with Excel® applications Dawn E. Lorimer Charles R. Rayhorn second edition ii Library of Congress Cataloging-in-Publication Data Lorimer, Dawn E., 1950- Financial modeling for managers : with Excel applications / Dawn E. Lorimer, Charles R. Rayhorn.— 2nd ed. p. cm. Rev. ed. of: Financial maths for managers / Dawn E. Lorimer, Charles R. Rayhorn. c1999. Includes bibliographical references and index. ISBN 0-9703333-1-5 (pbk.) 1. Business mathematics. 2. Microsoft Excel for Windows. 3. Electronic spreadsheets. 4. Financial futures. I. Rayhorn, Charles R., 1949- II. Lorimer, Dawn E., 1950- Financial maths for managers. III. Title. HF5691 .L58 2001 650'.01’513—dc21 2001005810 Copyright 2002 by Authors Academic Press Financial Modeling for Managers with Excel Applications All rights reserved. Previous edition copyright 1999 by Dunmore Press Limited. Printed in the United States of America. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a data base or retrieval system, without the prior written permission of the publisher. ISBN 0-9703333-1-5 Acquisition Editors: Trond Randoy, Jon Down, Don Herrmann Senior Production Manager: Cynthia Leonard Layout Support: Rebecca Herschell Marketing Manager: Nada Down Copyeditor: Michelle Abbott Cover Design: Tom Fenske and Cynthia Leonard Cover Photo: London Dealing Room. Courtesy National Australia Bank, London. Printer: EP Imaging Concepts Acknowledgments Robert Miller—Northern Michigan University, Michael G. Erickson—Albertson College, and Jacquelynne McLellan—Frostburg State University all contributed greatly to the production of this book through their thoughtful reviews. When ordering this title, use ISBN 0-9703333-1-5 www.AuthorsAP.com iii Contents Contents Preface 1 Part I. Interest rates and foreign exchange Chapter 1: Compounding and discounting 7 Chapter 2: The valuation of cash flows 31 Chapter 3: Zero’s, forwards, and the term structure 73 CONTENTS 1.1 Notation and definitions 8 1.2 Time value of money 8 1.3 Simple interest, bills and other money market securities 10 1.4 Compound interest 16 1.5 Linear interpolation 19 1.6 Real interest rates 20 2.1 Notation and definitions 32 2.2 Cash flow representation 34 2.3 Valuing annuities 36 2.4 Quotation of interest rates 39 2.5 Continuous time compounding and discounting 44 2.6 Fixed interest securities 47 2.7 Duration and value sensitivity 57 2.8 Interest rate futures 61 3.1 Notation and definitions 74 3.2 A brief mystery of time 75 3.3 Zero coupon rates 76 3.4 Implied forward rates 79 3.5 Forwards, futures and no-arbitrage 81 3.6 Computing zeros and forwards 86 3.7 Algorithm: computing zeros and forwards from swap data 89 3.8 Concluding remarks 97 iv Chapter 4: FX Spot and forwards 103 Part II. Doing it the Excel® way Chapter 5: Learning by doing: an introduction to financial spreadsheets 127 Part III. Statistical analysis and probability processes Chapter 6: Statistics without becoming one 151 Chapter 7: Regression and financial modeling 175 4.1 Notation and definitions 104 4.2 Spot exchange rate quotations 105 4.3 Inversions 108 4.4 Cross rates 109 4.5 Money market forward rates 114 5.1 Step-by-step bond valuation example 128 5.2 Do-it-yourself fixed interest workshop 137 6.1 Notation and definitions 152 6.2 Introduction to data 153 6.3 Downloading data 154 6.4 Data exploration 156 6.5 Summary measures 159 6.6 Distribution function and densities 164 6.7 Sampling distributions and hypothesis testing 168 7.1 Notation and definitions 176 7.2 Bivariate data exploration 177 7.3 Regression statistics 182 7.4 More regression theory: goodness of fit 187 7.5 The CAPM beta 189 7.6 Regression extensions: multiple regression 196 v Chapter 8: Introduction to stochastic processes 203 Part IV. Many variables Chapter 9: Many variables 235 Part V. Appendix General Mathematical review 264 8.1 Notation and definitions 204 8.2 Expectations 205 8.3 Hedging 206 8.4 Random walks and Ito processes. 213 8.5 How Ito processes are used 217 8.6 Volatility models 223 8.7 Other time series buzzwords 226 9.1 Vectors and matrices 236 9.2 Matrix inverses and equation solving 240 9.3 Statistics with matrices 243 9.4 Portfolio theory with matrices 245 9.5 Practicum 248 A1 Order of operations 264 A2 Multiplication and division with signed numbers 265 A3 Powers and indices 267 A4 Logarithms 272 A5 Calculus 273 vi 1 We wrote the book because we felt that financial professionals needed it; and those who are training to be financial professionals, as students in colleges, will need it by the time they finish. Not all of us are cut out to be Quants, or would even want to. But pretty much all of us in the financial world will sooner or later have to come to grips with two things. The first is basic financial math and models. The second is spreadsheeting. So we thought that the market should have a book that combined both. The origins of the book lie in financial market experience, where one of us (DEL), at the time running a swaps desk, had the problem of training staff fresh from colleges, even good universities, who arrived in a non operational state. Rather like a kitset that had to be assembled on the job: you know the bits are all there, but they can’t begin to work until someone puts all the bits together. Their theoretical knowledge might or might not have been OK, but instead of hitting the ground running, the new graduates collapsed in a heap when faced with the “what do I do here and now?” problem. The present book evolved out of notes and instructional guidelines developed at the time. In later versions, the notes took on an international flavor and in doing so, acquired a co author (CH), to become the present book, suitable for the U.S. and other international markets. The material you will find here has been selected for maximal relevance for the day to day jobs that you will find in the financial world, especially those concerned with financial markets, or running a corporate treasury. Everything that is here, so far as topics are concerned, you can dig up from some theoretical book or journal article in finance or financial economics. But the first problem is that busy Preface WHY READ THIS BOOK? 2 professionals simply do not have the time to go on library hunts. The second problem is that even if you do manage to find them, the techniques and topics are not implemented in terms of the kind of computational methods in almost universal use these days, namely Excel or similar spreadsheets. No spreadsheet, no solution, and that is pretty well how things stand throughout the financial world. Students who graduate without solid spreadsheeting skills automatically start out behind the eight ball. Of course, depending on where you work, there can be special purpose packages; treasury systems, funds management systems, database systems, and the like, and some of them are very good. But it is inadvisable to become completely locked into special purpose packages, for a number of reasons. For one thing, they are too specialized, and for another, they are subject to “package capture”, where firms become expensively locked into service agreements or upgrades. So in our own courses, whether at colleges or in the markets, we stress the flexibility and relative independence offered by a multipurpose package such as Excel or Lotus. Most practitioners continue to hedge their special systems around with Excel spreadsheets. Others who might use econometric or similar data crunching packages, continue to use Excel for operations like basic data handling or graphing. So, spreadsheets are the universal data and money handling tool. It is also a truism that the financial world is going high tech in its methodologies, which can become bewildering to managers faced with the latest buzzwords, usually acronymic and often incomprehensible. This leaves the manager at a moral disadvantage, and can become quite expensive in terms of “consultant capture”. In writing the book we also wanted to address this credibility gap, by showing that some, at least, of the buzzwords can be understood in relatively plain terms, and can even be spreadsheeted in one or two cases. So without trying to belittle the quants, or the consultants who trade in their work, we are striking a blow here for the common manager. It remains to thank the many people who have helped us in preparing the book. As the project progressed, more and more people from the financial and academic communities became involved, and some must be singled out for special mention. Larry Grannan from the Chicago Mercantile Exchange responded quickly to our questions on CME futures contracts. Cayne Dunnett from the National Bank of Australia (NAB) in London gave generously of his time to advise us on financial calculations. Together with Ken Pipe, he also organized the photo shoot for the front cover, taken in the NAB’s new London dealing room. Joe D’Maio from the New York office of the NAB pitched in with assistance on market conventions and products. Andy Morris at Westpac in New York provided helpful information on US financial products. Penny Ford from the BNZ in Wellington, New Zealand kindly assisted with technical advice and data. 3 Among the academic community, Jacquelynne McLellan from Frostburg State University in Maryland and Michael G. Erickson from Albertson College in Ohio read the entire manuscript and took the trouble to make detailed comments and recommendations. Roger Bowden at Victoria University of Wellington read through the manuscript making many helpful suggestions, and kept us straight on stochastic processes and econometric buzzwords. Finally, it has been great working with Cynthia Leonard and Tom Fenske of Authors Academic Press. They have been encouraging, patient, and responsive at all times, which has made this project a positive experience for all. 4 [...]... 0.0523 = 5.23% (14 / 365) 15 Financial Modeling for Managers Part I Interest Rates and Foreign Exchange 1.4 Compound interest Compound interest rates mean that interest is earned on interest previously paid Bonds are priced on this basis and most bank loans are as well Many deposit accounts also have interest calculated on a compound basis Before we formalize things, let’s start with a few examples Example... interest earned on a deposit of $1m for 45 days at an annual interest rate p.a of 4.75% What is the future value of this deposit? 45 = $5,856.16 365 45 FV = P0 + I = P0 (1 + (i × t)) = $1,000,000 (1 + (.0475 × )) 365 Interest = P0 × i × t = $1,000,000 × 0475 × = $1,005,856.16 11 (3) Financial Modeling for Managers Part I Interest Rates and Foreign Exchange Present value Formula (3) may be rearranged by... rate 9 Financial Modeling for Managers Part I Interest Rates and Foreign Exchange would actually be higher because of compounding, a subject we will discuss in more detail later The effective rate would be calculated as ((1 + 015)12 - 1) × 100% or 19.6% In general, the effective rate can be calculated by replacing 12 by the number of compounding periods (m) during the year Thus, the equation for the... that is neither the end date of the final cash flow nor the current date The following example illustrates the technique for calculating an accumulated value or future value to a specific date prior to the final cash flow 17 Financial Modeling for Managers Part I Interest Rates and Foreign Exchange Example 1.9 Find the value at one year and 60 days from today of $1 million due in two years and 132 days... and 40 days (or 1.109589 years) A picture often clarifies our thinking, so let i1.109589, the rate we are seeking, be equal to ∆%, and draw a timeline for it = f (time) 19 Financial Modeling for Managers it = f (time) Figure 1.2 Part I Interest Rates and Foreign Exchange 1.0 1.109589 2.0  _ A B C 4.2% 5.3% ∆ Timeline Length AB = 1.109589 - 1.0 = 109589 Length BC = 2.0 - 1.109589 = 890411... the same as what you started with The only way this can happen is if the real rate of interest you have earned is zero percent What you gained on the nominal rate of interest of 10%, you lost on the devalued dollar at the end of the period In this case, the purchasing power derived from this investment is zero 21 Financial Modeling for Managers Part I Interest Rates and Foreign Exchange Let us generalize... value P = purchase price (present value) FV = value due at maturity (also the face value of the security) i BD = bank discount rate = t FV − P 1 × FV t = D dpy dpy = 360 13 Financial Modeling for Managers P Part I Interest Rates and Foreign Exchange = FV × (1- (iBD × t )) = 100 × (1- (iBD × t )) (5) Securities priced using the bank discount approach use a non-present value equation because the interest... some time in the future This is because the amount due earlier can be invested and increased with earnings by the later date Many financial agreements are based on a flow (or flows) of money happening in the future (for instance, housing mortgages, government bonds, hire purchase agreements) To make informed financial decisions, it is crucial to understand the role that time plays in valuing flows of... at effective rate i per period (or for calculating its future value) is: (7) AV = FV = P0 × (1 + i) n n or FV = PV × (1 + i) (again, AV = FV) Note that this formula refers to n periods at effective rate i per period Thus, n and i can relate to quarterly, monthly, semi annual, or annual periods It is easy to see that Formula (7) can be rearranged to give a formula for the present value at time 0 of... ginseng to get through it all Once you have built up a bit of confidence with the basic skills, then you can think about going long in ginseng for the chapters that follow As well as interest rates, we have inserted a chapter on the arithmetic of foreign exchange, incorporating the quotation, pricing and trading of foreign currencies for much the same reasons These days everyone has to know a bit about . with Excel applications Dawn E. Lorimer Charles R. Rayhorn second edition ii Library of Congress Cataloging-in-Publication Data Lorimer, Dawn E., 1950- Financial modeling for managers : with. 650'.01’513—dc21 2001005810 Copyright 2002 by Authors Academic Press Financial Modeling for Managers with Excel Applications All rights reserved. Previous edition copyright 1999 by Dunmore. mathematics. 2. Microsoft Excel for Windows. 3. Electronic spreadsheets. 4. Financial futures. I. Rayhorn, Charles R., 1949- II. Lorimer, Dawn E., 1950- Financial maths for managers. III. Title.