Question

The U.S. nominal annual rate of interest is 3% and the European annual nominal rate of interest on the Euro is 2%. At the same time, the spot exchange rate is $1.20 per Euro and the real interest rate is 2% in both the U.S. and Europe.

1. What is the one year forecast of the U.S. dollar (USD) per Euro spot exchange rate, assuming the international Fisher effect holds? Show work.
2. What is the U.S. dollar (USD) per Euro one-year forward exchange rate, based on interest rate parity? Show work.
3. Can the forward exchange rate be considered a possible predictor of the future spot exchange rate? If so, why?

Answer 1

a) The expected future spot rate(S^e) is equal to the product of the spot exchange rate(S) and the ratio of the annual interest rate(i_$) in country with base currency to the annual interest rate (i_euro) in the other country.

S^e = S *(i_$/i_euro) = 1.20 * (3/2) = 1.20 *1.50 = $1.80 per euro

Hence, the expected spot exchange rate after an year will be $1.80 per euro. According to the International Fisher Effect (IFE), country with higher nominal rate of interest will tend to see its currency depreciate. In the given case, since US has higher nominal rate of interest, dollar is predicted to depreciate (earlier only $1.20 were needed to buy 1 euro while it is predicted that we will need $1.80 to buy an euro after an year) which is in concurrence with the IFE.

b) Forward Exchagne rate (F) = S [(1+i_$)/ (1+i_euro)]

F = 1.20 (1.03/1.02) = 1.20 *1.01 = $1.21 per euro

The Forward exchange rate is equal to $1.21 per euro. Since F is greater than S, in this case it shows forward premium.

c) When a bank agrees to exchange a currency at a future date through a forward contract at a particular exchange rate, the agreed exchange rate is known as the forward exchange rate.

Interest parity condition allows for no arbitrage opportunities and is given by: (1+i_d) = (F/S)(1+i_f)

i.e. the return in domestic on deposits should be equal to the return on foreign deposits. If interest parity doesn't hold, it implies that an investor could borrow currency in the country with the lower interest rate, convert to the foreign currency at today's spot exchange rate, and invest in the foreign country with the higher interest rate.

Forward exchange rate can be a predictor for the expected spot exchange rate if we assume the assumption of rationality and the risk neutrality of the investor. This is also known as the unbiasedness hypothesis. Risk neutrality implies no foreign exchange risk premium i.e. algebraically it can be shown as:

F_t = S^e_t+k

where, F_t is the forward exchange rate at time t, S^e_t+k is the expected future spot exchange rate at time t + k, and k is the number of periods into the future from time t

However, the predictability will depend on the assumption of rationality and risk neutrality. If the risk neitrality assumption is relaxed, then the relationship needs to include the exchange rate risk premium and the equation will look as follows:

F_t = S^e_t+k + P_t where, Pt is the risk premium in time t.