INSIDER TRADING: REGULATION OR TAXATION?

Transcription

1 ISIDE TDIG: EGULTIO O TXTIO? Javier Estrada * ** Carlos III University Department of Business Last version: pril, 996 bstract: I analyze in this paper the impact of a change of policy from insider trading regulation (IT) to a regime that allos insider trading and taxes insider trading profits. I argue belo that such a change of policy has a qualitative impact on securities markets and social elfare similar to that of a complete elimination of IT; in particular, they both generate an increase in social elfare. The proposed regime combines the beneficial efficiency effects of deregulating insider trading ith the explicit inclusion of a redistributive component; the latter is included in order to make the policy appealing to those lamakers ho base their decisions on fairness considerations. * This article follos from the third chapter of my Ph.D. dissertation at the Department of Economics of the University of Illinois at Urbana-Champaign. For their contributions to this article I ould like to thank Joe Finnerty, Jennie France, Mark Huggett, Charlie Kahn, Stan Kerr, oger Koenker, sani Sarkar, Tom Ulen, and participants of the seminars at: Torcuato Di Tella Institute (rgentina), University of Geneva (Sitzerland), e University of Lisbon (Portugal), Brooklyn College (US), Lund University (Seden), Gothenburg University (Seden), University of the Basque Country (Spain), Complutense University (Spain), and CEMFI (Spain). The vies expressed belo and any errors that may remain are entirely my on. ** Universidad Carlos III / Departamento de Empresa / 893 Getafe, Madrid. SPI TEL: (34-) / FX: (34-) / EMIL: estrada@eco.uc3m.es

2 I- ITODUCTIO There has been a significant amount of research on the benefits and costs generated by the imposition of insider trading regulation (IT). There has been very little research, on the other hand, on alternative policies to regulate insider trading. This may have been partly due to the extreme positions taken by many researchers ith respect to hether insider trading is beneficial or detrimental; such extreme positions resulted in calls for an outright ban of insider trading or the elimination of all regulations against this practice. In any case, this paper attempts to fill the mentioned gap. I have argued elsehere (Estrada, 995), based on a rather detailed elfare analysis, that the elimination of IT ould make society better off; I have further shon that this result is valid for a ide range of values of attitudes toard risk and volatility parameters. It thus follo from those arguments that IT should be eliminated, or, at least, significantly relaxed. Hoever, due to the (unfair?) lack of popularity of insider trading, there may be no government illing to make such a radical change of policy. In light of this problem, I consider in this paper an alternative policy that improves upon IT, namely, alloing insider trading and taxing insider trading profits. Thus, I evaluate belo the impact of a change in policy from IT to a policy that allos insider trading and taxes insider trading profits. There is no doubt that liquidity and informational efficiency, among others, are important characteristics of a securities market. Hoever, it is clear that these characteristics are not, or should not be, ends in themselves. There seems to be little doubt that, from a normative point of vie, the ultimate goal (hence, the ultimate concern of policy makers) is, or should be, to maximize social elfare. Hence, although I do analyze belo the impact of the proposed change of policy on securities markets, I place special emphasis on its impact on social elfare. I argue in this paper that the impact of a change of policy from regulation to taxation ould have an impact similar to that of a complete elimination of IT. That is, either change of policy ould decrease market liquidity, increase current-price volatility, decrease future-price volatility, increase the informational efficiency of the market, and increase price predictability. Further, in terms of elfare, either change of policy ould make insiders and orkers better off, outsiders and liquidity traders orse off, and society as a hole better off. In addition, I argue that a policy of alloing insider trading and taxing insider trading profits is politically more appealing than the complete elimination of IT. This is due to the fact that the proposed regime incorporates a scheme (a tax on insider trading profits) to redistribute ealth from insiders to the rest of society. Thus, such a scheme should satisfy some fairness considerations usually sought to be satisfied through the imposition of IT. more detailed introduction to the topic is omitted but can be found in Estrada (995). The rest of the paper is organized as follos. In part II, I introduce the model and derive to equilibria (one for a market under IT and another for a market under the proposed regime). In part III, I evaluate the impact of a change in policy from regulation to taxation on a securities markets and on social elfare. In part IV, I perform a sensitivity analysis n impressive amount of ork, mostly published in la journals by layer-economists, folloed the pioneering ork by Manne (966). See, for example Scott (98), Carlton and Fischel (983), Easterbrook (985), Haddock and Macey (987), and Macey (99). Economists, on the other hand, entered the debate more recently, folloing the pioneering ork by Kyle (985). See, for example, usubel (99), Subrahmanyam (99), Cornell and Sirri (99), Leland (99), and Meulbroek (99). Throughout the analysis I ill refer to a policy that restricts insider trading as regulation, and to a policy that allos insider trading and taxes insider trading profits as taxation.

3 3 in order to determine the generality of the results derived in part III. nd, finally, in part V, I summarize the most important conclusions of the analysis. n appendix concludes the article. II- THE MODEL.- Market microstructure The analytical frameork dras heavily from Estrada (995). Consider a to-date (one-period) economy here denotes the present (the beginning of the period) and denotes the future (the end of the period). Three types of traders interact in the market for a risky asset: insiders (indexed by ), outsiders (indexed by T), and liquidity traders (indexed by ). ll these traders interact ith a market maker either in a market that restricts insider trading (the regulated market, indexed by ) or in a market that allos insider trading and taxes insider trading profits (the alternative market, indexed by ). 3 Finally, there is a group of agents, referred to as orkers (indexed by K), that do not participate in speculative activities. 4 If IT is to be effective, resources have to be allocated to monitor the behavior of insiders. Thus, in the regulated market, insiders, outsiders, liquidity traders, and orkers are forced to forgo a proportion t j ( t j ) of their (certain) initial ealth ( i ) in order to bear this cost of IT. Thus, let t be the rate at hich the ealth of traders and orkers is taxed in the regulated market, and t ; that is, ealth is not taxed in the alternative market. 5 In the alternative market, on the other hand, ealth is not taxed but insider trading profits are. Thus, let λ i ( λ i ) be the rate at hich the trading profits of the ith trader are taxed, such that λ is the rate imposed on insider trading profits, and λ T λ ; that is, the trading profits of outsiders and liquidity traders are not taxed. The taxation of insider trading profits orks as follos. t the beginning of the period, a risk-neutral party (government) exogenously selects the tax rate λ, and announces that the amount ( p p ) x ] µ λ E[ ill be transferred to society, here E(π ) are the expected profits from insider trading in the alternative market. This transfer may be thought of as the governmental provision of a public good. t the end of the period, the government collects the amount λ π and provides the public good. Thus, let δ i ( δ i ) be the proportion of this public good received by the ith agent. Beteen the beginning and the end of the period, all traders and orkers engage in the production of a commodity. Thus, let Y ij be (the monetary value of) agent i s production of this commodity in the jth market. It is assumed that all traders produce the same amount of Y regardless of the type of market in hich they trade; that is, Y i Y i, for i,t,. Hoever, this cannot be the case for everybody in the economy. For, if insider trading is restricted, someone has to perform the task of enforcing IT, thus foregoing production of the commodity. It is 3 Throughout the analysis, a market that restricts insider trading ill be referred to as the regulated market, and a market that allos insider trading and taxes insider trading profits as the alternative market. Occasionally, a market that places no restriction on insider trading ill be referred to as the unregulated market. 4 In hat follos, subscripts i ill be used to index agents (i,t,,k) and subscripts j to index markets (j,). 5 The alternative system is assumed to be costless; that is, it is not costly to monitor hether insiders pay their taxes on insider trading profits. dmittedly, this is only a simplification. But it is not implausible to think that, if there exist economies of scale in enforcement (as is likely to be the case), the IS could monitor hether insiders pay their taxes at a (marginal) cost loer than the cost of IT. The assumption that the alternative regime is costless is simply an extreme version of the previous reasoning and its only purpose is to simplify the analysis.

4 4 assumed that, if the market is regulated, (some) orkers ill perform this task. Hence, orkers production of the commodity ill be larger in the alternative market; that is, Y K >Y K. ll traders observe all publicly available information about the future price of the risky asset, summarized in a parameter p. Further, insiders privately (and costlessly) observe a realization of a random variable ε ( ) and outsiders privately (and also costlessly) observe a realization of a random variable η (η ). The first random shock ( ε ) stems from the firm that issues the risky asset under consideration; hence, it is observed only by insiders. The other random shock ( η ) may be thought of as arising somehere else in the economy, perhaps in a firm hose activities are related to the activities of the firm under consideration; hence, it is observed only by outsiders. Folloing Fishman and Hagerty (99), it is assumed that insiders have access to information of higher quality; that is, ε < η, here ε and η are the variances of inside and outside information, respectively. The behavior of liquidity traders is not explicitly modelled. They are assumed to demand a random quantity x of the risky asset, such that x (, ). This demand is assumed to be independent from the type of market (regulated or alternative) in hich they trade. 6 It is further assumed that Cov( ε, x ) Cov( η, x ) ; that is, liquidity trading has no information content. It follos from the above discussion that agent i s terminal ealth in the jth market ( ) is given by: ij ( t j ) i Yij ( λ i )( p p j ) xij δ i µ i, T,, K j, () here xij is agent i s demand for the risky asset in the jth market, p j is the price of this asset in the jth market at the beginning of the period, and p its price at the end of the period. This terminal price is given by p ε p η, here p is the expected price of the risky asset given all publicly available information, and and ε and η are to random variables such that ε (, ε ), η (, η ), and Cov ( ε, η ). That is, the future price of the risky asset is determined by all publicly available information and by to independent, normally-distributed random shocks. The market maker is assumed to be risk neutral and constrained to make zero profits hen selecting the price that clears the market for the risky asset (hence, his elfare is not analyzed). Insiders, outsiders, liquidity traders, and orkers are assumed to be risk averse and to have a negative exponential utility function (V), thus displaying constant absolute risk aversion; 7 that is: V e a i i i ( i ) i, T,, K () ij ε, 6 It could alternatively be assumed that the amount of liquidity trading depends on the type of market in hich liquidity traders trade; hoever, an arbitrary difference in trading across markets ould have to be assumed. The assumption of no differential trading is just as arbitrary as any other difference and simplifies the analysis considerably. 7 Estrada (994a), an extended previous version of this article, considers in detail the impact of a change in policy from regulation to taxation in a model in hich all agents are risk neutral.

5 5 here a i (a i >) is the absolute risk aversion parameter. Since is normally distributed conditional on each trader s private information set ( ωi ) 8 then the expected value of V, conditional on ( ω i ), is given by: E a i E [ ( )] ( i i ) a i Var ( i i ) V ω ( / ) ω i i e [ ] ω i, T, K (3) i, Thus, insiders and outsiders (but not liquidity traders and orkers) are assumed to select, conditional on their private information, the demand for the risky asset that maximizes (3). 9 Hoever, it is clear that maximizing this expected utility function is equivalent to maximizing the (conditional) certainty equivalent of ealth (CE i ) hich is given by: ( ) a Var ( i i ( i / ) i i ) i, T, K CEi E ω ω, (4) This follos from the fact that (3) is monotonically increasing in (4). Therefore, in hat follos, insiders and outsiders ill be assumed to select the demand for the risky asset that maximizes (4)..- Strategies and equilibria Definition: n equilibrium is a realization of the random variable i x ij argmax x E V i ( ) [ ij ) ω i ωi ] i, T j U, ij p j such that the folloing to conditions hold: ( * * ii) p j E p xj xtj x ) j U,. That is, an equilibrium is a (current) price of the risky asset that: first, stems from demands that maximize the utility of insiders and outsiders, conditional on their private information ( ω i ); and, second, is efficient in the sense that it is equal to the expected (terminal) price of the risky asset, conditional on all the information available to the market maker. The timing of the model is as follos. t the beginning of the period, endoments are distributed, information and liquidity trading are realized, and demands are submitted to the market maker, ho sets the price that clears the market for the risky asset. In addition, the government announces the amount of the governmental transfer; that is, the amount of the public good to be provided. t the end of the period, all uncertainty is resolved, the payoffs of the portfolios are realized, the production of the commodity is finished, insiders pay their taxes on insider trading profits, and the government provides the public good. Trading, in particular, is structured in to steps: First, insiders and outsiders observe a realization of and, respectively, and submit their demand for the risky asset conditional on such a realization. Second, the market maker determines the price that clears the market for this asset. Folloing Kyle (985), it is assumed that, hen so doing, the market maker sets this price efficiently, thus making zero profits. That is, he sets the price of the risky asset by taking into account all publicly available information and the order flo. This implies that the market maker sets the current price of the risky asset according to the expression: 8 ote that ω ε and ω T η. 9 ecall that liquidity traders trade randomly and that orkers do not trade. ote that ω ε and ω T η. The order flo provides the market maker ith information beyond that hich is publicly available. This is due to the fact that, as ill be seen belo, the demand of informed traders is based on their private information, hich

6 6 p E p x x x p j j Tj j x j x ( Tj x ) j, (5) here j is a parameter hose reciprocal measures the liquidity of the jth market. When selecting their portfolio, insiders and outsiders behave strategically in the sense that they take into account the impact of their demand on the price of the risky asset. That is, they maximize their expected utility by taking the market maker s pricing function (but not the price of the risky asset) as given. Further, hen selecting their portfolio, insiders (outsiders) make a conjecture about hat the outsiders (insiders ) demand for the risky asset ill be. This yields the folloing conjectures: Conjecture : n insider s demand for the risky asset is given by x j jε, for a given parameter j. That is, an insider s demand is a linear function of his private information. Conjecture : n outsider s demand for the risky asset is given by x Tj jη, for a given parameter j. That is, an outsider s demand is a linear function of his private information. Thus, the structure of the model is such that the market maker selects the parameter that determines the liquidity of the market, and insiders and outsiders select the parameter that determines their demand. That is, the market maker selects j, insiders select j, and outsiders select j. It follos from (5) and conjectures - that µ λ [( ) E p p j x ] λ ( ) ε ; that is, the (unconditional) expected profits from insider trading are a function of knon parameters. ote that this implies that there is no uncertainty about the value of the governmental transfer. In other ords, the governmental transfer is a lump sum hose value follos from the parameters that determine the equilibrium of the model and the (unconditional) probability distribution of inside information. This concludes the analytical structure of the model in the alternative market; that is, in a market in hich insider trading is alloed and insider trading profits are taxed. In such a frameork, the folloing theorem holds: Theorem : When all traders are risk averse, insider trading is alloed, and insider trading profits are taxed, there exists an equilibrium characterized by the parameters: ε η (6) ε η (7) a ( λ ) ( ) η ( ) at ε (8) Proof: Using (), (5), and conjectures -, a representative insider s terminal ealth can be ritten as: is correlated to the future price of the risky asset. The plausibility of linear strategies has been strengthened by recent ork: Bhattacharya and Spiegel (99) analyze linear and nonlinear strategies and sho that, if informed traders had to choose beteen them, they ould choose the former over the latter.

7 7 Y ( λ ) ( ε η x η x ) x δ µ (9) The expected value and variance of (9), both conditional on the insider s private information, are given, respectively, by: 3 E ε ε Y ( λ )( ε x ) x δ µ () Var U ε ε ( λ ) ( ) η x () Thus, substituting () and () into (4), the insider s problem becomes: Maxx { Y ( λ ) ( ε ) x ( a i / ( ) [( ) ] } x δ µ ) λ x η () Taking derivatives and solving for the insider s demand yields: ε * x ε (3) a ( λ ) ( ) η from hich (7) follos directly. Similarly, using (), (5), and conjectures -, a representative outsider s terminal ealth can be ritten as: Y ( ε η ε x x ) x δ T T T T The expected value and variance of (4), both conditional on the outsider s private information, are given, respectively, by: T T µ (4) ( η x ) x δ µ T E T η η YT T T T (5) ( ) Var T η η ε xt (6) Thus, substituting (5) and (6) into (4), the outsider s problem becomes: Max x T [ ] T { Y η x ) x δ µ ( a / ) ( ) ε x } T ( T T T T T (7) Taking derivatives and solving for the outsider s demand yields: η * x T η (8) T a T ( ) ε from hich (8) follos directly. Equations (7) and (8) form a system in and hose solution yields the equilibrium of the model. This equilibrium, hoever, must satisfy the restriction that the market maker sets prices efficiently. This implies that: * * * * P E( p x xt x x xt x ) p ( x xt x ). (9) Finally, applying the projection theorem on (9) to solve for yields (6). In the regulated market, IT is assumed to be fully effective in the sense that it prevents insiders from trading; that is, in a regulated market, x. 4 Thus, in the regulated market, the folloing theorem holds: 3 It is important to recall at this point that, since the governmental transfer (µ) is a publicly-knon lump sum, then there is no uncertainty about its value.

8 8 Theorem : When all traders are risk averse and insider trading is restricted, there exists an equilibrium characterized by the parameters: η () η a T ( ε ) () Proof: Similar to the proof of Theorem. III- SIMULTIO OF THE MODEL: BSE CSE The complexity of the equilibria derived above precludes a tractable analysis in closed-form. Therefore, the impact of a change in policy from regulation to taxation on a securities market and on social elfare is evaluated belo using numerical analysis. The impact of such a change in policy on a securities market is evaluated through its effect on market liquidity, price volatility, informational efficiency, and price predictability. Its impact on social elfare, on the other hand, is evaluated through its effect on the elfare of insiders, outsiders, liquidity traders, and orkers. I perform belo an ex-ante analysis; that is, an analysis of the impact of a change in policy from regulation to taxation before the realization of the random variables of the model..- The expressions to be evaluated The liquidity of the market (L), hich is inversely related to the change in price that follos from the arrival of an order, can be measured by the inverse of the parameter j of the market maker s pricing function; that is: ( j ) j L j, () The volatility of current prices (CV) can be measured by the (unconditional) variance of p j ; that is: CV j j j ε jη j, (3) The volatility of future prices (FV), on the other hand, can be measured by the variance of p, conditional on the equilibrium value of p j ; that is: FV ( ) j ε j η j, ε η j (4) j ε j η The informational efficiency of the market (IE) reflects the amount of information revealed by securities prices, and can be measured by the inverse of the volatility of future prices; that is: ( FV j ) j IE j, (5) 4 This assumption is not crucial for the analysis (that is, its relaxation ould not significantly change the results derived belo) but it simplifies it substantially.

9 9 Finally, a measure of price predictability is given by the correlation coefficient beteen j p and p (r); that is: j r j j j j j, η ε η ε η ε (6) s stated above, special emphasis is placed on the impact of a change in policy from regulation to taxation on social elfare. The elfare analysis is performed in terms of a representative agent of each type, and is performed ex-ante. Hence, the expectations taken belo are unconditional expectations. n insider s expected terminal utility in the alternative market and that in the regulated market are given, respectively, by: ( ) [ ] ( ) ( ) ( ) ( ) ) ( ) / ( ) ( ) ( a Y a e V E ε ε η ε λ µ δ ε λ (7) ( ) { } Y t a e V E (8) n outsiders s expected terminal utility in the alternative market and that in the regulated market, on the other hand, are given, respectively, by: ( ) [ ] ( ) ( ) ( ) ) ( ) / ( ) ( at T YT T at T T e V E η η ε η µ δ η (9) ( ) [ ] ( ) ( ) ( ) ( ) ) / ( a T Y T T t a T T T e V E η η ε η η (3) liquidity trader s expected terminal utility in the alternative market and that in the regulated market are given, respectively, by: ( ) [ ] ( ) ( ) ) ( ) / ( a Y a e V E η ε µ δ (3) ( ) [ ] ( ) ) ( ) / ( ) ( a Y t a e V E η ε (3) orker s (certain) terminal utility in the alternative market is given by: { } δ K µ K K K Y a K K e V E (33) { } K K K Y t a K K e V E ) ( (34) When insider trading is restricted, on the other hand, some orkers are diverted to perform the task of enforcing IT, thus foregoing production of the commodity. Hence, as argued above, orkers produce a loer amount of this commodity in the regulated market. Under competitive conditions, the compensation received by those orkers diverted to enforce IT must equal their opportunity cost. Hence, the cost of IT, born by traders and orkers through the tax system, is given by the value of the production orkers forgo hen they act as regulators; that is, ( ) t K T Y K Y K. Therefore, a orker s (certain) terminal utility in the regulated market is given by:

10 This concludes the list of expressions to be evaluated. I turn no to consider the base case of the model ith parameters that reflect average market data. These parameters ill be used to find an explicit solution for both equilibria, hich, in turn, ill be used to evaluate the impact of a change in policy from regulation to taxation on a securities market and on social elfare..- The base case The values of the parameters for the base case are reported in Table. Volatility parameters and risk aversion coefficients ere taken from Leland (99). TBLE : PMETES FO THE BSE CSE ε ε t a i ε i Y i λ δ i lthough the volatility of ( ε.4) (.5) and (.5) ε η p η is taken from Leland (99), the partition beteen is arbitrary. ote that this partition satisfies the restriction that the information observed by insiders is more precise than that observed by outsiders; that is, ε < η. The variability of liquidity trading (.) and the risk-aversion parameters (a i ) are also taken from Leland (99). The initial ealth of traders and orkers ( i ) is normalized to, and so is their production of the commodity in the alternative market (Y i ). The tax rate imposed on traders and orkers in the regulated market (t ) follos from the cost of IT, hich, in turn, follos from the production foregone by the imposition of this regulation. The foregone production in the model attempts to mirror the foregone production in the economy, thus implying a cost of IT equal to.. 5 Finally, insiders are assumed to keep half of their insider trading profits (λ.5), and each representative trader is assumed to receive an equal amount of the governmental transfer (δ i.5). The values reported in Table can be used to compute an explicit solution for the model. The solution of the system for both the regulated and the alternative market is reported belo in Table. 6 It is orthhile to mention that the equilibria reported in this table are highly insensitive to the initial values needed to solve both systems numerically. TBLE : EUILIBIUM VLUES FO BEHVIOL PMETES These equilibria can no be used to evaluate the impact of a change in policy from regulation to taxation on a securities market. Thus, market liquidity, current and future price volatility, informational efficiency, and price predictability in both the regulated and the alternative market are reported belo in Table These calculations are shon in part I of the appendix of Estrada (995). 6 This table follos from equations (6)-(8), ()-(), and the values reported in Table. 7 This table follos from equations ()-(6) and the values reported in Tables -.

11 TBLE 3: SECUITIES MKETS (-) L CV FV IE r Table 3 shos that a change in policy from regulation to taxation ould have both beneficial and detrimental effects on a securities market. In particular, it ould decrease market liquidity, increase current-price volatility, decrease future-price volatility, increase the informational efficiency of the market, and increase price predictability. From a qualitative point of vie, all these results are the same as those that ould be obtained from the complete deregulation of insider trading; that is, from the elimination of IT. 8 The equilibria reported in Table can also be used to evaluate the impact of a change in policy from regulation to taxation on social elfare. To this purpose, let social elfare in the jth market (SW j ) be defined as the joint utility of insiders, outsiders, liquidity traders, and orkers; that is, SW j E(V j V Tj V j V Kj ), here V ij is agent i s utility in the jth market. The utility of each representative agent, as ell as social elfare, in both the regulated and the alternative market are reported belo in Table 4. 9 TBLE 4: SOCIL WELFE (-) E(V ) E(V T ) E(V ) E(V K ) SW Table 4 shos that a change in policy from regulation to taxation ould make insiders and orkers better off, and outsiders and liquidity traders orse off. ll these changes are explained by the changes in expected trading profits, in the taxation of ealth, and in the governmental transfer that stem from such a change in policy. In addition, Table 4 shos that a change in policy from regulation to taxation ould make society better off. Three reasons explain the result that the alternative regime yields a higher level of social elfare than the regulated regime; these three reasons are, in fact, the same three reasons that explain hy an unregulated market improves upon a regulated one. First, it can be shon that the sum of the variances of the terminal ealth of all 8 Estrada (995) analyzes in detail the impact of imposing IT on a previously unregulated market, and finds that such a regulation increases market liquidity, decreases current-price volatility, increases future-price volatility, decreases informational efficiency, and decreases price predictability. The impact of eliminating IT follos directly from those results, and, from a qualitative point of vie, is the same as that shon by Table 3. n intuitive explanation of the impact of imposing IT on a securities market is provided by Estrada (994b). 9 This table follos from equations (7)-(34) and the values reported in Tables -.

12 agents in the regulated market is larger than such a sum in the alternative market. This is explained by the fact that, hen insiders are alloed to trade, the inside information they channel into securities prices corrects these prices in the right direction, thus smoothing the price change that follos from the arrival of ne information. Therefore, a change in policy from regulation to taxation ould decrease the volatility of securities prices; that is, the alternative market is less risky than the regulated market. Second, it is important to note that a change in policy from regulation to taxation ould allo insiders not only to trade but also to bear risk. Thus, in the alternative market, the risk of the volatility of securities prices is spread across insiders, outsiders, and liquidity traders; in the regulated market, on the other hand, such risk is spread only across outsiders and liquidity traders. Put differently, the risk sharing in the alternative market is superior to that in the regulated market. Finally, as long as monitoring hether insiders pay their taxes on insider trading profits is less costly than monitoring their behavior, a change in policy from regulation to taxation ould reallocate resources to the productive sector of the economy. In other ords, the production of goods and services in the alternative market ould be higher than that in the regulated market. In sum, a change in policy from regulation to taxation ould decrease market liquidity, increase currentprice volatility, decrease future-price volatility, increase the informational efficiency of the market, and increase price predictability. In terms of elfare, such a change of policy ould force a reallocation of ealth and risk that ould make insiders and orkers better off, outsiders and liquidity traders orse off, and society as a hole better off. Three reasons explain this last result: First, a change in policy from regulation to taxation ould decrease price volatility, thus making the market less risky; second, it ould improve the risk sharing among traders; and, third, it ould reallocate resources to the productive sector of the economy. By comparing these results to those obtained by Estrada (995) it can be established that, from a qualitative point of vie, a change in policy from regulation to taxation ould have the same impact on a securities market and on social elfare as that of a complete deregulation of insider trading. Hence, the policy proposed preserves the beneficial effects of alloing insider trading. In addition, the governmental transfer, hich reallocates ealth from insiders to the rest of society, should satisfy some fairness considerations usually sought to be satisfied through the imposition of IT. Therefore, the proposed policy combines the beneficial efficiency effects of eliminating IT ith the fairness considerations necessary to make the policy appealing to lamakers. IV- SIMULTIO OF THE MODEL: SESITIVITY LYSIS I explore in this part hether the results derived in the previous part hold for a ider range of values of the parameters of the model. s before, I divide this inquiry into results related to securities markets and results related to social elfare. I perform the sensitivity analysis ith respect to changes in the variability of inside and < Var ( p p ).337 Var ( p p ) ecent empirical research by Cornell and Sirri (99) and Meulbroek (99) provides support to the argument that insider trading corrects securities prices significantly and in the right direction. The optimal regulation of insider trading is addressed in more detail in Estrada (994c).

13 elfare. 4.- Social elfare 3 outside information, the variability of liquidity trading, the risk aversion of all traders, and the tax rate on insider trading profits. 3.- Securities markets s shon in the previous part, a change in policy from regulation to taxation ould have the same qualitative impact on a regulated securities market as that of a complete deregulation of insider trading. That is, it ould decrease market liquidity, increase current-price volatility, decrease future-price volatility, increase informational efficiency, and increase price predictability. The sensitivity analysis, summarized in Table, in part II of the appendix, shos that the previous results hold for a ide range of values of the parameters of the model. Table shos that the superiority of regulation over taxation in terms of market liquidity and current-price volatility, and the superiority of taxation over regulation in terms of future-price volatility, informational efficiency, and price predictability hold for a ide range of values of the parameters of the model. I turn no to discuss the results of the sensitivity analysis on social s shon in the previous part, a change in policy from regulation to taxation ould have the same qualitative effect on traders and orkers as that of a complete deregulation of insider trading. That is, it ould make insiders and orkers better off, outsiders and liquidity traders orse off, and society as a hole better off. The sensitivity analysis, summarized in table, in part II of the appendix, shos that, except in the specific cases to be considered belo, these results hold for a ide range of values of the parameters of the model. Throughout the sensitivity analysis, it is alays the case that E(V -V ), E(V T -V T ), E(V -V ), and E(V K -V K ) ; that is, a change in policy from regulation to taxation never makes insiders and orkers orse off, or outsiders and liquidity traders better off. Put differently, changes in the parameters of the model change the magnitude, but not the sign, of the individual gains and losses that result from such a change in policy. The sensitivity analysis shos that an increase in the variability of inside or outside information, or in the variability of liquidity trading, increase the volatility of securities prices, thus increasing the risk to be born by society. Hence, both SW and SW decrease as ε, η or increase. Further, since the risk sharing under taxation is superior to that under regulation, then SW decreases more rapidly than SW. Therefore, the social gain of replacing IT by a tax on insider trading profits is increasing in the variability of inside and outside information, as ell as in the variability of liquidity trading. This result is illustrated in Figures -3, in part I of the appendix. 3 The range of variation of the parameters of the model in the sensitivity analysis is as follos: The variability of inside information ( ε ) ranges from. to.4; the variability of outside information ( η ) from.6 to.38; the variability of liquidity trading ( ) from. to.4; the risk aversion of insiders (a ), outsiders (a T ), and liquidity traders (a ) from.5 to 8; and, finally, the tax rate on insider trading profits from to. 4 ote that no sensitivity analysis as performed ith respect to changes in the risk aversion of liquidity traders. This is due to the fact that liquidity traders trade randomly, and, therefore, their attitude toards risk has no impact on a securities market.

14 4 The sensitivity analysis also shos that the gain obtained by insiders as a result of a change in policy from regulation to taxation is decreasing in their risk aversion. 5 Further, the loss imposed on outsiders and liquidity traders, as ell as the gain obtained by orkers, are not significantly affected by changes in the risk aversion of insiders. 6 Finally, the social gain of replacing IT by a tax on insider trading profits is decreasing in the risk aversion of insiders. Thus, somehere beteen a and a.5 the gain obtained by insiders and orkers ceases to outeigh the loss imposed on liquidity traders and orkers; that is, somehere beteen a and a.5 IT becomes socially beneficial. This result is explained as follos. change in policy from regulation to taxation reallocates ealth from outsiders and liquidity traders to insiders and orkers, and risk from outsiders and liquidity traders to insiders and the government. ote that, if insiders are more risk averse than outsiders and liquidity traders, then such a change in policy generates a reallocation of risk to traders (insiders) that bear that risk at a higher cost than outsiders and liquidity traders. Hence, as the risk aversion of insiders increases, the risk reallocation becomes more costly. Therefore, if the risk aversion of insiders is high, IT improves upon a tax on insider trading profits. This result is illustrated in Figure 4, in part I of the appendix. The sensitivity analysis also shos that the gain obtained by insiders and orkers as a result of a change in policy from regulation to taxation, as ell as the loss imposed on liquidity traders, are not significantly affected by changes in the risk aversion of outsiders. 7 The loss that such a change in policy imposes on outsiders, on the other hand, is decreasing in their risk aversion. 8 Finally, the social gain of replacing IT by a tax on insider trading profits is increasing in the risk aversion of outsiders. Thus, somehere beteen a T.5 and a T, the gain obtained by insiders and orkers begins to outeigh the loss imposed on outsiders and liquidity traders. This is due to the fact that, as the risk aversion of outsiders increases, the risk reallocation becomes more beneficial. On the other hand, the opposite situation implies that, if the risk aversion of outsiders is lo, IT improves upon a tax on insider trading profits. This result is illustrated in Figure 5, in part I of the appendix. The sensitivity analysis also shos that the gain obtained by insiders and orkers as a result of a change in policy from regulation to taxation, as ell as the loss imposed on outsiders, are not affected by changes in the risk aversion of liquidity traders. 9 The loss that such a change in policy imposes on liquidity traders, on the other hand, is decreasing in their risk aversion. 3 Finally, the social gain of replacing IT by a tax on insider trading profits is increasing in the risk aversion of liquidity traders. Thus, somehere beteen a.5 and a, the gain obtained by insiders and orkers begins to outeigh the loss imposed on liquidity traders and orkers. This is due to the fact that, as the risk aversion of liquidity traders increases, the risk reallocation becomes more beneficial. On 5 For a.5, E(V -V ).435, hereas for a 7.5, E(V -V ). 6 For.5 a 8, (V T -V T ).358, and E(V -V ).58. Further, for a.5, E(V K -V K ).89, hereas for a 8, E(V K -V K ) For a T.5, E(V -V ).8587, E(V -V ).58, and E(V K -V K ).88, hereas for a T 8, E(V - V ).859, E(V -V ).59, and E(V K -V K ).8. 8 For a T.5, E(V T -V T ).45, hereas for a T 7, E(V T -V T ). 9 For.5 a 8, E(V -V ).8587, E(V T -V T ).358, and E(V K -V K ) For a.5, E(V -V ).937, hereas for a 8, E(V -V ).

15 5 the other hand, the opposite situation implies that, if the risk aversion of liquidity traders is lo, IT improves upon a tax on insider trading profits. This result is illustrated in Figure 6, in part I of the appendix. ote from Figures 4, 5, and 6 that a change in policy from regulation to taxation turns from beneficial to detrimental slightly beyond a, and from detrimental to beneficial slightly before a T and a. This is due to the fact that, in the sensitivity analysis, the risk aversion of to representative traders is fixed at and the risk aversion of the third representative trader is subject to changes. Hence, levels of risk aversion around become a threshold. In other ords, high and lo levels of risk aversion should not be interpreted as higher or loer than, but as high and lo ith respect to the risk aversion of other traders. Therefore, the last three results derived above can be summarized as follos: IT improves upon a tax on insider trading profits only hen insiders are more risk averse than outsiders or liquidity traders. Finally, the sensitivity analysis shos that the gain obtained by insiders as a result of a change in policy from regulation to taxation, as ell as the loss imposed on outsiders and liquidity traders, are decreasing in the tax rate on insider trading profits. 3 The gain obtained by orkers as a result of such a change in policy, on the other hand, is increasing in this tax rate. 3 t the aggregate level, the sensitivity analysis shos that the social gain of replacing IT by a tax on insider trading profits is increasing in the tax rate on insider trading profits; this result is illustrated in Figure 7, in part I of the appendix. In fact, the sensitivity analysis shos that social elfare is maximized hen λ. 33 This result follos from the assumption that the government collects an uncertain amount (a fraction λ of insider trading profits) but redistributes a certain amount (a fraction λ of the expected value of these profits). That is, under taxation, the government bears (a fraction λ of) risk that ould be born by outsiders and liquidity traders under regulation. Further, since the government is assumed to be risk neutral, it can bear this risk at no cost. Therefore, it is alays optimal to have the government bearing as much risk as possible, and, as a result, λ. In sum, the sensitivity analysis establishes that regulation can improve over taxation only hen insiders are more risk averse than outsiders or liquidity traders. In this case, the proposed change of policy reallocates risk to traders (insiders) that bear that risk at a higher cost than outsiders or liquidity traders. Hoever, casual empiricism suggests that, in reality, the opposite pattern of risk aversion is observed; that is, insiders seem to be less risk averse than outsiders and liquidity traders. 34 In addition, it does not seem plausible to justify the imposition of IT on the basis of differences in risk aversion across traders, hen the latter is so difficult (if not impossible) to justify empirically. In other ords, the conditions under hich regulation improves upon taxation seem to be either inconsistent ith casual empiricism or very difficult to justify from an empirical point of vie. 3.- digression 3 For λ, E(V -V ).3466, E(V T -V T ).58, and E(V -V ).757, hereas for λ, E(V - V ).3533, E(V T -V T ).88, and E(V -V ) For λ, E(V K -V K )., hereas for λ, E(V K -V K ) For this tax rate to be optimal it is necessary to assume that, even if the government collects all the insider trading profits, insiders ould still trade. 34 Some of the most notorious insiders have been arbitrageurs (like Ivan Boesky) or investment bankers (like Dennis Levine). It seems plausible to think that these traders, ho frequently invest large sums of money in search for a quick profit, are inherently less risk averse that liquidity traders, ho trade for liquidity reasons.

16 6 The assumption that, under taxation, the government collects an uncertain amount (a fraction λ of insider trading profits) and redistributes a certain amount (a fraction λ of the expected value of these profits) seems to be consistent ith the ay a government ould act in such a regime. This is due to the fact that the amount of the public good to be provided ould have to be stated in the government budget, but the insider trading profits ould be collected in the folloing period. Hoever, the assumption that the government is risk neutral, thus being able to bear risk at no cost, may be more controversial. I briefly consider in this section to variations of the basic model. Consider first a situation in hich the government is risk averse. Under this assumption, it becomes costly for the government to bear the risk of the variability in (a fraction λ of) insider trading profits. In order to simplify the analysis of this case, assume that all members of the government are orkers; that is, individuals that do not participate in speculative activities. 35 In this frameork, hen IT is replaced by a tax on insider trading profits, a fraction λ of the variability in securities prices is reallocated from outsiders and liquidity traders to insiders and the government; that is, to insiders and orkers. Therefore, if all traders and orkers are equally risk averse, a tax on insider trading profits ould improve upon IT even if the government does not costlessly bear this risk. This is due to the fact that the risk sharing in the alternative market (the risk of the variability in securities prices ould be shared by all traders and orkers) ould be superior to the risk sharing in the regulated market (the risk ould be born only by outsiders and liquidity traders). 36 Consider no another variation, one in hich the government does not bear the risk of the variability in insider trading profits. That is, a situation in hich the government collects (a fraction λ of) insider trading profits and, at the end of the period, redistributes hatever amount it collected. ote that, in this case, the uncertainty about the value of the governmental transfer imposes a cost on traders and orkers. In this frameork, hen IT is replaced by a tax on insider trading profits, a fraction λ of the variability in securities prices is, as in the previous case, reallocated from outsiders and liquidity traders to insiders and the government. Hoever, in this case, the government does not bear any risk. ather, it spreads this risk across all members of society through an uncertain governmental transfer; that is, through an uncertain provision of a public good. Therefore, in this frameork, if all traders and orkers are equally risk averse, a tax on insider trading profits ould improve upon IT even if the government does not costlessly bear any risk. s in the previous case, this is due to the fact that the risk sharing in the alternative market (the risk of the variability in securities prices ould be shared by traders and orkers) ould be superior to the risk sharing in the regulated market (the risk ould be born only by outsiders and liquidity traders). V- COCLUSIOS I have evaluated in this paper the impact of a change in policy from IT to a regime that allos insider trading and taxes insider trading profits. I have shon that such a change in policy ould have, from a qualitative point of vie, an impact analogous to that of a complete deregulation of insider trading. That is, either change of policy ould decrease market liquidity, increase current-price volatility, decrease future-price volatility, increase 35 The sole purpose of this assumption is to capture the fact that the risk born by the government does not simply vanish from society; rather, it is borne by some of its members. 36 ecall, in addition, that the alternative market is less risky than the regulated market.

17 7 the informational efficiency of the market, and increase price predictability. The sensitivity analysis validated these results for a ide range of values of the parameters of the model. I have further shon that, in terms of elfare, a change in policy from regulation to taxation ould also have, from a qualitative point of vie, an impact analogous to that of a complete elimination of IT. In particular, I have shon that the proposed change of policy ould make insiders and orkers better off, outsiders and liquidity traders orse off, and society as a hole better off. Three reasons explain this last result: First, taxation enables inside information to be channelled into securities prices, thus reducing price volatility; second, taxation enables insiders to participate in the process of risk sharing; and, third, taxation enables a reallocation of resources to the productive sector of the economy. I have established specific conditions under hich a change in policy from regulation to taxation ould be socially detrimental. Such is the case hen the risk aversion of insiders is high relative to that of outsiders or liquidity traders. Under these circumstances the proposed change in policy generates a reallocation of ealth and risk that loers social elfare. Hoever, I have argued that the conditions under hich IT improves upon the proposed regime seem to be either inconsistent ith casual empiricism or very difficult to justify from an empirical point of vie. Finally, I have argued that the proposed policy combines the beneficial efficiency effects of eliminating IT ith the fairness component necessary to make the policy appealing to lamakers. In sum, I have argued in this paper that, if there is no government illing to deregulate insider trading completely, the replacement of IT by a policy that allos insider trading and taxes insider trading profits should be considered as a plausible alternative. Such a change in policy ould ultimately result in the reallocation of resources to a more efficient use and in a subsequent increase in social elfare. nd, as I have argued elsehere, that is hat economics is all about.