Mastering Financial Calculations market editions Mastering Financial Calculations A step-by-step guide to the mathematics of financial market instruments ROBERT STEINER London · New York · San Francisco · Toronto · Sydney Tokyo · Singapore · Hong Kong · Cape Town · Madrid Paris · Milan · Munich · Amsterdam PEARSON EDUCATION LIMITED Head Office: Edinburgh Gate Harlow CM20 2JE Tel: +44 (0)1279 623623 Fax: +44 (0)1279 431059 London Office: 128 Long Acre, London WC2E 9AN Tel: +44 (0)20 7447 2000 Fax: +44 (0)20 7240 5771 Website www.financialminds.com First published in Great Britain 1998 Reprinted and updated 1999 © Robert Steiner 1998 The right of Robert Steiner to be identified as author of this work has been asserted by him in accordance with the Copyright, Designs and Patents Act 1988. ISBN 0 273 62587 X British Library Cataloguing in Publication Data A CIP catalogue record for this book can be obtained from the British Library 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, or otherwise without either the prior written permission of the Publishers or a licence permitting restricted copying in the United Kingdom issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London W1P 0LP. This book may not be lent, resold, hired out or otherwise disposed of by way of trade in any form of binding or cover other than that in which it is published, without the prior consent of the Publishers. 20 19 18 17 16 15 14 13 12 11 Typeset by Pantek Arts, Maidstone, Kent. Printed and bound in Great Britain by Redwood Books, Trowbridge, Wiltshire. The Publishers’ policy is to use paper manufactured from sustainable forests. About the Author Robert Steiner is Managing Director of Markets International Ltd, an inde- pendent company specializing in training in a range of areas related to the international financial markets, treasury and banking. The company also provides advice to finance directors and treasurers of international compa- nies on foreign exchange, money markets and other treasury matters. This advice ranges from written studies reviewing existing management policies and procedures, through the development of appropriate hedging strategies, to short-term market advice. Robert was previously senior consultant with HongKong and Shanghai Banking Corporation, where he worked in London and New York in the dealing area as consultant to major US and European companies on treasury management. He has also been treasurer and fund manager of H P Bulmer Holdings PLC and English and American Insurance Group PLC, active in currency and interest rate management. He has thus been closely involved in treasury management as consultant and practitioner. He has also worked in the Overseas Department of the Bank of England, and with the European Commission in Brussels. Robert spends a considerable amount of time training bankers, systems staff, corporate staff and others involved in the financial markets. In particu- lar, he personally runs courses for several of the ACI exams – the ACI Diploma, the Dealing Certificate, Repo Markets and the Settlements Certificate. He is the author of Mastering Repo Markets, also published by Financial Times Prentice Hall. His academic background is an honours degree in mathematics from Cambridge University followed by further studies in economics with London University. He is an associate member of ACI UK, and a member of the Association of Corporate Treasurers. TO MY PARENTS without whom none of this would have been possible AND TO MY FAMILY who have suffered while I’ve been writing it CONTENTS Foreword xi Introduction xiii Part 1: THE BASICS 1Financial Arithmetic Basics 3 Some opening remarks on formulas 4 Use of an HP calculator 4 Simple and compound interest 5 Nominal and effective rates 10 Future value / present value; time value of money 12 Discount factors 15 Cashflow analysis 17 Interpolation and extrapolation 23 Exercises 25 Part 2: INTEREST RATE INSTRUMENTS 2 The Money Market 29 Overview 30 Day/year conventions 32 Money market instruments 34 Money market calculations 38 Discount instruments 40 CDs paying more than one coupon 43 Exercises 47 3Forward-Forwards and Forward Rate Agreements (FRAs) 51 Forward-forwards, FRAs and futures 52 Applications of FRAs 58 Exercises 60 vii Contents 4Interest Rate Futures 63 Overview 64 Exchange structure and margins 66 Futures compared with FRAs 67 Pricing and hedging FRAs with futures 69 Trading with interest rate futures 74 Exercises 79 5 Bond Market Calculations 81 Overview of capital markets instruments 82 Features and variations 84 Introduction to bond pricing 86 Different yield measures and price calculations 95 A summary of the various approaches to price / yield 105 Duration, modified duration and convexity 107 Bond futures 114 Cash-and-carry arbitrage 121 Exercises 130 6 Zero-Coupon Rates and Yield Curves 135 Zero-coupon yields and par yields 136 Forward-forward yields 140 Summary 142 Longer-dated FRAs 143 Exercises 146 Part 3: FOREIGN EXCHANGE 7Foreign Exchange 149 Introduction 149 Spot exchange rates 150 Forward exchange rates 156 Cross-rate forwards 167 Short dates 169 Calculation summary 171 Value dates 172 Forward-forwards 173 Time options 175 Long-dated forwards 176 Synthetic agreements for forward exchange (SAFEs) 176 Arbitraging and creating FRAs 181 Discounting future foreign exchange risk 186 Exercises 189 viii Contents Part 4: SWAPS AND OPTIONS 8Interest Rate and Currency Swaps 195 Basic concepts and applications 196 Pricing 200 Valuing swaps 208 Hedging an interest rate swap 213 Amortising and forward-start swaps 214 Currency swaps 216 Exercises 218 9 Options 221 Overview 222 The ideas behind option pricing 223 Pricing models 228 OTC options vs. exchange-traded options 237 The Greek letters 238 Hedging with options 242 Some “packaged” options 244 Some trading strategies 246 Some less straightforward options 252 Exercises 254 Part 5: FURTHER EXERCISES, HINTS AND ANSWERS 10 Further exercises 257 11 Hints and Answers to Exercises 263 Hints on exercises 264 Answers to exercises 276 Answers to further exercises 316 Appendix 1 Using an HP calculator 329 Appendix 2 A summary of market day/year conventions 337 Appendix 3 A summary of calculation procedures 341 Appendix 4 Glossary 359 Appendix 5 ISO (SWIFT) codes for currencies 381 Select Bibliography 387 Index 389 ix FOREWORD ACI Education (formerly The ACI Institute) is the educational division of ACI – the Financial Markets Association, the primary international profes- sional body for the international financial markets, founded in 1955 and now represented in 59 countries internationally with over 24,000 members. The task of ACI Education is simple to state and is embodied in the Charter of ACI. It is to ensure that educational programmes that reflect the constantly changing nature of the industry are made available to both new entrants to the profession and seasoned professionals, and to set professional standards for the industry globally. This task is both challenging and excit- ing. Recent innovations include the decision to convert the examinations to an electronically delivered format, a change that will facilitate the availability of ACI’s professional testing programme, on a daily basis via a network of over 2,000 test centres globally. One of the component ACI examinations is the Level 2 ACI Diploma that has been running successfully since 1990. Research into ACI’s large database of results yields some interesting findings. Among these it can be seen that one of the best predictors of overall success in the examination has been a good performance on the part of the candidate in the financial calculations section. Conversely, candidates performing badly in this section have often performed poorly, overall, in the examination. ACI, as part of its educational programmes encourages authors, publishers and tutors to provide a wide variety of routes to its examinations as possible. For this reason it is delighted that Robert Steiner and Financial Times Prentice Hall have produced Mastering Financial Calculations. It captures the professional knowledge necessary to appreciate fully the topic, and provides an excellent additional source of study for both the ACI Dealing Certificate and key sections of the ACI Diploma. It also believes that the publication will be appreciated not only by examination candidates but also by the market professionals seeking an ‘easy-to-read’ reference manual on this highly important subject. Heering Ligthart President ACI – The Financial Markets Association xi INTRODUCTION The aim of the book This book is aimed at the very many people in financial institutions, universi- ties and elsewhere who will benefit from a solid grounding in the calculations behind the various financial instruments – dealers, treasurers, investors, pro- grammers, students, auditors and risk managers – but who do not necessarily do complex mathematical puzzles for fun. There is also a strong emphasis on the mechanics, background and applications of all the various instruments. Many dealers would claim to be able to perform their job – essentially buying and selling – very profitably, without using much maths. On the other hand, the different dealing areas in a bank overlap increasingly and it is essential to understand the basis for pricing each instrument, in order to understand how the bank’s position in one relates to a position in another. Almost all the concepts in this book regarding pricing the different instru- ments can be reduced to only two basic ideas. The first concerns the ‘time value of money’: a hundred dollars is worth more if I have it in my hand today than if I do not receive it until next year; or alternatively, for a given amount of cash which I will receive in the future, I can calculate an equiva- lent ‘present value’ now. The second is the ‘no free lunch’ principle: in theory, it should not generally be possible to put together a series of simulta- neous financial transactions which lock in a guaranteed no-risk profit.