Mispricing, Convergence, and Arbitrage
Arbitrage exploits violations of the Law of One Price by buying and selling assets, separately or in combination, that should be priced the same but are not. Implicit in an arbitrage strategy is the expectation that the prices of the misvalued assets will ultimately move to their appropriate values. Indeed, arbitrage should push prices to their appropriate levels. Thus, an arbitrage strategy has two key aspects: execution and convergence. Execution includes how the arbitrage opportunity is identified in the first place, how the strategy is put together, how it is maintained over its life, and how it is ultimately closed out. Convergence is the movement of misvalued asset prices to their appropriate values.15 Of particular importance are the time frame over which convergence is expected to occur and the process driving the convergence. These two are the primary factors that determine the design of the appropriate arbitrage strategy in a given situation.
The processes driving convergence fall into two categories: mechanical or absolute, and behavioral or correlation. A mechanical or absolute convergence process has an explicit link that forces prices to converge over a well-defined time period. An example is index arbitrage, in which the futures price of an index is mechanically linked to the spot (cash) value of the index through the cost-of-carry pricing relation. This is examined in Chapter 3, "Cost of Carry Pricing." In index arbitrage, the convergence time period is deterministically dictated by the delivery/expiration date of the index futures contract.
A behavioral or correlation convergence process exists when there is historical evidence of a systematic relationship or a correlation in the behavior of the assets’ prices. However, the mispriced assets fall short of being linked mechanically. An example of a behavioral or correlation convergence process is pairs trading. Pairs trading identifies two stocks that have historically tended to move closely, as measured by the average spread between their prices. It is common to identify pairs of stocks that are highly correlated in large part due to being in the same industry. The essence of this strategy is to identify pairs whose spreads are significantly higher or lower than usual and then sell the higher-priced stock and buy the lower-priced stock under the expectation that the spread will eventually revert to its historical average. Thus, pairs trading relies on an estimated correlation and projected convergence toward the historical mean spread. Importantly, no mechanical link guarantees this convergence, and no deterministic model indicates how long such convergence should take. Although they are commonly referred to as arbitrage, behavioral/correlation convergence process-based strategies are not true arbitrage, because they can be quite risky. This book is concerned primarily with mechanical/absolute convergence process-based arbitrage because that is the fertile soil from which modern finance has grown.