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**

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