Currency Investment Strategy: Analyzing Interest Rate Parities for US Dollars and Euros”

QUESTION

Today, the annual interest rate on bank deposits is 8.15% in New York and 3% in Paris, the spot exchange rate is 1.2 US dollars per euro, and the one-year forward exchange rate is 1.236 US dollars per euro. Emily plans to deposit 1,000 US dollars in either New York or Paris for one year. Answer the following questions, using the exact equations for the UIP/CIP.

(a). Where should Emily deposit her funds? Given today’s spot exchange rate and interest rates, what is the equilibrium forward rate, if covered interest parity (CIP) holds? Report the intermediate steps.

(b). Suppose the forward rate takes the value given by your answer to question (a). If UIP also holds, is the US dollar expected to appreciate or depreciate against the euro over one year? By how much? Report the intermediate steps.

ANSWER

Currency Investment Strategy: Analyzing Interest Rate Parities for US Dollars and Euros”

To determine where Emily should deposit her funds and calculate the equilibrium forward rate under the Covered Interest Parity (CIP), we need to compare the expected returns from depositing in New York and Paris. CIP states that the interest rate differential between two countries should be equal to the forward premium or discount of the exchange rate between those two currencies.

First, let’s calculate the expected return from depositing in New York:

1. In New York, the annual interest rate is 8.15%. If Emily deposits $1,000, she will receive $1,000 * 8.15% = $81.50 in interest after one year.

2. In Paris, the annual interest rate is 3%, but she needs to convert her US dollars to euros at the spot exchange rate of 1.2. So, she would get €1,000 / 1.2 = €833.33.

3. If Emily deposits her funds in Paris, after one year, she will have €833.33 * 3% = €25 in interest.

Now, let’s calculate the equilibrium forward rate using CIP. CIP can be expressed as follows:

Forward Premium/Discount = (Interest Rate Differential – Expected Exchange Rate Change)

In this case:

Interest Rate Differential = 8.15% – 3% = 5.15%

Expected Exchange Rate Change = (Forward Rate – Spot Rate) / Spot Rate

Let’s assume the equilibrium forward rate is F US dollars per euro.

5.15% = (F – 1.2) / 1.2

Now, solve for F:

F – 1.2 = 0.0515 * 1.2

F – 1.2 = 0.0618

F = 1.2 + 0.0618

F ≈ 1.2618 US dollars per euro

So, if covered interest parity (CIP) holds, the equilibrium forward rate should be approximately 1.2618 US dollars per euro.

Now, let’s answer part (b):

(b) To determine whether the US dollar is expected to appreciate or depreciate against the euro over one year under the Uncovered Interest Parity (UIP), we need to compare the difference between the interest rate differential and the expected exchange rate change based on the equilibrium forward rate calculated in part (a).

Interest Rate Differential = 8.15% – 3% = 5.15%

Expected Exchange Rate Change = (Equilibrium Forward Rate – Spot Rate) / Spot Rate

Expected Exchange Rate Change = (1.2618 – 1.2) / 1.2 ≈ 0.0515 or 5.15%

Under UIP, the interest rate differential should be equal to the expected exchange rate change. However, in this case, the interest rate differential (5.15%) is greater than the expected exchange rate change (5.15%).

This means that according to UIP, the US dollar is expected to appreciate against the euro over one year by approximately 5.15%.

In conclusion, if both Covered Interest Parity (CIP) and Uncovered Interest Parity (UIP) hold, Emily should deposit her funds in New York, and the US dollar is expected to appreciate against the euro by approximately 5.15% over one year.