Question

You have the following market data.

• Spot price for the British pound is $1.475 per pound.
• Futures price is $1.27 per pound on a contract that expires in four months.
• U.S. dollar LIBOR for four months is a continously compounded rate of 1.43% per annum.
• British LIBOR for four months is a continuously compounded rate of 3.41% per annum.
• The contract size is 62,500 British pounds.

What is the total net profit if you execute the arbitrage strategy with one futures contract?

Do not round values at intermediate steps in your calculations. Enter your answer in dollars and cents to two decimal places, but omit the $ symbol and commas. For example, enter $1,234.56 as 1234.56 as your answer.

Answer 1

So = $1.457/pound

** if the quote is say $1.41 CAD per 1 USD, then domestic currency is CAD and foreign currency is USD**

domestic currency: $

foreign currency: pound

F: Theoretical Forward rate

S: spot rate = $1.457/pound

r: risk-free rate in domestic currency ($) = 1.43%

rf: risk-free rate in foreign currency (pound) = 3.41%

t: time in years = 4months = 0.25 year

e: natural exponent

F = S * e^((r - rf)*t)

F = 1.457*e^((1.43%-3.41%)*0.25) = $1.4498/pound

Future price (quoted) = $1.27/pound

Since future price (quoted) < forward price (theoretical)

The future is undervalued and we will go long on it

Arbitrage profit = $1.4498/pound - $1.27/pound = $0.1798/pound

Contract size = 62,500 pounds

Arbitrage profit = ($0.1798/pound)*62,500 pounds = $11237.85