QUADERNI DI FINANZA THE DETECTION OF MARKET ABUSE STUDI E RICERCHE ON FINANCIAL MARKETS: A QUANTITATIVE APPROACH M. MINENNA

Transcription

1 QUADERNI DI FINANZA STUDI E RICERCHE THE DETECTION OF MARKET ABUSE ON FINANCIAL MARKETS: A QUANTITATIVE APPROACH M. MINENNA N MAGGIO 2003 ENGLISH VERSION

2 I Quaderni di Finanza anno lo scopo di promuovere la diffusione dell informazione e della riflessione economica sui temi relativi ai mercati mobiliari ed alla loro regolamentazione. Nella collana «Studi e Ricerce» vengono pubblicati i lavori di ricerca prodotti o promossi dalla Consob; nella collana «Documenti» trovano spazio gli interventi istituzionali e gli atti di convegni. Direttore Responsabile: Alberto Agemo Comitato di Redazione: Marcello Bianci, Giuseppe D Agostino, Salvatore Providenti, Adriana Rossetti, Claudio Salini, Giovanni Siciliano. Segreteria di Redazione: Eugenia Della Libera e Francesca Tempestini. Quaderni di Finanza Autorizzazione del Tribunale di Roma n. 432 del Consob : Via G.B. Martini, Roma Tel.: Fax: quaderni_finanza@consob.it

3 Te detection of market abuse on nancial markets: a quantitative approac. Marcello Minenna * Key words: insider trading, market manipulation, abnormal return, detection of market abuse, alert, di usion process. Summary. In every country wit legislation on market abuse, i.e. on market manipulation and insider trading, te repression of tese o ences is entrusted to supervisory and judicial autorities wit powers tat vary wit te legislation in question. A procedure permitting cases of market abuse to be detected in real time is a need tat is strongly felt by nancial market supervisory autorities. Suc a procedure consists basically in te analysis of te transactions carried out on te market by traders in order to detect anomalies tat could be symptomatic of market abuse. Te aim of tis paper is to develop, troug recourse to probability teory, a metod for identifying cases of market abuse more e ectively. * I wis to tank Emilio Barucci of te University of Pisa for is assistance in searcing and analyzing te literature and for is comments and suggestions wit regard to te quantitative modelling tat underlies te procedure for detecting market abuses. My tanks also go to Veronica Faralli (CORIPE) and Maddalena Lenzi (Consob) for repeatedly reprocessing te data for te di erent quantitative solutions prepared in order to calibrate te procedure for detecting market abuse, Luca Doveri (CORIPE) and Enrico Maria Scurati for te analyses needed to develop te indicators of market concentration, and Giovanni Portioli, Paola Deriu and Carlo Milia (Consob) for collecting te data and information tat permitted te empirical veri cation of te procedure. I am also very grateful to Luigi Spaventa, Claudio Salini (Consob) and Francesco Tuccari for aving encouraged te development of tis procedure in te belief tat quantitative analysis can e ectively support supervisory activity. As regards te matematics contained in Appendix A, I am grateful for te suggestions made by Mavira Mancino of te University of Florence for Section A.2 and by Ennio Arlandi (FINARM) for Section A1.

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5 Introduction In eac country tat as legislation on market abuse, i.e. market manipulation and insider trading, te repression of tese o ences is entrusted to te supervisory and judicial autorities. Depending on te legislation in place, te powers of investigation and enforcement of te supervisory autority are quite broad. For an analysis of te di erent legal frameworks in Europe and elsewere in te world, see te bibliograpy [Minenna, 2001]. Te aim of te manipulation of a security on a nancial market (so-called market manipulation) is to cange its price or market participants perception of its underlying value. Tis can be acieved in two ways, known respectively as market-based manipulation and information-based manipulation. Te former is carried out directly on nancial markets by means of transactions, including sam transactions, wereas te latter involves disclosing false or misleading information about issuing companies or securities traded on nancial markets. Insider trading consists in trading on nancial markets wit a view to exploiting information wic is not yet publicly available (privileged or inside information) and wic, if made public, would probably ave a signi cant e ect on te prices of te securities in question. On te basis of tese de nitions, te elements tat distinguis te two types of market abuse are discussed below. A comparison of te aims of market manipulation wit tose of insider trading, from te perspective of pro t maximization for te agents involved, reveals te rst di erence: a market manipulator may ave an interest in te market knowing wat e as done, wereas an insider trader seeks to ide is presence on te market. Tis di erence implies tat an insider, unlike a manipulator, is a price taker. Anoter di erence is tat insider trading is always based on exploiting privileged information, wereas tis is not necessarily te case for market manipulation. A tird di erence is tat insiders will always act in te direction in wic te information in teir possession will cause te price of te security to move, wereas for a manipulator te direction is indi erent and will depend on te type of manipulation undertaken. Te need to de ne a procedure tat will permit nancial market abuse to be detected is strongly felt by supervisory autorities. Te question of market abuse detection as noneteless been largely ignored in te nancial literature, partly owing to te di culty of accessing detailed data on trading, wic is available instead to supervisory autorities. Te aim of tis paper is to construct a procedure for identifying market abuses tat can detect, for eac security and on a daily basis, te possible presence of illicit beaviour. On te basis of te information available to market supervisory autorities, te procedure is designed to verify, for eac security, te presence of anomalies, known as market failures. To tis end, te metod used identi es a reference model for te various nancial variables tat make up te ow of information on trading in a given security tat makes it possible to develop an indicator based on dynamic tresolds; te crossing of tese tresolds indicates an anomalous 5

6 movement in te variable in question (known as an alert). Te nancial variables analyzed on te basis of te model tus become a series of alerts tat signal te possible presence of market abuse. Te tripwires of te market abuse detection procedure were identi ed by analyzing wat te teory of nancial markets, supervisory experience and te empirical observation of te various cases of market abuse found by Consob suggested in relation to te various variables tat comprise te ow of information on trading in securities on nancial markets. Once te tripwires ave been cosen, te calibration of a market abuse detection procedure consists in calibrating te corresponding reference models, i.e. in teir parametric speci cation for predictive purposes, and in identifying an algoritm tat will permit te joint interpretation of te various alerts. Te observation of te cases of insider trading and market manipulation found by Consob permitted a valuable empirical veri cation for te calibration of te market abuse detection procedure. Te paper is divided into two parts: te rst consists of a survey of te nancial literature and of supervisory experience, in wic elements useful for te construction of te tripwires are identi ed (see Section 1); te second outlines te procedure developed and contains a detailed description of te various tripwires and an explanation of ow te procedure was calibrated (see Section 2). 1 Review of te literature and supervisory experience Every procedure for detecting market abuses is based on an analysis of di erent traders trades. Te ows of elementary information on trades comprise: te prices, te quantities and te names of te traders wo carried tem out. Tis section contains an analysis of te nancial literature and Consob s supervisory experience designed to sow ow tese ows of elementary information can be processed to construct te nancial variables tat serve to de ne te tripwires of te model. In particular, te following are addressed: 1. te teory of e cient markets wit information tat is omogeneous among traders (so-called classical asset-pricing teory); 2. te teory of nancial markets wit eterogeneous or asymmetric information; 3. te literature on te e ects of insider trading and market manipulation on nancial markets; As regards te last of tese points, tree issues ave been analyzed: te information content of trades by insiders for te purpose of inferring te future returns on securities [Minenna, 2001, Seyun, 1998]; te estimation of te economic value of privileged information as a proxy for te calculation of te abnormal returns acieved by insiders [Minenna, 2002]; and te ability of te 6

7 market to read insider information and ence of prices to incorporate its value before it is made public [Meulbroek, 1992, Cackravarty, 1999, Cornell and Sirri, 1992, Battacarya et al., 2000]. Te bibliograpy contains details on te literature referred to in tis section [Barucci, 2002] and on supervisory experience [Tuccari, 1999]. 1.1 Some teoretical aspects: classical asset-pricing teory Some results of classical asset-pricing teory (in wic agents ave omogeneous information) sow tat te various ows of elementary information on trading in a security can be e ectively summarized in two nancial variables: te rate of return and te volume of trading. Te analysis of tis branc of teory wit a view to identifying a set of tripwires serving to de ne a procedure for market abuse detection as terefore been carried out wit reference to tese two variables Te rate of return Classical asset-pricing teory is based on ypoteses tat ave already been widely applied in economic teory; tose of perfectly competitive markets, wic are complete (trades can be conditioned on all futures dates and events), agents wo maximize an objective function (expected utility), and rational expectations (agents are risk neutral). Wen markets are in equilibrium and tere are no opportunities for arbitrage, it as been sown tat tere exists a measure of equivalent probability, known as te risk-neutral probability, suc tat te expected conditioned single-period rates of return of securities portfolios are equal to te rate of return on te risk-free security. Wit respect to tis measure of risk-neutral probability, it follows tat: tere does not exist an investment strategy capable of generating iger expected returns tan tat of te market portfolio or of te buy and old strategy; te price of a security and te wealt generated by a discounted investment strategy, or a function tereof, are Martingale di usion processes; excess returns (te return on a security net of te return on te risk-free security) are not autocorrelated and te information available at a given time does not permit future returns to be predicted. Tese caracteristics are summarized in te fact tat te logaritm of te price of a security tat does not distribute dividends follows a stocastic process known as random walk. 7

8 It can easily be seen tat tese ypoteses (risk neutrality and agents preferences constant over time) are unrealistic and tat te results tey lead to are of little elp in understanding te beaviour of te return on a security. Dropping te ypotesis of risk-neutral agents, te implications of te teory of asset pricing become more complex. Te measure of risk-neutral probability no longer coincides wit te istorical value (obtained from market data). Furtermore, te dynamic of te conditional expected return on a security no longer corresponds to tat of te risk-free return. Tis dynamic is analyzed in te literature by comparing te return on a security wit some state variables tat describe te cange in investment opportunities and agents preferences. In particular, in te case of complete markets, in relation to te state variable used to describe te dynamic of te return on a security, te relevant teoretical models are te CCAPM (Consumption Capital Asset Pricing Model) [Rubinstein, 1976] and te ICAPM (Investment Capital Asset Pricing Model) [Breeden, 1979]. Tus, were agents are not risk neutral, tere is no reason wy te returns on securities sould not be autocorrelated or wy some currently available information sould not be of value in forecasting future returns [Fama, 1991]. In te most recent literature it as been noted tat te returns on portfolios and stock indices are caracterized by mean reversion in te long run (negative autocorrelation of te returns) and by a trend (momentum e ect) in te sort run (positive autocorrelation of returns). Leman and Jegadees con rmed te presence of autocorrelation in te weekly returns on securities [Leman, 1990, Jegadees, 1990]. Roll found evidence tat te daily returns on individual securities are a ected by te e ects of te market s microstructure (e.g. transaction costs), wic can lead to sort-term mean reversion penomena [Roll, 1984]. In particular, illiquid securities, caracterized by a sallow market, are marked by a ig price pressure, so tat te returns may cange sign in a sort span of time. Fama and Frenc sowed tat an auto-regressive model based on te log of returns captures bot te mean reversion and te momentum e ect components [Fama and Frenc, 1988]. In te ligt of tese observations, te autocorrelation of returns, or teir examination according to a mean-reverting dynamic, can provide an interesting indicator of te dynamic of a security. An anomaly in tis dynamic signals a cange in investment opportunities, and terefore in te riskiness of a security, te occurrence of a structural break or of a case of market abuse. Moreover, given te natural tendency for a security to be caracterized by a mean-reversion component, and for tis tendency to be inversely related to te security s liquidity, it can be seen tat a joint analysis of returns and trading volumes is likely to be of elp in discriminating between te di erent ypoteses of market failure. 8

9 1.1.2 Transactions: Trading volumes In te literature agents are considered to trade securities on te nancial market for te following reasons: risk saring-edging; speculation. Trading tat is connected wit risk saring-edging serves to meet agents need to edge against te nancial risk associated wit teir outstanding positions. Speculative reasons are connected instead wit te possibility of making pro ts, owing in part to te presence of eterogeneous information sets among agents. In classical asset-pricing teory tese reasons nd scarce treatment; indeed, wit complete markets, trading in connection wit risk saring-edging can be explained only in an initial state of te market generated by an exogenous sock, wic, given its nature, causes a structural break in te market. Were tis occurs, suc trading is necessary to reac a Pareto optimum allocation. Once tis as been reaced, under te ypotesis of rational expectations tere will be no reason for any furter trading. Speculative trading is excluded a priori given te ypotesis of agents wit omogeneous information. In tis context, terefore, te literature fails to o er an e ective explanation of te ig turnover observed on nancial markets and te large autoregressive component of suc trading [Gallant et al., 1992]. Dropping te ypotesis of competitive markets, te absence of some markets and of speci c nancial instruments leads to an increase in trading volumes since agents, unable to edge risk completely, tend to trade more frequently in te market. All told, te teory of nancial markets wit operators possessing omogenous information does not lead to a model tat explains te empirical evidence of ig turnovers and teir large autoregressive components. On te oter and, it sows tat a cange in investment opportunities in agents portfolio coices owing to a structural break will undoubtedly generate turnover wit a certain autoregressive component. Te literature examined above tus does not identify a speci c reference model tat would explain te canges in trading volumes over time, altoug empirically it notes te presence of autoregressive components tat sould suggest te construction of a tripwire based on tis variable. Te literature on nancial markets in possession of non-omogeneous information surveyed in te following section o ers greater insigts into te dynamic of tis nancial variable. 9

10 1.2 Some teoretical insigts: eterogeneous and asymmetric information Te ypotesis of eterogeneous and asymmetric information complicates te teoretical picture described above; indeed te existence of di erent information sets among agents leads to trading, not only for risk saring-edging reasons but also for speculative reasons. Te analysis of te beaviour of te returns on securities and trading volumes depends on te structure of te market (weter or not it is perfectly competitive) and on te nature of agents information (eterogeneous or asymmetric). A market is perfectly competitive wen agents beaviour does not in uence te price (tat is to say tey are price takers); vice versa, if tey are found to in uence te price, te market is imperfectly competitive. Information is eterogeneous wen all te agents (or a large set of agents) receive private signals correlated wit te fundamental value of te security; it is asymmetric wen only a small subset of agents is in possession of privileged information regarding te fundamental value of te security. Te following presents te principal results in te literature on nancial markets wit eterogeneous and asymmetric information, wit a view to identifying a set of useful tripwires for te de nition of a Market Abuse Detection (M.A.D.) procedure Financial markets wit eterogeneous information Two important results found in te literature on nancial markets in te presence of eterogeneous information are: 1. te existence of fully-revealing equilibrium prices; 2. te no-trade teorem. Te rst result implies tat, in te absence of noise (suc as random demand on te part of noise traders), equilibrium prices promptly and accurately incorporate te value of te private information in agents possession. Tis caracteristic of prices was attributed by Grossman to te fact tat, by trading on te market, agents transmit te value of te information in teir possession to te oters [Grossman, 1989]. In tis context, te size of te excange is an increasing function of te accuracy of te information (a closed-form relationsip is establised in te case of normal random variables and an exponential utility function). Te second result sows tat, by itself, eterogeneous information does not give rise to turnover. In fact, if agents ave acieved an ex ante Pareto optimal allocation in te absence of suc information, di erentiation of te information tey possess will not generate trading [Milgrom and Stockey, 1982, Tirole, 1982]. 10

11 Since tese results lead te analysis of nancial markets wit eterogeneous information back to classical teory, tey do not add anyting to te analysis of te beaviour of te returns on securities and trading volumes. (see Section 1.1). By adding a noise component, some later models make it possible to overcome te limitations connected wit te existence of fully-revealing equilibrium prices and wit te no-trade teorem under te ypotesis of perfectly competitive markets. Kim and Verreccia analyzed a model wit private information obtained at a cost and a noise component in a two-period economy [Kim and Verreccia, 1991]: in te rst period agents trade on te basis of teir eterogeneous private information regarding te fundamental value of te security; in te second a public announcement causes te expectations of te security s value to be omogeneous. Te autors sow tat volumes in te second period are positively correlated wit te absolute value of te cange in price between te two periods considered and tat te multiplier depends on te degree of eterogeneity of te agents information. Tis static model igligts two important results: 1. volumes and absolute price canges are positively correlated; 2. te relationsip between volumes and absolute price canges is positively related to te degree of eterogeneity of agents information. Tese results ave also been obtained using models in wic agents are caracterized by opinions di erentiated ex ante (and terefore not connected wit private information) [Salen, 1993] or by di erent interpretations of a public signal [Kandel and Pearson, 1995]. He and Wang developed a dynamic model tat provides for te arrival on te market of private and public information togeter wit a noise component. Agents can trade eiter to accommodate a sock on te supply side (non-informational trading) or to speculate on te performance of te security (informational trading). Te autors sow tat te autocorrelation of volumes distinguises private from public information. In particular, wen a public announcement is made, large volumes are found only in a sort interval around te announcement; wen, instead, te information is private, te volumes tend to be autocorrelated, insofar as te information is transmitted via prices over time troug trading, including tat, subsequent to te arrival of te information, of uninformed agents wo act as followers [He and Wang, 1995]. Harris and Raviv obtained a similar result by establising a link between large volumes and autocorrelation among tem wit private information present in te market [Harris and Raviv, 1993]. Oter models examine te relationsip between volumes and returns, distinguising between volumes tat are information based and tose tat are not. Campbell et al. veri ed empirically tat, if volumes are large for oter tan informational reasons (liquidity, preference socks), ten returns accompanied by ig volumes will be followed by returns of te opposite sign (price reversal 11

12 or mean reversion) [Campbell et al., 1993, Conrad et al., 1994]. Llorente et al. sowed, instead, tat if volumes are generated by new private information arriving on te market (informational trading), te relationsip may be of te opposite sign, but not necessarily so [Llorente, et al., 2001]. Te latter models terefore sow tat tere will be mean reversion if te volumes are based on non-informational reasons and a momentum e ect (presence of a trend and positive autocorrelation among te returns) if tey are based on private information. Dropping te ypotesis of perfectly competitive markets, te fact tat agents transactions can in uence te prices of securities on nancial markets invalidates te results concerning te existence of fully-revealing equilibrium prices and te no-trade teorem. Te literature is scant, partly because imperfectly competitive markets are generally associated wit te presence of asymmetric rater tan eterogeneous information (see Section 1.2.2). An interesting study is tat of Foster and Viswanatan, wic sows tat agents aving di erent perceptions of te fundamental value of te security will fuel a cain reaction, since tey will continue to trade owing to teir di erent interpretations of te oter agents trading [Foster and Viswanatan, 1996]. Te analysis of te literature on nancial markets wit eterogeneous information con rms tat, for te purpose of de ning a tripwire based on turnover, examining te time series according to an autocorrelated process can be of particular assistance. It also strongly suggests te desirability of de ning a tripwire tat examines returns in te ligt of a mean-reversion model and a calibration procedure tat jointly evaluates te results of te tripwires based on volumes and returns Financial markets wit asymmetric information Te literature on nancial markets wit asymmetric information sows ow adverse selection penomena due to te fear of trading wit an agent in possession of privileged information can cause individual uninformed agents to decide not to carry out any trades and tus reduce te volume of trading on te market. Assuming perfectly competitive markets, Wang analyzed a model wit informed and uninformed agents, were te former can also trade o -market (private investment opportunities) for reasons not connected wit te value of te security. Te informed agents trade in response to private information or socks related to private investment opportunities. Te uninformed agents terefore face a problem of adverse selection linked to te risk of carrying out a trade wit an informed agent and may be led not to trade on te market at all. Consequently, te volume of trading diminises wit te degree of information asymmetry, wile it increases wen information is disclosed because tis reduces te problem of adverse selection. Even toug te absolute e ect is di erent from tat found in te case of eterogeneous information (see Section 1.2.1), 12

13 te dynamic e ect produced by te arrival of information in te public domain is te same. Dropping te ypotesis of perfectly competitive markets, te picture becomes more variegated because an agent in possession of privileged information will de ne is beaviour taking into account te e ect it will ave on te price. Kyle sowed tat in an imperfectly competitive market wit a noise component te information transmitted by prices is inferior to tat transmitted in a perfectly competitive market [Kyle, 1989]. In tis context te nancial literature presents some models tat examine te beaviour of returns and trading volumes in relation to: 1. te microstructure of te market, and in particular to weter te market is order driven or quote driven; 2. te level of competitiveness from te point of view of dealers-market makers; 3. te e ect of adverse selection on agents in te presence of informed agents. Some interesting results are linked to te ypotesis of a dealer wo sets bid and ask prices knowing tat tere are some informed and some uninformed agents in te market. In tis case te dealer, fearing te e ect of adverse selection (carrying out a transaction wit an informed agent), tends to set a ig bid-ask spread and, terefore, does not contribute to increasing te liquidity of te market. Easley and O Hara sowed tat a dealer in a quote-driven market, knowing of te existence of informed traders, tends to set a iger bid-ask spread tat produces ine cient conditions for trading [Easley and O Hara, 1987]. In extreme situations, Glosten and Milgrom sowed tat tis type of beaviour on te part of a dealer can lead to price levels tat result in no transactions at all being carried out [Glosten and Milgrom, 1985]. Kyle analyzed a model in wic an insider trader operates in a market wit noise traders (wose demand is given by a random variable tat does not depend on price) and a market maker wo undertakes to clear te market at a price equal to te expected value of te dividend conditional on te ow of market orders. In an economy wit only one opportunity to trade te insider trader, wo knows te exact value of te dividend, tends to ide is information to prevent te market maker s price discovery process from re ecting te value of te private information exactly. Tis beaviour on te part of te insider translates operationally into an elasticity of is demand for private information tat is inversely proportional to te dept of te market and directly proportional to te noise component. In particular, te insider, in order to maximize te pro ts obtained by exploiting te privileged information, may be led to trade modest quantities, so as to prevent is trading from revealing te value of te information to te market [Kyle, 1985]. Foster and Viswanatan, using reasoning analogous to Kyle s, sowed tat volumes are autocorrelated in an imperfectly competitive market in te presence of market abuse penomena [Foster and Viswanatan, 1993]. 13

14 Te analysis of te literature on te nancial markets in te presence of asymmetric information con rms te usefulness of observing te time series of volumes according to an autocorrelated process in order to construct a tripwire based on tis nancial variable. Wat is more, it suggests te desirability of examining factors related to te microstructure of markets and te trading metods used, wit particular reference to te dept of te market and te presence of dominant traders. Tis analysis sould be carried out troug te construction of speci c tripwires capable of revealing te presence of dominant operators in te market and te evolution of market concentration. Moreover, te consideration tat market concentration sould always be examined in relation to volumes and te dept of te market, suggests tat te calibration of te procedure sould be de ned in a way tat permits te joint evaluation of te results of te volume and market concentration tripwires. 1.3 Te literature on te e ects of insider trading and market manipulation. Te literature on market abuse is very limited and often connected to researc carried out by supervisory autorities in support of teir own activities. In particular, te teme of manipulation is almost completely absent, partly owing to te unavailability of data on te trading of te various market participants, wereas insider trading as attracted te attention of several writers. Among tese, Meulbroek sowed tat iger volumes and abnormal returns are found on days marked by insider trading, since some uninformed agents follow te beaviour of te insiders (te so-called erd e ect) and tus elp te price of te security to rise more rapidly to te level it would reac if te information were disclosed [Meulbroek, 1992]. Similar results were obtained by Cornell and Sirri by examining te Campbell and Taggart case [Cornell and Sirri, 1992]. Tis analysis sows tat insiders tend to ide teir operations by carrying out rater small transactions, a fact already igligted in te analysis of te nancial literature Battacarya et al. sowed tat te disclosure of information on companies listed on te Mexican market does not ave any e ect on returns, volumes or volatility. Tis is due to te intense trading by insiders wo anticipate te di usion in te market of te value of te privileged information.(so-called pre-announcement information leakage) [Battacarya et al., 2000]. Cackravarty, analyzing te Carnation case, sowed instead tat a price e ect does exist upon te disclosure of information, but also tat it is not possible to distinguis te price e ect due to te trading of insiders from tat produced by te transactions of agents not in possession of privileged information [Cackravarty, 1999]. Bagliano et al. in an analysis of te Italian market sowed tat insider trading does not bring about a cange in te autocorrelation of te time series of volumes and returns [Bagliano et al., 2001]. 14

15 Wit reference to researc carried out by supervisory autorities, Mitcell and Netter described te procedure adopted by te United States Securities and Excange Commission (SEC) to estimate te abnormal returns connected wit te disclosure of privileged information. Tis procedure uses te market model and, by means of an econometric approac of te event-studies type, estimates te abnormal return on a security in relation to te return on te market index. Te results of te estimation form te basis for determining te value of te privileged information appropriated by te insider to te detriment of te market. On te basis of tis value te SEC determines te sanctions to apply to te insider (so-called disgorgement) [Mitcell and Netter, 1994]. Minenna as recently proposed, as an alternative to te market model, te adoption of a di usion process tat infers future returns on te basis of a calibration based on te returns recorded by te security in a certain period. Tis innovative procedure detects te presence of abnormal returns in relation to te disclosure of privileged information. He as also sown tat, by calibrating te di usion process on te basis of an insider s trading strategy (information available to te supervisory autority), it is possible to calculate te value of te privileged information appropriated by te insider to te detriment of te market and ence te disgorgement [Minenna, 2001]. All told, tese studies do not clarify weter te information possessed by insiders is incorporated in te price before te information is disclosed; owever, tey do con rm tat volumes increase, tat uninformed agents account for a substantial part of te increase, tat insider traders tend to ide teir presence in te market, tat abnormal returns occur in te presence of privileged information and tat tey can be estimated using di usion processes [Minenna, 2002]. In de ning alerts based on trading volumes and returns, tese considerations terefore con rm te need to analyze: te dynamic of trading volumes determined by te activity of te di erent market participants according to an autocorrelated process; te beaviour of te return on a security wit a view to identifying te presence of abnormal returns using di usion processes. 1.4 Consob s supervisory experience Consob s supervisory experience as been acquired since 1991, te year in wic Law 157/1991 provided a speci c legal framework for countering insider trading and market manipulation. Since te law entered into force Consob as reported 140 cases of market abuse to te judicial autorities. Consob carries out its supervisory action against market abuse by means of operational and analytical investigations. Te former include not only analysis of intermediaries market operations, te positions in cas and securities of individual clients, records of orders and transactions but also te collection of information on issuers, te analysis of teir nancial statements and researc 15

16 reports, etc. Tese instruments permit te veri cation of te existence of te fumus of abusive conduct in te market and to ascertain te elements necessary to determine its scope. Te analytical instruments serve, instead, to evaluate te economic impact of abusive conduct on market integrity and any losses incurred by investors. In cases of insider trading, after identifying te privileged information, it is necessary to evaluate its price sensitivity and te value of te information tat te insiders exploit at te expense of te market [Minenna, 2002]; in cases of market manipulation, after identifying te type of manipulation, it is necessary to examine te anomaly produced in te performance of te security and to quantify te damage caused to te market [Milia, 2001]. It needs to be remembered, in fact, tat te sanction to be imposed on manipulators as to consider te economic and nancial e ects of teir conduct on te market and investors. Te ex-post examination of te cases of market abuse found by Consob sow tat suc conduct leaves a trace in te nancial markets, in terms of bot te price of te security and te volume of trading [Tuccari, 1999]. As for insider trading, considering te tendency of insiders to ide teir presence in te market, it is te value of te privileged information and te moment of disclosure to te market, in relation among oter tings to te possible advance propagation of rumours, tat determine anomalous movements in te security s price and te volume of trading. Hence te importance of te supervisory autority keeping a database of company information and setting up special enforcement units to monitor continuous and periodic information on companies. In its experience wit market manipulation Consob as found cases of bot market-based manipulation and information-based manipulation. Te cases of market-based manipulation sow tat prices can be altered eiter wit actual transactions (trade-based manipulation) or wit sam transactions (was sales/matced orders) and tat some prices (speci cally opening and closing prices) ave a greater information value tan oters since tey are referred to in rules on te functioning of te microstructure of markets. For example, manipulation of te opening price as been found in some cases because it determines te pay-o of te derivative component of structured products placed in te retail market. It as also been found tat market value, concentration of ownersip and liquidity are factors tat a ect te probability of listed securities being manipulated. For example, in te case of tinly trade securities, agents may be tempted to carry out transactions so as to create te appearance of an active market, to drive te price above te level te market would oterwise express, and to boost te market value of a company tat is about to be disposed of, etc. Manipulators are generally connected to te company s controlling sareolders and te organization of te market abuse requires agreements wit intermediaries and institutional investors. Tese interventions often resemble tose undertaken to stabilize te price of a security or in anticipation of te announcement of company news. Turning to information-based manipulation, te cases found are connected 16

17 wit te fundamental role tat information plays in all nancial investments. Two problems emerge in tis connection: te rst is te con ict of interest typical of nancial intermediaries tat publis researc and investment advice and also operate directly in te market; te second is more typically Italian and regards te lack of pure publisers. Tat aving been said, one type of manipulation found by Consob consists in te release of false information on company events or te situation of te company wit te aim of in uencing te prices of listed securities. Tis conduct is usually connected wit te presence of controlling sareolders, wo are often in nancial di culties. In some cases misleading or biased press reports ave been found, by means of wic te company communicates te existence of restructuring projects to te market, sometimes troug cannels not directly connected to te company. Anoter type of manipulation consists in te publication by intermediaries of researc reports wit exaggerated and/or false forecasts. In tese cases te trading for own account of te intermediaries in question as often been found to be inconsistent wit teir recommendations. Te examples of market manipulation given above igligt te fact tat bot te prices of securities and te related returns generally undergo sarp canges (for example at te moment privileged information is disclosed), or sow movements tat cannot be attributed to a dynamic of te mean-reverting type (for example in te presence of manipulation). Furtermore, tey sow tat trade volumes vary bot in absolute terms, generally conserving an autoregressive component, and in terms of te composition of intermediaries and traders. Wit reference to te composition, it is necessary to consider two variables in particular: 1. te level of concentration of te intermediaries, tat is te number of intermediaries and teir sares of trading volumes (so-called static concentration); 2. te evolution of te concentration of te intermediaries, tat is te cange in eac intermediary s sare of te volume of trading in a given security (so-called dynamic concentration). Tese considerations, wic summarize Consob s supervisory experience, con rm te desirability of de ning a tripwire based on trading volumes by examining te time series of volumes using an autoregressive model and on returns by calibrating a regression process of te mean-reverting type. Tey also suggest de ning two tripwires tat examine te composition of intermediaries-traders, distinguising between static and dynamic concentration. Lastly, te empirical evidence sows ow market abuse penomena give rise to canges in te beaviour of several nancial variables at te same time, wic implies tat te calibration of te procedure needs to be de ned in a way tat permits a summary evaluation of te results of all te tripwires. 17

18 2 Te Market Abuse Detection procedure 2.1 Preamble A M.A.D. procedure identi es, on a daily basis, te securities a ected by illicit beaviour in te form of market manipulation or insider trading. It igligts te possible presence of market abuse penomena by examining te beaviour of nancial variables tat correspond to te ows of elementary information on trading available to te supervisory autority. Te examination of te beaviour of te nancial variables requires te definition of a reference model for eac of tem. Te development of te reference models is aimed at te identi cation of dynamic tresolds, te crossing of wic signals an anomalous movement in te variable in question (so-called alerts). Te nancial variable and te related model tus become a tripwire of potential market abuse penomena for te procedure. Having identi ed te tripwires, te calibration of a M.A.D. procedure consists in calibrating teir models, tat is in specifying teir parameters and in identifying an algoritm permitting several alerts to be interpreted jointly. As mentioned in te Introduction, te identi cation and calibration of te tripwires of te M.A.D. procedure ave been identi ed and calibrated by analyzing: wat te teory of nancial markets and Consob s experience suggest; te cases of insider trading and market manipulation found by Consob. 2.2 Te tripwires Te examination of te literature and supervisory experience ave provided te following indications as to ow transaction prices, te quantities traded and te names of te traders wo carried out te transactions (i.e. te ows of elementary information on trading available to te supervisory autority) must be analyzed in order to construct nancial variables wose beaviour can reveal market abuses: transaction prices are analyzed in terms of returns by studying te movements in te log of te price; returns generally undergo sarp canges (for example at te time privileged information is disclosed) or follow pats tat are not of te meanreverting type (for example in te presence of manipulative penomena); te presence of abnormal returns is detected by estimating returns using di usion processes; autoregressive models can capture bot te discrete mean-reversion and momentum-e ect components of returns; 18

19 te quantities traded by individual agents are examined in terms of daily trading volumes according to an autocorrelated process; te agents are analyzed in relation to te quantities tey ave traded in a day, taking into account te dept of te market, te presence of dominant traders and te composition of te various intermediaries-traders; te composition of te market is evaluated using a two-stage process: te level of concentration of te intermediaries, tat is te number of intermediaries and teir sares of trading volumes (so-called static concentration); te evolution of te concentration of te intermediaries, tat is te movement in eac intermediary s sare of te volume of trading in a given security (so-called dynamic concentration). On te basis of tese indications four nancial variables ave been constructed tat represent te beaviour of: 1. te volumes of trading in te security; 2. te returns on te security; 3. te static market concentration; 4. te dynamic market concentration. Te de nition of a tripwire of a M.A.D. procedure requires te examination of tese variables to be based on a reference model; appropriately calibrated, tis de nes te dynamic tresolds tat trigger te procedure s alerts. In particular, te construction of te tripwires must guarantee te detection, in real time, of te securities tat may be te subject of market abuse. Te examination of te di erent cases of market abuse found by Consob as provided important support in de ning te di usion processes tat describe te beaviour of te nancial variables and tus caracterize te reference models. A description follows of te construction and functioning of te tripwires based on te four nancial variables considered, wit reference to te ows of elementary information on te trading in any security listed on te sare market. To tis end, P t and Q t are used to denote respectively te o cial price and te volume of trading observed in te nancial markets for a generic security on day t: Te analysis of trading volumes Te examination of te time series of trading volumes Q t was conducted according to an autocorrelated process, as suggested by te literature on nancial markets and supervisory experience. It sould be noted, owever, tat te literature does not indicate a particular reference model for tis examination. 19

20 Considering te objective of de ning a tripwire tat is capable of revealing anomalies in te movement of tis nancial variable wit a view to detecting market abuses, te analysis of te di erent cases found by Consob suggested assuming tat volumes are governed in discrete time by te following autoregressive process, wic, by construction, sows autocorrelation: Q k = Q k 1 + bz k (1) were is a deterministic function of time; Q 0 = q 0 and (Z k ) k0 is a sequence of random variables identically independently distributed as a normal wit a zero mean and a unit variance on R 1. Te variability of b in relation to time is guaranteed by te fact tat it multiplies a random variable wose variance is de ned in relation to te unit of time. For expository convenience, putting = 1 ; (1) can be rewritten as follows: Q k Q k 1 = Q k 1 + bz k (2) A rst consideration concerning (2) is tat, since q 0 is a constant and Z 1 ; : : : ; Z k a sequence of independent random variables distributed as a normal wit a zero mean and a unit variance, te solution fq k g k0 is a Markov cain wit respect to te ltration f= k g k0 generated by te sequence Z 1 ; : : : ; Z k ; wic assumes values on R 1 and were k is te indicator of discrete time. Te pair (R 1 ; B(R 1 )) de nes te measurable space of fq k g k0 were B(R 1 ) is te Borel eld on R 1 : Every discrete Markov process de ned in tis way is identi- ed by te initial distribution v 0 () and by te probability of transition 1;k (; ) de ned on (R 1 ; B(R 1 )): 1 Te properties of te reference model sub (2) do not permit te beaviour of volumes to be forecast using a number of daily observations tat refer to a time orizon of a mont or less, if te statistical signi cance of te analysis is not to be lost or numerous procedural complications are not to be encountered. 2 In order to construct a tripwire tat responds to te objectives of te procedure, attention is focused on te distributive caracteristics of te corresponding continuous-time version of (2) [Nelson, 1990]. Te advantage of te continuous time approac is tat by referring to a stocastic di erential equation, if tis as an integrated solution or if te distributive properties of te solution are known, it is possible to construct a con dence interval for te prediction of te variable described by te di usion process. Tis interval de nes te trading volume dynamic tresolds tat identify te alerts of te M.A.D. procedure. Te logic underlying te indicator to be constructed is taken over from tat used by Minenna to predict te beaviour of te return on a security and detect te presence of abnormal returns [Minenna, 2001]. 1 In particular 8 2 B(R 1 ): 1. P (Q 0 2 ) = v 0 ; 2. P (Q k+1 2 j= k ) = P (Q k+1 2 jq k ) = 1;k (Q k ; ): 2 For a discussion of te problems connected wit te estimation of te parameters of te model in question, see te bibliograpy [Greene, 1993]. 20

21 By rescaling te discrete Markov process fq k g k0, it can be sown tat (2) converges weakly to te di usion process fq t g ; given by te following stocastic di erential equation: dq t = Q t dt + dw t (3) were and are deterministic time functions and W t is a standard unidimensional Brownian motion. Te proof is given wit reference to te generic di usion process fx t g in appendix A. (3) is te continuous-time version of (2). Tis stocastic di erential equation is known in te literature as an Ornstein-Ulenbeck aritmetic di usion process, wic as te following distributive properties wit reference to any constant initial condition identi ed at time s, wit s < t; equal to Q s : r! Q t N Q s e (t s) 2 ; 1 e 2(t s) (4) 2 Te proof of tese distributive properties is given in appendix A wit reference to te generic di usion process fx t g. Te relationsip between (2) and (3) and te distributive properties of te latter stocastic di erential equation (4) de ne te reference model to be used in examining te time series of trading volumes and tus uniquely de ne te tripwire wit reference to tis nancial variable. Te dynamic tresolds tat make it possible to identify te alerts for trading volumes ave been constructed, in fact, by exploiting te properties of te reference model. In Section te construction of tese tresolds and teir calibration are described in detail Te analysis of returns Te teory of nancial markets and supervisory experience indicated te desirability of using an autoregressive model to examine te time series of a security s returns. In particular, considering te objective of de ning a tripwire capable of revealing anomalies in te beaviour of tis variable wit a view to detecting market abuses, te examination of te cases found by Consob sowed tat te following model appropriately describes te beaviour of tis variable in discrete time: R k = + R k 1 + bz k (5) were R = ln(p ); and are deterministic functions of time, 3 R 0 = r 0 and (Z k ) k0 is a sequence of random variables identically independently distributed as a normal wit a zero mean and a unit variance on R 1. For expository convenience, putting = 1 and = ; (5) can be rewritten as follows: 3 Te variability of b in relation to time is guaranteed by te fact tat it multiplies a random variable wose variance is de ned in relation to te unit of time. 21

22 R k R k 1 = ( R k 1 ) + bz k (6) As in Section 2.2.1, in order to construct a tripwire tat acieves te objectives of te procedure, we focus on te distributive caracteristics of te corresponding continuous-time version of (6) [Nelson, 1990]. As already sown in te previous section, te advantage of te sift to continuous time consists in te identi cation a priori of te distributive properties of te process fr k g and tus in te possibility of easily de ning a con dence interval for te prediction of te variable described by te di usion process; by de ning te dynamic tresolds tat identify te alerts of te procedure, tis process turns a nancial variable into an alert. By time rescaling, as in Section 2.2.1, te discrete Markov process fr k g k0 and sowing (6) converges weakly towards te di usion process fr t g given by te following stocastic di erential equation: dr t = q ( R t ) dt + dw t (7) were q and are deterministic time functions and W t is a standard unidimensional Brownian motion. 4 (7) is te continuous-time version of (6). Tis is again an Ornstein-Ulenbeck aritmetic di usion process, wic as te following distributive properties wit reference to any constant initial condition identi ed at time s, wit s < t; equal to R s : 5 R t N (R s )e q(t s) + ; s 2 2q 1 e 2q(t s) Te relationsip between (6) and (7) and te distributive properties of te latter stocastic di erential equation (8) de ne te reference model to be used in examining te time series of returns and tus uniquely de ne te tripwire wit reference to tis nancial variable. Te dynamic tresolds tat make it possible to identify te alerts for returns were in fact constructed by exploiting te properties of te reference model. In Section we describe te construction of tese tresolds and teir calibration in detail Te analysis of static concentration Consob s supervisory experience and te nancial literature sowed te desirability, wit a view to detecting market abuses, of examining te composition of te intermediaries-traders present on te market. A rst analysis of tis kind can be made by examining te so-called static concentration, tat is te level of 4 Te proof is given wit reference to te generic di usion process fx tg in appendix A. 5 Te proof of tese distributive properties is given in appendix A wit reference to te generic di usion process fx tg.! (8) 22