Law of One Price

The Law of One Price says that identical goods should sell for the same price in two separate markets. This assumes no transportation costs and no differential taxes applied in the two markets.

Economists generally assume that the law of one price can be applied in liquid financial markets because of the possibility of arbitrage. Unlike in international trade, where it takes time and effort to move goods physically from one place to another, there are very little barriers in global financial markets.

What makes the law of one price work?

For example, an ounce of gold should cost the same on commodity exchanges in Chicago and London. If the gold costs more on one exchange, then traders would have incentive to purchase the gold on one exchange and sell it at the other one. They would do what is called an arbitrage.

An arbitrage is a trading strategy that requires the investment of no capital, with no risk of capital loss, and where there is some positive probability of making money. Traders with gold would know how much they pay at one exchange and receive at the other one. They could borrow money to realize immediate beforehand known profit. They would realize arbitrage risk free profit.

This law does not always hold in practice. The reason is mostly transaction costs and trade barriers. There may be limits on how much gold one can export or import out of the country. It costs something to buy gold in Chicago and have it shipped to London.

The law of one price in financial markets

The law of one price is an economic rule saying that a security must have a single price in an efficient market regardless of how that security is created.

For example, if a financial instrument or a position can be created using two different sets of underlying securities, then the aggregate price for each would be the same or else an arbitrage opportunity would exist. Let's show this using an example.

The purchase of a Put option while owning shares in XYZ company is a strategy with a limited loss and (after subtracting the Put premium) unlimited profit. Profit potential is unlimited. Losses limited as long as the Put option is owned. The payoff of this strategy is the same like the payoff of a Long Call option position.

The law of one price and purchasing power parity

The purchasing power parity theory is an aggregate application of the law of one price.

If the law of one price says that identical goods should sell for identical prices in different markets, then the law should apply to all identical goods sold in both markets.

In other words, if the law of one price holds for each individual item in the market basket, then it should hold for the market baskets as well.