Question

How much is your arbitrage profit in $ at expiration, if you know that the current exchange rate is $ 1.25 / GBP, the 60-day forward rate is $ 1.41 /GBP, the risk free rate in the U.S. is 2% and the risk free rate in the UK is 4%? Make your calculation so that the spot transaction is for $100,000. Provide your arbitrage profit in $ rounded to two decimals.

Answer 1

	Exchange Rate = $ 1.25 / £
	As per Interest Rate Parity Theorem,
	Fair Forward Rate = $ (1 + i $)/(1 + i£)
	Fair Forward Rate = 1.25 (1 + (0.02*(60/360)))/(1 + (0.04*(60/360)))
	Fair Forward Rate = 1.2458
	60-day forward rate is $ 1.41 /GBP
	As the Actual Forward Rate is higher than fair forward Rate, Forwards are over priced hence Sell forward
A	If $100,000 is deposited, after 60 days, We get $100,000*2%*(60/360) = $100,333.33
B	Purchase £ in Spot and enter into Forward Contract
	Purchase £ with $100,000 available, We get $100,000/$1.25 = £ 80,000
	Deposit £ we got for 60 days, We get £ 0.9674 + Interest = 0.9746
	Interest = £80,000 * 4% * 60/360 = £ 80,533.33
	Convert £ we received to $ using Forward Rate
	We get £80,533.33/$1.41 = $ 113,552
C	Arbitrage Gain = $ 113,552 - $ 100,333.33
	Arbitrage Gain = $ 13,218.67