1. Bernstein (1992, p. 171).
2. A variation of this is the purchase of a target’s stock at the announcement of an acquisition and the sale of this stock after the acquisition takes place. However, the risk associated with such strategies precludes it from being true arbitrage. Another example of risk arbitrage is the strategy pursued by Long-Term Capital Management (LTCM). LTCM is a now-defunct hedge fund that caused great concern in the financial markets in 1998. LTCM had large, levered positions in bonds with close maturities but wide yield spreads. Rather than narrowing to more normal yield spreads, the spreads widened further and wiped out LTCM’s equity capital. See Dunbar (2000) and Lowenstein (2000).
3. Indeed, in futures markets, a theory exists that hedgers must effectively pay speculators to take the other side of a futures contract that allows them to hedge their risk. For example, a farmer who hedges the risk of a decline in corn prices by selling a futures contract must get a speculator to buy that futures contract. Thus, hedgers can be viewed as losing to speculators.
4. The Law of One Price and the Law of One Expected Return are used interchangeably in this chapter because they are conceptually similar.
5. See Neftci (2000, pp. 13–14).
6. Hence the question, "How about them apples?"
7. It is generally assumed that investors are risk-averse, which implies that they require higher expected returns to compensate for higher risk. Envision an extremely risk-averse person wearing both a belt and suspenders.
8. Violation of this assumption would limit the ability to implement arbitrage strategies that keep prices properly aligned.
9. An efficient financial market is one in which security prices rapidly reflect all information available concerning securities.
10. While this is the classic definition of arbitrage, it is possible for such a position to require a net initial outlay if the strategy generates a return in excess of the risk-free rate of return without exposing the investor to risk.
11. Long positions in stocks and bonds profit when prices rise and lose when prices fall. Alternatively, short positions profit when prices fall and lose when prices rise. A stock is sold short when an investor borrows the shares from their owner (usually through a broker) with a promise to return them later. Upon entering the agreement, the short seller then sells the shares. The short seller predicts that the price of the stock will drop so that he can repurchase it below the price at which he sold it short. Thus, if the goal of a long position is to "buy low, sell high," the goal of a short position is the same, but in reverse order—"sell short high, buy back low." Note that it is common for many equity managers to be prohibited from selling short stocks by their governing portfolio policy statements.
12. This is called "going short against the box." In the past, it was more common for investors to hold stock certificates registered in their names rather than the currently common practice of allowing brokers to hold shares in the name of the brokerage firm ("street name") while crediting the owned shares to investors’ individual accounts. Thus, "going short against the box" refers to the practice of selling short shares that are already owned by an investor, which were commonly retained by the investor in a safe deposit box. Although it’s a bit anachronistic, the term has survived and is used commonly.
13. In the U.S., tax laws are complicated. The Internal Revenue Service has published rulings concerning the treatment and legality of such tax-motivated trades. Investors should consult a tax expert before engaging in any trades designed to minimize taxes.
14. Thus, it is obviously possible for an investor to be both long and short. The net position is what is important in assessing an investor’s risk exposure. An investor who is short a position that is not completely offset by an associated long position is considered a "naked short" or uncovered.
15. See the related discussions in Taleb (1997, pp. 80–87) and Reverre (2001, pp. 3–16).
16. See Reinganum (1986).
17. Reinganum (1986, pp. 10-11).
18. See Neftci (2000, p. 13).
19. This presentation of arbitrage conditions was inspired by Jarrow (1988, pp. 21–24).
20. SPDR stands for Standard & Poor’s Depositary Receipts, which is a pooled investment designed to match the price and yield performance, before fees and expenses, of the S&P 500 index. It trades in the same manner as an individual stock on the American Stock Exchange.