# The Law of One Price and Arbitrage

by Christopher Chen

The Law of One Price is the economic theory that identical goods sell for the same price after exchange rates are taken into consideration. However, this is not the case. Therefore, an arbitrageur (someone who finds discrepancies in the market) looks to purchase an asset in a cheaper market and sell it where prices are higher.

From the Law of One Price, we can deduce five other parity (equilibrium) conditions. Thus, if the markets are not impeded, we can deduce a set of parity conditions for exchange rates. As such, investors can take “advantage” of the imbalances in the market and potentially make a profit.

The Five Parity Conditions:

1. Purchasing Power Parity: If the law of one price holds out, a unit of home currency (HC) should have the same purchasing power worldwide. For the theory, we can deduce that a pound of bread in the United States should buy a pound of bread in Great Britain. For this to actually occur in real life, the inflation rates of both the United States and Great Britain have to be the same. However, they are not, and their discrepancy is the foreign exchange rate. If purchasing power parity were true, one could deduce countries with higher inflation rates would devalue and those with lower inflation rates would rise in value. Traders could then take advantage of this idea.
2. The Fischer Effect: According to the Fischer International Effect, a country’s real interest rate (the interest rate without inflation) plus its expected inflation rate should equal to the country’s nominal interest rate (the interest rate with inflation). If the Fischer Effect were to be true, the expected inflation rate of a country is the country’s nominal minus its real interest rate. Thus, if a trader believes this effect to be true, then whenever the expected and actual inflation rates differ, s/he can take advantage of the discrepancy.
3. Covered Interest-Rate Parity: According to the covered interest-rate parity, an investment in the domestic currency and subsequent purchase of a future exchange contract should be equal to exchanging a domestic to foreign currency. If they do not equal to one another, then an investor can exploit the difference.
4. Forward Rate as an Unbiased Predictor of the Future Spot Rate: If the covered and uncovered interest-rate parity hold, then the forward discount (this is when a currency’s spot exchange rate trades at a higher level than a currency’s future spot rate) will be equal to the expected change in the spot exchange rate. (This is the present-day exchange rate of a currency) If the covered interest-rate parity and the uncovered interest-rate parity are equal to another, but the actual spot rate is different from the expected spot rate, a trader could potentially make a profit.
5. Uncovered Interest-Rate Parity: This is the idea that the yield between the foreign and domestic currency deposits should equal the expected exchange rate. If the differences between the foreign and domestic currency deposits are not equal to the expected exchange rate, a trader can take advantage of the discrepancies and make a profit.