## What is the 'Uncovered Interest Rate Parity - UIP'

The uncovered interest rate parity (UIP) is a parity condition stating that the difference in interest rates between two countries is equal to the expected change in exchange rates between the countries' currencies. If this parity does not exist, there is an opportunity to make a risk-free profit using arbitrage techniques.

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## BREAKING DOWN 'Uncovered Interest Rate Parity - UIP'

Assuming foreign exchange equilibrium, interest rate parity implies that the expected return of a domestic asset will equal the expected return of a foreign asset once adjusted for exchange rates. There are two types of interest rate parity: covered interest rate parity and uncovered interest rate parity. When this no-arbitrage condition exists without the use of forward contracts, which are used to hedge foreign currency risk, it is called uncovered interest rate parity.

## Uncovered Interest Rate Parity Formula and Example

The formula for uncovered interest rate parity takes into account the following variables:

E(t + k) / S(t) = the expected rate of change in the exchange rate, which is simply the projected exchange rate at time (t + k) divided by the spot rate at time t

k = the number of time periods into the future from time t

i(c) = the foreign interest rate

i(d) = the domestic interest rate.

Using these variables, the formula is:

(1 + i(d)) = E(t + k) / S(t) x (1 + i(c))

For example, assume the following situation. The current USD/euro spot rate is 1.15 and the expected exchange rate one year into the future is 1.175 USD/euro. Currently, the one-year interest rate in the euro zone is 3%. Given this information, an analyst can calculate what the expected one-year interest rate in the United States would be using uncovered interest rate parity. The calculation would be:

(1 + i(c)) = 1.175 / 1.15 x (1 + 3%)

When solving for i(c), it is calculated to be 5.24%

There is only limited evidence to support uncovered interest rate parity, but economists, academics and analysts still use the theory as a theoretical device to represent rational expectation models. This is because of the assumption that capital markets are efficient. If capital markets are efficient, the price of a currency forward contract at any time in the future would equal E(t + k), making the uncovered interest rate parity equation valid. Based on market data, there is evidence to support covered interest rate parity, as shown by deviations from covered interest parity over time.

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