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Unformatted text preview: Trim: 246mm × 189mm CUUK2581-FM Top: 9.841mm CUUK2581/Brooks Gutter: 18.98mm 978 1 107 03466 2 December 20, 2013 3:48 Trim: 246mm × 189mm CUUK2581-FM Top: 9.841mm CUUK2581/Brooks Gutter: 18.98mm 978 1 107 03466 2 December 20, 2013 Introductory Econometrics for Finance This bestselling and thoroughly classroom-tested textbook is a complete resource for finance students. A comprehensive and illustrated discussion of the most common empirical approaches in finance prepares students for using econometrics in practice, while detailed financial case studies help them understand how the techniques are used in relevant financial contexts. Worked examples from the latest version of the popular statistical software EViews guide students to implement their own models and interpret results. Learning outcomes, key concepts and end-of-chapter review questions (with full solutions online) highlight the main chapter takeaways and allow students to self-assess their understanding. Building on the successful data- and problem-driven approach of previous editions, this third edition has been updated with new data, extensive examples and additional introductory material on mathematics, making the book more accessible to students encountering econometrics for the first time. A companion website, with numerous student and instructor resources, completes the learning package. Chris Brooks is Professor of Finance and Director of Research at the ICMA Centre, Henley Business School, University of Reading, UK where he also obtained his PhD. He has diverse research interests and has published over a hundred articles in leading academic and practitioner journals, and six books. He is Associate Editor of several journals, including the Journal of Business Finance and Accounting, the International Journal of Forecasting and the British Accounting Review. He acts as consultant and advisor for various banks, corporations and professional bodies in the fields of finance, real estate, and econometrics. 3:48 Trim: 246mm × 189mm CUUK2581-FM Top: 9.841mm CUUK2581/Brooks Gutter: 18.98mm 978 1 107 03466 2 December 20, 2013 3:48 Trim: 246mm × 189mm CUUK2581-FM Top: 9.841mm CUUK2581/Brooks Gutter: 18.98mm 978 1 107 03466 2 December 20, 2013 Introductory Econometrics for Finance THIRD EDITION Chris Brooks The ICMA Centre, Henley Business School, University of Reading 3:48 Trim: 246mm × 189mm CUUK2581-FM Top: 9.841mm CUUK2581/Brooks Gutter: 18.98mm 978 1 107 03466 2 University Printing House, Cambridge CB2 8BS, United Kingdom Published in the United States of America by Cambridge University Press, New York Cambridge University Press is a part of the University of Cambridge. It furthers the University’s mission by disseminating knowledge in the pursuit of education, learning and research at the highest international levels of excellence. Information on this title:  C Chris Brooks 2014 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2002 Second edition 2008 Third edition published 2014 Printed in the United Kingdom by MPG Printgroup Ltd, Cambridge A catalogue record for this publication is available from the British Library Library of Congress Cataloguing in Publication data ISBN 978-1-107-03466-2 Hardback ISBN 978-1-107-66145-5 Paperback Additional resources for this publication at Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. December 20, 2013 3:48 Trim: 246mm × 189mm CUUK2581-FM Top: 9.841mm CUUK2581/Brooks Gutter: 18.98mm 978 1 107 03466 2 December 20, 2013 Contents List of figures List of tables List of boxes List of screenshots Preface to the third edition Acknowledgements 1 Introduction 1.1 1.2 What is econometrics? Is financial econometrics different from ‘economic econometrics’? 1.3 Types of data 1.4 Returns in financial modelling 1.5 Steps involved in formulating an econometric model 1.6 Points to consider when reading articles in empirical finance 1.7 A note on Bayesian versus classical statistics 1.8 An introduction to EViews 1.9 Further reading 1.10 Outline of the remainder of this book 2 Mathematical and statistical foundations 2.1 2.2 2.3 2.4 2.5 3 Functions Differential calculus Matrices Probability and probability distributions Descriptive statistics A brief overview of the classical linear regression model 3.1 3.2 3.3 3.4 3.5 What is a regression model? Regression versus correlation Simple regression Some further terminology Simple linear regression in EViews – estimation of an optimal hedge ratio page xii xv xvii xix xxi xxv 1 2 2 4 7 11 12 13 14 24 24 28 28 37 41 56 61 75 75 76 76 84 86 3:48 Trim: 246mm × 189mm CUUK2581-FM vi • • • • • • • • • Top: 9.841mm CUUK2581/Brooks Gutter: 18.98mm 978 1 107 03466 2 December 20, 2013 Contents 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 3.14 3.15 3.16 4 The assumptions underlying the classical linear regression model Properties of the OLS estimator Precision and standard errors An introduction to statistical inference A special type of hypothesis test: the t -ratio An example of a simple t-test of a theory in finance: can US mutual funds beat the market? Can UK unit trust managers beat the market? The overreaction hypothesis and the UK stock market The exact significance level Hypothesis testing in EViews – example 1: hedging revisited Hypothesis testing in EViews – example 2: the CAPM Appendix: Mathematical derivations of CLRM results Further development and analysis of the classical linear regression model 4.1 4.2 4.3 Generalising the simple model to multiple linear regression The constant term How are the parameters (the elements of the β vector) calculated in the generalised case? 4.4 Testing multiple hypotheses: the F -test 4.5 Sample EViews output for multiple hypothesis tests 4.6 Multiple regression in EViews using an APT-style model 4.7 Data mining and the true size of the test 4.8 Goodness of fit statistics 4.9 Hedonic pricing models 4.10 Tests of non-nested hypotheses 4.11 Quantile regression Appendix 4.1: Mathematical derivations of CLRM results Appendix 4.2: A brief introduction to factor models and principal components analysis 5 Classical linear regression model assumptions and diagnostic tests 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11 Introduction Statistical distributions for diagnostic tests Assumption 1: E(u t ) = 0 Assumption 2: var(u t ) = σ 2 < ∞ Assumption 3: cov(u i , u j ) = 0 for i = j Assumption 4: the xt are non-stochastic Assumption 5: the disturbances are normally distributed Multicollinearity Adopting the wrong functional form Omission of an important variable Inclusion of an irrelevant variable 90 91 93 98 111 113 115 116 120 121 123 127 134 134 135 137 139 144 145 150 151 156 159 161 168 170 179 179 180 181 181 188 208 209 217 220 224 225 3:48 Trim: 246mm × 189mm CUUK2581-FM Top: 9.841mm CUUK2581/Brooks Gutter: 18.98mm 978 1 107 03466 2 December 20, 2013 Contents 6 226 235 Univariate time series modelling and forecasting 251 251 252 256 259 266 268 273 276 281 283 285 296 298 Introduction Some notation and concepts Moving average processes Autoregressive processes The partial autocorrelation function ARMA processes Building ARMA models: the Box–Jenkins approach Constructing ARMA models in EViews Examples of time series modelling in finance Exponential smoothing Forecasting in econometrics Forecasting using ARMA models in EViews Exponential smoothing models in EViews Multivariate models 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 7.10 7.11 7.12 7.13 7.14 7.15 7.16 7.17 8 vii 5.12 Parameter stability tests 5.13 Measurement errors 5.14 A strategy for constructing econometric models and a discussion of model-building philosophies 5.15 Determinants of sovereign credit ratings 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 6.11 6.12 6.13 7 • • • • • • • • • Motivations Simultaneous equations bias So how can simultaneous equations models be validly estimated? Can the original coefficients be retrieved from the π s ? Simultaneous equations in finance A definition of exogeneity Triangular systems Estimation procedures for simultaneous equations systems An application of a simultaneous equations approach to modelling bid–ask spreads and trading activity Simultaneous equations modelling using EViews Vector autoregressive models Does the VAR include contemporaneous terms? Block significance and causality tests VARs with exogenous variables Impulse responses and variance decompositions VAR model example: the interaction between property returns and the macroeconomy VAR estimation in EViews Modelling long-run relationships in finance 8.1 8.2 Stationarity and unit root testing Tests for unit roots in the presence of structural breaks 238 240 305 305 307 308 309 311 312 314 315 318 323 326 332 333 335 336 338 344 353 353 365 3:48 Trim: 246mm × 189mm CUUK2581-FM viii • • • • • • • • • Top: 9.841mm CUUK2581/Brooks Gutter: 18.98mm 978 1 107 03466 2 December 20, 2013 Contents 8.3 8.4 8.5 8.6 8.7 8.8 8.9 8.10 8.11 8.12 8.13 9 Testing for unit roots in EViews Cointegration Equilibrium correction or error correction models Testing for cointegration in regression: a residuals-based approach Methods of parameter estimation in cointegrated systems Lead–lag and long-term relationships between spot and futures markets Testing for and estimating cointegrating systems using the Johansen technique based on VARs Purchasing power parity Cointegration between international bond markets Testing the expectations hypothesis of the term structure of interest rates Testing for cointegration and modelling cointegrated systems using EViews Modelling volatility and correlation 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 9.10 9.11 9.12 9.13 9.14 9.15 9.16 9.17 9.18 9.19 9.20 9.21 9.22 9.23 9.24 9.25 Motivations: an excursion into non-linearity land Models for volatility Historical volatility Implied volatility models Exponentially weighted moving average models Autoregressive volatility models Autoregressive conditionally heteroscedastic (ARCH) models Generalised ARCH (GARCH) models Estimation of ARCH/GARCH models Extensions to the basic GARCH model Asymmetric GARCH models The GJR model The EGARCH model GJR and EGARCH in EViews Tests for asymmetries in volatility GARCH-in-mean Uses of GARCH-type models including volatility forecasting Testing non-linear restrictions or testing hypotheses about non-linear models Volatility forecasting: some examples and results from the literature Stochastic volatility models revisited Forecasting covariances and correlations Covariance modelling and forecasting in finance: some examples Simple covariance models Multivariate GARCH models Direct correlation models 369 373 375 376 377 380 386 390 391 398 400 415 415 420 420 421 421 422 423 428 431 439 440 440 441 441 443 445 446 452 454 461 463 464 466 467 471 3:48 Trim: 246mm × 189mm CUUK2581-FM Top: 9.841mm CUUK2581/Brooks Gutter: 18.98mm 978 1 107 03466 2 December 20, 2013 Contents 9.26 9.27 9.28 9.29 9.30 Extensions to the basic multivariate GARCH model A multivariate GARCH model for the CAPM with time-varying covariances Estimating a time-varying hedge ratio for FTSE stock index returns Multivariate stochastic volatility models Estimating multivariate GARCH models using EViews Appendix: Parameter estimation using maximum likelihood 10 Switching models 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9 10.10 10.11 10.12 10.13 10.14 Motivations Seasonalities in financial markets: introduction and literature review Modelling seasonality in financial data Estimating simple piecewise linear functions Markov switching models A Markov switching model for the real exchange rate A Markov switching model for the gilt–equity yield ratio Estimating Markov switching models in EViews Threshold autoregressive models Estimation of threshold autoregressive models Specification tests in the context of Markov switching and threshold autoregressive models: a cautionary note A SETAR model for the French franc–German mark exchange rate Threshold models and the dynamics of the FTSE 100 index and index futures markets A note on regime switching models and forecasting accuracy 11 Panel data 11.1 11.2 11.3 11.4 11.5 11.6 11.7 Introduction – what are panel techniques and why are they used? What panel techniques are available? The fixed effects model Time-fixed effects models Investigating banking competition using a fixed effects model The random effects model Panel data application to credit stability of banks in Central and Eastern Europe 11.8 Panel data with EViews 11.9 Panel unit root and cointegration tests 11.10 Further reading 12 Limited dependent variable models 12.1 12.2 Introduction and motivation The linear probability model • • • • • • • • • ix 472 474 475 478 480 484 490 490 492 493 500 502 503 506 510 513 515 516 517 519 523 526 526 528 529 531 532 536 537 541 547 557 559 559 560 3:48 Trim: 246mm × 189mm CUUK2581-FM x • • • • • • • • • Top: 9.841mm CUUK2581/Brooks Gutter: 18.98mm 978 1 107 03466 2 December 20, 2013 Contents 12.3 12.4 12.5 12.6 12.7 12.8 12.9 12.10 12.11 12.12 12.13 12.14 The logit model Using a logit to test the pecking order hypothesis The probit model Choosing between the logit and probit models Estimation of limited dependent variable models Goodness of fit measures for linear dependent variable models Multinomial linear dependent variables The pecking order hypothesis revisited – the choice between financing methods Ordered response linear dependent variables models Are unsolicited credit ratings biased downwards? An ordered probit analysis Censored and truncated dependent variables Limited dependent variable models in EViews Appendix: The maximum likelihood estimator for logit and probit models 13 Simulation methods 13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 13.9 Motivations Monte Carlo simulations Variance reduction techniques Bootstrapping Random number generation Disadvantages of the simulation approach to econometric or financial problem solving An example of Monte Carlo simulation in econometrics: deriving a set of critical values for a Dickey–Fuller test An example of how to simulate the price of a financial option An example of bootstrapping to calculate capital risk requirements 14 Conducting empirical research or doing a project or dissertation in finance 14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 14.9 14.10 What is an empirical research project and what is it for? Selecting the topic Sponsored or independent research? The research proposal Working papers and literature on the internet Getting the data Choice of computer software Methodology Event studies Tests of the CAPM and the Fama–French Methodology 562 563 565 565 565 567 568 571 574 574 579 583 589 591 591 592 593 597 600 601 603 608 613 626 626 627 629 631 631 633 634 634 634 648 3:48 Trim: 246mm × 189mm CUUK2581-FM Top: 9.841mm CUUK2581/Brooks Gutter: 18.98mm 978 1 107 03466 2 December 20, 2013 Contents Appendix 1 Appendix 2 • • • • • • • • • xi 14.11 How might the finished project look? 14.12 Presentational issues 662 666 Sources of data used in this book Tables of statistical distributions 667 668 Glossary References Index 680 697 710 3:48 Trim: 246mm × 189mm CUUK2581-FM Top: 9.841mm CUUK2581/Brooks Gutter: 18.98mm 978 1 107 03466 2 December 20, 2013 Figures Steps involved in forming an econometric model page 11 2.1 A plot of hours studied (x) against grade-point average (y) 30 2.2 Examples of different straight line graphs 30 2.3 Examples of quadratic functions 31 2.4 A plot of an exponential function 34 2.5 A plot of a logarithmic function 35 2.6 The tangent to a curve 39 2.7 The probability distribution function for the sum of two dice 58 2.8 The pdf for a normal distribution 59 2.9 The cdf for a normal distribution 60 2.10 A normal versus a skewed distribution 67 2.11 A normal versus a leptokurtic distribution 67 3.1 Scatter plot of two variables, y and x 77 3.2 Scatter plot of two variables with a line of best fit chosen by eye 79 3.3 Method of OLS fitting a line to the data by minimising the sum of squared residuals 79 3.4 Plot of a single observation, together with the line of best fit, the residual and the fitted value 80 3.5 Scatter plot of excess returns on fund XXX versus excess returns on the market portfolio 82 3.6 No observations close to the y-axis 84 3.7 Effect on the standard errors of the coefficient estimates when ¯ are narrowly dispersed (xt − x) 95 1.1 3.8 3.9 3.10 3.11 3.12 3.13 3.14 3.15 3.16 3.17 3.18 4.1 4.2 Effect on the standard errors of the coefficient estimates when ¯ are widely dispersed (xt − x) Effect on the standard errors of xt2 large Effect on the standard errors of xt2 small The t-distribution versus the normal Rejection regions for a two-sided 5% hypothesis test Rejection region for a one-sided hypothesis test of the form H0 : β = β ∗ , H1 : β < β ∗ Rejection region for a one-sided hypothesis test of the form H0 : β = β ∗ , H1 : β > β ∗ Critical values and rejection regions for a t20;5% Frequency distribution of t-ratios of mutual fund alphas (gross of transactions costs). Source: Jensen (1968). Reprinted with the permission of Blackwell Publishers Frequency distribution of t-ratios of mutual fund alphas (net of transactions costs). Source: Jensen (1968). Reprinted with the permission of Blackwell Publishers Performance of UK unit trusts, 1979–2000 R2 = 0 demonstrated by a flat estimated line, i.e. a zero slope coefficient R2 = 1 when all data points lie exactly on the estimated line 96 96 97 101 103 104 104 108 114 114 116 153 154 3:48 Trim: 246mm × 189mm CUUK2581-FM Top: 9.841mm CUUK2581/Brooks Gutter: 18.98mm 978 1 107 03466 2 December 20, 2013 List of figures Effect of no intercept on a regression line 5.2 Graphical illustration of heteroscedasticity 5.3 Plot of uˆ t against uˆ t −1 , showing positive autocorrelation 5.4 Plot of uˆ t over time, showing positive autocorrelation 5.5 Plot of uˆ t against uˆ t −1 , showing negative autocorrelation 5.6 Plot of uˆ t over time, showing negative autocorrelation 5.7 Plot of uˆ t against uˆ t −1 , showing no autocorrelation 5.8 Plot of uˆ t over time, showing no autocorrelation 5.9 Rejection and non-rejection regions for DW test 5.10 Regression residuals from stock return data, showing large outlier for October 1987 5.11 Possible effect of an outlier on OLS estimation 5.12 Plot of a variable showing suggestion for break date 6.1 Autocorrelation function for sample MA(2) process 6.2 Sample autocorrelation and partial autocorrelation functions for an MA(1) model: yt = −0.5u t −1 + u t 6.3 Sample autocorrelation and partial autocorrelation functions for an MA(2) model: yt = 0.5u t −1 − 0.25u t −2 + u t 6.4 Sample autocorrelation and partial autocorrelation functions for a slowly decaying AR(1) model: yt = 0.9yt −1 + u t 6.5 Sample autocorrelation and partial autocorrelation functions for a more rapidly decaying AR(1) model: yt = 0.5yt −1 + u t 6.6 Sample autocorrelation and partial autocorrelation functions for a more rapidly decaying AR(1) 5.1 181 6.7 182 191 6.8 191 192 6.9 192 7.1 193 193 7.2 196 8.1 212 213 8.2 231 259 8.3 8.4 270 8.5 270 8.6 9.1 271 9.2 9.3 271 9.4 • • • • • • • • • model with negative coefficient: yt = −0.5yt −1 + u t Sample autocorrelation and partial autocorrelation functions for a non-stationary model (i.e. a unit coefficient): yt = yt −1 + u t Sample autocorrelation and partial autocorrelation functions for an ARMA(1, 1) model: yt = 0.5yt −1 + 0.5u t −1 + u t Use of in-sample and out-ofsample periods for analysis Impulse responses and standard error bands for innovations in unexpected inflation equation errors Impulse responses and standard error ban...
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