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Portfolio Management Under Transaction Costs Portfolio management under transaction costs: Model development and Swedish evidence Umeå School of Business Umeå University SE-901 87 Umeå Sweden Studies in Business Administration, Series B, No. 56. ISSN 0346-8291 ISBN 91-7305-986-2 Print & Media, Umeå University © 2005 Rickard Olsson All rights reserved. Except for the quotation of short passages for the purposes of criticism and review, 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, or otherwise, without the prior consent of the author. Portfolio management under transaction costs: Model development and Swedish evidence Rickard Olsson Master of Science Umeå Studies in Business Administration No. 56 Umeå School of Business Umeå University Abstract Portfolio performance evaluations indicate that managed stock portfolios on average underperform relevant benchmarks. Transaction costs arise inevitably when stocks are bought and sold, but the majority of the research on portfolio management does not consider such costs, let alone transaction costs including price impact costs. The conjecture of the thesis is that transaction cost control improves portfolio performance. The research questions addressed are: Do transaction costs matter in portfolio management? and Could transaction cost control improve portfolio performance? The questions are studied within the context of mean-variance (MV) and index fund management. The treatment of transaction costs includes price impact costs and is throughout based on the premises that the trading is uninformed, immediate, and conducted in an open electronic limit order book system. These premises characterize a considerable amount of all trading in stocks. First, cross-sectional models of price impact costs for Swedish stocks are developed using limit order book information in a novel fashion. Theoretical analysis shows that the price impact cost function of order volume in a limit order book with discrete prices is increasing and piecewise concave. The estimated price impact cost functions are negatively related to market capitalization and historical trading activity, while positively related to order size and stock return volatility. Total transaction costs are obtained by adding the relevant commission rate to the price impact cost. Second, the importance of transaction costs and transaction cost control is examined within MV portfolio management. I extend the standard MV model by formulating a quadratic program for MV portfolio revisions under transaction costs including price impact costs. The extended portfolio model is integrated with the empirical transaction cost models developed. The integrated model is applied to revise portfolios with different net asset values and across a wide range of risk attitudes. The initial (unrevised) portfolios are capitalization- weighted and contain all Swedish stocks with sufficient data. The standard MV model, which neglects transaction costs, realizes non-trivial certainty equivalent losses relative to the extended model, which, in addition, exhibits lower turnover, higher diversification, and lower transaction costs incurred. The evidence suggests that transaction cost control improves performance in MV revisions, and that price impact costs are worthwhile to consider. Third, the research questions are studied within index fund management. I formulate two index fund revision models under transaction costs including price impact costs. Each model is integrated with the empirical transaction cost models. Transaction costs including price impact costs, cash flows, and corporate actions are incorporated in the empirical tests, which use ten years of daily data. In the tests, the two index fund revision models and several alternative approaches, including full replication, are applied to track a Swedish capitalization-weighted stock index. Instead of using an extant index, an index is independently calculated according to a consistent methodology, mimicking that of the most used index in the Nordic region, the OMX(S30). The alternative approaches are tested under a number of variations including different tracking error measures and different types and degrees of transaction cost control. Index funds implemented by the index fund revision models under transaction cost control dominate, in all dimensions of tracking performance considered, their counterparts implemented without transaction cost control as well as the funds implemented by full replication. Price impact costs constitute the majority of the transaction costs incurred. Additional results indicate that some common tracking error measures perform similar and that the technique to control transaction cost by constructing an index fund from a pre-defined subset of the most liquid index stocks is not efficient. The overall conclusion of the thesis is that transaction costs matter, that transaction cost control improves portfolio performance, and that price impact costs are important to consider. To the memory of my father Acknowledgments I would like to thank without implicating in any way the following persons and organizations for aid of various kinds: Professor Lars Hassel - main supervisor Doctor Claes-Göran Larsson - supervisor Professor Johan Knif - reviewer of the manuscript at the pre-defense seminar Doctor Jörgen Hellström - reviewer of the manuscript at the pre-defense seminar Associate Professor Xavier de Luna Professor Kurt Brännäs Associate Professor Barbara Cornelius Professor Maria Bengtsson Professor Emeritus Nils Hakansson Doctor Mattias Hamberg Doctor Henrik Nilsson, Anders Isaksson, Anneli Linde, and Tobias Svanström Christian Fagerlund, Gabriel Fogelsjöö, Mattias Lundgren, Mattias Olofsson, and Joakim Oscarsson Jan Wallanders och Tom Hedelius Stiftelse, Sparbanksstiftelsen Norrland, J.C. Kempes Minnes Stipendiefond och J.C. Kempes Minnes Akademiska Fond, and Borgerskapets i Umeå Forskningsstiftelse And to family and friends, to whom I at times during this work have not paid the attention they deserve, I sincerely apologize. Umeå, October 2005 Contents 1 Contents LIST OF FIGURES ...........................................................................................................4 LIST OF TABLES ............................................................................................................4 CHAPTER 1 INTRODUCTION.................................................................. 5 1.1 BACKGROUND AND MOTIVATION .......................................................................5 1.2 RESEARCH QUESTIONS......................................................................................10 1.3 INITIAL LITERATURE REVIEW............................................................................11 1.4 PREMISES REGARDING TRADING AND TRANSACTION COSTS ............................14 1.5 PURPOSE ...........................................................................................................17 1.6 RESEARCH TASKS..............................................................................................18 1.7 METHODS AND DATA ........................................................................................18 1.8 DISPOSITION......................................................................................................20 CHAPTER 2 TRANSACTION COSTS.................................................... 23 2.1 INTRODUCTION .................................................................................................23 2.2 THE STOCKHOLM STOCK EXCHANGE TRADING SYSTEM ..................................27 2.3 PRICE IMPACT COST AS A FUNCTION OF ORDER VOLUME IN THE LIMIT ORDER BOOK .................................................................................................................30 2.4 PRICE IMPACT COST MODELING USING LIMIT ORDER BOOK DATA ....................36 2.4.1 Background................................................................................................36 2.4.2 Modeling of transaction costs: Estimation approaches and data...............39 2.4.3 Cross-sectional determinants of trading costs ...........................................43 2.5 DATA.................................................................................................................54 2.6 EMPIRICAL ANALYSIS .......................................................................................57 2.6.1 Regression results ......................................................................................61 2.6.2 Simulation analysis....................................................................................63 2.6.3 Improvements and extensions....................................................................67 2.7 CONCLUSIONS ...................................................................................................67 CHAPTER 3 MEAN-VARIANCE PORTFOLIO MANAGEMENT UNDER TRANSACTION COSTS.................................................................. 69 3.1 INTRODUCTION .................................................................................................69 3.2 BACKGROUND...................................................................................................72 3.2.1 Mean-variance portfolio selection .............................................................72 3.3 MODEL DEVELOPMENT .....................................................................................76 3.3.1 Transaction costs........................................................................................76
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