Question

Suppose that domestic risk-free rate is 5% annually, and foreign risk free rate is 6% annually. Spot exchange rate between domestic currency and foreign currency is 1:1. (a) According to uncovered interest rate parity, which currency is expected to worth more in one year? (b) According to uncovered interest rate parity, what is the expected exchange rate in one year? (c) According to covered interest rate parity, what is the arbitrage-free one-year forward exchange rate?

Answer 1

a) Uncovered interest rate parity is the scenario in which the difference in the interest rate will be negated by the change in forward exchange rate. So that there will be no discrepancy in the rates and there will not be any arbitrage opportunity.
However, this is based on expectations and there is no any agreement or contract for the forward rate.

If the interest rate parity holds then there will not be any gain in the arbitrage domestic currency will appreciate.

b) Uncovered interest rate parity can be given by the following formula
Forward Rate / Spot Rate = ( 1+Domestic Interest Rate ) / ( 1+Foreign Interest Rate )

Forward Rate = 1 * ( 1.05 / 1.06 )
Forward Rate = 1.0095

c) The covered interest rate parity is the situation where there is no arbitrage gain because of the interest rate or exchange rate difference. The exchange rate will adjust according to the difference in the interest rate to eliminate any opportunity of arbitrage profit. The covered interest rate parity differs from the uncovered interest rate parity in the aspect that its forward rate is locked by the forward rate agreement or contract.

Forward Rate / Spot Rate = ( 1+Domestic Interest Rate ) / ( 1+Foreign Interest Rate )

Forward Rate = 1 * ( 1.05 / 1.06 )
Forward Rate = 1.0095