Arbitrage, Hedging, and the Law of One Price
- Nov 4, 2005
...[Arbs] keep the markets honest. They bring perfection to imperfect markets as their hunger for free lunches prompts them to bid away the discrepancies that attract them to the lunch counter. In the process, they make certain that prices for the same assets in different markets will be identical.
Peter L. Bernstein1
"Buy low, sell high." "A fool and his money are soon parted." "Greed is good." All these adages illustrate the profit-oriented impulses of Wall Street traders, who stand ready to buy and sell. In pursuit of profits, undervalued assets are bought, and overvalued ones are sold. While risk is routinely borne in trading assets, most investors prefer to exploit mispriced assets with as little risk as possible. The goal is to enhance expected returns without adding risk. Think how seductive an investment that offers attractive returns but no risk is! One approach to identifying and profiting from misvalued assets is called arbitrage. Those who do it are called arbitrageurs or simply "arbs."
Arbitrage is the process of buying assets in one market and selling them in another to profit from unjustifiable price differences. "True" arbitrage is both riskless and self-financing, which means that the investor uses someone else's money. Although this is the traditional definition of arbitrage, use of the term has broadened to include often-risky variations such as the following:
Risk arbitrage, which is commonly the simultaneous buying of an acquisition target's stock and the selling of the acquirer's stock.2
Tax arbitrage, which shifts income from one investment tax category to another to take advantage of different tax rates across income categories.
Regulatory arbitrage, which reflects the tendency of firms to move toward the least-restrictive regulations. An example is the historic tendency of U.S. commercial banks to move toward the least-restrictive regulatorstate versus federal. Thus, as regulators in the past pursued a strategy of "competition in laxity," banks sought to arbitrage regulatory differences.
Pairs trading, which identifies two stocks whose prices have moved closely in the past. When the relative price spread widens abnormally, the stock with the lower price is bought, and the stock with the higher price is sold short.
Index arbitrage, which establishes offsetting long and short positions in a stock index futures contract and a replicating cash market portfolio when the futures price differs significantly from its theoretical value.
Even though arbitrage may be motivated by greed, it is nonetheless a finely tuned economic mechanism that imposes structure on asset prices. This structure ensures that investors earn expected returns that are, on average, commensurate with the risks they bear. Indeed, prices and expected returns are not at rest unless they are "arbitrage-free." Arbitrage provides both the carrot and the stick in efficiently operating financial markets.
Closely related to arbitrage is hedging, which is a strategy that reduces or eliminates risk and possibly locks in profits. By buying and selling specific investments, an investor can reduce the risk associated with a portfolio of investments. And by buying and selling specific assets, a target profit can be assured. Although all arbitrage strategies rely on hedging to render a position riskless, not all hedging involves arbitrage. "Pure" arbitrage is the riskless pursuit of profits resulting from mispriced assets. Hedging strategies seek to reduce, if not eliminate, risk, but do not necessarily involve mispriced assets. Thus, hedging does not purse profits.3
A guiding principle in investments is the Law of One Price. This states that the "same" investment must have the same price no matter how that investment is created. It is often possible to create identical investments using different securities or other assets. These investments must have the same expected cash flow payoffs to be considered identical. Indeed, the threat of arbitrage ensures that investments with identical payoffs are, at least on average, priced the same at a given point in time. If not, arbitrageurs take advantage of the differential, and the resulting buying and selling should eliminate the mispricing.
Similar to the Law of One Price is the Law of One Expected Return,4 which asserts that equivalent investments should have the same expected return. This is a bit different from the prior requirement that the same assets must have the same prices across markets. While subtle, this distinction will help you understand arbitrage in the context of specific pricing models.
The concepts of arbitrage, hedging, and the Law of One Price are backbones of asset pricing in modern financial markets. They provide insight into a variety of portfolio management strategies and the pricing of assets. This chapter explores the nature and significance of arbitrage and illustrates how it is used to exploit both mispriced individual assets and portfolios. It consequently provides a broad analytical framework to build on in subsequent chapters. For example, the next chapter illustrates arbitrage strategies in terms of the capital asset pricing model (CAPM) and the Arbitrage Pricing Theory (APT).
Why Is Arbitrage So Important?
True arbitrage opportunities are rare. When they are discovered, they do not last long. So why is it important to explore arbitrage in detail? Does the benefit justify the cost of such analysis? There are compelling reasons for going to the trouble.
Investors are interested in whether a financial asset’s price is correct or "fair." They search for attractive conditions or characteristics in an asset associated with misvaluation. For example, evidence exists that some low price/earnings (P/E) stocks are perennial bargains, so investors look carefully for this characteristic along with other signals of value. Yet the absence of an arbitrage opportunity is at least as important as its presence! While the presence of an arbitrage opportunity implies that a riskless strategy can be designed to generate a return in excess of the risk-free rate, its absence indicates that an asset’s price is at rest. Of course, just because an asset’s price is at rest does not necessarily mean that it is "correct." Resting and correct prices can differ for economically meaningful reasons, such as transactions costs. For example, a $1.00 difference between correct and resting prices cannot be profitably exploited if it costs $1.25 to execute the needed transactions. Furthermore, sometimes many market participants believe that prices are wrong, trade under that perception, and thereby influence prices. Yet there may not be an arbitrage opportunity in the true sense of a riskless profit in the absence of an initial required investment. Thus, it is important to carefully relate price discrepancies to the concept of arbitrage because one size does not fit all.
Arbitrage-free prices act as a benchmark that structures asset prices. Indeed, understanding arbitrage has practical significance. First, the no-arbitrage principle can help in pricing new financial products for which no market prices yet exist. Second, arbitrage can be used to estimate the prices for illiquid assets held in a portfolio for which there are no recent trades. Finally, no-arbitrage prices can be used as benchmark prices against which market prices can be compared in seeking misvalued assets.5