Delegated portfolio management

ISSN 1518-3548 Working Paper Series Delegated Portfolio Management Paulo Coutinho and Benjamin Miranda Tabak December, 2002 ISSN 1518-3548 CGC 00.038.166/0001-05 Working Paper Series Brasília n. 60 Dec 2002 P. 1-22 Working Paper Series Edited by: Research Department (Depep) (E-mail: workingpaper@bcb.gov.br) Reproduction permitted only if source is stated as follows: Working Paper Series n. 60 Authorized by Ilan Goldfajn (Deputy Governor for Economic Policy). General Control of Subscription: Banco Central do Brasil Demap/Disud/Subip SBS – Quadra 3 – Bloco B – Edifício-Sede – 2º subsolo 70074-900 Brasília – DF – Brazil Phone: (5561) 414-1392 Fax: (5561) 414-3165 The views expressed in this work are those of the authors and do not reflect those of the Banco Central or its members. Although these Working Papers often represent preliminary work, citation of source is required when used or reproduced. As opiniões expressas neste trabalho são exclusivamente do(s) autor(es) e não refletem a visão do Banco Central do Brasil. Ainda que este artigo represente trabalho preliminar, citação da fonte é requerida mesmo quando reproduzido parcialmente. Banco Central do Brasil Information Bureau Address: Secre/Surel/Diate SBS – Quadra 3 – Bloco B Edifício-Sede – 2º subsolo 70074-900 Brasília – DF – Brazil Phones: (5561) 414 (....) 2401, 2402, 2403, 2404, 2405, 2406 DDG: 0800 992345 Fax: (5561) 321-9453 Internet: http://www.bcb.gov.br E-mails: cap.secre@bcb.gov.br dinfo.secre@bcb.gov.br Delegated Portfolio Management Paulo Coutinho* Benjamin Miranda Tabak** Abstract In this paper, we examine optimal portfolio decisions within a decentralized framework. There are many portfolio managers choosing optimal portfolio weights in a mean-variance framework and taking decisions in a decentralized way. However, the overall portfolio may not be efficient, as the portfolio managers do not take into account the overall covariance matrix. We show that the initial endowment that portfolio managers can use within the firm in order to manage their portfolios can be used as a control variable by the top administration and redistributed within the firm in order to achieve overall efficiency. Keywords: Optimal Portfolio, Decentralized, Efficient Frontier, Portfolio Management. * Economics Department, Universidade de Brasília. E-mail address: coutinho@unb.br ** Research Department, Central Bank of Brazil. E-mail address: benjamin.tabak@bcb.gov.br 3 1. Introduction One of the main tasks of portfolio managers is to achieve the best possible trade-off between risk and return. This task involves the determination of the best risk-return opportunities available from feasible portfolios and the choice of the best portfolio from this feasible set. However, in many situations, the portfolio is managed in a decentralized way, with the top administration of the firm delegating to different portfolio managers partial control about investment in subclasses of assets. In general, the top administration of trading firms decides the amount of wealth invested in certain asset classes. The top administration however delegates to portfolio managers the control of which specific securities to hold and the proportions of these securities in the portfolio. 1 The delegation process may imply in an overall inefficient portfolio. Even if all portfolio managers are in the efficient frontier for their particular asset class it may be the case that, in the aggregate, the resulting portfolio is an inefficient one as portfolio managers are not taking into account the overall covariance matrix and all possible combinations that would result in the best trade-off between risk and return. These considerations has led us to examine which conditions should be met so that even in a decentralized decision making set the overall portfolio would be efficient. Our findings suggest that the initial endowment available for investing by the portfolio managers and the risk free interest rate they face when taking investment decisions can be used as control variables to attain overall efficiency. Although we recognize that asymmetry of information play a crucial role in the delegation process, in this paper, we put these considerations to concentrate in the pure compatibility of solutions between the different portfolio managers with the overall 1 Classical articles in asset allocation choice are Tobin (1958) and Markowitz (1952, 1959). 4 solution. Bhattacharya and Pfleiderer (1985) develop a model of decentralized investment management under asymmetric information, where they are especially concerned about screening agents with superior information and on the surplus extraction from the agent. Barry and Starks (1984) show that risk sharing considerations are sufficient to motivate the use of multiple managers. Stoughton (1993) investigate the significance of nonlinear contracts on the incentive for portfolio managers to collect information, justifying employment of portfolio managers with the notion of superior skills at acquiring and interpreting information related to movement in security prices. We solve the problem of finding equivalence between decentralized and centralized portfolio management analytically within a mean-variance framework, which provides some insights on how to enhance the delegation process.2 Our findings suggest that it is possible to decentralize investment decisions and construct portfolios that are still optimal in an aggregate sense. All that is needed are some instruments to control decisions taken by portfolio managers such as their available initial endowment and the risk free interest rate that they face, which may be determined endogenously in our model. We solve a general case with many portfolio managers that are specialized in some particular asset class (which may intersect or not in some cases), and show that the initial endowment that portfolio managers have to invest in their portfolios can be used by the top administration to achieve overall efficiency. The organization of the paper is as follows. In section II, we develop the model. Section III gives some interpretations of the results. Section IV concludes and gives directions for further research. 2 There may be other difficulties in implementing mean-variance analysis such as the extreme weights that may arise when sample efficient portfolios are constructed. As Genotte (1986) and Britten-Jones (1999) noticed, there are huge estimation errors in expected returns estimation, which cannot be ignored. However, we will not address these points in this paper. 5 2. The model We start with n risky assets. Let w be the n x 1 vector of portfolio weights for risky assets, V the n x n covariance matrix, r the n x 1 expected return vector for all risky assets, rf the risk free interest rate and rp the portfolio’s expected rate of return. We characterize an investor’s preferences by utility curves of the following general form: 1 1 U ( rp , σ p ) = rp − λ σ p2 = w Tr + (1 − w T 1) rf − λ w T Vw . 2 2 (1) The first part of this utility function is the expected return of one dollar invested in the portfolio and the second part is half of the variance of one dollar invested in the portfolio multiplied by a scalar λ . The convenience of this utility function is that maximizing it is equivalent to find a frontier portfolio, as we will show below. The coefficient λ may be interpreted as a coefficient of risk aversion.3 Higher levels for U ( ⋅, ⋅) imply in higher utility for managers and (1) shows that utility increases if the expected return increases, and it decreases when the variance increases. The relative magnitude of these changes is governed by λ . An efficient portfolio is one that maximizes expected return for a given level of variance (when there is a solution to this problem). We can represent this problem as: max w ȉr + (1 − w T 1) rf {w} s.t. (2) 1 T w Ȉw = σ p2 . 2 The Lagrangean for this problem is: 1 l = w ȉr + (1 − w T 1) rf − λ  w T Vw − σ 2p 2  .  3 However, this is not the absolute risk aversion as defined in Arrow (1970) which is given by − U '' ( ⋅) U ' ( ⋅) . 6 (3) where λ is a positive constant. The first order conditions are: ∂l = r − 1rf − λ V w p = 0 , ∂w (4) ∂l = rp - w Tp r − (1 − w T 1) rf = 0 . ∂λ (5) Observe that (3) is essentially equivalent to (1). The first order condition of (1) is exactly (4). As V is a positive definite matrix, it follows that the first order conditions are necessary and sufficient for a global optimum. In this case, we can solve for the portfolio weights: wp = V −1 ( r − 1rf ) . 1 λ (6) In what follows, we will show equation (6) in a more convenient way. If we have n risky assets, the covariance matrix is:  σ 12 σ 12  2 σ 21 σ 2 V= ⋅ ⋅  ⋅  ⋅ σ ⋅  n1 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ σ 1n   σ 2n  .  σ ( n−1) n  σ n2  ⋅ ⋅ σ n ( n −1) Using Stevens’ (1998) direct characterization of the inverse of the covariance matrix, we have that the inverse of the covariance matrix is given by: 1   σ 2 1 − R2 1 )  1(  β  − 2 21 2  σ 2 (1 − R2 ) V -1 =  ⋅   ⋅  β n1 − 2  σ (1 − R 2 ) n  n − β12 σ (1 − R 2 1 2 1 ) 1 σ (1 − R22 ) ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 2 2 − β n2 σ (1 − Rn2 ) 2 n 7   σ (1 − R )   β − 2 2N 2  σ 2 (1 − R2 )  . ⋅   ⋅  1  σ n2 (1 − Rn2 )  ⋅ ⋅ − ⋅ ⋅ β1n 2 1 2 1 (7) where R i2 and β ij are the R-squared and the coefficient for the multiple regression of the excess return for the k-th asset on the excess returns of all the other assets. The factor σ 12 (1 − R12 ) is the part of the variance of the excess return for the k-th asset that cannot be explained by the regression on the other risky excess return returns, which is equivalent to the estimate of the variance of the residual of that regression. Using this result, we can rewrite (6) as: 1   σ 2 1 − R2 1 )  1( w  1  β 21 w  −  2  2  1  σ 2 (1 − R22 )  ⋅ =    λ ⋅  ⋅   ⋅ w    n β n1 −  σ 2 (1 − R 2 ) n  n − β12 σ (1 − R 2 1 2 1 ) 1 2 σ 2 (1 − R22 ) ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ − βn2 σ (1 − Rn2 ) 2 n   σ (1 − R )    r1 − rf β2N − 2   r2 − rf 2 σ 2 (1 − R2 )    ⋅ ⋅  ⋅  ⋅   rn − rf 1  2 σ n (1 − Rn2 )  ⋅ ⋅ − ⋅ ⋅ β1n 2 1 2 1    .     (8) Letting ei = ri − rf be the excess expected return, the optimal weight for the first risky asset is: w1 = n 1   β1i ei  , − e ∑ 2 2  1 λσ 1 (1 − R1 )  i =2  (9) and for the second risky asset is:   n 1  w2 = e − ∑ β 2i ei  . 2 2  2  λσ 2 (1 − R2 )  i =1 i≠2   (10) In general, for a k-th risky asset we have:   n 1  wk = ek − ∑ β ki ei  .  λσ k2 (1 − Rk2 )  i =1 i≠k   8 (11) This is the optimal solution for the top administration that takes decisions on an n risky asset framework. It is interesting to notice that the numerator ek − ∑ β ki ei can be seen n i =1 i≠k as the constant of the regression of excess return of asset k on the excess returns of the other risky assets and the denominator σ k2 (1 − Rk2 ) is the residual variance of that regression. To generate the equivalence between the solution of the top administration and of the decentralized decision made by portfolio managers, it is necessary to guarantee that wealth allocated by the top administration is the same as the wealth allocated by portfolio managers in each risky asset. We will now see some examples of how the equivalence problem may be solved. 2.1 Example 1. One portfolio manager for each risky asset Suppose that we have a k-th portfolio manager that takes decisions regarding one risky asset, denominated asset k. Then the optimal weight for this portfolio manager would be: wk ,k = rk − rf , k λkσ k2 where λk is the coefficient of risk aversion of the k-th portfolio manager and rf ,k is the risk free rate that he faces. The solution above shows that optimal weight in the risky asset is inversely proportional to the risk aversion and the level of risk and directly proportional to the risk premium offered by the risky asset. As this portfolio manager does not take into account the overall covariance matrix there is a small probability that this portfolio will be efficient in an overall sense. A sufficient condition for efficiency would be that the optimal weight of the top administration multiplied by this wealth would be equal to the portfolio manager’s optimal weight multiplied by the portfolio manager’s initial endowment. This equivalence result may be expressed as: 9 (12) rk − rf ,k λkσ k2 W0, k   n 1  = e − ∑ β ki ei  W0 2 2  k  λσ k (1 − Rk )  i≠k i =1   (13) We can explicitly find a risk free interest rate that would make this condition true:  rf , k  n λ W 1  = rk − k − β ki ei  0 . e ∑ 2  k  W0,k λ (1 − Rk )  i =1  i≠k  (14) We could solve the problem using the portfolio manager’s initial endowment instead:  W0,k  n λ e 1  = k − β ki i  W0 , 1 ∑ 2  λ (1 − Rk )  i =1 ek   i≠k  (15) where we used rf , k = rf (in this case we can allow the risk free interest rate to be the same for both the top administration and the portfolio manager). Equation (14) and (15) must hold for all n portfolio managers for each risky asset. This implies that the risk free interest rate or initial endowment may be different for portfolio managers. However, in general portfolio managers do not trade on one asset but in an asset class where there may be many assets. This motivates generalizations of the results obtained above. 2.2 Example 2. One portfolio manager trading on two risky assets We can assume a k-th portfolio manager that takes decisions regarding two risky, assets 1 and 2. Thus the optimal weights for this portfolio manager would be: w1, k = 1 ( e1 − β12e2 ) , λkσ (1 − R1,2k ) (16) w2,k = 1 ( e2 − β 21e1 ) , λkσ (1 − R2,2 k ) (17) 2 1 2 2 10 where w1,k and w2,k are the optimal weights for assets 1 and 2, respectively and Ri2,k is the r-squared of the regression of excess return of the i-th risky asset on excess return of the other risky assets managed by the portfolio manager k. Equivalence of results can be derived using the condition that the amount invested in each risky asset is the same. This condition for the first and second risky assets can be written, respectively, as: n 1 1   1 e e W e β β1i ei W0 − = − ( ) ∑ 1 12 2 0, k 2 2 2 2  1 λkσ 1 (1 − R1,k ) λσ 1 (1 − R1 )  i =2    n 1 1 2  e2 − ∑ β 2 i ei W0 ( e2 − β 21e1 )W0,k = 2  λkσ 22 (1 − R2,2 k ) λσ 2 (1 − R22 )  i =1 ≠ 2 i   (18) (19) 1 2 where W0,k and W0,k are the available initial endowments that portfolio manager k has to invest in assets 1 and 2, respectively. We can find endogenously the amount of initial endowments that the top administration must dispose to portfolio manager k by solving (18) and (19): W0,1 k W0,2k n 1   β1i ei  e − ∑ 2  1 i =2  λ (1 − R1 )  = k W0 1 λ (e − β e ) (1 − R1,2k ) 1 12 2 n  1  − β 2i ei  e ∑ 2  2 i =2  λ (1 − R2 )  = k W0 1 λ (e − β e ) (1 − R2,2 k ) 2 21 1 It is important to notice that this initial endowment depends of the risk aversion of individual portfolio managers and the top administration. It is interesting to notice that initial endowment available to the portfolio manager rises as the portfolio managers are more risk averse relatively to the top administration. As the ratio λk λ increases, more initial endowment can be disposed to portfolio manager 11 (20) (21) k. In general, the initial endowment disposed for portfolio manager k for a risky asset m should be given by: W0,mk 2.3   n 1  e − ∑ β mi ei  2  m  1 − Rm )  i =1 λk ( i≠m  W = 0 1 λ e e β − ( ) 2 2 m m (1 − Rk2,m ) (22) Example 3. Two portfolio managers trading in the same risky asset m An interesting example to analyze would be the case where there are two portfolio managers (k and j) trading on the same asset, say asset m. In this particular case, equivalence could be obtained by: wm,kW0,mk + wm , jW0,mj = wmW0 . (23) As there is no particular reason for the top administration to use different initial endowments for portfolio managers, we have that W0,mk = W0,mj and (23) can be rewritten as: W0,mk = W0,mj    n 1   e − β e  mi i   λ (1 − R 2 )  m ∑  i =1 m    i m ≠    W0 . =  em em   +   λk λ j  (24) Expression (24) could be easily generalized for any number of portfolio managers trading on any specific risky asset. The top administration may choose to give different initial endowments for different portfolio managers to invest in the same asset, in this case (23) can be rewritten as: W0,mk = wm wm, k W0 12 − wm, j wm , k W0,mj . (25) In this case the initial endowment available for portfolio manager k would depend on the initial endowment available for portfolio manager j. We will analyze the general case in the next subsection section. 2.4 A more general case: there are l portfolio managers and n risky assets Suppose that we have l portfolio managers and n risky assets. Portfolio managers are specialized in subsets m1 , m2 ,K , ml where mk corresponds to the subset that the k-th portfolio manager trades. It is assumed that mk I m j ≠ ∅ for some k , j; k ≠ j . The restrictions that should apply are given by: ∑w l 1, k W0,1 k = wW 1 0 2, k W0,2k = w2W0 ∑w k =1 l k =1 ∑w M l k =1 n,k W0,nk = wnW0 In this case the top administration decides which assets each portfolio manager should trade. The examples above help to understand how the top administration would solve his problem. If there are more than one portfolio manager in a single asset then the top administration could solve the problem as shown in example 3. If there is only one portfolio manager in a single asset then he could solve the equivalence result as shown in example 1. Finally, if portfolio managers trade in more than one asset, all that the top administration has to do is to use different initial endowment for each risky asset. 3. Interpreting the results In this section, we do some comparative static and interpret the expressions previously found. It would be interesting to understand what happens to portfolio managers’ initial endowment (or the risk free interest rate) when the exogenous parameters change. 13 If we use expression (15) then the initial endowment would depend on changes in the expected return for asset k as given below: ∂W0,k ∂rk = n λk ei 1 W 0 ∑ β ki 2 . 2 λ (1 − Rk ) i =1 ek (26) i≠k The sign of this derivative is positive, reflecting the growth of interest in investing in risky asset k by the top administration (which can be seen from (11)). We could also answer how the wealth would change for a given portfolio manager that trades on asset k when the expected return on asset j changes: ∂W0,k ∂rj =− e λk 1 W0 β kj j 2 ek λ (1 − Rk ) The sign of this derivative depends on the beta coefficient, i.e., in the correlation between assets. If the correlation is negative then the top administration would increase the initial endowment to induce an increase in investment in asset k. The increase investment in an asset negatively correlated with the asset that improved its expected return is due to a hedge effect. On the other hand, if correlation were positive then the initial endowment would be reduced to reduce the risk exposure of the overall portfolio. We can interpret expression (22), which gives the optimal initial endowment that should be available for a portfolio manager in order to obtain the equivalence result. The initial endowment available depends on the ratio of the risk aversion coefficients. The greater λk the more risk averse is portfolio manager k. If this portfolio manager is more risk averse than the top administration then he would be propense to underinvest in asset m. In that case the top administration would increase the portfolio manager’s initial endowment in order to induce an increase in the portfolio manager’s risk exposure. W0,mk also depends on the ratio of the Residual Sharpe Ratios. The greater the Residual Sharpe Ratio of the top administration relative to the Residual Sharpe Ratio of the portfolio manager for asset m the more willing the top administration is to increase the portfolio manager’s initial endowment in asset m. Increasing the initial endowment would make the portfolio manager invest more in that particular asset. 14 (27) From expression (29) we can derive an interesting relation between the initial endowments of portfolio managers. The partial derivative of portfolio manager’s k initial endowment for asset m with respect to the initial endowment of portfolio manager j for asset m is: ∂W0,mk ∂W m 0, j =− wm , j wm ,k   mk 1 e − β e  ∑ m mi i  1 − Rm2 ,k )  i =1 λj ( i m ≠   =− λk   mj 1 e − β e  mi i  i =1 (1 − Rm2 , j )  m ∑ i≠m  This expression gives us the rate at which the top administration would decrease (increase) portfolio manager k initial endowment after increasing (decreasing) portfolio manager j initial endowment. This trading rate is dependent on the risk aversion coefficients ratio and the Residual Sharpe Ratio Coefficients. 4. Conclusions In general, decentralization of portfolio allocation would not generate an efficient global portfolio as decentralized decisions do no take into account the overall covariance matrix. It is possible to use the risk free interest rate and the available initial endowment for portfolio managers in order to generate an equivalence of portfolio allocation results and find an efficient global portfolio. If portfolio managers trade in more than one risky asset then the top administration could use the initial endowment available for investing in each risky asset as a control variable to obtain the equivalence result. This means that the top administration could redistribute the initial endowment among portfolio managers as exogenous parameters change at the beginning of the portfolio building process. We used here a type of second welfare theorem. Our findings suggest that the risk free interest rate and the initial endowment used as control variables depend on a number of parameters and on risk aversion coefficients. This motivates further research on estimation of risk aversion coefficients. As it is widely known these coefficients are not directly observable and to our knowledge there 15 (28) are not many published work that estimates individual risk aversion coefficients4. This is left for further research. Another interesting question would be to answer what is the optimal number of portfolio managers that a firm should have. This is a very important problem that trading firms deal with all the time and is still an open question. Agency considerations and the use of multi-period portfolio selection models would be another important route to explore within decentralized investment management5. However, our approach could be use in a dynamic framework. The top administration must define the investment horizon for the firm and other portfolio managers and at the end of each period he would coordinate and redistribute initial endowment among portfolio managers. Nonetheless, this extension raises the question of how well portfolio managers would have performed within the investment horizon period and this would lead to asymmetric information considerations among portfolio managers as well. There are many open questions yet. As the literature on this theme is almost nonexistent, we answered very simple questions. This is a first step, yet important, towards an understanding of how delegation of portfolios can be made without loosing overall efficiency. However, there are many questions to be made and answered. They are left for further research. 4 Sharpe et alli (1999) derive the risk tolerance for an investor using the equation for an indifference curve of an investor having constant risk tolerance. Their solution depends of the optimal weights given by managers for risky assets, on the variance and expected excess return of the portfolio. 5 Sharpe (1981) analyzes decentralized investment management in a different framework. 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Review of Economic Studies, 25: 65-86. 18 Banco Central do Brasil Trabalhos para Discussão Os Trabalhos para Discussão podem ser acessados na internet, no formato PDF, no endereço: http://www.bc.gov.br Working Paper Series Working Papers in PDF format can be downloaded from: http://www.bc.gov.br July/2000 1 Implementing Inflation Targeting in Brazil Joel Bogdanski, Alexandre Antonio Tombini and Sérgio Ribeiro da Costa Werlang 2 Política Monetária e Supervisão do Sistema Financeiro Nacional no Banco Central do Brasil Eduardo Lundberg Jul/2000 Monetary Policy and Banking Supervision Functions on the Central Bank Eduardo Lundberg July/2000 3 Private Sector Participation: a Theoretical Justification of the Brazilian Position Sérgio Ribeiro da Costa Werlang July/2000 4 An Information Theory Approach to the Aggregation of Log-Linear Models Pedro H. Albuquerque July/2000 5 The Pass-Through from Depreciation to Inflation: a Panel Study Ilan Goldfajn and Sérgio Ribeiro da Costa Werlang July/2000 6 Optimal Interest Rate Rules in Inflation Targeting Frameworks José Alvaro Rodrigues Neto, Fabio Araújo and Marta Baltar J. Moreira July/2000 7 Leading Indicators of Inflation for Brazil Marcelle Chauvet Set/2000 8 The Correlation Matrix of the Brazilian Central Bank’s Standard Model for Interest Rate Market Risk José Alvaro Rodrigues Neto Set/2000 9 Estimating Exchange Market Pressure and Intervention Activity Emanuel-Werner Kohlscheen Nov/2000 10 Análise do Financiamento Externo a uma Pequena Economia Aplicação da Teoria do Prêmio Monetário ao Caso Brasileiro: 1991–1998 Carlos Hamilton Vasconcelos Araújo e Renato Galvão Flôres Júnior Mar/2001 11 A Note on the Efficient Estimation of Inflation in Brazil Michael F. Bryan and Stephen G. Cecchetti Mar/2001 12 A Test of Competition in Brazilian Banking Márcio I. Nakane Mar/2001 19 13 Modelos de Previsão de Insolvência Bancária no Brasil Marcio Magalhães Janot Mar/2001 14 Evaluating Core Inflation Measures for Brazil Francisco Marcos Rodrigues Figueiredo Mar/2001 15 Is It Worth Tracking Dollar/Real Implied Volatility? Sandro Canesso de Andrade and Benjamin Miranda Tabak Mar/2001 16 Avaliação das Projeções do Modelo Estrutural do Banco Central do Brasil Para a Taxa de Variação do IPCA Sergio Afonso Lago Alves Mar/2001 Evaluation of the Central Bank of Brazil Structural Model’s Inflation Forecasts in an Inflation Targeting Framework Sergio Afonso Lago Alves July/2001 Estimando o Produto Potencial Brasileiro: uma Abordagem de Função de Produção Tito Nícias Teixeira da Silva Filho Abr/2001 Estimating Brazilian Potential Output: a Production Function Approach Tito Nícias Teixeira da Silva Filho Aug/2002 18 A Simple Model for Inflation Targeting in Brazil Paulo Springer de Freitas and Marcelo Kfoury Muinhos Apr/2001 19 Uncovered Interest Parity with Fundamentals: a Brazilian Exchange Rate Forecast Model Marcelo Kfoury Muinhos, Paulo Springer de Freitas and Fabio Araújo May/2001 20 Credit Channel without the LM Curve Victorio Y. T. Chu and Márcio I. Nakane May/2001 21 Os Impactos Econômicos da CPMF: Teoria e Evidência Pedro H. Albuquerque 22 Decentralized Portfolio Management Paulo Coutinho and Benjamin Miranda Tabak 23 Os Efeitos da CPMF sobre a Intermediação Financeira Sérgio Mikio Koyama e Márcio I. Nakane 24 Inflation Targeting in Brazil: Shocks, Backward-Looking Prices, and IMF Conditionality Joel Bogdanski, Paulo Springer de Freitas, Ilan Goldfajn and Alexandre Antonio Tombini Aug/2001 25 Inflation Targeting in Brazil: Reviewing Two Years of Monetary Policy 1999/00 Pedro Fachada Aug/2001 26 Inflation Targeting in an Open Financially Integrated Emerging Economy: the Case of Brazil Marcelo Kfoury Muinhos Aug/2001 27 Complementaridade e Fungibilidade dos Fluxos de Capitais Internacionais Carlos Hamilton Vasconcelos Araújo e Renato Galvão Flôres Júnior Set/2001 17 20 Jun/2001 June/2001 Jul/2001 28 Regras Monetárias e Dinâmica Macroeconômica no Brasil: uma Abordagem de Expectativas Racionais Marco Antonio Bonomo e Ricardo D. Brito Nov/2001 29 Using a Money Demand Model to Evaluate Monetary Policies in Brazil Pedro H. Albuquerque and Solange Gouvêa Nov/2001 30 Testing the Expectations Hypothesis in the Brazilian Term Structure of Interest Rates Benjamin Miranda Tabak and Sandro Canesso de Andrade Nov/2001 31 Algumas Considerações sobre a Sazonalidade no IPCA Francisco Marcos R. Figueiredo e Roberta Blass Staub Nov/2001 32 Crises Cambiais e Ataques Especulativos no Brasil Mauro Costa Miranda Nov/2001 33 Monetary Policy and Inflation in Brazil (1975-2000): a VAR Estimation André Minella Nov/2001 34 Constrained Discretion and Collective Action Problems: Reflections on the Resolution of International Financial Crises Arminio Fraga and Daniel Luiz Gleizer Nov/2001 35 Uma Definição Operacional de Estabilidade de Preços Tito Nícias Teixeira da Silva Filho Dez/2001 36 Can Emerging Markets Float? Should They Inflation Target? Barry Eichengreen Feb/2002 37 Monetary Policy in Brazil: Remarks on the Inflation Targeting Regime, Public Debt Management and Open Market Operations Luiz Fernando Figueiredo, Pedro Fachada and Sérgio Goldenstein Mar/2002 38 Volatilidade Implícita e Antecipação de Eventos de Stress: um Teste para o Mercado Brasileiro Frederico Pechir Gomes Mar/2002 39 Opções sobre Dólar Comercial e Expectativas a Respeito do Comportamento da Taxa de Câmbio Paulo Castor de Castro Mar/2002 40 Speculative Attacks on Debts, Dollarization and Optimum Currency Areas Aloisio Araujo and Márcia Leon Abr/2002 41 Mudanças de Regime no Câmbio Brasileiro Carlos Hamilton V. Araújo e Getúlio B. da Silveira Filho Jun/2002 42 Modelo Estrutural com Setor Externo: Endogenização do Prêmio de Risco e do Câmbio Marcelo Kfoury Muinhos, Sérgio Afonso Lago Alves e Gil Riella Jun/2002 43 The Effects of the Brazilian ADRs Program on Domestic Market Efficiency Benjamin Miranda Tabak and Eduardo José Araújo Lima 44 Estrutura Competitiva, Produtividade Industrial e Liberação Comercial no Brasil Pedro Cavalcanti Ferreira e Osmani Teixeira de Carvalho Guillén 21 June/2002 Jun/2002 45 Optimal Monetary Policy, Gains from Commitment, and Inflation Persistence André Minella Aug/2002 46 The Determinants of Bank Interest Spread in Brazil Tarsila Segalla Afanasieff, Priscilla Maria Villa Lhacer and Márcio I. Nakane Aug/2002 47 Indicadores Derivados de Agregados Monetários Fernando de Aquino Fonseca Neto e José Albuquerque Júnior Sep/2002 48 Should Government Smooth Exchange Rate Risk? Ilan Goldfajn and Marcos Antonio Silveira Sep/2002 49 Desenvolvimento do Sistema Financeiro e Crescimento Econômico no Brasil: Evidências de Causalidade Orlando Carneiro de Matos Set/2002 50 Macroeconomic Coordination and Inflation Targeting in a TwoCountry Model Eui Jung Chang, Marcelo Kfoury Muinhos and Joanílio Rodolpho Teixeira Sep/2002 51 Credit Channel with Sovereign Credit Risk: an Empirical Test Victorio Yi Tson Chu Sep/2002 52 Generalized Hyperbolic Distributions and Brazilian Data José Fajardo and Aquiles Farias Sep/2002 53 Inflation Targeting in Brazil: Lessons and Challenges André Minella, Paulo Springer de Freitas, Ilan Goldfajn and Marcelo Kfoury Muinhos Nov/2002 54 Stock Returns and Volatility Benjamin Miranda Tabak and Solange Maria Guerra Nov/2002 55 Componentes de Curto e Longo Prazo das Taxas de Juros no Brasil Carlos Hamilton Vasconcelos Araújo e Osmani Teixeira de Carvalho de Guillén Nov/2002 56 Causality and Cointegration in Stock Markets: the Case of Latin America Benjamin Miranda Tabak and Eduardo José Araújo Lima Dec/2002 57 As Leis de Falência: uma Abordagem Econômica Aloisio Araujo Dez/2002 58 The Random Walk Hypothesis and the Behavior of Foreign Capital Portfolio Flows: the Brazilian Stock Market Case Benjamin Miranda Tabak Dec/2002 59 Os Preços Administrados e a Inflação no Brasil Francisco Marcos R. Figueiredo e Thaís Porto Ferreira Dez/2002 22