The covered interest parity : the no arbitrage condition



The covered interest parity states that the relative value of 2 currencies should be such that borrowing (shorting) in a low yield currency and lending (investing) the proceeds in a higher yield foreign currency while hedging the exchange rate risk using spot and forward exchange risk should earn the domestic risk free rate. 


In sum, in the context of an hedged exchange rate risk position the investor should be indifferent between investing in both currencies. 




Suppose the interest rate on US dollars is 10% while the interest rate in Europe is 6%. 


Suppose now that the spot rate for $/€ is 1 euro = 1.1 dollar and the forward rate that forces the no-arbitrage condition on the investment time horizon is 1 euro=1*(1.1/1.06)= 1.0377$ according to the CIRP.


An investor could borrow the euro (short the euro), lend the proceeds in USD and hedge the exchange rate risk by buying the pair.*


*he wants to hedge the decrease in USD since lending in dollars means being long USD. Since buying the pair is buying (being long) the base currency (euro) and shorting the price currency (USD).


Initial investment: 100 euros 


1- borrow 100 € , and lend the dollar equivalent at the spot rate, 100$. 


2 at end of the holding period , convert the initial investment + interest 110$ back to euros at the new spot rate of 1.0377, that is 106€ (+0%)


3-Pay back the loan in euro + interest rate 


Total return is: 106-106=0%


Hence an investment in a foreign currency fully hedge against exchange risk should yield the domestic free rate. 


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