Dominant trading strategy

A dominant trading strategy is a portfolio that costs the same as another one, but which is always guaranteed to out-perform it.

Equivalently, a dominant trading strategy exists if it is possible to start with no money and make a guaranteed trading profit. The difference between this and arbitrage is that an arbitrage opportunity does not guarantee making money, it is merely a chance to make money with no risk of a loss.

The concept is similar to those of no arbitrage and the law of one price, and it is similarly useful in proving much of financial theory.

It can be proved that:

• If there is no arbitrage there is no dominant trading strategy, but there may be arbitrage opportunities even if there are no dominant trading strategies.
• If there is no dominant trading strategy then the law of one price holds, but the law of one price may hold even when trading strategies exist.
• If there are no dominant trading strategies then it can be shown that there must exist a linear pricing measure.

The last of these cannot be fully explained here. In essence it is a weighting for each possible "state of the universe"; each possible combination of securities prices. The value of a security can be calculated by multiplying its price in each possible state by the value of the pricing measure for that state. The existence of a linear pricing measure can be used to prove a number of important results in financial economics.