ARBITRAGE

Arbitrage, within the context of financial markets, refers to the practice of trading on, and profiting from, a current or expected inconsistency in the pricing of an asset or group of assets. For example, consider a dual listed stock selling for $30 on one stock exchange and $40 on another. To make a guaranteed profit one need only buy the security for $30 on one exchange and sell it for $40 on the other. This is an example of an immediate arbitrage opportunity. An arbitrage opportunity is created when an asset has two different expected returns. However, apparent arbitrages must be examined carefully, to make sure that the price differential is an actual mispricing and does not represent a risk premium or compensation for a perceived utility.

Arbitrage is very closely related to the concept of market efficiency. Proponents of the Efficient Market Hypothesis (EMH) maintain that the only way to reliably earn more than a risk free return in the market is to accept economic risk. The only way that this premise can be true is if the market is free of arbitrage opportunities. The rationale for arguing against the existence of arbitrage lies in the assumption that an efficient market always allocates funds to their most productive use. This is achieved through competition among wealth maximizing investors. The moment an arbitrage opportunity presents itself, the potential arbitrageurs respond with transactions that remove it from the marketplace. In practice, this hypothesis cannot always be true or there would not be enough willing arbitrageurs to keep the markets efficient. Determining the degree to which markets display efficiency, and hence the degree to which arbitrage opportunities exist, is an ongoing topic of research. Few researchers maintain that the market is perfectly efficient, and few maintain that arbitrage opportunities exist for long periods of time before the actions of arbitrageurs negate them.

When investing money, a portfolio manager's belief about the existence of arbitrage opportunities will greatly affect his management style. At one extreme, a manager may choose to invest according to the Capital Asset Pricing Model (CAPM) or the Arbitrage Pricing Theory (APT). These models rely solely on the quantification of economic risk as the basis for making investment decisions. Furthermore, they look only at average long-term results, ignoring the possibility that the market may occasionally have short-term inconsistencies and mispricing. In fact, the APT derives its name from its primary assumption that no arbitrage is possible.

At the opposite end of the spectrum are professional arbitrageurs. These are managers who specifically and exclusively seek market price aberrations when making their investment decisions. Arbitrageurs are not concerned with the concept of economic risk because their rationale is to make investments that profit without taking such risk. Also, the arbitrageur is commonly considering too brief an investment period for economic risk to be a relevant concern.

Arbitrageurs look for opportunities in many different markets. One of the most common is in foreign currency exchange. For example, if the Canadian Dollar (CAD) to U.S. dollar exchange rate is 1.5 and the French Franc (FFR) to U.S. dollar exchange rate is 5.0, then the CAD to FFR rate must be 1.5/5.0 = 0.3 or else there is arbitrage. To illustrate, suppose that the CAD to FFR rate is actually at 0.4. An arbitrageur could sell $1,000,000 to receive FFR 5,000,000. Then the arbitrageur could sell the FFR 5,000,000 to receive CAD 2,000,000. Finally, the arbitrageur could sell the CAD 2,000,000 to receive $1,333,333.33. Since all transactions are done simultaneously, the transaction is self-financing and nets $333,333.33 with no risk. In reality, the discrepancies are rarely this obvious or large. Typically, an arbitrage opportunity exists for a very short time before market buying and selling activity acts to close the gap created by temporary mispricing.

Derivative securities are also favorite tools of arbitrageurs. Important relationships among the futures, options, bonds, stocks, and currency markets exist, which if violated signal an arbitrage opportunity. One such relationship, called interest rate parity, links the future and spot (current) markets of a currency to the interest rate differential between the two countries. If the percentage difference between the futures and spot markets' exchange rates is greater or less than the percentage difference in the respective interest rates, the arbitrageur has an opportunity.

As an example, assume that German Deutsche Marks (DEM) are currently 1.5 per U.S. Dollar (USD), and a DEM futures contract obligates the holder to pay 1.2 in three months. Now, suppose the interest rates for three months are 3 percent (.03) in the United States and 2 percent (.02) in Germany. An arbitrageur would borrow $1,000,000, buy and invest DEM 1,500,000. The arbitrageur would also enter into a futures contract. In three months, the arbitrageur would receive DEM 1,530,000 that could be converted back to USD at 1.2 to $1,275,000. The USD loan is paid back for $1,030,000 leaving a riskless profit of $245,000.

The preceding examples are immediate arbitrage opportunities. Market mispricing allows immediate riskless profits to be realized. Two types of expected arbitrage opportunities are index arbitrage and interest rate arbitrage. Index arbitrage arises when the futures price of a stock index moves out of alignment with the net costs of buying the index today. This cost includes the interest income foregone on the funds used to buy the index futures, net of the expected dividends.

The arbitrageur buys the cheaper position and sells the more expensive one to make a profit. The problem is that dividends paid in the future are uncertain, so one can expect the profit but not guarantee it. To make this kind of arbitrage profit, the arbitrageur must have very good forecasting ability.

Interest rate arbitrage uses the U.S. Treasury bond futures market. Treasury futures markets provide prices for government debt in the future and hence can be used to estimate future interest rates. The actual bond market, however, may also be used to estimate future interest rates. For example, if one-year bonds are at 8.0 percent and two-year bonds are at 10.0 percent, then a good estimate of next year's one-year rate should be about 9.0 percent, since 8.0 percent plus 10.0 percent would average to 9.0 percent for the two-years. If, however, the estimated interest rate from the futures contract did not indicate 10.0 percent for the second year, the arbitrageur would attempt to capitalize on the pricing discrepancy. Once again, the arbitrageur must be a good forecaster, and may or may not be actually accepting economic risk.