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. If the spot rate is 1.5 euros per pound, and interest rates are as stated previously, what should be the forward rate if CIP is held? ?

b. Suppose the forward rate takes the value given by your answer to (b). Calculate the forward premium on the British pound for the Dutch investor (where exchange rates are in euros per pound). Is it positive or negative?

c. If UIP holds, what is the expected euro–pound exchange rate one year ahead?

d. Based on your answer to (f) (d), ? what is the expected depreciation of the euro against the pound over one year? ?

e. Now assume that the Expected exchange rate does not change, but the interest rate in Europe dropped to 2%. What is the new euro-pound spot rate if the UIP holds.

Answer 1

Hello,

a) Spot rate,S = 1.5 euros per pound
i_d = interest rate in domestic country (here, Europe)
i_f = interest rate in foreign country (Britain)

Covered interest rate parity is a condition where there is no scope of arbitrage as both the spot and forward rates are in equilibrium with the exchange rates.

(1 + i_d) = (S / F) * (1 + i_f)
F = S * ((1 + i_f) / (1 + i_d))
Substituting the values,
F = 1.5((1 + .03)/(1+.04))
= 1.5(.99)
= 1.485 euros per pound

b) A forward premium is the difference between current the spot rate and the forward rate.

Forward premium = (F/S - 1)*100
= (1.485/1.5 - 1)*100
= -1%
Since the premium is coming out to be negative, therefore it's a forward discount.

c) (1 + i_d) = E(t + k) / S(t) x (1 + i_f)
(1 + i_d)/(1 + i_f) = E(t + k) / S(t)
Where, E(t + k) = expected exchange rate at the time t+k
Other notations similar as in the above parts.

Calculating E(t+k),
(1+.04)/(1+.03) = E(t + k)/(1.5)
E(t+k) = 1.515 euros per pound

d) Spot Rate = 1.5 euros per pound
Expected exchange rate after one year = 1.515 euros per pound

Expected depreciation = (E(t+k) - S)/S x 100
= (1.515 - 1.5)/1.5*100
= 1%

e) (1 + i_d)/(1 + i_f) = E(t + k) / S(t)
New i_d = 2% =.02
Substituting the values:

(1+.02)/(1+.03) = 1.515/ S(t)
S(t) = 1.53 Euros per Pound
  
Hope you understood!:)