Question

Suppose the spot exchange rate be $1.45 per euro, the interest rate on one-year euro-denominated German government bond is 2%, and the expected future spot rate be $1.50 per euro. At the same time, the interest rate on dollar-denominated US government bond with the same maturity is 3%. a. Calculate the expected dollar return on the German government bond. b. Does your answer in Part (a) imply free capital mobility between the US and Germany? Explain your reasoning. c. Suppose both governments implement financial liberalization to achieve free capital mobility. Will the US receive capital inflows from Germany? Explain your reasoning. d. Suppose both governments implement financial liberalization to achieve free capital mobility, and government bonds interest rate remain unchanged. Calculate the spot exchange rate that is consistent with financial liberalization, given no change in the expected future spot rate. e. Suppose both governments implement financial liberalization to achieve free capital mobility. However, the US government is willing to raise its bond interest rate to 4%, while the German government continues to keep its bond interest rate at 3%. Calculate the spot exchange rate that is consistent with financial liberalization, given no change in the expected future spot rate.

Answer 1

Interest Rate Parity (IRP) is considered as the interest rates differential between the two countries remains equal to the differential calculated by using the forward exchange rate and the spot exchange rate techniques. Interest rate provides the relation between foreign exchange rates, spot rate and risk-free interest rate

According to this theory, there will be no arbitrage in interest rate differentials between two different currencies and the differential will be reflected in the discount or premium for the forward exchange rate on the foreign exchange.

A.

Let's say we are investing € 1000 for 1 year.

Scenario 1: Investment in the US (Dollar)

In the US, as per the spot exchange rate $1.45 / €1.

So, we get an exchange for our €1000 @ $1.45 = $1450

We can invest this money $1450 at the rate of 3% for 1 year which gives a return of $1493.50 at the end of the year.

Scenario 2: Investment in Germany (Dollar)

We can also invest €1000 in Geman market, where the rate of interest is 2.0% for 1 year.

So, €1000 @ of 2% for 1 year = €1020

The forward exchange rate is $1.50 / €1.

So, we buy forward 1 year in the future exchange rate at $1.50 /€1 since we need to convert our €1000 back to the domestic currency, i.e., the U.S. Dollar.

Then, we can convert € 1020 @ $1.50 = $1530

Thus, an expected dollar return on the german government bond of $1530 - $1493.50 = $36.50 for € 1000

B.

Yes, Part (A) implies that there is free capital mobility between the US and Germany, as the arbitrage or difference in the interest rates and the exchange rates can be taken advantage of when there is easy capital mobility between countries along with complete substitutability of assets, for example, a deposit in a foreign bank is considered the same as a deposit in a domestic bank.

Thus in order to achieve the riskless return by taking advantage of the interest rate differential and exchange rate differential, there should be free capital mobility, or else the arbitrage will be minimized due to the tax laws difference, and conversion cost difference, etc.

C.

If both governments implement financial liberalization to achieve free capital mobility the US will receive capital inflow from Germany because of the interest rate paid on the one-year government bonds is higher when compared to those in Germany as well as there seems to be a strengthening of the Euro against the US Dollar after a period of 1 year.

D.

F=S*(1+ Rqc)/(1+ Rbc)

F = Foward Rate Here, $1.50 / €1.

S = Spot rate

Rqc = interest rate on quoting currency Here USD = 3%

Rbc = interest rate on base currency Here Euro = 2%

Spot exchange rate = 1.50 x (1.02) / (1.03) = 1.4854

E.

F=S*(1+ Rqc)/(1+ Rbc)

F = Foward Rate Here, $1.50 / €1.

S = Spot rate

Rqc = interest rate on quoting currency Here USD = 4%

Rbc = interest rate on base currency Here Euro = 3%

Spot exchange rate = 1.50 x (1.03) / (1.04) = 1.4855