Question

In the table below, exchange rate is defined as US dollars per Euro, E_$/€. Given the information below, using UIP (in approximate form), fill in the blanks marked with letters. Round your answers to 3 decimals.

Interest Rate on Dollar Deposit (annual)	Interest Rate on Euro Deposit (annual)	Spot Exchange Rate, E$/€ (today)	Expected Future Exchange Rate, Ee$/€ (in one year)	Expected Rate of Change in Exchange Rate (Ee$/€-E$/€)/E$/€	Expected Dollar Return on Euro Deposit (annual)	Investors Prefer
0.025 (2.5%)	0.005 (0.5%)	1.10	1.326	0.205 (20.5%)	0.21	A
0.025	0.005 (0.5%)	B	1.326	0.105	C	D
0.025	0.005	E	1.326	F	G	Indifferent
0.025	0.005	1.4	1.326	H	I	J

Answer 1

Let’s assume dollar is the home currency country and Euro be the foreign currency. So, according to UIP the following relation should hold.

=> i_Dollar = i_Euro + d, where “i_Dollar = home rate of return”, “i_Euro = foreign rate of return”, “d = Expected rate of change in exchange rate ”and “i_Euro + d = Expected dollar return on Euro deposits”.

a).

In the 1^st case “i_Dollar = 2.5% = 0.025” which is less than “Expected dollar return on Euro deposits = i_Euro + d = 21% = 0.21”. So, the investor will prefer “Euro Deposit”.

b).

Here the expected exchange rate is “Ee = 1.326” and the “Expected Rate of change in exchange rate = (Ee-E)/E = 0.105.

=> (Ee-E)/E = 0.105, => Ee/E - 1 = 0.105, => Ee/E = 1.105, where “Ee=1.326”.

=> E = Ee/1.105 = 1326/1.105 = 1.2, => E = 1.2. The Spot Exchange rate is “E=1.2”.

The “expected dollar return on Euro deposit” is the sum of “i_Euro = foreign rate of return” and “d = Expected rate of change in exchange rate”, the “expected dollar return on Euro deposit” is “i_Euro + d = 0.005 + 0.105 = 0.11 = 11%”.

Here “i_Dollar = 2.5% = 0.025” which is less than “Expected dollar return on Euro deposits = i_Euro + d = 11% = 0.11”. So, the investor will prefer “Euro Deposit”.

c).

Here the investor is indifferent between “dollar deposit” and “Euro deposit” implied “interest rate on dollar deposit” must be equal to “Expected dollar return on Euro deposits = i_Euro + d”.

=> i_Dollar = i_Euro + d, => 0.025 = 0.005 + (Ee-E)/E, => 0.025 = 0.005 + Ee/E – 1.

=> Ee/E = 1.02, => E = Ee/1.02, => E = 1.326/1.02 = 1.3, => E = 1.3.

So, the “expected rate of change in exchange rate” is given by “Ee/E – 1 = 1.326/1.3 -1 = 0.02”, => “d=0.02 = 2%”.

Here “Expected dollar return on Euro deposit” should be same “i_Dollar= 0.025 = 2.5%”.

d).

Here the spot exchange rate is “E=1.4” and the expected exchange rate is “Ee=1.326”. So, the “Expected Rate of change in Exchange rate = d” is given by.

=> d = Ee/E -1 = 1.326/1.4 -1 = (-0.0529).

So, the “expected dollar return on euro deposit” is “i_Euro + d = 0.005 – 0.0529 = (-0.0479)”.

Here “i_Dollar = 2.5% = 0.025” which is more than “Expected dollar return on Euro deposits = i_Euro + d = (-0.048)”. So, the investor will prefer “Dollar Deposit”.

Consider the following fig.

Interest Rate on Interest Rate on Spot Exchange Expected Future Expected Change in Expected Dollar Return Dollar Deposit Euro Deposit Rate (E) Exchange Rate (Ee) Exchange Rate(d) on Euro Deposit Investors Prefer 0.025 0.005 1.1 1.326 0.205 0.21 A = Euro Deposit 0.025 0.005 B = 1.2 1.326 0.105 C = 0.11 D = Euro Deposit 0.025 0.005 E = 1.3 1.326 F = 0.02 G = 0.025 Indifferent 0.025 0.005 1.4 1.326 H = (-0.053) 1 = (-0.048) J = Dollar Deposit