Question

The following are quotes for several U.S. currency dealers. Please do number 10 and 11

Dealer	A	B	C	D	E
Japanese yen	109.03 109.06	109.04 109.08	109.06 109.10	109.05 109.07	109.07 109.09
British pounds	1.3115 1.3119	1.3118 1.3120	1.3115 1.3118	1.3116 1.3117	1.3115 1.3118

Covered interest arbitrage (Inter-temporal) - assume that the highest bid and lowest ask are equal (i.e., that the bid-ask spread is zero)

9. Assume the interest rate of 1-year risk free debt denominated in US dollars is 2.57% and the interest rate on 1-year risk free debt denominated in Uruguayan pesos is 9.25%. If the spot market exchange rate for the Uruguayan peso (USD/UYU) is 32.545, what is the 1-year forward exchange rate if interest rate parity holds?

Spot rate(1+ interest rate of USD)/(1+interest rate of uruguayan)

= 32.545*1.0257/1.0925

= 30.555

10 a. If the actual 1-year forward exchange rate for Uruguayan pesos is 34.636 and the spot market exchange rate and interest rates are as indicated in question 9, what trades should you make to take advantage of the arbitrage opportunity? Be specific about both current and future transactions (i.e., be sure to specify what currency/currencies are involved and how, and the amount of each – you can make any assumption you like about the amount of currency to start).

b. How profitable is the trade? (State the profitability, either in dollars or pesos, or as a percent of initial amount borrowed.)

Answer 1

Answer to Q10 a and b

Spot rate: 32.545 (USD/UYU)

1 year Forward rate: 34.636 (USD/UYU)

Taking into consideration the same interest rate as mentioned in Q9, there would be an arbitrage opportunity.

Say you want to trade for USD 1000, then one can Borrow dollar for 1 year @ 2.57% risk free rate and Sell USD at spot rate of 32.545 to get UYU,

=1000* 32.545

=UYU 32545.

Invest UYU 32545 at a risk free rate @ 9.25% for 1 year and get UYU

= 32545*1.0925

=UYU 35555 approx

Sell this UYU 35555 after 1 year actual forward rate @ 34.636, getting USD

= 35555/34.636

=USD 1026.545

Borrowed Dollar payment after 1 year:-

=1000*1.0257

=USD 1025.70

Arbitrage profit amount: USD(1026.545-1025.70) = USD 0.845

Percentage of profitable amount to the initial amount borrowed = 0.845/1000 = 0.08%

NOTES & ASSUMPTIONS

1. The borrowings in USD is assumed to be 1000 USD.

2. This concept can be understand through Borrow-Sell-Invest-Sell for easy understanding.

3. The percentage of profit amount will remain same. However the profit amount can change with the amount of borrowings.

4. While answering this question, you should follow by borrowing in both the currencies. While one currency will give you the loss, thus not making it viable to borrow and the other will give you the profit. Follow the same procedure for practicing purpose by Borrowing say 100000 UYU @ 9.25% and sell it spot @ 32.545 to get USD. Invest this USD @ 2.57% for 1 year and then sell after 1 year to get UYU. Compare this received amount with the payable amount on borrowing. If payable is more than received amount then it is not viable to borrow the currency.