The uncovered interest parity (UIP) is a non-arbitrage condition. It postulates that the nominal interest differential between two countries () should be equal to the expected depreciation of the exchange rate ()1. The UIP assumes perfect capital mobility. It states that the returns from borrowing in foreign currency, exchanged against national currency in the forex market and then invested in interest-bearing instruments, while simultaneously purchasing futures contracts to convert the currency back to the original one at the end of the holding period, must be equal to the returns from purchasing and holding the same interest-bearing instruments denominated in national currency. If those returns are different, the non-arbitrage condition is violated and a risk-free return exists.
In formulas: 
where the LHS is the return from purchasing and holding a domestic financial asset and the RHS is the return from purchasing and holding a similar foreign financial asset. Needless to say, if the equality does not hold, it will give rise to an arbitrage opportunity. The equation (1) can be rewritten as follows:
where . The equation (1’) implies that:
1 Here S measures the number of units of national currency needed to buy one unit of the foreign currency.
Editor: Lorenzo CARBONARI