Question

A U.S. investor and an Italian investor are considering investments in the U.S. and the Eurozone. Both investors are quoted the following rates from their banks:

Spot exchange rate (e_$/€):                                $1.10/€

One-year forward rate (f_$/€):                           $1.06/€

One-year interest rate on dollars (i_$):             3.0%

One-year interest rate on euros (i_€):               5.0%

1. Does Covered Interest Rate Parity hold given the rates quoted above?
2. Should the U.S. investor make a one-year covered investment in euros or simply invest in dollars?
3. Should the Italian investor make a one-year covered investment in dollars or simply invest in euros?
4. If Uncovered Interest Rate Parity holds, what is the spot rate expected in one year?

Answer 1

A. Interest rate parity is a no-arbitrage condition in which there is no possibility of gaining money and the end result being indifferent to choice of where the money is invested in, and the exchange rate risk is hedged against a forward rate, or

(1+iUS)/(1+iEU) = F/S
Since, inserting the values from the question, we have

1.03/1.05=1.06/1.10 which is not true, we get that given the rates quoted above, covered interest rate parity doesn't hold.

B In this case, let's suppose we start with 100$, if we invest it in the US, we have a total of 103$ in the end after 3% interest,
However,if we invest in the EU, first we convert it to Euros to get 100/1.10 = 90.9090 euros, which become 90.9090*1.05= 95.4545 At 5% interest after 1 year, and converting back at the forward exchange rate, we have 95.4545*1.06=101.1818 $

Since the Investor in US has more money if he just invests in dollars, he should simply invest in dollars.

C. Similarly, now we take an investor in Italy and suppose he starts with 100$, he will have a total of 105$ if he invests in Euros at 5% interest in a year

If he invests in US, he will have 100*1.10= 110$ in the beginning at the spot exchange rate, which becomes 113.3$ At 3% interest rate in a year, and converting back at the forward exchange rate we have, 113.3/1.06 = 106.8868$

Therefore the Italian investor should make a one year covered interest in dollars

D. If uncovered interest rate parity holds i.e. there is the "no-arbitrage condition" satisfied without the use of forward exchange rates,and so the spot rate expected in a year will be such that the condition holds, or

(1+iUS)/(1+iEU) = St+1/St

1.03/1.05 = x/1.10

x=1.079047

Or the expected spot exchange rate is 1.08$/Euros

Hope it helps. Do ask for any clarifications if required.