Table Of ContentQUANTITATIVE METHODS FOR PORTFOLIO ANALYSIS
THEORY AND DECISION LIBRARY
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QUANTITATIVE METHODS
FOR
PORTFOLIO ANAL YSIS
AflllAfodelApproach
by
T AKEAKI KARIY A
The Institute of Economic Research,
Hitotsubashi University, Tokyo, Japan
...
"
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
Library of Congress Cataloging-in-Publication Data
Kariya, Takeaki.
Ouantitative methods for portfolio analysis MTV model approach I
by Takeaki Kariya.
p. cm. -- (Theory and decision library. Series B,
Mathematical and statistical methods ; v. 23)
Includes bibl iographical references (p. ) and index.
ISBN 978-94-010-4754-8 ISBN 978-94-011-1721-0 (eBook)
DOI 10.1007/978-94-011-1721-0
1. Portfolio management--Mathematical models, 2. Investment
analysis--Mathematical models. 3. Time-series analysis. I. Title.
II. Series.
HG4529.5.K37 1993
332.6'Ol'51--dc20 93-7416
ISBN 978-94-010-4754-8
Printed on acid-free paper
AlI Rights Reserved
© 1993 Springer Science+Business Media Dordrecht
Originally published by Kluwer Academic Publishers in 1993
Softcover reprint of the hardcover 1 st edition 1993
No part of the material protected by this copyright notice may be reproduced or
utilized in any form or by any means, electronic or mechanical,
incIuding photocopying, recording or by any information storage and
retrieval system, without written permission from the copyright owner.
CONTENTS
Preface ... ... ... ... ... ... ... ... ... ...... ... ... ... ... ... ... ... ... ...... ... ... ............ vii
PART I QUANTITATIVE MODELS FOR PORTFOLIO ANALYSIS
Chapter 1 Quant i tat i ve Approach to Asset A II ocat ion ............... 1
1. The aim of this book (1) 2. Demand for variability
and for quants portfolio construction system (3)
3. Modern portfolio theory (MPT) and quants (9)
Chapter 2 Emp i rica I Features of F i nanc i a I Returns ... ............... 15
1. Introduction (15) 2. Random walk and
nonnormality (19) 3. Nonindependent and
nonlinear features of a return process (24)
Chapter 3 Univariate Financial Time Series Models .................. 33
1. Modelling financial time series (33)
2. Stationarity, trend and return (35)
3. Taylor model (41) 4. ARCH model (44)
5. Some other nonlinear models (51)
Chapter 4 Multivariate Financial Time Series Models ............... 58
1. Multifactor models (58) 2. A review on some
basic multivariate time series models (59) 3. State
space approach and Kalman Filter model (65)
4. Some special multifactor models (75)
Chapt er 5 MTV Mode I and Its App I i cat ions ............ ..................... 83
1. Introduction (83) 2. Theoretical foundation
of MTV model (84) 3. How to use the MTV model and
estimation (90) 4. MTV exchange rate analysis (95)
5. Prediction of stock prices (101)
PART IT QUANTITATIVE ASSET ALLOCATION SYSTEMS
Chapter 6 Quant i tat i ve Portfo I i a Canst ruct i on Procedures ......... 108
1. A comprehensive asset allocation (108)
2. Basic notation and concept (113)
3. Markowitz theory and its implications (116)
4. Mathematical structure of asset allocation (123)
Chapter 7 Mu It i factor Mode I s and the i r App I i cat ions ............... 130
1. Introduction (130) 2. CAPM (131) 3. APT
(Arbitrage pricing theory) (139) 4. Two multifactor
models in Japan (146) 5. Regression-MTV model (152)
Chapter 8 B. Rosenberg Models and their Applications ···············159
1. Market model portfolio (159) 2. Time-varying
coefficient models (162) 3. Prediction of future
returns and risk (164) 4. A model in Japan (169)
5. Convergent parameter model (174)
VI CONTENTS
Chapter 9 Selection of Portfol io Population ···························177
1. Introduction (177) 2. Information coefficient
(IC) for selection of a portfolio population (179)
3. Classification procedure (181) 4. Robust
classification analysis (189)
Chapter 10 Opt imal MTV Market Portfol io ................................. 195
1. MTV-MP system (195) 2. Extraction of
common market components and selection of a target
population (196) 3. Optimal MTV portfolio (200)
4. Prediction errors in MTV model (203)
Chapter 11 Index Portfol io and Canonical
Correlation Portfol io ............................................. 205
1. Basic concept of index portfolio (205)
2. MTV Index portfolio (207) 3. Cluster analysis
for grouping (209) 4. Index plus a premium minus
~ risk historical portfolio (212) 5. Canonical
correlation portfolio (215)
PART ill STATISTICAL APPROACH TO OPTION PRICING AND BOND PRICING
Chapter 12 Black-Scholes Option Theory and
Its App I i cat ions ................................................... 220
1. Introduction (220) 2. Black-Scholes option
pricing formula (224) 3. Basic formulae for BS
option portfolios (231) 4. Portfolio insurance (235)
5. Estimation of volatilities (239)
Chapter 13 Practical Option Pricing and Related Topics ............ 242
1. Practical option pricing (242) 2. Gram-Charlier
option pricing (245) 3. Practical option pricing
under a Taylor model and under an ARCH model (249)
4. Fractional Brownian motion and option pricing (254)
5. Asian options (260)
Chapter 14 Statistical Bond Pricing Models .............................. 263
1. Introduction (263) 2. Basic structure of bond
analysis (264) 3. Market spot rate function (266)
4. Market spot rate function of zero coupon bond (270)
5. Statistical model for market discount function of
coupon bonds (275) 6. Prediction of market discount
function (278) 7. Duration in our statistical models (278)
Appendix ................................................................................. 283
References ...... ..................... ................................................... 295
Index ....................................................................................... 305
PREFACE
This book aims to provide practically useful models and methods
for quantitative analysis of financial asset prices, construction
of various portfolios, and computer-assisted trading systems. In
particular, this book will be beneficial for
1) "quants" (quantitatively-inclined analysts) III financial
industries,
2) financial engineers In investment banks, securities companIes,
derivative-trading companies, software houses, etc., who are
developing portfolio trading systems,
3) graduate students and specialists in the areas of finance,
business, economics, statistics, financial engineering, and
4) investors who are interested in Japanese financial markets.
Throughout the book a great emphasis is put on the practical use
fulness of models and methods for investment decision-making, and
some examples are demonstrated with practical analyses and models on
Japanese financial markets. The statistical procedures treated in
this book are somewhat advanced because our financial world is of
many complexities. In fact, the time series variations of financial
asset prices are of the complicated features;
(a) they are multi-dimensional phenomena,
(b) their variational structure is evolving over time and
(c) profitable structure of variations will be eventually
exploited.
Hence to make effective portfolios, it will be important to empiri
cally model the evolving multi-dimensional variations by a proper
multivariate time series model and to manage portfolios constructed
from the model with proper trading (rebalancing) rules for profita
ble investment. Therefore our methods and models for analysis of
prices, construction of portfolios and management of portfolios are
closely associated with various multivariate time series methods In
statistics. In particular, the MTV (multivariate time series
VIl
viii PREFACE
variance component) model the author (1987) proposed plays an im
portant role as a basic information-summarizing and result-stabiliz
ing model in many ways. In this book we respect the MPT (modern
portfolio theory) to the extent that the models derived from the MPT
perform well empirically as statistical models for investment
decision making. In other words, from our viewpoint of practical
usefulness we consider it more important to extract by statistically
scientific methods significant and useful information for invest
ments from available data than to follow the MPT or traditional
finance theory. The relationship between our approach and the MPT
approach is fully discussed in Chapter 1. The book consists of the
following three parts:
Part I Quantitative models for portfolio analysis,
Part [ Quantitative asset-allocation systems,
Part m Statistical approaches to option pricing and bond pricing.
In general, the procedure of making and managing a portfolio
consists of the following five elements:
(1) Selection of investment stances.
(2) Selection of a population of financial assets for investment.
(3) Modelling and predicting future prices of financial assets.
(4) Construction of an optimal portfolio.
(5) Choice of a trading (rebalance) rule for managing the
portfolio.
The most important element in this procedure will be (3) because
an investment is a commitment to uncertainties in future and a bet
ter prediction leads us to a better performance. In Part I, we
introduce basic and practical models and methods for analyzing and
predicting financial asset prices. In particular, univariate non
linear models and multivariate time series models are focussed upon.
In addition, we observe some empirical features of returns on
stocks and exchange rates, which can be taken into account in
selecting or screening assets for a portfolio population in (2) and
forming an optimal portfolio in (4). One of the features is non
linearity for a time series process of (one-period) returns and it
will provide profitable information in option trading. In Part n,
multivariate time series models introduced in Part I are used to
develop various procedures of making portfolios. Above all, we
propose some new procedures such as the procedures of making predic
tive MTV market portfolios, MTV index portfolios, MTV canonical
correlation portfolios, predictive classification portfolios, etc.
Also some procedures associated with the APT (arbitrage pricing
theory) and Rosenberg's models are introduced with some practices
in the Japanese financial industries. In Part ill, practical option
pricing is discussed, where the variational features observed in
Part I are taken into account. A review and development is also
made on the Black-Scholes type option theory. Some new bond pricing
models are also presented in Part ill.
Some parts of this book have been adapted from my Japanese book
"Portfolio Keiryo Bunseki no Kiso (Foundation for Quantitative Port
folio Analysis)" Toyo Keizai-shimposha. Some portions of this book
have been used in the course I taught at the Graduate School of
Business of the University of Chicago while I was a visiting profes
sor. I would like to express my deep gratitude to professors
George.C. Tiao, Ruey.S.Tsay and Arnold Zellner of the University of
Chicago for their various comments, communications and encourage
ments. I also thank Professors Stanley Pliska of University of
Illinois at Chicago, Edward George of University of Texas A&M,
Regina Liu, Arthur Cohen, Robert Berk, William Strawderman, and
Hiroki Tsurumi of Rutgers University, Narayan C. Giri and Martin
Bilodeau of University of Montreal, Morris L. Eaton of University
of Minnesota, Robert Wijsman of University of Illinois at Urbana,
Jeff C. Wu of University of Waterloo, Peter Kim of University of
Guelph, Bimal K. Sinha of University of Maryland. Arjun K. Gupta of
Bowling Green University. Yoshihiko Tsukuda of Tohoku University.
x PREFACE
and Hajime Takahashi of Hitotsubashi University for communications
and encouragements. I would like to thank Mr.'s Takehiro Enomoto,
Masahiro Fukuyama, Ryuichiro Hirayama, Kimio Horiguchi, Koji Itoh,
Satoshi Kimura, Hiroaki Maruyama, Minoru Masuda, Norikazu Minoshima,
Masayoshi Mizuno, Tei Moriya, Katsuto Ono, Masao Shigematsu, Hideaki
Suzuki, Masafumi Takahashi, Naoya Tatebe, Hiroshi Tsuda, Yukio
Un-no, and Mikio Yamada for personal communications and encourage
ments in various occasions, and Ms. Midori Shibano for skilled
typing. Finally I acknowledge the New Japan Securities Financial
Science Foundation, the Nomura Foundation for Social Sciences, the
Trust Companies Association of Japan and the Postal Life Insurance
Foundation of Japan for some financial support.
To my daughter Emi,
Takeaki KARIYA
