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1 ISSN Worig Paper Series Delegated Portfolio Maagemet Paulo Coutiho ad Bejami Mirada Taba December, 00

2 ISSN CGC / Worig Paper Series Brasília. 60 Dec 00 P. -

3 Worig Paper Series Edited by: Research Departmet (Depep ( Reproductio permitted oly if source is stated as follows: Worig Paper Series. 60 Authorized by Ila Goldfaj (Deputy Goveror for Ecoomic Policy. Geeral Cotrol of Subscriptio: Baco Cetral do Brasil Demap/Disud/Subip SBS Quadra 3 Bloco B Edifício-Sede º subsolo Brasília DF Brazil Phoe: ( Fax: ( The views expressed i this wor are those of the authors ad do ot reflect those of the Baco Cetral or its members. Although these Worig Papers ofte represet prelimiary wor, citatio of source is required whe used or reproduced. As opiiões expressas este trabalho são exclusivamete do(s autor(es e ão refletem a visão do Baco Cetral do Brasil. Aida que este artigo represete trabalho prelimiar, citação da fote é requerida mesmo quado reproduzido parcialmete. Baco Cetral do Brasil Iformatio Bureau Address: Secre/Surel/Diate SBS Quadra 3 Bloco B Edifício-Sede º subsolo Brasília DF Brazil Phoes: ( (... 40, 40, 403, 404, 405, 406 DDG: Fax: ( Iteret: s: cap.secre@bcb.gov.br difo.secre@bcb.gov.br

4 Delegated Portfolio Maagemet Paulo Coutiho* Bejami Mirada Taba** Abstract I this paper, we examie optimal portfolio decisios withi a decetralized framewor. There are may portfolio maagers choosig optimal portfolio weights i a mea-variace framewor ad taig decisios i a decetralized way. However, the overall portfolio may ot be efficiet, as the portfolio maagers do ot tae ito accout the overall covariace matrix. We show that the iitial edowmet that portfolio maagers ca use withi the firm i order to maage their portfolios ca be used as a cotrol variable by the top admiistratio ad redistributed withi the firm i order to achieve overall efficiecy. Keywords: Optimal Portfolio, Decetralized, Efficiet Frotier, Portfolio Maagemet. * Ecoomics Departmet, Uiversidade de Brasília. address: coutiho@ub.br ** Research Departmet, Cetral Ba of Brazil. address: bejami.taba@bcb.gov.br 3

5 . Itroductio Oe of the mai tass of portfolio maagers is to achieve the best possible trade-off betwee ris ad retur. This tas ivolves the determiatio of the best ris-retur opportuities available from feasible portfolios ad the choice of the best portfolio from this feasible set. However, i may situatios, the portfolio is maaged i a decetralized way, with the top admiistratio of the firm delegatig to differet portfolio maagers partial cotrol about ivestmet i subclasses of assets. I geeral, the top admiistratio of tradig firms decides the amout of wealth ivested i certai asset classes. The top admiistratio however delegates to portfolio maagers the cotrol of which specific securities to hold ad the proportios of these securities i the portfolio. The delegatio process may imply i a overall iefficiet portfolio. Eve if all portfolio maagers are i the efficiet frotier for their particular asset class it may be the case that, i the aggregate, the resultig portfolio is a iefficiet oe as portfolio maagers are ot taig ito accout the overall covariace matrix ad all possible combiatios that would result i the best trade-off betwee ris ad retur. These cosideratios has led us to examie which coditios should be met so that eve i a decetralized decisio maig set the overall portfolio would be efficiet. Our fidigs suggest that the iitial edowmet available for ivestig by the portfolio maagers ad the ris free iterest rate they face whe taig ivestmet decisios ca be used as cotrol variables to attai overall efficiecy. Although we recogize that asymmetry of iformatio play a crucial role i the delegatio process, i this paper, we put these cosideratios to cocetrate i the pure compatibility of solutios betwee the differet portfolio maagers with the overall Classical articles i asset allocatio choice are Tobi (958 ad Marowitz (95,

6 solutio. Bhattacharya ad Pfleiderer (985 develop a model of decetralized ivestmet maagemet uder asymmetric iformatio, where they are especially cocered about screeig agets with superior iformatio ad o the surplus extractio from the aget. Barry ad Stars (984 show that ris sharig cosideratios are sufficiet to motivate the use of multiple maagers. Stoughto (993 ivestigate the sigificace of oliear cotracts o the icetive for portfolio maagers to collect iformatio, justifyig employmet of portfolio maagers with the otio of superior sills at acquirig ad iterpretig iformatio related to movemet i security prices. We solve the problem of fidig equivalece betwee decetralized ad cetralized portfolio maagemet aalytically withi a mea-variace framewor, which provides some isights o how to ehace the delegatio process. Our fidigs suggest that it is possible to decetralize ivestmet decisios ad costruct portfolios that are still optimal i a aggregate sese. All that is eeded are some istrumets to cotrol decisios tae by portfolio maagers such as their available iitial edowmet ad the ris free iterest rate that they face, which may be determied edogeously i our model. We solve a geeral case with may portfolio maagers that are specialized i some particular asset class (which may itersect or ot i some cases, ad show that the iitial edowmet that portfolio maagers have to ivest i their portfolios ca be used by the top admiistratio to achieve overall efficiecy. The orgaizatio of the paper is as follows. I sectio II, we develop the model. Sectio III gives some iterpretatios of the results. Sectio IV cocludes ad gives directios for further research. There may be other difficulties i implemetig mea-variace aalysis such as the extreme weights that may arise whe sample efficiet portfolios are costructed. As Geotte (986 ad Britte-Joes (999 oticed, there are huge estimatio errors i expected returs estimatio, which caot be igored. However, we will ot address these poits i this paper. 5

7 . The model We start with risy assets. Let w be the x vector of portfolio weights for risy assets, V the x covariace matrix, r the x expected retur vector for all risy assets, r f the ris free iterest rate ad r p the portfolio s expected rate of retur. We characterize a ivestor s prefereces by utility curves of the followig geeral form: ( T T T U rp, σ p = rp λ σ p = wr+ ( w rf λ wvw. ( The first part of this utility fuctio is the expected retur of oe dollar ivested i the portfolio ad the secod part is half of the variace of oe dollar ivested i the portfolio multiplied by a scalar λ. The coveiece of this utility fuctio is that maximizig it is equivalet to fid a frotier portfolio, as we will show below. The coefficiet λ may be iterpreted as a coefficiet of ris aversio.3 Higher levels for U (, imply i higher utility for maagers ad ( shows that utility icreases if the expected retur icreases, ad it decreases whe the variace icreases. The relative magitude of these chages is govered by λ. A efficiet portfolio is oe that maximizes expected retur for a give level of variace (whe there is a solutio to this problem. We ca represet this problem as: max Τ T wr+ ( w { w} s.t. T w Σw = σ p. r f ( The Lagragea for this problem is: Τ T T l = wr+ ( w rf λ wvw σ p. (3 3 However, this is ot the absolute ris aversio as defied i Arrow (970 which is give by ( U' ( U''. 6

8 where λ is a positive costat. The first order coditios are: l = r r f λvw = p 0, (4 w l = T r p p ( T -w r w r = f 0. (5 λ Observe that (3 is essetially equivalet to (. The first order coditio of ( is exactly (4. As V is a positive defiite matrix, it follows that the first order coditios are ecessary ad sufficiet for a global optimum. I this case, we ca solve for the portfolio weights: wp = V ( r rf. (6 λ I what follows, we will show equatio (6 i a more coveiet way. If we have risy assets, the covariace matrix is: σ σ σ σ σ σ V =. σ ( σ σ( σ Usig Steves (998 direct characterizatio of the iverse of the covariace matrix, we have that the iverse of the covariace matrix is give by: β β σ ( R σ ( R σ ( R β β N σ ( R σ ( R σ ( R - V =. (7 β β σ ( R σ ( R σ ( R 7

9 where R i ad β ij are the R-squared ad the coefficiet for the multiple regressio of the excess retur for the -th asset o the excess returs of all the other assets. The factor ( R σ is the part of the variace of the excess retur for the -th asset that caot be explaied by the regressio o the other risy excess retur returs, which is equivalet to the estimate of the variace of the residual of that regressio. Usig this result, we ca rewrite (6 as: β σ ( R σ ( R σ ( R w r rf β β N w r r f σ σ σ ( R ( R ( R =. (8 λ w r r f β β σ ( R σ ( R σ ( R β Lettig ei = ri rf be the excess expected retur, the optimal weight for the first risy asset is: w = e β ei, (9 ( R i λσ i= ad for the secod risy asset is: w = e β ie i λσ ( R. (0 i= i I geeral, for a -th risy asset we have: w = e ( βie i λσ R. ( i= i 8

10 This is the optimal solutio for the top admiistratio that taes decisios o a risy asset framewor. It is iterestig to otice that the umerator e β e ca be see i i i= i as the costat of the regressio of excess retur of asset o the excess returs of the other risy assets ad the deomiator ( R σ is the residual variace of that regressio. To geerate the equivalece betwee the solutio of the top admiistratio ad of the decetralized decisio made by portfolio maagers, it is ecessary to guaratee that wealth allocated by the top admiistratio is the same as the wealth allocated by portfolio maagers i each risy asset. We will ow see some examples of how the equivalece problem may be solved.. Example. Oe portfolio maager for each risy asset Suppose that we have a -th portfolio maager that taes decisios regardig oe risy asset, deomiated asset. The the optimal weight for this portfolio maager would be: w r r = ( f,, λσ where λ is the coefficiet of ris aversio of the -th portfolio maager ad rf, is the ris free rate that he faces. The solutio above shows that optimal weight i the risy asset is iversely proportioal to the ris aversio ad the level of ris ad directly proportioal to the ris premium offered by the risy asset. As this portfolio maager does ot tae ito accout the overall covariace matrix there is a small probability that this portfolio will be efficiet i a overall sese. A sufficiet coditio for efficiecy would be that the optimal weight of the top admiistratio multiplied by this wealth would be equal to the portfolio maager s optimal weight multiplied by the portfolio maager s iitial edowmet. This equivalece result may be expressed as: 9

11 r rf, W 0, = e β ie i W0 λσ λσ ( R (3 i i= We ca explicitly fid a ris free iterest rate that would mae this coditio true: λ W r r e e W 0 f, = β i i λ ( R. (4 i= 0, i We could solve the problem usig the portfolio maager s iitial edowmet istead: W λ i 0, = β i W0 λ ( R i= e i e, (5 where we used r, f = r (i this case we ca allow the ris free iterest rate to be the f same for both the top admiistratio ad the portfolio maager. Equatio (4 ad (5 must hold for all portfolio maagers for each risy asset. This implies that the ris free iterest rate or iitial edowmet may be differet for portfolio maagers. However, i geeral portfolio maagers do ot trade o oe asset but i a asset class where there may be may assets. This motivates geeralizatios of the results obtaied above.. Example. Oe portfolio maager tradig o two risy assets We ca assume a -th portfolio maager that taes decisios regardig two risy, assets ad. Thus the optimal weights for this portfolio maager would be: w = e e ( ( β R, λσ, w = e e ( ( β R, λσ,, (6, (7 0

12 where w, ad w, are the optimal weights for assets ad, respectively ad R is the r-squared of the regressio of excess retur of the i-th risy asset o excess retur of the other risy assets maaged by the portfolio maager. Equivalece of results ca be derived usig the coditio that the amout ivested i each risy asset is the same. This coditio for the first ad secod risy assets ca be writte, respectively, as: (8 λσ λσ = e βe W0, = e β iei W0, i ( ( R ( R ( ( e β e W0, = e βie i W0 λσ R, λσ ( R (9 i= i i, where W 0, ad W 0, are the available iitial edowmets that portfolio maager has to ivest i assets ad, respectively. We ca fid edogeously the amout of iitial edowmets that the top admiistratio must dispose to portfolio maager by solvig (8 ad (9: W W ( R i i λ i= 0, = W0 λ e ( ( e β e R, ( R β e i i λ i= 0, = W0 λ e ( ( e β e R, β e (0 ( It is importat to otice that this iitial edowmet depeds of the ris aversio of idividual portfolio maagers ad the top admiistratio. It is iterestig to otice that iitial edowmet available to the portfolio maager rises as the portfolio maagers are more ris averse relatively to the top admiistratio. As the ratio λ λ icreases, more iitial edowmet ca be disposed to portfolio maager

13 . I geeral, the iitial edowmet disposed for portfolio maager for a risy asset m should be give by: W ( Rm m mi i i m λ = i m 0, = W0 λ e ( ( e m βme Rm, β e (.3 Example 3. Two portfolio maagers tradig i the same risy asset m A iterestig example to aalyze would be the case where there are two portfolio maagers ( ad j tradig o the same asset, say asset m. I this particular case, equivalece could be obtaied by: w W + w W = w W. (3 m m m, 0, m, j 0, j m 0 As there is o particular reaso for the top admiistratio to use differet iitial m m edowmets for portfolio maagers, we have that W0, = W0, j ad (3 ca be rewritte as: ( Rm e m mi i λ i= m m i m 0, = 0, j = 0 β e W W W. (4 em e m + λ λ j Expressio (4 could be easily geeralized for ay umber of portfolio maagers tradig o ay specific risy asset. The top admiistratio may choose to give differet iitial edowmets for differet portfolio maagers to ivest i the same asset, i this case (3 ca be rewritte as: W w w = W. (5 m m m, j m 0, W 0 0, j wm, wm,

14 I this case the iitial edowmet available for portfolio maager would deped o the iitial edowmet available for portfolio maager j. We will aalyze the geeral case i the ext subsectio sectio..4 A more geeral case: there are l portfolio maagers ad risy assets Suppose that we have l portfolio maagers ad risy assets. Portfolio maagers are specialized i subsets m, m, K, ml where m correspods to the subset that the -th portfolio maager trades. It is assumed that m I mj for some, j; j. The restrictios that should apply are give by: l = l = l = w W = ww, 0, 0 w W = ww, 0, 0 w W M = ww, 0, 0 I this case the top admiistratio decides which assets each portfolio maager should trade. The examples above help to uderstad how the top admiistratio would solve his problem. If there are more tha oe portfolio maager i a sigle asset the the top admiistratio could solve the problem as show i example 3. If there is oly oe portfolio maager i a sigle asset the he could solve the equivalece result as show i example. Fially, if portfolio maagers trade i more tha oe asset, all that the top admiistratio has to do is to use differet iitial edowmet for each risy asset. 3. Iterpretig the results I this sectio, we do some comparative static ad iterpret the expressios previously foud. It would be iterestig to uderstad what happes to portfolio maagers iitial edowmet (or the ris free iterest rate whe the exogeous parameters chage. 3

15 If we use expressio (5 the the iitial edowmet would deped o chages i the expected retur for asset as give below: W r λ 0, i = W 0 βi λ ( R i= e i e. (6 The sig of this derivative is positive, reflectig the growth of iterest i ivestig i risy asset by the top admiistratio (which ca be see from (. We could also aswer how the wealth would chage for a give portfolio maager that trades o asset whe the expected retur o asset j chages: W r 0, j λ = λ ( R W β 0 j e e j (7 The sig of this derivative depeds o the beta coefficiet, i.e., i the correlatio betwee assets. If the correlatio is egative the the top admiistratio would icrease the iitial edowmet to iduce a icrease i ivestmet i asset. The icrease ivestmet i a asset egatively correlated with the asset that improved its expected retur is due to a hedge effect. O the other had, if correlatio were positive the the iitial edowmet would be reduced to reduce the ris exposure of the overall portfolio. We ca iterpret expressio (, which gives the optimal iitial edowmet that should be available for a portfolio maager i order to obtai the equivalece result. The iitial edowmet available depeds o the ratio of the ris aversio coefficiets. The greater λ the more ris averse is portfolio maager. If this portfolio maager is more ris averse tha the top admiistratio the he would be propese to uderivest i asset m. I that case the top admiistratio would icrease the portfolio maager s iitial edowmet i order to iduce a icrease i the portfolio maager s ris exposure. W also depeds o the ratio of the Residual Sharpe Ratios. The greater the Residual m 0, Sharpe Ratio of the top admiistratio relative to the Residual Sharpe Ratio of the portfolio maager for asset m the more willig the top admiistratio is to icrease the portfolio maager s iitial edowmet i asset m. Icreasig the iitial edowmet would mae the portfolio maager ivest more i that particular asset. 4

16 From expressio (9 we ca derive a iterestig relatio betwee the iitial edowmets of portfolio maagers. The partial derivative of portfolio maager s iitial edowmet for asset m with respect to the iitial edowmet of portfolio maager j for asset m is: ( Rm, m mi i m i= W w 0, m, j λ j i m = = m W0, j wm, λ m j ( Rm, j e m β e em βmie i i= i m (8 This expressio gives us the rate at which the top admiistratio would decrease (icrease portfolio maager iitial edowmet after icreasig (decreasig portfolio maager j iitial edowmet. This tradig rate is depedet o the ris aversio coefficiets ratio ad the Residual Sharpe Ratio Coefficiets. 4. Coclusios I geeral, decetralizatio of portfolio allocatio would ot geerate a efficiet global portfolio as decetralized decisios do o tae ito accout the overall covariace matrix. It is possible to use the ris free iterest rate ad the available iitial edowmet for portfolio maagers i order to geerate a equivalece of portfolio allocatio results ad fid a efficiet global portfolio. If portfolio maagers trade i more tha oe risy asset the the top admiistratio could use the iitial edowmet available for ivestig i each risy asset as a cotrol variable to obtai the equivalece result. This meas that the top admiistratio could redistribute the iitial edowmet amog portfolio maagers as exogeous parameters chage at the begiig of the portfolio buildig process. We used here a type of secod welfare theorem. Our fidigs suggest that the ris free iterest rate ad the iitial edowmet used as cotrol variables deped o a umber of parameters ad o ris aversio coefficiets. This motivates further research o estimatio of ris aversio coefficiets. As it is widely ow these coefficiets are ot directly observable ad to our owledge there 5

17 are ot may published wor that estimates idividual ris aversio coefficiets4. This is left for further research. Aother iterestig questio would be to aswer what is the optimal umber of portfolio maagers that a firm should have. This is a very importat problem that tradig firms deal with all the time ad is still a ope questio. Agecy cosideratios ad the use of multi-period portfolio selectio models would be aother importat route to explore withi decetralized ivestmet maagemet5. However, our approach could be use i a dyamic framewor. The top admiistratio must defie the ivestmet horizo for the firm ad other portfolio maagers ad at the ed of each period he would coordiate ad redistribute iitial edowmet amog portfolio maagers. Noetheless, this extesio raises the questio of how well portfolio maagers would have performed withi the ivestmet horizo period ad this would lead to asymmetric iformatio cosideratios amog portfolio maagers as well. There are may ope questios yet. As the literature o this theme is almost oexistet, we aswered very simple questios. This is a first step, yet importat, towards a uderstadig of how delegatio of portfolios ca be made without loosig overall efficiecy. However, there are may questios to be made ad aswered. They are left for further research. 4 Sharpe et alli (999 derive the ris tolerace for a ivestor usig the equatio for a idifferece curve of a ivestor havig costat ris tolerace. Their solutio depeds of the optimal weights give by maagers for risy assets, o the variace ad expected excess retur of the portfolio. 5 Sharpe (98 aalyzes decetralized ivestmet maagemet i a differet framewor. Koo ad Yamazai (99, Porter (973, Pyle ad Turovsy (970, Roy (95 ad Pye (97 aalyze differet approaches to the mea-variace portfolio criteria such as the safety-first ad stochastic domiace criteria. 6

18 Refereces Alexader, G The derivatio of efficiet sets. Joural of Fiacial ad Quatitative Aalysis : Arrow, K Essays i the Theory of Ris-Bearig. Amsterdam: North-Hollad. Barry, C.B., Stars, L.T Ivestmet Maagers ad ris sharig with multiple maagers. Joural of Fiace, 39: Bhattacharya, S., Pfleiderer, P Delegated portfolio maagemet, Joural of Ecoomic Theory, 36: -5. Britte-Joes, M The samplig error i estimates of mea-variace efficiet portfolio weights. Joural of Fiace, 54: Elto, E.J., Gruber, M.J Moder Portfolio Theory ad Ivestmet Aalysis. New Yor: Joh Wiley & Sos. Elto, E.J., Gruber, M. J., Padberg, M.W Simple criteria for optimal portfolio selectio. Joural of Fiace, : Elto, E.J., Gruber, M. J., Padberg, M.W Simple criteria for optimal portfolio selectio: tracig out the efficiet frotier. Joural of Fiace, 4: Geotte, G Optimal portfolio choice uder icomplete iformatio. Joural of Fiace, 4: Huag, C., Litzeberger, R.H Foudatios for Fiacial Ecoomics. New Yor: Elsevier Sciece Publishig Co. Koo, H., Yamazai, H. 99. Mea absolute deviatio portfolio optimizatio ad it s applicatios to Toyo stoc maret. Maagemet Sciece, 39: Marowitz, H. 95. Portfolio Selectio. Joural of Fiace, 7: Marowitz, H Portfolio selectio: efficiet diversificatio of ivestmets. New Yor: Joh Wiley & Sos. Porter, B A empirical compariso of stochastic domiace ad mea-variace portfolio choice criteria. Joural of Fiacial ad Quatitative Aalysis, 8: Pye, G. 97. Miimax Portfolio choices. Fiacial Aalyst Joural, 8: Pyle, D., Turovsy, S Safety-first ad expected utility maximizatio i meastadard deviatio portfolio aalysis. Review of Ecoomic ad Statistics, 5: Roy, A.D. 95. Safety-first ad the holdig of assets. Ecoometrics, 0:

19 Steves, G.V.G O the Iverse of the covariace matrix i portfolio aalysis. Joural of Fiace, 53: Sharpe, W. F. 98. Decetralized ivestmet maagemet. Joural of Fiace, 36: Sharpe, W.F.,Alexader, G. J., Bailey, J. V Ivestmets. New Jersey: Pretice Hall. Stoughto, N.M Moral hazard ad the portfolio maagemet problem. Joural of Fiace, 48: Tobi, J Liquidity preferece as behavior towards ris. Review of Ecoomic Studies, 5:

20 Baco Cetral do Brasil Trabalhos para Discussão Os Trabalhos para Discussão podem ser acessados a iteret, o formato PDF, o edereço: Worig Paper Series Worig Papers i PDF format ca be dowloaded from: Implemetig Iflatio Targetig i Brazil Joel Bogdasi, Alexadre Atoio Tombii ad Sérgio Ribeiro da Costa Werlag Política Moetária e Supervisão do Sistema Fiaceiro Nacioal o Baco Cetral do Brasil Eduardo Ludberg Moetary Policy ad Baig Supervisio Fuctios o the Cetral Ba Eduardo Ludberg 3 Private Sector Participatio: a Theoretical Justificatio of the Brazilia Positio Sérgio Ribeiro da Costa Werlag 4 A Iformatio Theory Approach to the Aggregatio of Log-Liear Models Pedro H. Albuquerque 5 The Pass-Through from Depreciatio to Iflatio: a Pael Study Ila Goldfaj ad Sérgio Ribeiro da Costa Werlag 6 Optimal Iterest Rate Rules i Iflatio Targetig Framewors José Alvaro Rodrigues Neto, Fabio Araújo ad Marta Baltar J. Moreira 7 Leadig Idicators of Iflatio for Brazil Marcelle Chauvet 8 The Correlatio Matrix of the Brazilia Cetral Ba s Stadard Model for Iterest Rate Maret Ris José Alvaro Rodrigues Neto 9 Estimatig Exchage Maret Pressure ad Itervetio Activity Emauel-Werer Kohlschee 0 Aálise do Fiaciameto Extero a uma Pequea Ecoomia Aplicação da Teoria do Prêmio Moetário ao Caso Brasileiro: Carlos Hamilto Vascocelos Araújo e Reato Galvão Flôres Júior A Note o the Efficiet Estimatio of Iflatio i Brazil Michael F. Brya ad Stephe G. Cecchetti A Test of Competitio i Brazilia Baig Márcio I. Naae July/000 Jul/000 July/000 July/000 July/000 July/000 July/000 Set/000 Set/000 Nov/000 Mar/00 Mar/00 Mar/00 9

21 3 Modelos de Previsão de Isolvêcia Bacária o Brasil Marcio Magalhães Jaot 4 Evaluatig Core Iflatio Measures for Brazil Fracisco Marcos Rodrigues Figueiredo 5 Is It Worth Tracig Dollar/Real Implied Volatility? Sadro Caesso de Adrade ad Bejami Mirada Taba 6 Avaliação das Projeções do Modelo Estrutural do Baco Cetral do Brasil Para a Taxa de Variação do IPCA Sergio Afoso Lago Alves Evaluatio of the Cetral Ba of Brazil Structural Model s Iflatio Forecasts i a Iflatio Targetig Framewor Sergio Afoso Lago Alves 7 Estimado o Produto Potecial Brasileiro: uma Abordagem de Fução de Produção Tito Nícias Teixeira da Silva Filho Estimatig Brazilia Potetial Output: a Productio Fuctio Approach Tito Nícias Teixeira da Silva Filho 8 A Simple Model for Iflatio Targetig i Brazil Paulo Spriger de Freitas ad Marcelo Kfoury Muihos 9 Ucovered Iterest Parity with Fudametals: a Brazilia Exchage Rate Forecast Model Marcelo Kfoury Muihos, Paulo Spriger de Freitas ad Fabio Araújo 0 Credit Chael without the LM Curve Victorio Y. T. Chu ad Márcio I. Naae Os Impactos Ecoômicos da CPMF: Teoria e Evidêcia Pedro H. Albuquerque Decetralized Portfolio Maagemet Paulo Coutiho ad Bejami Mirada Taba 3 Os Efeitos da CPMF sobre a Itermediação Fiaceira Sérgio Miio Koyama e Márcio I. Naae 4 Iflatio Targetig i Brazil: Shocs, Bacward-Looig Prices, ad IMF Coditioality Joel Bogdasi, Paulo Spriger de Freitas, Ila Goldfaj ad Alexadre Atoio Tombii 5 Iflatio Targetig i Brazil: Reviewig Two Years of Moetary Policy 999/00 Pedro Fachada 6 Iflatio Targetig i a Ope Fiacially Itegrated Emergig Ecoomy: the Case of Brazil Marcelo Kfoury Muihos 7 Complemetaridade e Fugibilidade dos Fluxos de Capitais Iteracioais Carlos Hamilto Vascocelos Araújo e Reato Galvão Flôres Júior Mar/00 Mar/00 Mar/00 Mar/00 July/00 Abr/00 Aug/00 Apr/00 May/00 May/00 Ju/00 Jue/00 Jul/00 Aug/00 Aug/00 Aug/00 Set/00 0

22 8 Regras Moetárias e Diâmica Macroecoômica o Brasil: uma Abordagem de Expectativas Racioais Marco Atoio Boomo e Ricardo D. Brito 9 Usig a Moey Demad Model to Evaluate Moetary Policies i Brazil Pedro H. Albuquerque ad Solage Gouvêa 30 Testig the Expectatios Hypothesis i the Brazilia Term Structure of Iterest Rates Bejami Mirada Taba ad Sadro Caesso de Adrade 3 Algumas Cosiderações sobre a Sazoalidade o IPCA Fracisco Marcos R. Figueiredo e Roberta Blass Staub 3 Crises Cambiais e Ataques Especulativos o Brasil Mauro Costa Mirada 33 Moetary Policy ad Iflatio i Brazil ( : a VAR Estimatio Adré Miella 34 Costraied Discretio ad Collective Actio Problems: Reflectios o the Resolutio of Iteratioal Fiacial Crises Armiio Fraga ad Daiel Luiz Gleizer 35 Uma Defiição Operacioal de Estabilidade de Preços Tito Nícias Teixeira da Silva Filho 36 Ca Emergig Marets Float? Should They Iflatio Target? Barry Eichegree 37 Moetary Policy i Brazil: Remars o the Iflatio Targetig Regime, Public Debt Maagemet ad Ope Maret Operatios Luiz Ferado Figueiredo, Pedro Fachada ad Sérgio Goldestei 38 Volatilidade Implícita e Atecipação de Evetos de Stress: um Teste para o Mercado Brasileiro Frederico Pechir Gomes 39 Opções sobre Dólar Comercial e Expectativas a Respeito do Comportameto da Taxa de Câmbio Paulo Castor de Castro 40 Speculative Attacs o Debts, Dollarizatio ad Optimum Currecy Areas Aloisio Araujo ad Márcia Leo 4 Mudaças de Regime o Câmbio Brasileiro Carlos Hamilto V. Araújo e Getúlio B. da Silveira Filho 4 Modelo Estrutural com Setor Extero: Edogeização do Prêmio de Risco e do Câmbio Marcelo Kfoury Muihos, Sérgio Afoso Lago Alves e Gil Riella 43 The Effects of the Brazilia ADRs Program o Domestic Maret Efficiecy Bejami Mirada Taba ad Eduardo José Araújo Lima 44 Estrutura Competitiva, Produtividade Idustrial e Liberação Comercial o Brasil Pedro Cavalcati Ferreira e Osmai Teixeira de Carvalho Guillé Nov/00 Nov/00 Nov/00 Nov/00 Nov/00 Nov/00 Nov/00 Dez/00 Feb/00 Mar/00 Mar/00 Mar/00 Abr/00 Ju/00 Ju/00 Jue/00 Ju/00

23 45 Optimal Moetary Policy, Gais from Commitmet, ad Iflatio Persistece Adré Miella 46 The Determiats of Ba Iterest Spread i Brazil Tarsila Segalla Afaasieff, Priscilla Maria Villa Lhacer ad Márcio I. Naae 47 Idicadores Derivados de Agregados Moetários Ferado de Aquio Foseca Neto e José Albuquerque Júior 48 Should Govermet Smooth Exchage Rate Ris? Ila Goldfaj ad Marcos Atoio Silveira 49 Desevolvimeto do Sistema Fiaceiro e Crescimeto Ecoômico o Brasil: Evidêcias de Causalidade Orlado Careiro de Matos 50 Macroecoomic Coordiatio ad Iflatio Targetig i a Two- Coutry Model Eui Jug Chag, Marcelo Kfoury Muihos ad Joaílio Rodolpho Teixeira 5 Credit Chael with Sovereig Credit Ris: a Empirical Test Victorio Yi Tso Chu 5 Geeralized Hyperbolic Distributios ad Brazilia Data José Fajardo ad Aquiles Farias 53 Iflatio Targetig i Brazil: Lessos ad Challeges Adré Miella, Paulo Spriger de Freitas, Ila Goldfaj ad Marcelo Kfoury Muihos 54 Stoc Returs ad Volatility Bejami Mirada Taba ad Solage Maria Guerra 55 Compoetes de Curto e Logo Prazo das Taxas de Juros o Brasil Carlos Hamilto Vascocelos Araújo e Osmai Teixeira de Carvalho de Guillé 56 Causality ad Coitegratio i Stoc Marets: the Case of Lati America Bejami Mirada Taba ad Eduardo José Araújo Lima 57 As Leis de Falêcia: uma Abordagem Ecoômica Aloisio Araujo 58 The Radom Wal Hypothesis ad the Behavior of Foreig Capital Portfolio Flows: the Brazilia Stoc Maret Case Bejami Mirada Taba 59 Os Preços Admiistrados e a Iflação o Brasil Fracisco Marcos R. Figueiredo e Thaís Porto Ferreira Aug/00 Aug/00 Sep/00 Sep/00 Set/00 Sep/00 Sep/00 Sep/00 Nov/00 Nov/00 Nov/00 Dec/00 Dez/00 Dec/00 Dez/00