (MET-t) and using this de®nition of the risk premium, yields the following expression for the managerial trade vector: 2 1 b : RP T-M hm 1 b 1 b Expression (T-M) is fairly intuitive. If the risk premium is 0, the manager will hedge all the risk associated with the b share of value she receives from employment by selling b= 1 b of the ®rm's shares. As the risk premium increases, so does the manager's net trade vector. Thus, any eort and trade strategies for the manager satisfying (MET-e) and (TM) must satisfy the general condition (MR) for managerial rationality in a rational expectations equilibrium. Next consider the problem of the shareholder. The shareholder maximizes her expected date 0 utility conditional on her information. The only information the shareholder has at date 0 that she can use to infer the manager's eort level is the clearing price, P. Assume, as we verify later, that a fully revealing rational expectations equilibrium exists. In such an equilibrium, price reveals managerial eort. Given the price conjecture, the manager's eort decision, e , is measurable with respect to the shareholder's information set. Thus, the shareholder's date 0 utility under the REE conjecture is h n oi E exp 1 b 1 hs V~ e hs P c b; c : Dierentiating this expression with respect to the shareholder's net trade, hs , yields the following necessary and sucient condition for an optimal net trade vector, hs : 1

be P 1 hs 1

2

b 0:

Thus, the optimal net trade vector for the shareholder is given by 2 1 be P 1 T-S hs 1 RP 1: 1 b 1 b2 Like expression (T-M), expression (T-S) is also fairly intuitive. If the risk premium is 0, the shareholder eliminates all risk exposure by selling her entire endowment of one unit of the ®rm's stock. As the risk premium increases, the shareholder increases her stock holdings. Any shareholder trading strategy satisfying (T-S) satis®es the sequential rationality condition for shareholder

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trades given by expression (SR). Note that the market clearing condition, (MC), combined with (T-S) and (T-M), implies that 2 1 1 : 02 RP 1 b 1 b Thus, in any rational expectations equilibrium, it must be the case that RP

1

b 2

:

From the de®nition of the risk premium, RP, this equation implies that the only possible rational expectations conjecture is REE

e

P 1

b

1 : 2

Next note that, under (REE), eort is a 1 1 function of the market price, P. Thus, our initial conjecture that price reveals eort is veri®ed. Because the other conditions for a rational expectations equilibrium, (T-M), (T-S), (MC), and (MET-e), were shown to be satis®ed in the process of constructing the equilibrium, we have established the existence of a rational expectations equilibrium. 4. Investment in the governance technology in the parametric model In this section, we characterize the optimal investment in corporate governance in the parametric framework speci®ed in the previous section. 4.1. Investment in governance without trade In Section 2.3, we provided a general characterization of shareholder policies in the absence of trading. However, because our results when trade is permitted are restricted by the parametric restrictions (P1)±(P3), and the quadratic eort preference assumption (QE), for comparison we need to derive speci®c function forms for agent payos in the absence of trade. To initiate this process, note that under (QE) the managerial eort decision is given by (8). Thus, for a ®xed r~, the date 1 payo to the shareholder (in utility terms) in the parametric model is given as follows: 1 2 exp c b; c 1 be ~ 1 b r; b : 2 Taking expectations over ~ r yields

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exp

1 c b; c 1 2

b b r

1 1 2

b

2

r2 1 r 4

701

:

Thus, the certainty equivalent of the shareholder's date 0 expected payo when managerial trading is not allowed is given as follows: 5 1 1 r2r 2 1 b 1 WN b c b; c 1 b b r : 36 2 2 4 Thus, the optimal policy for the shareholder when there are no trading opportunities is the solution to the problem NTP

max WN b:

b2 0;1

In order to gain insight into this maximization problem we dierentiate WN with respect to b. This dierentiation yields the following ®rst-order condition: 1 r2 o c b ; c 0: WN0 b 6 2r r2r b 2 r 37 4 ob 4 From the ®rst-order condition (37), the tradeos surrounding the optimal policy problem are apparent. First, note that even if contracting is costless (implying that c0 0), the optimal fraction of value to concede to the manager will still generally be interior. This follows because conceding value to the manager (increasing b) has the positive incentive eect of inducing the manager to work harder; this eect makes a positive b viable even in the absence of contracting costs. The incentive eect of increasing b is countered by the direct loss from conceding value to the manager. The tension between these two effects can yield an interior solution. Because the second derivative of WN0 is given by r2r o 00 WN b 2 c b; c < 0; 4 ob2 we see that the marginal bene®t of conceding value to the manager is strictly decreasing. Thus, under both costless and costly contracting, the optimal fraction of value to concede to the manager is unique. Qualitatively, the tradeos in the managerial compensation decision are clear from the expression (37). However, it is not possible to solve (37) explicitly for b , the optimal policy, without imposing additional assumptions on the cost-of-contracting 5

Henceforth, we measure payos using certainty equivalents rather than raw utilities. This is standard in CARA-Normal models. Because the certainty equivalent is an increasing function of utility, this approach produces equivalent inferences. The advantage of using certainty equivalents is that the expressions for the certainty equivalents are simpler than the expressions for raw utilities in the CARA-Normal setting.

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function c. To produce explicit solutions, we henceforth assume that the costof-contracting function technology has the following simple form: CF

c b; c

c log b; 4

0 6 c < 2 1 r:

The cost expression given by (CF) satis®es the general conditions imposed by assumption (G1). The parametric restriction c < 2 1 r is imposed to avoid corner solutions in which the technology is so inecient that shareholder utility is maximized by simply giving the project to the manager, i.e., setting b 1. Given the functional form speci®ed in (CF), characterizing the solution to this problem is a simple exercise. The required characterization is provided below. Theorem 2. The equilibrium fraction of firm value appropriated by the manager, b , when managerial insider trading is precluded, is given by q 2 2 6 r 2r 6 r2r 2r 4 8 r2r c r : bN 2 8 r2r Proof. The ®rst-order condition for (NTP) is r2r br 1 b c 1 b 1 0: 2 2 4b 4

38

The second-order condition is clearly satis®ed at any point satisfying the ®rstorder condition. The quadratic formula ensures that there exists a unique b 2 0; 1 satisfying (38). The characterization in Theorem 2 of bN also follows from the quadratic formula. 4.2. Investment in governance with trade Given the equilibrium date 1 trading and action decisions given by (T-M), (T-S) and (MET-e), the ex ante utility of the shareholder is given by 1 1 1 E exp r b c b; c : 1 b ~ 8 2 4 Taking expectations yields 1 1 1 exp r 1 b 1 8 2 8

b2 r2r

1 b c b; c : 4

Thus, the certainty equivalent of the shareholder's ex ante utility can be expressed as

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1 WT b r 1 2

b

1 1 8

1 2 b r2r b 4

1 8

c b; c:

703

39

The above problem is a simple optimization problem whose solution is characterized below. Theorem 3. The optimal policy when the shareholder permits the manager to engage in insider trading is given by bT 1 if c > 2r 1, and by bT

1

2 r r2r

q 2 1 2 r r2r 4cr2r 2r2r

;

otherwise. Proof. The proof is virtually identical to the proof of Theorem 2 and thus will be omitted. 4.3. Comparative statics when trading is permitted The comparative statics describing the eects of the three exogenous parameters, r, rr , and c, on the optimal policies followed by the ®rm are identical to those obtained when insider trading is prohibited. These comparative statics are required for comparisons with the no-trade analysis. Of course, because the rational expectations analysis required us to restrict our analysis to the CARANormal setting, the comparative statics are derived in a more restrictive setting than were the results for the no-trade case derived in Section 2.3. Because these comparative statics have been established only in a highly parameterized setting and because the intuition supporting them is identical to the intuition supporting more general comparative static analysis of the no-trade analysis, we will keep our discussion of these results brief. Lemma 2. When insider trading is permitted, increasing average managerial effort preference, r, increases the level of shareholder investment in the governance technology and the fraction of firm value captured by the shareholder. Increasing uncertainty regarding managerial effort preferences, rr , increases the optimal fraction of value captured by the shareholder and decreases investment in the governance technology. Reducing the efficacy of the governance technology (i.e., increasing c) decreases the fraction of firm value captured by shareholder and may increase or decrease investment in the governance technology. Proof. The proof is a straightforward application of the implicit function theorem and thus will be omitted.

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5. The eect of allowing insider trading on shareholder welfare The dierence in ex ante shareholder welfare when insider trading is permitted versus when it is prohibited is given by WN b

WT b

1 8

1 b 1 2

b

1 1 2

2

b

1 b 4

3 5 b 8 4

b2 : 40

Expression (40) is quadratic in b. 6 From the quadratic formula we see that (40) has two roots, one at b 12 and the other at b 34. This establishes the following basic characterization of the insider trading decision. Theorem 4. The firm will permit managerial insider trading if and only if it chooses an investment in the governance technology that induces either a large or small share of the firm value to be captured by the manager. That is, permitting insider trading is optimal if and only if the optimal fraction of value to concede to the manager, b , satisfies 12 6 b < 34. Theorem 3 follows from the trade-os between the two eects of insider trading: Trading impounds information and aects managerial rewards. When the fraction of value captured by the manager through employment, b, is very small, permitting insider trading induces the manager to increase her holdings in the ®rm. Thus, insider trading improves managerial incentives. Because the information eect of insider trading is always positive for the shareholder, in this low b case insider trading improves the welfare of the shareholder. As b increases to a moderate level, the incentive of the manager to increase her personal holding above and beyond that which she obtains from employment falls, and in fact the manager may start to use insider trading to liquidate his personal holding to lower risk. This attenuates eort incentives. Because in this intermediate b case, the shareholder is still endowed with a large fraction of the ®rm value, the loss from eort attenuation trumps their gains from increased price informativeness. Thus, for moderately high b, the shareholder gains from prohibiting managerial insider trading. As b becomes so high that the manager eectively owns the ®rm, the shareholder acquires most of her ownership in the ®rm through trading in the market. Trade prices impound the eort attenuation caused by permitting insider trading. Thus, the shareholder is not very concerned with the eort attenu6 Also note that because the cost-of-governance function, c , appears in both WN and WT , it cancels out in expression (40), which represents the dierence between these two functions. Thus, expression (40) holds independently of our speci®c assumptions regarding the functional form of the cost-of-governance function.

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ation eects of insider trading. Because, in equilibrium, she still ends up, thorough trade, owning a large fraction of the ®rm's shares, she nevertheless gains from price informativeness. In the high b case, then, permitting insider trading once again bene®ts the shareholder. 5.1. Comparative statics of the shareholder-preferred policy Our next result describes the shareholder's optimal compensation/insider trading policy as a function of the exogenous parameters of the model. Our basic result is that, when the shareholder optimizes over insider trading policies, the relationship between the fraction of value to concede to the manager, b, and the exogenous parameters of the model inherits monotonicity from the monotonicity of the relationship between b and the exogenous parameters found when the insider trading policy is ®xed. However, in contrast to the ®xed-regime case, when the ®rm is allowed to choose an insider trading policy, the b-parameter relationships are discontinuous at those levels of the parameters at which the optimal insider trading regime shifts. Such regime shifts always occur at some point when the mean managerial eort parameter is varied across its admissible range. However, regime shifts need not always occur with variations in the other parameters of the model. To formalize these ideas, we ®rst need to formalize the set of admissible parameters for the model. To this end, de®ne R C to represent the values of r c satisfying the admissibility condition 0 < c < 2 1 r. Thus, R and C represent the feasible range of the mean managerial eort, r, and the governance technology, c. The dependence of each of these sets on the value of the other parameter is suppressed in the notation. The basic comparative static result is given below. Lemma 3. (a) There exist r , r 2 R such that insider trading is prohibited if and only if r 2 r ; r . The fraction of the firm that the manager is permitted to appropriate, b , is a decreasing function of r. Further, this function is discontinuous at r and r . (b) There exist c , c 2 R such that insider trading is prohibited if and only if c 2 C \ c ; c . The fraction of the firm that the manager is permitted to appropriate is a decreasing function of c defined on C. Further, this function is discontinuous at c and c , whenever c , c 2 C. (c) There exist rr , rr 2 R such that insider trading is prohibited if and only if rr 2 0; 1 \ rr ; rr . The fraction of the firm that the manager is permitted to appropriate is a decreasing function of rr defined on 0; 1. Further, this function is discontinuous at rr and rr , whenever rr , rr 2 0; 1. Proof. We prove only (a) because the proofs for (b) and (c) are virtually identical. Let B : R ! 0; 1 represent the function that maps mean levels of managerial eort preference, r 2 R, into fractions of value to concede to the

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manager, b , under the optimal insider trading policy (dependence on the other parameters being suppressed in the notation for simplicity). Let BT : R ! 0; 1 represent the function that maps mean levels of managerial eort, r 2 R, into fractions of value to concede to the manager, b , when insider trading is permitted. De®ne BN : R ! 0; 1 analogously when insider trading is prohibited. Let WT ; r : 0; 1 ! R represent, for each ®xed r, the function mapping b into ex ante payo to the shareholder when insider trading is permitted. De®ne WN ; r : 0; 1 ! R analogously for the case where insider trading is not allowed, and de®ne W ; r : 0; 1 ! R by W b; r maxfWT b; r; WN b; rg. We ®rst show that B is 1 1. To see this, ®rst note that BN and BT depend continuously on r. Next, note that B never attains the values 12 or 34. To see this, note that if B 12, for example, then, because the ex ante wealth function under trade and no trade are the same at this point, we prove that BT BN 12. Thus, both ®rst-order conditions are satis®ed at this point, i.e., WT0 12 ; r WN0 12 ; r 0. Thus, WT0 12 ; r WN0 12 ; r 0. But this is impossible, as can be seen from inspecting the derivative of expression (40). A similar argument shows that B never attains the value 34. By Theorem 3, B r BT r whenever B r 2 0; 12 [ 34 ; 1, and B r 1 3 BN r whenever B r 2 2 ; 4. Moreover both BT and BN are decreasing. Thus, the only points at which B cannot be 1 1 are those points where the function attains the values 12 or 34. However our earlier argument shows that B never attains these values. Thus, B is a 1 1 function of r. Because B is not continuous, the fact that B is 1 1 does not prove that it is monotone. However, monotonicity results from the following argument. Let R0 f r 2 R : B r 2 12 ; 34g; let R f r 2 R : B r > 34g; let R fr 2 R : B r < 12g. Because B can have at most two points of discontinuity and is decreasing at continuity points, the sets R0 , R , and R are intervals because B r BN r; whenever r 2 R [ R , we have that R > R . As the union of the three intervals exhausts R, we must have that R P R0 P R . Thus, the function B is monotonically decreasing. Because both BN and BT converge to 1 as r # r and converge to 0 as r " 1, we have that R and R are both nonempty. Because B BT on R [ R and BT is a continuous function, we must also have that R0 is nonempty. For, if R0 were empty, then we would have that R R [ R and that B BT everywhere. But BT is continuous. Thus, if R0 were empty, B would never attain the values 12 ; 34, violating the intermediate-value property of continuous functions. A typical example of the functional relationship between the exogenous parameters, r, rr , and c, and the optimal insider trading /compensation policy for the ®rm is diagrammed in Figs. 2±4. Consistent with the results in the theorem, these relationships are monotonic but not continuous.

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Fig. 2. Optimal share of ®rm value to concede to the manager and optimal insider trading policy as a function of managerial eort preferences. Note: In this diagram, the optimal share of ®rm value to concede to the manager, b , and the optimal insider trading policy as a function of mean managerial eort preference, r, is plotted. In the plot, c is ®xed at 0.50 and r2r is ®xed at 1. The range of values over which permitting insider trading is optimal is given by the horizontal dotted lines.

Fig. 3. Optimal share of ®rm value to concede to the manager and optimal insider trading policy as a function of uncertainty regarding managerial eort preferences. Note: In this diagram, the optimal share of ®rm value to concede to the manager, b , and the optimal insider trading policy as a function of degrees of uncertainty regarding managerial eort preference, r2r , is plotted. In the plot, r is ®xed at 1.20 and c is ®xed at 0.50. The range of values over which permitting insider trading is optimal is given by the horizontal dotted lines.

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Fig. 4. Optimal share of ®rm value to concede to the manager and optimal insider trading policy as a function of the governance technology. Note: In this diagram, the optimal share of ®rm value to concede to the manager, b , and the optimal insider trading policy as a function of the costs of governance, c, is plotted. In the plot, r is ®xed at 1.00 and r2r is ®xed at 1. The range of values over which permitting insider trading is optimal is given by the horizontal dotted lines.

6. General welfare eects of insider trading The earlier analysis has identi®ed situations in which the welfare of owners is improved by permitting insider trading. If allowed to determine corporate insider trading policies, owners will permit insider trading under certain circumstances. Is it the case that allowing owners to determine insider trading policies improves overall welfare? To answer this question we need to consider both channels through which insider trading aects the welfare of each of the agents. Insider trading aects welfare in three ways: First, it in¯uences price informativeness; second, it in¯uences the manager's optimal eort decision and thus the level of output; third, it in¯uences the shareholder's optimal compensation policy, thereby aecting investment in the governance technology and the division of output between the ®rm and the manager. The eects of permitting insider trading, both on price informativeness and on eort incentives, are the two eects considered in the classical law-and-economics defense of insider trading. We can see that the eect of insider trading on price informativeness is positive, almost by de®nition, in our rational expectations model of capital markets. The eect of insider trading on eort incentives, given a ®xed investment in the governance technology resulting in the fraction b of ®rm value accruing to the manager, is given by 12 b. This implies that, when sucient resources are invested in the governance technology to allow the shareholder to capture most of corporate value, output is higher when

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insider trading is permitted. Thus, permitting insider trading appears to increase output and price informativeness, at least when the ®rm is following fairly aggressive governance-technology investment policies. However, policies are endogenous and, as we have demonstrated, permitting insider trading alters the ®rm's optimal investment in governance and this eect can reverse the earlier conclusions reached under the assumption of a ®xed governance policy. The routes through which insider trading in¯uences agents in the economy are fairly intricate, and this makes welfare analysis complex. Given our model structure, we need consider how these factors aect only two types of agents ± managers and owners. On the output side, there are no externalities from production which might bene®t other ®rms or agents in the economy. Thus, if permitting insider trading improves the welfare of both the shareholder and the manager, it unambiguously improves overall welfare. In Fig. 5, owner welfare is measured by shareholder utility evaluated at the optimal managerial compensation policy. In more technical terms, shareholder welfare under the notrade and trade regimes is measured by WN bN and WT bT , respectively.

Fig. 5. Insider trading and owner welfare. Note: In this diagram, rr is ®xed at 1, and average eort preference of managers (r) and cost of governance (c) are varied. In the regions labeled T, permitting insider trading leads to equilibria in which owner welfare is higher. In the region marked NT, prohibiting trade leads to higher owner welfare.

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The shareholder will permit insider trading by the manager only if such trading is in her interest. Thus, the previous section, which derived the conditions under which the shareholder would permit the manager to engage in insider trade, implicitly determined the welfare eects of insider trading on the shareholder. However, to facilitate comparison with the eects on the manager that we shall subsequently detail, we present, in Fig. 5, a graphical representation of the welfare eect of insider trading on the shareholder. Managerial welfare is measured by the expected utility of wealth of the manager conditioned on the information the manager has at date 1. This is consistent with the risk-and-eort-averse managerial objective function, U, posited earlier. 7 To understand the eect on the manager, note that by permitting trade the shareholder can induce fairly high levels of output from the manager even if the manager is allowed only a small portion of ®rm output as part of her employment agreement. If governance is not costly, then extracting this large portion of output is not very costly for the shareholder. But when trade is prohibited, even when governance is cheap, the shareholder will be forced to concede a large fraction of ®rm value to the manager in order to provide her with an incentive to produce. Thus, when governance is inexpensive, permitting insider trading allows the shareholder to pro®tably capture a much larger fraction of ®rm output. This eect more than osets the gains to the manager from trading on information. When governance is costly, however, the strategy of permitting insider trading does not, to any great extent, lead the shareholder to force down the fraction of value captured by the manager. Thus, insider trading induces only an insigni®cant redistribution of project value between the manager and the shareholder. In this case, the portfolio bene®ts to the manager of permitting insider trading ensure that managerial welfare is always higher when trade is permitted. These eects on managerial welfare are illustrated in Fig. 6. As demonstrated in the previous section, the shareholder will tend to permit insider trading when the equilibrium fraction of output extracted by the shareholder is either very high or very low. On the one hand, when insider trading is connected to high rent extractions by the shareholder, permitting trading is redistributive in that it decreases the welfare of the manager while, simultaneously, increasing the welfare of the shareholder. On the other hand, when the shareholder chooses to allow insider trading in conjunction with a low-rent extraction policy, insider trading equilibrium produces greater welfare for both the manager and the shareholder than would the equilibrium compensation/trading policy in the absence of insider trading opportunities. These observations are illustrated in Fig. 7, which identi®es the subset of the

7 Numerical computations and formulae underlying these graphs are available from the authors upon request. Graphs were prepared using Mathematica.

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Fig. 6. Insider trading and managerial welfare. Note: In this diagram, rr is ®xed at 1, and average eort preference of managers (r) and cost of governance (c) are varied. In the regions labeled T, permitting insider trading leads to equilibria in which managerial welfare is higher. In the region marked NT, prohibiting trade leads to higher managerial welfare.

parameter space over which permitting insider trading is favored by both the manager and the shareholder (region OY±MY in the ®gure). One question unanswered by Fig. 7 and the above analysis is exactly why permitting insider trading increases the welfare of both the manager and the shareholder. As stated earlier, insider trading aects agent welfare through a number of routes. Moreover, the price discovery eect is always positive. Thus, a natural question follows: Does the price discovery eect, in and of itself, account for the welfare gain from permitting insider trading? One way to address this issue is to determine the eect of permitting insider trading on net output, i.e., the dierence between expected output and costs of investing in the governance technology. The next diagram, Fig. 8, investigates this question. The region over which net output is increased if insider trading is permitted is represented by T T1 [ T2 . As can be seen by comparing with Fig. 5, in both regions, T1 and T2 , shareholder welfare is also higher when trading is permitted. Thus, the shareholder will permit insider trading whenever trading leads to higher net output. In region T1 , permitting trade also leads to increased managerial welfare. In this region, the fraction of output

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Fig. 7. The disparate impact of permitting insider trade on owners and managers. Note: In this diagram, rr is ®xed at 1, and average eort preference of managers (r) and cost of governance (c) are varied. In the regions labeled OY (ON) permitting insider trading leads to equilibria in which owner welfare is greater (smaller). In the region marked MY MN) prohibiting trade leads to greater (smaller) managerial welfare.

captured by management when trading is permitted does not fall signi®cantly relative to the no-trade fraction. Thus, the overall bene®ts from improved eort incentives and greater price informativeness lead to higher managerial welfare. In contrast, in T2 , although output is higher and shareholder wealth is higher when insider trading is permitted, managerial welfare declines. This occurs because prohibiting insider trading forces the shareholder to rely on granting the manager a large share of ®rm output in order to increase managerial eort incentives. Thus, permitting insider trading, by allowing ®rms to move away from these manager-favored divisions of output, reduces managerial welfare. 7. Concluding remarks Initial arguments in the law and economics literature opposing blanket prohibitions of insider trading oer two reasons to permit insider trading: increasing the informativeness of prices and improving managerial incentives. The extant literature on insider trading considers informativeness of prices in

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Fig. 8. Regions over which permitting insider trade increases net output, the dierence between expected total ®rm output and contracting costs. Note: In this diagram, rr is ®xed at 1, and average eort preference of managers (r) and costs of governance (c) are varied. In the regions labeled T1 and T2 , permitting insider trading leads to equilibria in which net output is higher. In the region marked NT, prohibiting trade leads to higher net output.

the absence of managerial moral hazard, or considers moral hazard in the absence of any informational role for prices. The conclusions of these analyses generally do not support the ability of insider trading to induce welfare gains. In contrast, in this paper we develop a model which links moral hazard with price informativeness by assuming that managers have private information about their own potential gains from moral hazard. In this setting, we show that permitting insider trading sometimes increases both the equilibrium level of output and shareholder welfare. This result, which contrasts with the negative conclusions reached in much of the extant literature on insider trading, follows for two reasons. First, insider trading impounds information regarding managerial taste for perk consumption into asset prices, and this increases shareholders' ability to choose more ecient investment portfolios. Second, allowing insider trading can induce managers to increase their stake in the ®rm beyond that obtained through their compensation contract. This eect leads to reduced managerial perk consumption and/or increased managerial eort. Despite these welfare gains from insider trading, managers may support

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blanket prohibitions on insider trading because granting shareholders discretionary control over insider trading policy may lead shareholders to follow polices leading to reduced managerial welfare ± speci®cally, shareholders may simultaneously permit trade and reduce the fraction of output captured by management through employment. Because our results point to a broad range of situations in which informed insider trading is bene®cial to shareholders, it seems natural for us to ask why trading is generally prohibited under the US legal system and condemned in the popular business press. In order to answer this question, we ®rst note that our results do prove that insider trading is uniformly bene®cial to shareholders. In fact, we explicitly identify, in Theorem 3, a region of the parameter space in which insider trading is not bene®cial to shareholders. It may be the case that a preponderance of US ®rms fall in this region, and, for this reason, the legal system simply codi®es what would in fact be best corporate practice in the absence of codi®cation. Alternatively, since Manne (1966), commentators have pointed out that pressure in favor of the regulation of insider trading has not come from corporate shareholders, but rather from the courts and the political system. This pressure may be based on a misunderstanding of the eects of insider trade arising from a narrow concentration on the insider pro®ts, along with a refusal to acknowledge the positive incentive eects of trading. A ``political economy'' explanation for the prohibition of insider trading also suggests itself. As we have shown, regions in which the eort-preference parameter r is small correspond to regions in which managers capture only a small fraction of total output. Thus, the parametric region where r is small and the costs of governance are also small corresponds with the region of the parameter space where the fraction of value captured by management is small and the costs of governance are small. Within this region, managers lose from permitting insider trade (see Fig. 6). It can be argued that in most large professionally managed corporations in developed markets, governance costs are small relative to output and managers capture a relatively small fraction of total ®rm value. Our analysis predicts such managers will lose if insider trading is permitted because managerial gains from trade will be more than oset by reductions in explicit compensation. It is possible to argue that, because shareholders of large public ®rms are diuse, the interests of managers are more salient in determining public policy regarding public governance than the interests of shareholders. Thus, anti-insider-trading positions within the legal system may simply re¯ect the interests of corporate management. In contrast, consider the region when the cost of governance, c, is large and the eort preference, r, is small. As we explained earlier, this region corresponds to economic situations in which management is well entrenched and has valuable outside options and/or other business interests. In this region, permitting insider trading bene®ts both shareholders and managers. This situation roughly corresponds to the situation in many emerging market economies. Our

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analysis predicts, then, that legal restrictions on insider trading will be less common in such economies and that ®rms operating in these emerging markets will make few eorts to restrict their ocers from trading on personal account. The above observations suggest a direct empirical prediction. Insider trading is typically regulated at the national level. As documented by Hart (1988), there are considerable cross-sectional dierences between the legal systems of various countries with respect to the degree to which they protect incumbent management/insider shareholders. Thus, ceteris paribus, we would expect countries with insider-friendly legal systems to exhibit high governance costs, or, in the terminology of our analysis, high c's. As illustrated above, high values of c induce a preference for insider trading on the part of both managers and shareholders. Thus, our analysis predicts that countries with insider-friendly legal systems will be less prone to limit insider trading through legal restrictions, and that outside shareholders in these countries will make few attempts to limit insider trading through the corporate charter.

Acknowledgements We would like to thank the participants in the Atlanta Finance workshop for comments on an earlier draft of this manuscript. Special thanks are extended to two anonymous referees whose comments greatly improved the quality of this manuscript. The usual disclaimer applies.

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