Question

Consider a Dutch investor with 2,000 euros to place in a bank deposit in either the Europe or Great Britain. The one-year interest rate on bank deposits is 3% in Britain and 4% in Europe. The one-year forward euro–pound exchange rate is 1.6 euros per pound and the spot rate is 1.5 euros per pound. Answer the following questions, using the exact equations for Covered Interest Rate Parity (CIP) and Uncovered Interest Rate Parity (UIP) as necessary.

a. What is the euro-denominated return on European deposits for this investor?

b. What is the riskless euro-denominated return on British deposits for this investor using forward cover? ?

c. Do the above values depict an equilibrium in the forward exchange rate market? ?

d. If not, show how to profit from any arbitrage opportunity?

Answer 1

We shall assume that the foreign currency (and consequently foreign territory) in this example is the British Pound and the home currency (and consequently home country) is the Euro.

British Interest Rate = r(b) = 3 % per annum and European Interest Rate = r(e) = 4 %

Current Spot Exchange Rate = S0 = 1.5 EUR / Pound and Forward Exchange Rate = F = 1.6 EUR / Pound

(a) European Deposit would mean a deposit made in the originally held denomination of 2000 euros at the end of 1 year at the European deposit rate.

Therefore, Deposit Value after on year in Europe = 2000 x (1.04) = $ 2080

Euro Denominated Return = (2080-2000) / 2000 = 0.04 or 4 % as would be expected because the deposit promises a return of 4 %.

(b) British Deposit would mean converting the 2000 euros into British Pounds at the existing spot exchange rate of 1.5 EUR/ Pound and then depositing the same into a British Bank for a year. After one year the deposit value is converted into Euros at the then existing (and stated) forward exchange rate of 1.6 EUR/Pound and the further calculations made to determine euro-denominated returns on British deposit.

Initial Deposit = 2000 euros = 2000 / 1.5 = 1333.334 Pounds

Deposit Value after one year = 1333.334 x (1.03) = 1373.334 Pounds

Deposit Value in Euros = 1373.334 x 1.6 = 2197.334

Euro Denominated Return = (2197.334 - 2000) / 2000 = 0.098667 or 9.8667 %

The Euro Denominated Return is greater than the expected return of 4% (prevalent deposit rate in Europe) as the exchange rate one year later is mispriced with respect to the arbitrage-free Covered Interest Parity Equation.

(c) As already mentioned above, the above rates do not demonstrate an equilibrium. This is so because converting the deposit into Pounds, putting it in a British Bank and reconverting at the mispriced forward exchange rate generates a greater return than the expected European deposit rate of 4 %.

(d) Arbitrage would be executed as described below:

- Borrow 2000 euros at the European Deposit Rate of 4 % per annum

- Convert the borrowings into pounds at the existing spot rate of 1.5 EUR/Pound to yield (2000 / 1.5) = 1333.334 Pounds

- Deposit this converted amount in a British bank at the British deposit rate of 3 % per annum.

- Value of Deposit after one year = 1333.334 x (1.03) = 1373.334 pounds

- Convert deposit value into euros at the forward rate of 1.6 EUR/ pound to yield (1373.334 x 1.6) = 2197.3344 Euros

- Borrowings to be repaid (2000 x 1.04) = 2080 euros

- Risk Less profit made = Deposit Value in Euros after one year - Borrowings to be repaid after one year = 2197.3344 - 2080 = 117.3344 euros.

As this strategy makes a riskless profit, it is an example of an arbitrage strategy.