Preface

You can make even a parrot into a learned political economist—all he must learn are the two words “supply” and “demand”.... To make the parrot into a learned financial economist, he only needs to learn the single word ‘arbitrage.’

—Stephen A. Ross¹

This book traces the common thread binding together much of financial thought—arbitrage. Distilled to its essence, arbitrage is about identifying mispricing and developing strategies to exploit it. An inherently simple concept—the act of exploiting different prices for the same asset or portfolio—arbitrage is as important as it is commonly misunderstood. This is because arbitrage is so often presented in financial arguments that are long on technical detail but short on economic intuition. Many business professionals’ exposure to the concept is limited to the media occasionally associating arbitrage with high-profile financiers, like foreign currency speculator George Soros, or former Secretary of the U.S. Treasury Robert Rubin, once head of arbitrage at Goldman Sachs. Yet such casual mentions do not convey the pervasive importance and usefulness of arbitrage in the world economy or in financial thought. Hence, the goal of this book is to emphasize the intuition of arbitrage and explain how it functions as a common thread in financial analysis. In so doing, I’ll provide concrete examples that illustrate arbitrage in action.

How do I convey the intuition of arbitrage? In teaching and discussing the concept with many investment professionals, CFA® charterholders, CFA candidates, and university students, I have found that arbitrage is best understood by exploring it across the major areas of finance. When you compare and contrast the argument in different applications, the common elements stand in clearer relief, and an integrated picture of arbitrage emerges. Thus, in this book, I explore the role of arbitrage in pricing forward contracts using the cost of carry framework; in examining the relationship among puts, calls, stock, and riskless securities through the put-call parity relation; in understanding foreign exchange rate behavior; in option pricing and strategy; and in understanding corporate capital structure decisions. These topics are of enduring significance in financial thought and in the functioning of the world economy. Indeed, as I discuss in the book, arbitrage-related contributions have garnered several Nobel Prizes in recent years.

The benefit of focusing on the intuition of arbitrage comes at a cost. I deal largely with classic arbitrage, which is riskless and self-financing. While I acknowledge various applications called arbitrage that are risky or are not self-financing, departures from classic arbitrage are not emphasized. Yet I discuss how various market frictions can affect the ability to implement classic arbitrage strategies. What remains is a presentation of arbitrage-based arguments and strategies that conveys strong economic intuition, which can fuel further explorations of this pervasively important concept in finance.

Chapter 1, “Arbitrage, Hedging, and the Law of One Price,” explores the core concepts in arbitrage analysis. The chapter shows that the Law of One Price defines the resting place for asset prices and that arbitrage is the action that draws prices to that resting place. The chapter also explains how hedging is used to reduce or eliminate the risk in implementing an arbitrage strategy and identifies the conditions associated with an arbitrage opportunity. The Law of One Price is shown to impose structure on asset prices through the discipline of the profit motive.

Chapter 2, “Arbitrage in Action,” illustrates the nature of arbitrage and hedging using several examples, including a simple commodity, gold, and arbitrage applications in the context of the Nobel Prize-winning capital asset pricing model and the arbitrage pricing theory.

Chapter 3, “Cost of Carry Pricing,” presents the cost of carry approach to identifying and exploiting mispriced assets. This simple framework is first used to portray the appropriate relationship between spot (cash) and forward contract prices. Mispriced forward prices are exploited using one of two strategies: cash and carry arbitrage or reverse cash and carry arbitrage. The cost of carry framework is then used to identify and exploit imbalances among interest rates. The chapter concludes with an overview of practical market imperfections that influence the implementation of cost of carry-based arbitrage strategies. These imperfections include transactions costs and limited access to the proceeds generated by short sales.

Chapter 4, “International Arbitrage,” shows how arbitrage influences currency exchange rates in light of international interest rate and inflation differences. Specifically, the chapter explains how foreign exchange rates are structured through absolute purchasing power parity, relative purchasing power parity, and covered interest rate parity. Further, triangular currency arbitrage is examined, which exploits imbalances between quoted and implied exchanges rates across multiple currencies.

Chapter 5, “Put-Call Parity and Arbitrage,” explains the systematic relationship among European call and put prices, the underlying stock, and riskless securities. It then shows how to exploit deviations from the relationship using arbitrage strategies and explains how put-call parity can be used to create synthetic securities. The chapter also shows how put-call parity yields insight into basic option/stock combination strategies that include the covered call and protective put. The framework is shown to support the Law of One Price, which argues that a synthetic position should be priced the same as the underlying position it successfully emulates.

Chapter 6, “Option Pricing,” explains how arbitrage is the basis of modern option pricing. The one-period binomial model is examined to reveal the essential intuition of how arbitrage forms option prices. The two-period model is then developed to show how portfolios should be revised so as to remain riskless over multiple periods. The chapter concludes by explaining how the Nobel Prize-winning Black-Scholes-Merton option pricing model relates to the binomial option pricing approach.

Chapter 7, “Arbitrage and the (Ir)relevance of Capital Structure,” explains the role of arbitrage in valuing capital structure decisions in the context of the Nobel prize-winning Modigliani-Miller theory (M&M). The chapter shows that no matter how you cut up the financial claims to the firm sold in the capital markets, the real assets that determine the value of the firm remain the same. The chapter explains that the irrelevance of capital structure decisions depends on the ability of investors to “undo” a firm’s corporate leverage using a strategy that involves personal borrowing. The chapter also shows how the firm may be viewed as put and call options and then uses the put-call parity framework to explain how a firm is valued from the distinct though linked perspectives of bondholders and stockholders.

One of the great lessons of the book is that arbitrage allows the creation of distinct new assets by artfully combining more basic building-block assets. And so I hope it is with this book. I explore well-known financial concepts and hopefully combine them in a way that adds value.

Randall S. Billingsley

Blacksburg, Virginia

August 2005

¹ Ross (1987, p. 30) presents the quote concerning political economists as from one of Professor Paul Samuelson’s economics textbooks. He then adds the comment concerning financial economists.