Question

4. Consider two countries: Japan and France. Suppose you saw the following information in the newspaper: Interest rate on one-year Japanese deposits = 8%; Interest rate on one-year French deposits = 6%; Current spot rate: 100 yens per euro. Further suppose that based on your research on the two countries, you expect the spot rate is going to be 105 yens per euro a year from now. Round numbers to 3 decimal points. Pick home and foreign country and setup your equation appropriately

1. Does uncovered interest parity (in exact form) hold?
2. If not, at what current spot rate would the uncovered interest parity hold (be satisfied)?
3. How might the current spot rate be driven to this level you found in (b)? Explain. (Explain the adjustment mechanism that occurs through trade of currencies that makes arbitrage disappear).

Answer 1

a]

As per uncovered interest parity, the difference in interest rates should equal the change in exchange rate over the period

Home country is France and foreign country is Japan

For uncovered interest parity to hold, future exchange rate = current exchange rate * (1 + foreign rate) / (1 + domestic rate)], where the exchange rate is quoted as number of foreign currency per unit of domestic currency

Future exchange rate = 100 * [(1 + 8%) / (1+ 6%)] = 101.887

However, the expected future exchange rate is 105.

Therefor uncovered interest parity does not hold

b]

let us say current spot rate is X. Then, uncovered interest parity would be satisfied if :

105 = X * [(1 + 8%) / (1 + 6%)]

X = 103.056

The current spot rate should be 103.056 Yen per Euro for uncovered interest parity to hold

c]

Since the uncovered interest parity does not hold currently, the arbitrage players in the currency markets would take these steps to make arbitrage profits :

• Borrow Euro, and sell the Euros to buy Yen
• Invest in Yen for one year
• After one year, convert the Yen back into Euro at the spot rate after one year
• Repay the Euro loan

This demand for Yen would increase the exchange rate until it reaches the equilibrium rate of 103.056. At this exchange rate, no arbitrage would be possible