QUANTITATIVE FINANCIAL ECONOMICS STOCKS, BONDS AND FOREIGN EXCHANGE Second Edition KEITH CUTHBERTSON AND DIRK NITZSCHE QUANTITATIVE FINANCIAL ECONOMICS QUANTITATIVE FINANCIAL ECONOMICS STOCKS, BONDS AND FOREIGN EXCHANGE Second Edition KEITH CUTHBERTSON AND DIRK NITZSCHE Copyright  2004 John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England Telephone (+44) 1243 779777 Email (for orders and customer service enquiries): cs-books@wiley.co.uk Visit our Home Page on www.wileyeurope.com or www.wiley.com All Rights Reserved No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except under the terms of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London W1T 4LP, UK, without the permission in writing of the Publisher Requests to the Publisher should be addressed to the Permissions Department, John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England, or emailed to permreq@wiley.co.uk, or faxed to (+44) 1243 770620 Designations used by companies to distinguish their products are often claimed as trademarks All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners The Publisher is not associated with any product or vendor mentioned in this book This publication is designed to provide accurate and authoritative information in regard to the subject matter covered It is sold on the understanding that the Publisher is not engaged in rendering professional services If professional advice or other expert assistance is required, the services of a competent professional should be sought Other Wiley Editorial Offices John Wiley & Sons Inc., 111 River Street, Hoboken, NJ 07030, USA Jossey-Bass, 989 Market Street, San Francisco, CA 94103-1741, USA Wiley-VCH Verlag GmbH, Boschstr 12, D-69469 Weinheim, Germany John Wiley & Sons Australia Ltd, 33 Park Road, Milton, Queensland 4064, Australia John Wiley & Sons (Asia) Pte Ltd, Clementi Loop #02-01, Jin Xing Distripark, Singapore 129809 John Wiley & Sons Canada Ltd, 22 Worcester Road, Etobicoke, Ontario, Canada M9W 1L1 Wiley also publishes its books in a variety of electronic formats Some content that appears in print may not be available in electronic books Library of Congress Cataloging-in-Publication Data Cuthbertson, Keith Quantitative financial economics : stocks, bonds and foreign exchange / Keith Cuthbertson and Dirk Nitzsche – 2nd ed p cm Includes bibliographical references and index ISBN 0-470-09171-1 (pbk : alk paper) Investments – Mathematical models Capital assets pricing model Stocks – Mathematical models Bonds – Mathematical models Foreign exchange – Mathematical models I Nitzsche, Dirk II Title HG4515.2.C87 2005 332.6 – dc22 2004018706 British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN 0-470-09171-1 Typeset in 10/13pt Times by Laserwords Private Limited, Chennai, India Printed and bound in Great Britain by Antony Rowe Ltd, Chippenham, Wiltshire This book is printed on acid-free paper responsibly manufactured from sustainable forestry in which at least two trees are planted for each one used for paper production To all our students who have done well enough to be in a position to hire finance consultants CONTENTS Preface Acknowledgements Basic Concepts in Finance Aims 1.1 Returns on Stocks, Bonds and Real Assets 1.2 Discounted Present Value, DPV 1.3 Utility and Indifference Curves 1.4 Asset Demands 1.5 Indifference Curves and Intertemporal Utility 1.6 Investment Decisions and Optimal Consumption 1.7 Summary Appendix: Mean-Variance Model and Utility Functions xiii xv 1 13 19 25 28 32 33 Basic Statistics in Finance 35 Aims 2.1 Lognormality and Jensen’s Inequality 35 35 2.2 Unit Roots, Random Walk and Cointegration 2.3 Monte Carlo Simulation (MCS) and Bootstrapping 2.4 Bayesian Learning 2.5 Summary Efficient Markets Hypothesis Aims 3.1 Overview 3.2 Implications of the EMH 3.3 Expectations, Martingales and Fair Game 3.4 Testing the EMH 3.5 Using Survey Data 3.6 Summary Appendix: Cross-Equation Restrictions Are Stock Returns Predictable? Aims 4.1 A Century of Returns 36 40 47 50 53 53 54 56 59 65 66 70 71 73 73 73 viii CONTENTS 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 Simple Models Univariate Tests Multivariate Tests Cointegration and Error Correction Models (ECM) Non-Linear Models Markov Switching Models Profitable Trading Strategies? Summary 82 85 95 100 103 106 109 113 Mean-Variance Portfolio Theory and the CAPM 115 5.1 5.2 5.3 5.4 5.5 Aims An Overview Mean-Variance Model Capital Asset Pricing Model Beta and Systematic Risk Summary International Portfolio Diversification 6.1 6.2 6.3 6.4 Aims Mathematics of the Mean-Variance Model International Diversification Mean-Variance Optimisation in Practice Summary Appendix I: Efficient Frontier and the CML Appendix II: Market Portfolio Performance Measures, CAPM and APT 7.1 7.2 7.3 7.4 7.5 Aims Performance Measures Extensions of the CAPM Single Index Model Arbitrage Pricing Theory Summary 115 115 119 132 134 138 141 141 142 152 156 163 164 167 169 169 169 176 179 181 187 Empirical Evidence: CAPM and APT 189 Aims 8.1 CAPM: Time-Series Tests 8.2 CAPM: Cross-Section Tests 8.3 CAPM, Multifactor Models and APT 8.4 Summary Appendix: Fama–MacBeth Two-Step Procedure 189 189 190 195 202 203 Applications of Linear Factor Models 205 Aims Event Studies Mutual Fund Performance Mutual Fund ‘Stars’? Summary 205 206 209 227 243 10 Valuation Models and Asset Returns 245 9.1 9.2 9.3 9.4 Aims 10.1 The Rational Valuation Formula (RVF) 10.2 Special Cases of the RVF 10.3 Time-Varying Expected Returns 10.4 Summary 11 Stock Price Volatility Aims 11.1 Shiller Volatility Tests 11.2 Volatility Tests and Stationarity 11.3 Peso Problems and Variance Bounds Tests 11.4 Volatility and Regression Tests 11.5 Summary Appendix: LeRoy–Porter and West Tests 12 Stock Prices: The VAR Approach Aims 245 245 248 249 254 255 255 257 261 267 268 269 270 273 273 706 REFERENCES Pesando, J.E (1983) ‘On Expectations, Term Premiums and the Volatility of Long-term Interest Rates’, Journal of Monetary Economics, 12(3), 467–474 Pesaran, M.H (1987) The Limits to Rational Expectations, Blackwell, Oxford Pesaran, M.H and Timmermann, A (1994) ‘Forecasting Stock Returns: An Examination of Stock Market Trading in the Presence of Transaction Costs’, Journal of Forecasting, 13(4), 335–367 Pesaran, M.H and Timmermann, A (1995) ‘Predictability of Stock Returns: Robustness and Economic Significance’, Journal of Finance, 50(4), 1201–1228 Pesaran, M.H and Timmermann, A (2000) ‘A Recursive Modelling Approach to Predicting UK Stock Returns’, Economic Journal, 110(460), 159–191 Phillips, P.C.B and Hansen, B.E (1990) ‘Statistical Inference in Instrumental Variables Regression with I(1) Processes’, Review of Economic Studies, 57, 99–125 Phillips, P.C.B and Perron, P (1988) ‘Testing for a Unit Root in Time Series Regression’, Biometrika, 75(2), 335–346 Piazzesi, M (2002) ‘Affine Term Structure Models’, Handbook of Financial Econometrics, North Holland Politis, D.N and Romano, J.P (1994) ‘The Stationary Bootstrap’, Journal of the American Statistical Association, 89, 1303–1313 Poterba, J.M and Summers, L.H (1986) ‘The Persistence of Volatility and Stock Market Fluctuations’, American Economic Review, 76(5), 1142–1151 Poterba, J.M and Summers, L.H (1988) ‘Mean Reversion in Stock Prices: Evidence and Implications’, Journal of Financial Economics, 22, 26–59 Prat, G and Uctum, R (1994) ‘Formation des Anticipations de Change: les Enseignements des Enqueteres du Consensus Forecasts’, AFFI 16 th Annual Meeting, Paris, December Psaradakis, Z (2001) ‘On Bootstrap Inference in Cointegrating Regressions’, Economics Letters, 72, 1–10 Quigley, G and Sinquefield, R (1999) ‘The Performance of UK Equity Unit Trusts’, Report by Dimensional Fund Advisors for Institute for Fiduciary Education Rabin, M (1998) ‘Psychology and Economics’, Journal of Economic Literature, XXXVI(1), 11–46 Rabin, M (2000) ‘Risk Aversion and Expected Utility Theory: A Calibration Theorem’, Econometrica, 68(5), Rabin, M and Thaler, R.H (2001) ‘Anomalies: Risk Aversion’, Journal of Economic Perspectives, 15(1), 219–232 Rapach, D.E and Wohar, M.E (2002) ‘Testing the Monetary Model of Exchange Rate Determination: New Evidence from a Century of Data’, Journal of International Economics, 58(1), 359–386 Reinganum, M.R (1982) ‘A Direct Test of Roll’s Conjecture on the Firm Size Effect’, Journal of Finance, 37(1), 27–35 Reinganum, M.R (1983) ‘The Anomalous Stock Market Behavior of Small Firms in January: Empirical Tests for Tax-loss Selling Effects’, Journal of Financial Economics, 12(1), 89–104 Remola, E.M., Kleiman, P and Gruenstein, D (1997) ‘Market Returns and Mutual Fund Flows’, Economic Policy Review, Federal Reserve Bank of New York, July Remolona, E.M., Wickens, M.R and Gong, F.F (1998) ‘What was the Market’s View of UK Monetary Policy? 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New York REFERENCES 711 WM Company (1999) ‘Comparison of Active and Passive Management of Unit Trusts for Virgin Direct Financial Services’ Womack, K.L (1996) ‘Do Brokerage Analysts’ Recommendations Have Investment Value?’ Journal of Finance, 51(1), 137–167 Woodford, M (2003) Interest and Prices: Foundations of a Theory of Monetary Policy, Princeton University Press, Princeton, N.J Wurgler, J and Zhuravskaya, K (2002) ‘Does Arbitrage Flatten Demand Curves for Stocks?’, Journal of Business, 75, 583–608 Xia, T (2001) ‘Learning about Predictability: The Effects of Parameter Uncertainty on Dynamic Asset Allocation’, Journal of Finance, 56(1), 205–246 Zheng, L (1999) ‘Is Money Smart? A Study of Mutual Fund Investors’ Fund Selection Ability’, Journal of Finance, 54(3), 901–933 Recommended Reading Here is a highly selective list of texts for ‘recommended reading’ These are our ‘desirable dozen’ books in the finance-economics area that we think complement QFE-II and which our M.Sc./Ph.D students have also found useful Some are financial economics, some econometrics and others lead you on to derivatives and financial engineering – all are worth dipping into Campbell, J.Y., Lo, A.W and MacKinlay, A.C (1997) The Econometrics of Financial Markets, Princeton University Press – still a classic reference in this area Cochrane, J.H (2001) Asset Pricing, Princeton University Press – a classic on the theoretical basis of asset pricing, expertly interwoven with relevant econometric techniques Cerny, A (2004) Mathematical Techniques in Finance, Princeton University Press – clear, practical approach to the math of derivatives and hedging Cuthbertson, K and Nitzsche, D (2001) Investments Spot and Derivative Markets, John Wiley – useful and accessible introduction to financial markets Cuthbertson, K and Nitzsche, D (2001) Financial Engineering: Derivatives & Risk Management, John Wiley – concentrates on pricing of derivatives and their use in risk management – both the above texts have a website (www.wiley.co.uk/cuthbertson), with Powerpoint, Excel and Gauss files and other student material Hamilton, J.D (1994) Time Series Analysis, Princeton University Press – ‘The Bible’ – but weighs in a few pounds heavier Hull, J.C (2003) Options, Futures and Other Derivatives, Prentice Hall – concise, accessible text on derivatives 712 REFERENCES Luenberger, D.G (1998) Investment Science, Oxford University Press – nice mix of intuitive ideas and math examples of theory of spot and derivative assets Patterson, K (2000) An Introduction to Applied Econometrics, Palgrave – a very clear introduction to modern time series econometrics Sarno, L and Taylor M.P.T (2002) The Economics of Exchange Rates, Cambridge University Press – concise, comprehensive and up-to-date coverage Shiller, R.J (2001) Irrational Exhuberance, Princeton University Press – classic, popular account of stock market investment – quite simply, read anything he writes (www.econ.yale.edu) Sydsaeter, K and Hammond, P (2002) Essential Mathematics for Economic Analysis, Prentice Hall – very well presented introduction to basic math INDEX 401(k) funds 439 abnormal return 207, 209 absolute risk aversion 25 coefficient of 21 active funds 80 adaptive expectations 409, 410 ADRs 437 affine models 537, 541–45, 597–98 aggregate equity index 342 aggregate price indices 555–6 ambiguity aversion 430, 440 annual average geometric return annuity factor anomalies 88, 114, 424, 433–47, 484 arbitrage 427–8 arbitrage pricing theory 181–7, 195–202 arbitrageurs 427–8 arithmetic average 3–4 Arrow-Pratt measure of (local) absolute risk aversion 17 asset allocation 116, 141, 157, 375, 389, 472, 475 and uncertainty 389, 391, 393 intertemporal 355–68, 375–92 asset demands 19–25 Augmented Dickey–Fuller (ADF) test see Dickey-Fuller test autocorrelation 231, 459, 473 autoregressive conditional heteroscedasticity (ARCH) 55, 75, 103, 158, 342, 420, 638, 653, 654–656 Autoregressive Moving Average (ARMA) 39, 83, 93–5 bandwagon effect 453, 676 Bayes Theorem 161–3, 393–6 Bayesian learning 47–50, 51, 414, 588–9 BDS-test 105 bed and breakfasting 434 behavioural finance 423–49 BEKK 594, 667 Bellman equation 346, 356, 362–7, 369, 370, 371, 372, 396 benefit scheme 80 beta 80–1, 115, 134–8, 191, 192, 194 CAPM 117–19 beta risk 170, 176 bid-ask bounce 679 bid-ask spread 673–4 Black–Scholes equation 631, 654 Black Wednesday 551 bliss point 18 block exogeneity tests 511 bond-equivalent yield 12 bond market 663–4, 670–1 bond returns 668–70 bond 1–7, 79, 637–8 coupon-paying 11–12, 492 index-linked 78 non-callable 11 plain vanilla coupon paying 490 zero coupon 10, 12, 13, 491, 492, 522–3, 637–8 book-to-market ratio 210–11 book-to-market factor (HML) 211 bootstrap snooper 434, 680 bootstrapping 39, 51, 155, 198–9, 201–2, 229–31, 236–40, 536, 640 block bootstrap 46, 202 Box-Muller transformation 650 bubble intrinsic 404–8 periodically collapsing 403 rational 397–401, 623–4 South Sea bubble 397 Tulipmania bubble 397 714 INDEX budget constraint 363 bull run 443 calendar effects 433–4 calibration 47 Campbell–Shiller linearised formula for stock returns 296–7 candlestick charts 426 Capital Asset Pricing Model (CAPM) 13, 115, 132–4, 143, 151, 186–7, 210, 235 and beta 117–19 conditional 190, 316 conditional-beta 211 cross-equation restrictions and APT 199–201 cross-section tests 190–5 domestic 346 extensions of 176–9 heterogeneous expectations 179 international 346 intertemporal 658 multifactor models and APT 195–202 time-series tests 189–90 UK cross-section data 198–9 unconditional 316 United States cross-section data 195–8 vs C-CAPM 309–14 zero-beta 177–8, 187, 190 see also consumption-CAPM capital market line (CML) 115, 129, 143, 165–7 Carhart’s alpha 210–11 Carhart’s four-factor model 212, 218–19, 230, 235 cash-in-advance models 598–605 FRU and 598–605 habit persistence 599–604 standard 598–9 change-in-long-rate equation 522 change-in-short rate equation 522 Chartists 426, 458, 675, 676, 677–8, 682 see also noise traders Choleski decomposition 648, 650 closed-end funds 437–8, 457 cointegration 36–8, 100–3, 516–18 co-movement in stock returns 438–9 compound interest 1, conditional-alpha 212, 235 conditional-beta 235 conditional-CAPM 190, 211, 316 conditional covariance 382, 669 conditional density function 60 conditional expectation 60–1 conditional models 228 conditional performance measures 211–12 conditional probability distribution 60 conditional volatility 656, 668 conservatism bias 444 constant absolute risk aversion (CARA) 18–19, 414, 469, 472 constant excess returns model 283, 284 constant relative risk aversion (CRRA) 18, 95, 383–5, 413 consumption 28–32, 330–1, 382, 539 consumption-CAPM (C-CAPM) 94, 303–9, 309–17, 323–53, 361, 539, 540, 593–7 testing Euler equations of 332–6 vs standard CAPM 309–14 See also Stochastic Discount Factor 94 consumption habit persistence model (Campbell-Cochrane) 347–9, 430, 483 consumption-portfolio problem 369–70 consumption-wealth ratio 99, 199 contagion 463–6 continuous compounding 2, 3, 4–5, 502 continuous distribution 24–5 Cornish-Fisher expansion 634 coupon-paying bonds 11–12, 492 coupon stripping 492 covered-interest parity (CIP) 560–1, 576–72, 584 Cox-Ingersoll-Ross CIR, multi-factor model 544 single-factor Cox, Ingersoll and Ross model 541, 542–3, 547 cumulative abnormal return (CAR) 207 data-mining 99, 101, 434 data-snooping bias 86, 434, 680–1 debt-equity ratio 59, 657, 664 default spread 99 defined benefit schemes 80 delta (of an option) 631–5, 641, 644–5 delta approximation 642 delta-gamma approximation 635, 641, 644–5 delta hedging 458 delta-normal approach 627, 638 delta valuation method 633, 634 derived utility of wealth function 363 Dickey-Fuller test 37, 40, 556 diffusion of opinions models 433 disappointment aversion (DA) 385–6 discount rate 411–13 discounted present value (DPV) 7–13, 33, 245 dispersion of opinions 467 disposition effect 440 dividend-price ratio 84, 96–9, 100, 102, 105–6, 190, 252, 266, 274–5, 277–8, 281, 293, 389, 390, 393, 410, 453, 482, 483, 653 see also earnings price ratio dividend valuation models 10 dot.com boom 96 earnings price ratio 99, 100, 102 effective annual rate of return 1, 2, efficient frontier 115, 124–6, 143–4, 164–5 efficient markets hypothesis (EMH) 53–72, 256, 424–5, 453 efficient-portfolios 119 EGARCH 664, 665 Ellsberg paradox 429–30 INDEX Engle-Granger representation theorem 38–9, 101, 574, 577 envelope condition 366, 369–70 epidemics 463 Epstein-Zin C-CAPM model 339–40, 341, 343 Epstein-Zin utility function 341–3, 392 equilibrium expected return 62, 117 equity premium 78, 350–3 equity premium puzzle 114, 323, 327–32, 353, 383, 484 equity premium, forecasts of 81–2 error correction model (ECM) 38, 100–3, 618, 619, 620 errors-in-variables problem 191, 193 ESTAR 104–106 estimation error 157–9, 160 Euler equation 94–5, 332–6, 342, 378, 381, 398–401, 405, 482 event studies 206–9, 250 ex post average equity return 81 excess holding period return 520 excess volatility 114, 412 Exchange Rate Mechanism (ERM) 551 exchange rate overshooting 550, 608, 610–13, 615, 625 exchange rate regimes 549–52 exchange rates 574, 604–5 expectations 59–65, 246, 360–1, 611, 674–9 see also rational expectations expectations hypothesis 494–5, 498–500, 501–14, 522–38, 584 alternative representations 502–5 case study 523–32 divergent results 535–6 forward rates 499 future short-rate equation 513–14 long-rate equation 513 testing 585 UK studies 530–2 US studies 532–5 VAR approach 506–11, 526–8 variance bounds tests 504–6 yield curve 499–500 expected returns 82, 92, 120 expected utility 14 expected value 15 exponential-STAR (ESTAR) model 104–6, 559, 620 exponentially weighted moving average (EWMA) 158, 170, 630, 638, 639, 655 extrapolative model 676 extreme value theory 628, 646–7 factor analysis 186, 195 factor mimicking portfolio 234–5 factor models 315–17 fair bet/game 14, 17, 56, 59–65 fair value 10, 53, 247 Fama-French regressions 88, 94, 95 Fama-French three-factor model 196, 197, 200, 207, 230, 235, 236, 442 Fama-MacBeth rolling regression 193–4, 200, 201 fat tails 46, 75, 343, 654 feasible set 124 feedback trader hypothesis 224 filter rules 679 finite horizon 461 first-order conditions (FOC) 342, 356, 358–9, 360–1, 368–9, 538 Fisher hypothesis 544, 609, 610 flex-price monetary model (FPMM) 607, 608–10, 623, 624 forecast equity premium 81–2 foreign exchange market 549–65, 568, 569, 591–605, 672–4 foreign investment 6–7, 56 forward-looking models 616–17, 620–2 forward premium puzzle 576 forward rate regressions 520–1 forward rate unbiasedness (FRU) 155, 562, 574–80, 585–6, 592–3, 598–605 Full Valuation Method 635 fundamental risk 425 715 fundamental (fair) value 10, 53, 247 future-short-rate equation 501 futures hedge 667–8 gambler’s fallacy 429 gamma (of an option) 632, 633 GARCH 103, 159, 170, 340, 342, 343, 535, 539, 595, 638, 639, 653, 654, 664–5 GARCH-in-mean 252, 578, 659–60, 670, 681 GARCH(1,1) model 75, 76, 138 multivariate GARCH 665–71 multivariate GARCH-in-mean (MGM) model 342, 540, 541 generalised expected utility (GEU) function 339–40 Generalized Method of Moments (GMM) 41, 180, 201, 276, 302 geometric average 3–4 geometric Brownian motion (GBM) 642 gilt-equity yield ratio (GEYR) 100–1, 107 Gordon Growth Model 10, 82, 245, 249, 252, 275, 405, 409–11 Granger causality 50, 101 group behaviour 432–3 habit persistence 336, 338, 346–507, 599–604 Hansen-Jagannathan bounds 325–7, 333–6, 354 Hansen’s J-test 420 Hedge Funds 226–27, 426 hedging 378–9, 382 herding 398, 463 heterogeneity 676 heteroscedasticity 75, 265, 495 high minus low (HML) book-to-market portfolio 195 historic alphas 212, 213 historic simulation approach 646 holding period return (HPR) 12–13, 492, 522–3, 539, 663 holding period yield (HPY) (see holding period return) 716 INDEX Home Bias Problem 155–56, 439 horizon effects 386–9 hostile takeovers 58 hubris hypothesis 448 hyperbolic absolute risk aversion (HARA) 19 hyperinflation 610 index effect 437 index fund 56 index-linked bonds 78 index tracking 160–1 indifference curves 13–19, 25–7 information ratio 172 informational efficiency 65, 83 test for 65, 66, 68 initial public offering (IPO) of shares 206 inside spread 672 insurance principle 121–2 integrated GARCH (IGARCH) 656 Interest rate parity covered (CIP) 560–61 real interest rate 562–63 uncovered (UIP) 561 Interest (risk free) rate (puzzle–see also Equity Premium Puzzle) 114, 255, 323, 331–2, 480 internal rate of return (IRR) 9, 11, 33 international CAPM 346 international diversification 152–6 International Fisher hypothesis (see Fisher hypothesis) International Monetary Fund (IMF) 550 intertemporal asset allocation multiperiod model 362–7 preferences and budget constraint 363 recursions unlimited 365–7 value function 363–5 SDF model of expected returns 368 two-period model 356–62 C-CAPM/SDF model of equilibrium returns 361–2 optimal asset shares 358–9 optimal consumption: power utility 358 solution: logarithmic utility 360 solution: power utility 359–60 intertemporal CAPM 658 intertemporal consumption 27, 624 intertemporal model 416, 475 intertemporal utility 25–7 intrinsic bubbles 404–8 inverse gamma distribution (IG) 396 investment analysts 56–7 investment opportunity set 358 investment styles 440–1 irrational managers 448–9 iterated expectations 61, 246 January effect 434 Jarque-Bera test 236 Jensen inequality terms (JIT) 577–8 Jensen’s alpha 111, 112, 162, 170, 175–6, 187, 190, 209, 210, 218, 222, 231, 436 Jensen’s inequality 35–6, 50, 320 Johansen procedure 39, 516, 556, 621 joint lognormality 318–20, 341 Kalman filter 50 Kuhn-Tucker conditions 148, 149 labour income 376–7 Lagrange multiplier (LM) test 585 Law of one price LOOP (see also purchasing power parity) 7, 552–9 law of small numbers 428 learning 161–3 learning costs 427 learning model 409–20 leveraged buyouts 58 levered portfolio 126 likelihood ratio tests 105, 190, 507–9 limits to arbitrage hypothesis 104 liquidity preference hypothesis (LPH) 495–7 local currency return local expectations hypothesis 501 lognormal consumption growth 307–8, 320–1 lognormality 35–6, 320–1 long-horizon returns 84, 91 long-horizon risk 91 long-rate equation 501 Long-Term Capital Management 58 loser portfolio 435–6 loss aversion (LA) 383, 392, 393, 424, 430, 475 LSTAR model 105 Mankiw-Miron hypothesis 534 marginal rate of substitution (MRS) 131, 206 marginal utility 18 market microstructure 672–4 market model 206, 207, 652 market portfolio 115, 129, 130, 137, 167–8, 668, 669 market psychology 398 market risk 78, 122, 182 market segmentation hypothesis 497 market timing 171, 389–90 Markov process 50, 463 Markov switching models 106–9 in a VECM (MS-VECM) 107–9 martingale 59–65 maximum likelihood 201 mean absolute error (MAE) 108 mean reversion 88–90, 92, 114, 435, 466 mean square error 620 mean-variance analysis/optimisation 20–1, 155–63, 162 mean-variance criteria (MVC) 119 mean-variance model 119–32, 452 memory biases 429 mental accounting 430 mergers and acquisitions (M&A) 206 INDEX Merton-Henriksson model 225, 235 minimum funding requirement (MFR) 156 minimum variance portfolio 124, 146 model risk 426 Modigliani-Miller theorem 59 momentum effect 218 momentum stocks 198 momentum strategy 84, 440, 443–6, 468–70 monetary models 607–17 money market line 29 Monte Carlo simulation (MCS) 39, 40–7, 51, 94, 159, 413, 533, 536, 558, 618, 628, 632, 635, 640, 641–5, 646, 648–50 multiple-asset portfolio 642–3 single-asset portfolio 642 standard deviations 44 under non-linearity 105 variance bounds 262–4, 265, 266–7 multivariate tests 95–100 Muth-RE 61 mutual fund performance 209–27 fund characteristics and performance 220–1 hedge funds 226–7 investment flows and performance 221–4 market timing 225–6 mutual fund managers, SAT scores of 224–5 UK studies 212–16 US studies 216–18 mutual fund ‘stars’ 227–43 UK studies 232–43 US studies 229–32 myopic behaviour 365, 367, 382, 383, 390 myopic portfolio choice 376 narrow framing 287, 430 negative exponential utility 21 net asset value (NAV) 437, 438 Net present value (see discounted present value) neural networks 426–7 neutral stocks 119 new open-economy models (NOEM) 624–5 Newey-West 231, 236 newswatchers 468–70 noise trader behaviour, optimising model of 454–60 noise trader risk finite horizon and 425–6 serial correlation and 661–3 noise traders 83–5, 423 DeLong et al model of 485–6 destabilising rational traders 458–60 group behaviour 432–3 survival of 430–3, 456–7 nominal return 5–6 to foreign investment 6–7 noninformative prior 48 non-linear function 21 non-linear models 103–6 non-parametric measures 638–41 non-state separable utility function 338 Non-stationarity (see stationarity) normal distribution 343 open-economy models 624 optimal proportions of risky assets 116, 117 optimal weights 155 Options 141, 142, 154, 163, 227, 257, 627–29, 631–35, 639, 641–45, 647, 648, 654, 655, 658, 665 order flow 674 ordinary annuity ordinary least squares (OLS) regression 37, 41–5, 103, 180, 199, 201, 276, 412, 417, 418, 522, 533–4, 618–19 Ornstein-Uhlenbeck process 391 orthogonality 54, 61, 67–8 orthogonality test 266, 270, 271 overconfidence 428, 467–8 overpricing 462 over-reaction hypothesis 501, 510, 532 overshooting, Dornbusch 610–13 panel data 556 717 parameter uncertainty 387–8, 389–90, 393–6 parametric approach 645 pensions 380–1 perceived risk 447 perfect foresight long rate 503, 504 price 290–1 performance measures 169–76 see also Jensen index; Sharpe index; Treynor index performance-portfolios 212, 213, 218 periodic interest rate periodically collapsing bubbles 403 perpetuity 8, 12, 490 persistence 212–16, 218–20, 291–5, 455, 555 Peso problems 267–8, 337, 412, 537, 586–8 plain vanilla coupon paying bonds 490 Poisson distribution 47 portfolio balance model of exchange rates (PBM) 608, 615–16 Portfolio diversification 58, 73, 116, 118–20, 122, 136, 141–63, 180, 181, 184, 251, 442, 652 Portfolio (market/optimal) 32, 57, 111, 115–19, 122, 129–31, 133, 134, 136, 138, 142, 148–51, 155, 166, 168, 170, 177, 194, 250–51, 281, 311, 304, 341 portfolio risk 118, 120, 125 positive feedback theory 224 post-earnings announcement drift 208 posterior distribution 48, 49, 395, 396 Poterba–Summers variance-ratio statistic 94, 95 power utility 23–4, 307–8, 320–1 precautionary saving 348 predictability 73–114, 137–8 predictive density 161–2 predictive distribution 394, 395, 414 preferred habitat hypothesis 497–8 718 INDEX Present value (PV) (see discounted present value) Price competitiveness 490, 549, 550, 554, 563, 608, 610, 612 price-dividend ratio see dividend-price ratio price-earnings ratio 466, 467 price expectations augmented Phillips curve (PEAPC) 564, 608 price misperception 454 pricing kernel 306 pricing to market (PTM) hypothesis 554 prior losses 476 prospect theory 475–84, 485 model 476–7 purchasing power parity (PPP) 7, 156, 345, 552–9, 612, 620 absolute 553, 554 evidence on 554–5 PPP-LOOP 617–18 relative 7, 553–4 unit roots and non-linearities 557–9 wage-price spiral 564–5 pure discount bonds 10–11, 491, 522–3 pure expectations hypothesis (PEH) 494–5 quadratic programming 148 quadratic utility 18, 22–3 quasi-Monte Carlo (QMC) techniques 650 Rabin paradox 329–30, 385, 393, 477 Ramsey reset test 105 random walk model 36–8, 63, 88, 93, 208, 263, 324, 556–7, 619, 620 range estimator 655 rate of time preference 27 rational behaviour 440 rational bubbles 397–401, 623–4 rational expectations (RE) 54, 64, 578–9 rational valuation formula (RVF) 102–3, 245–8, 255–6, 274–80, 398–401 real assets, returns on 1–7 real exchange rate 554 Real interest rate (see interest rate) real interest rate monetary model (RIMM) (Frankel) 607–8, 613–15 real interest rate parity 562–3 real return 5–6, 7, 77 redemption yield 493–4 Regime switching 106–8, 418–21, 533 regressive model 676 single-equation 525–6 relative risk aversion 17, 25 relative strength strategy 444 representative agent model 398 response surface 40, 46 retirement income 375–81 return regressions 40–5 reward-to-risk ratio 22 reward-to-variability ratio 170 risk 14–15, 78–9, 578–9, 441–3 fundamental 425 long-horizon 91 market 78, 122, 182 noise trade 425–6, 661–3 perceived 447 portfolio 118, 120, 125 specific (idiosyncratic) 122, 180, 182 systematic (non-diversifiable; portfolio; market) 58, 134–8, 180, 182 unsystematic (idiosyncratic or specific) risk 122, 180, 182 risk aversion 14–7, 25, 260, 328–30, 339, 348, 379, 383 risk-free rate puzzle (see also Equity premium puzzle) 114, 331–2, 323, 353 114 risk lover 15 risk neutrality 15, 314, 561, 573, 575 risk premium 17, 252, 528–30, 575, 591–605 risk-return frontier 124 risky arbitrage hypothesis 104 risky assets 308–9, 320, 381–3 robustness 391–2 rolling cross-section regression 193–4 Roll’s critique 176, 194–5 root T -rule 630 sample size neglect 428 SDF-affine model 538 second units 233 security market line (SML) 134–5, 157, 190, 210, 332 self-attribution bias 444, 467 self-insurance 351 sensitivity analysis 46 separation principle 28, 33, 116, 130 Sharpe ratio 22, 23, 78–9, 88, 111–13, 154, 155, 159, 162, 170–5, 187, 325–7, 336–8, 348, 446 ex-ante 170 ex-post 78–9 for Campbell-Cochrane model 348 initial investment contains risky assets 172–3 Shiller volatility tests 65, 257–61, 288–90 short horizon 428 short selling 126, 148, 426 short-termism 58, 248, 457–8, 460–2, 486–8 shoulder pattern 675 Siegel’s paradox 36 sieve bootstrap 46 sign test 209 simple interest rate 1–3, 33 single-factor affine models 541–3, 546–8 Vasicek model 54, 543 single index model (SIM) 179–81, 187, 206, 635–6, 650–2 size effect 197 small firm effect 192, 435 smart money 83–5 smooth transition autoregressive (STAR) model 103, 104 social security 380–1 specific (idiosyncratic) risk 122, 180, 182 spirit of capitalism model 338, 347 spline model 104 spot rates of interest INDEX spot yields (spot rates) 10–11, 491–2, 502 stationarity 261–7 sticky-price monetary models (SPMM) 607, 608, 610–13 stochastic discount factor (SDF) 13, 306, 315, 323–4, 325–7, 348, 537–41 extensions of 336–46 international CAPM 345–6 model of FX returns 595–6 of term structure 545–6 stochastic dominance 155 stochastic income 375–81 stochastic parameters 390–1 stocks discounted present value 10 returns on 1–7 stress testing 627, 628, 644–6 Student’s t-distribution 37, 41, 343 style investing 470–5, 484 subjective expectations 61 survey data and expectations 674–9 switching strategy 110–12 symmetric triangle pattern 675 systematic (non-diversifiable; portfolio; market) risk 58, 134–8, 180, 182 takeovers 58–60 tangent portfolio 170 target threshold model (TAR) 517 T-bills 99, 522–3 technical trading rules 679–81 term premium see risk premium term structure 515–36, 577 data and cointegration 516–18 of forward premia 584 single-equation tests 520–3 Theil U statistic 620 theoretical spread 505, 621 threshold (asymmetric) model 103 time-series model (TSM) 542 time-varying expected returns 249–54 time-varying term premium (TVP) 502, 533 Tobin’s mean-variance model 20 Total Expense Ratios (TERs) 234 tracker fund 80 tracking error 222 transactions costs 446–7 transformation line 126–8 transversality condition 247 Treasury bill 95, 101, 115, 210, 234, 293, 491, 494, 497, 504, 517, 522 Treynor index 111, 154, 170, 174–5, 187 Treynor-Mazuy model 225, 235 twin shares 436–7 two-fund theorem 143, 178 uncertainty 14–17, 386–90, 393 uncertainty aversion 391 unconditional-CAPM 316 uncovered interest parity (UIP) 561, 572–4, 583–4, 585, 607 underpricing 462 underreaction 208 unhedged portfolio 153 unit root 36–8 univariate tests 85–95 unsystematic (idiosyncratic or specific) risk 122, 180, 182 utility 13–19, 33–4 value at risk (VaR) 87, 91, 92, 109, 206, 620–2, 627–35, 639, 648–50, 665 Bootstrap 640 forecasting 630–1 foreign equities 636–7 Historic simulation 638–41, 645, 646 measurement 628–35 Monte Carlo Simulation 159, 628, 632, 635, 641–45 portfolio of assets 628–30 Variance-Covariance method 627, 629, 630, 638–40 value function 356, 362, 363–5 value-growth strategy 84, 440, 441 value stocks 440, 442 variance bounds tests 267–8, 270–1, 272, 518–20 variance-covariance (VCV) approach 627, 629, 640, 646, 665 719 variance decomposition 297–9, 299–300 variance of portfolio 120 variance ratio 88–9, 518, 533 VECH-GARCH model 67 VECH notation 666 Vector Autoregressive (VAR) model 92, 109, 275–302, 382–3, 526–8, 536 vector error correction model (VECM) 39, 516–7,537, 619 companion form 509 empirical results 280–91 linearisation of returns and RVF 274–80 perfect foresight price and multi-period returns 290–1 persistence and 291–5 RVF and predictability of returns 281–7 Shiller volatility tests and multi-period returns 288–90 testing FRU 581–6 volatility and 291–5 volatility 58, 75–8, 82, 87–90, 248–9, 265, 287, 291–5, 654–6 and regression tests 268–9 in spot-FX markets 671 influences on 656–65 of spot rate and fundamentals 622–3 returns and 657–9 volatility contagion 671 volatility puzzle 114, 255 volatility tests 84, 261–7 Shiller volatility tests 65, 257–61, 288–90 first-generation volatility tests 258–60 statistical issues 260–1 VR-statistic 88 Wald test 105, 190, 277, 282, 283, 289, 507–9, 511, 532, 536, 585 weak form information 64 wealth portfolio 310 weekend effect 56, 85 720 INDEX weighted average cost of capital (WACC) 194 West inequality test 271–2 White noise 38, 39, 54, 55, 85, 248, 249, 252, 262, 409, 442, 453, 534, 599, 612, 658 winner’s curse 435–6 worst case scenario (WCS) 646 628, yield (see interest rate) yield curve 499–500 yield spread 99 yield to maturity (redemption yield) 493–4 Index compiled by Annette Musker zero-beta CAPM 177–8, 185–7, 190–1 zero coupon bond 10, 12, 13, 491, 492, 522–3, 637–8 zero-investment portfolio 1–3, 17 ... QUANTITATIVE FINANCIAL ECONOMICS QUANTITATIVE FINANCIAL ECONOMICS STOCKS, BONDS AND FOREIGN EXCHANGE Second Edition KEITH CUTHBERTSON... electronic books Library of Congress Cataloging-in-Publication Data Cuthbertson, Keith Quantitative financial economics : stocks, bonds and foreign exchange / Keith Cuthbertson and Dirk Nitzsche... The Money’ xiv P R E FA C E Who’s it for? The book is aimed at students on quantitative MSc’s in finance and financial economics and should also be useful on PhD programmes All you need as a pre-requisite