Interest rate parity

Interest rate parity is an economic concept, expressed as a basic algebraic identity that relates interest rates and exchange rates. The identity is theoretical, and usually follows from assumptions imposed in economics models. There is evidence to support as well as to refute the concept.
Interest rate parity is a non-arbitrage condition which says that the returns from borrowing in one currency, exchanging that currency for another currency and investing in interest-bearing instruments of the second currency, while simultaneously purchasing futures contracts to convert the currency back at the end of the holding period, should be equal to the returns from purchasing and holding similar interest-bearing instruments of the first currency. If the returns are different, an arbitrage transaction could, in theory, produce a risk-free return.
Looked at differently, interest rate parity says that the spot price and the forward or futures price of a currency incorporate any interest rate differentials between the two currencies.
Two versions of the identity are commonly presented in academic literature: covered interest rate parity and uncovered interest rate parity.
Covered interest rate parity :
The equality assumes that the risk premium is zero, which is the case if investors are risk-neutral. If investors are not risk-neutral then the forward rate (F + 1) can differ from the expected future spot rate (E[S + 1]), and covered and uncovered interest rate parities cannot both hold.
The uncovered parity is not directly testable in the absence of market expectations of future exchange rates. Moreover, the above rather simple demonstration assumes no transaction cost, equal default risk over foreign and domestic currency denominated assets, perfect capital flow and no simultaneity induced by monetary authorities. Note also that it is possible to construct the UIP condition in real terms, which is more plausible.
Uncovered interest parity example:
An example for the uncovered interest parity condition: Consider an initial situation, where interest rates in the US (home country) and a foreign country (e.g. Japan) are equal. Except for exchange rate risk, investing in the US or Japan would yield the same return. If the dollar depreciates against the yen, an investment in Japan would become more profitable than a US-investment - in other words, for the same amount of yen, more dollars can be purchased. By investing in Japan and converting back to the dollar at the favorable exchange rate, the return from the investment in Japan, in the dollar term, is higher than the return from the direct investment in the US. In order to persuade an Investor to invest in the US nonetheless, the dollar interest rate would have to be higher than the yen interest rate by an amount equal to the devaluation (a 20% depreciation of the dollar implies a 20% rise in the dollar interest rate).