Wharton School Publishing
Finally: Arbitrage for the Rest of Us

Arbitrage is the common thread that binds together much of contemporary financial thought. You'll find it at work in corporate risk management, derivatives analysis, asset pricing, portfolio management, and beyond. The underlying goal of arbitrage seems simple enough: identifying fleeting "mispricings" of assets or portfolios and exploiting them for profit. But many managers, financial professionals, and investors would benefit from a far deeper understanding of arbitrage than they possess.

The subject has attracted more than its share of mystification. On one hand: breathless, low-content articles about enigmatic hedge fund traders and secretive currency speculators. On the other hand: intensely mathematical treatments that daunt all but the most technical.

Into the breach rides Randall Billingsley, associate professor of finance at Virginia Tech's Pamplin College of Business. In Understanding Arbitrage, newly published by Wharton School Publishing, Billingsley provides readers with a strong intuitive understanding of classic arbitrage.

Billingsley brings exceptional experience to this assignment. He's spent 14 years teaching CFA candidates about derivatives and risk management. His case study on equity valuation was designated as assigned reading by AIMR (now the CFA Institute), the organization that awards the CFA designation.

Students find arbitrage slippery, he notes, because it's often presented in arguments that are "long on technical detail but short on economic intuition." To remedy that, he focuses on a wide array of examples. That allows him to compare and contrast and to illuminate elements common to all. Instead of touching just "one part of the elephant" — say, M&A — Understanding Arbitrage offers an integrated picture.

This book begins where any treatment of arbitrage must: with the Law of One Price, which posits that investments with identical payoffs, however structured, should be priced the same; when they aren't, arbitrageurs' transactions rapidly eliminate the differences.

Billingsley captures the essence of arbitrage with one of the simplest examples imaginable: What happens if gold's trading for $10 more in Hong Kong than in New York? Why might that happen? Is it sustainable? How can it be exploited?
He demonstrates what happens when you incorporate asset valuation models into arbitrage (e.g., CAPM and APT). Then, using scenarios involving gold and interest rates, Billingsley shows how the cost-of-carry model can reveal arbitrage opportunities arising when spot and forward or futures prices don't accurately reflect the value of time.

International Arbitrage

Next, he turns to international arbitrage and currency exchange, showing how to assess cross-border differences in interest rates and inflation and walking through the specific steps needed to arbitrage rate differentials. (Many readers will recall that George Soros "broke" the Bank of England: Billingsley explains how that was accomplished.)

Understanding Arbitrage carefully explains the relationships among call put, exercise, and stock prices; time to expiration; and risk-free rates — and shows how these relationships are used to create synthetic securities. Billingsley then turns to an area where the power of arbitrage is "particularly compelling and elegant": options. This material is indispensable. In addition to generating two Nobel prizes, arbitrage-related options pricing touches business decision making constantly: from determining whether to expand a profitable new business line to valuing executive stock options.

Dividing the Pie

In his final chapter, Billingsley addresses capital structure: especially the revolutionary Modigliani-Miller theorems. He begins by noting that just as "cutting an extra-large pizza into eight rather than six pieces does not increase the amount of pizza you can eat for dinner," neither are capital structure decisions relevant to a firm's valuation. (Modigliani himself used this analogy, quoting Yogi Berra as his source. Billingsley doesn't go quite that far.)

Working with an idealized example, readers walk through measuring the effects of financial leverage, arbitraging misvalued capital structure, and analyzing capital structure from the standpoints of bondholders and equityholders.

What's missing from this book? For one thing, the advanced math: a solid understanding of basic algebra will be sufficient. Second, Billingsley focuses primarily on "classic" approaches to arbitrage that are riskless and self-financing. He'll prepare you to encounter other forms — such as tax, regulatory, or index arbitrage — but you'll have to look elsewhere for detailed discussions. (He does, however, offer a cogent two-page précis of the Long Term Capital Management affair and LTCM's far-from-riskless strategies.)

Billingsley is an elegant, careful writer with deep knowledge. He's insightful enough to focus on what's important, well-tuned to newcomers' questions, and comfortable using real-world metaphors to humanize his subject. If you keep bumping up against arbitrage — and you keep intending to get your arms around it — he's written the book you've been waiting for.

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