Question

1. The present exchange rate between US dollars and Euros is 1.34 $/Euro. The price of a domestic 180-day Treasury bill is S99.50 per $100 face value. The price of the analogous Buro instrument is 98.50 Euros per 100 Euro face value (a) What is the theoretical 180-day forward exchange rate? (b) Suppose the 180-day forward exchange rate available in the marketplace is 1.31 $/Euro. This is less than the theoretical forward exchange rate, so an arbitrage is possible. Describe a risk-free strategy for making money in this market. How much does it gain (in dollars), for a contract size of 100 Euro?

Answer 1

Interest Rate Parity Theorem(IRPT)

There is strong relationship between the Foreign exchange market and the money market. the relationship between the interest rates in Two countries affect the rate of exchange, and the relationship between the spot rate of exchange and the forward rate of exchange.

there are many factors other than interest rates that affect movement in exchange rate overtime. However, all things being equal, the currency with higher interest rate will sell at a discount in the forward market against the currency with the lower interest rate.

In other words, if a country has a higher domestic rate of interest than its trading partner, it will find that this interest rate difference will attract foreign investors, and their desire to invest in that country will lead them to purchase the domestic currency, thus increasing that currency spot rate.

Thus, According to IRPT, equilibrium Forward rate or theoretical rate can be calculated as below

F/S = (1+rh)/(1+rf)

Where,

F = Forward exchange rate

S = Spot rate

rh = home currency interest rate

rf = foreign currency interest rate

Further, If Forward rate is not at equilibrium then there will arbitrage opportunity which means gain without making any investment and taking risk.

Strategy for Arbitrage

Interest rate differential (rf-rh) < domestic currency forward premium      

Borrow in foreign currency and bring borrowed money to home country at spot rate and invest it with home currency interest rate and cover this with forward contract. On Maturity, sell the home currency at forward rate and pay the loan liability of foreign currency.

The difference between investment proceeds in home country and home currency required to sell at forward rate to pay foreign currency loan is Arbitrage gain.

For calculations please refer to following spreadsheet.

Formula Reference -

1(a).

Theoretical 180-day Forward exchange rate = $ 1.33/euro

1(b).

Arbitrage gain in Dollar = $ 1.65

Please note the forward contract size is 100 euro, thus borrowing amount in euro should be 98.5 euro so that after 180 days amounts payable would be 100 euro.