Leveraged Exchange-Traded Funds

Leveraged Exchange-Traded Funds

Leveraged Exchange- Traded Funds A Comprehensive Guide to Structure, Pricing, and Performance Narat Charupat and Peter Miu

LEVERAGED EXCHANGE-TRADED FUNDS Copyright Narat Charupat and Peter Miu 2016 Softcover reprint of the hardcover 1st edition 2016 978-1-137-47820-7 All rights reserved. No reproduction, copy or transmission of this publication may be made without written permission. No portion of this publication may be reproduced, copied or transmitted save with written permission. In accordance with the provisions of the Copyright, Designs and Patents Act 1988, or under the terms of any licence permitting limited copying issued by the Copyright Licensing Agency, Saffron House, 6-10 Kirby Street, London EC1N 8TS. Any person who does any unauthorized act in relation to this publication may be liable to criminal prosecution and civil claims for damages. First published 2016 by PALGRAVE MACMILLAN The authors have asserted their rights to be identified as the authors of this work in accordance with the Copyright, Designs and Patents Act 1988. Palgrave Macmillan in the UK is an imprint of Macmillan Publishers Limited, registered in England, company number 785998, of Houndmills, Basingstoke, Hampshire, RG21 6XS. Palgrave Macmillan in the US is a division of Nature America, Inc., One New York Plaza, Suite 4500, New York, NY 10004-1562. Palgrave Macmillan is the global academic imprint of the above companies and has companies and representatives throughout the world. Hardback ISBN: 978 1 349 56501 6 E-PDF ISBN: 978 1 137 47821 4 DOI: 10.1057/9781137478214 Distribution in the UK, Europe and the rest of the world is by Palgrave Macmillan, a division of Macmillan Publishers Limited, registered in England, company number 785998, of Houndmills, Basingstoke, Hampshire RG21 6XS. Library of Congress Cataloging-in-Publication Data Charupat, Narat, author. Leveraged exchange-traded funds : a comprehensive guide to structure, pricing, and performance / Narat Charupat, Peter Miu. pages cm Includes bibliographical references and index. 1. Exchange traded funds. I. Miu, Peter, author. II. Title. HG6043.C43 2015 332.63 27 dc23 2015026190 A catalogue record for the book is available from the British Library. Printed in the United States of America.

Contents List of Figures List of Tables vii ix 1 Introduction 1 2 Regulations and Taxations 13 3 Mechanics 21 4 Return Dynamics and Compounding Effects 35 5 Pricing Efficiency 49 6 Performance and Tracking Errors 73 7 Trading Strategies 111 8 Options on LETFs 139 Notes 165 Bibliography 171 Index 175 v

Figures 4.1a Payoffs of a One-Year $100 Investment in a 2x ETF under Low Volatility 44 4.1b Payoffs of a One-Year $100 Investment in a 2x ETF under Low Volatility 45 4.2a Payoffs of a One-Year $100 Investment in a 2x ETF under High Volatility 47 4.2b Payoffs of a One-Year $100 Investment in a 2x ETF under High Volatility 47 7.1 Expected Return under Low-Volatility Bullish Market Conditions 116 7.2 Expected Return under High-Volatility Bullish Market Conditions 116 7.3 Expected Return under Low-Volatility Bearish Market Conditions 117 7.4 Expected Return under High-Volatility Bearish Market Conditions 117 7.5 A Plot of Expected Two-Year Holding Period Returns against the Corresponding Standard Deviations of Returns for Different LETFs with Hypothetical Leverage Ratios of +1x, +1.5x, +2x, +2.5x, and +3x, Respectively 119 7.6 Cumulative Investment Value of Long-Only versus Short-Only Strategy 124 8.1 A Plot of Implied Volatility against Natural Logarithm of Moneyness Ratio for Call Options on SPY and SSO 154 8.2 A Plot of Implied Volatility against Natural Logarithm of Moneyness Ratio for Call Options on SPY and SDS 155 8.3 A Plot of Implied Volatility against Transformed Moneyness Measure for Call Options on SPY and SSO 159 8.4 A Plot of Implied Volatility against Transformed Moneyness Measure for Call Options on SPY and SDS 159 vii

Tables 1.1 Total Number, Assets under Management, and Average Daily Volume of LETFs in United States in 2012 by Underlying Asset Classes 6 1.2 Top Ten LETFs in United States in 2012 by Their Assets under Management 7 1.3 Top Ten LETFs Based on the Annual Contract Volume of Their Options Trading on the Chicago Board of Exchange in 2013 10 3.1 Trading Statistics of Selected LETFs 31 4.1 LETF s Two-Day Compounded Returns under Different Scenarios 40 4.2 Simulation Results 46 5.1 Descriptive Statistics 54 5.2 Price Deviations 56 5.3 Correlations among Price Deviations 59 5.4 Price Deviations Based on the Returns on Their Underlying Indices 61 5.5 Relative Size of LETFs and Inversed ETFs 67 5.6 Regression Estimates 69 6.1 Descriptive Statistics 99 6.2 Half-Year Performance (in Percentage Points) of Funds Relative to Underlying Benchmarks 102 6.3 Single-Variable Regression Results 105 6.4 Three-Variable Regression Results 108 7.1 Optimal Leverage Ratio under Different Market Conditions 116 7.2 Expected Returns and Standard Deviations of Returns for Different LETFs 119 7.3 Long-Only versus Short-Only Strategy 122 7.4 Proportion of Time in Which Shorting the 3x LETF Gives Us a Higher One-Year Compounded Return Than Going Long on the +3x LETF 132 7.5 Sharpe Ratio from Shorting the 3x LETF 134 7.6 Simulated Median One-Year Compounded Return on Pair Strategy 136 ix

x Tables 7.7 Sharpe Ratio of Pair Strategy 137 8.1 Call Option Prices as Fractions of Underlying ETF and LETF Prices (i.e., c t /L t ) Based on Black-Scholes Model for Different Moneyness Ratios 146 8.2 Put Option Prices as Fractions of Underlying ETF and LETF Prices (i.e., p t /L t ) Based on Black-Scholes Model for Different Moneyness Ratios 147 8.3 Deltas of Call Options on ETFs and LETFs for Different Moneyness Ratios Based on Black-Scholes Model 149 8.4 Hypothetical Implied Volatility Table 152