Question

Suppose you observe the following spot exchange rates:

S(€/$) = 0.67, S($/£) = 2.00, S(£/€) = 0.80

a.Show if there exists a triangular arbitrage. If there exists an arbitrage, what is your strategy for a dollar profit (Start from selling the dollars and end with buying the dollars)?(4 points)

b.Start with $100,000, calculate the dollar profit. (2 points)

Answer 1

a)	€ / $
	= € / £ * £ / $
	= 1/0.80 * 1/2
	= 1.25 * 0.50
	= 0.625
	S(€ / $) = 0.67, so traingular arbitrage exists as follows
	1) Convert $100 into € at Spot Rate €0.67
	2) We will receive €67 ($100 * €0.67)
	3) Convert €67 into £ at Spot Rate £0.80/€
	4) We will receive £53.60 (€67*£0.80)
	5) Convert £53.60 into $ at Spot Rate $2.00/£
	6) We will receive $107.20 (£53.60*$2)
	7) Arbitrage Profit will be $7.20 ($107.20 - $100)
b)	1) Convert $100,000 into € at Spot Rate €0.67
	2) We will receive €67,000 ($100,000 * €0.67)
	3) Convert €67,000 into £ at Spot Rate £0.80/€
	4) We will receive £53,600 (€67,000*£0.80)
	5) Convert £53,600 into $ at Spot Rate $2.00/£
	6) We will receive $107,200 (£53,600*$2)
	7) Arbitrage Profit will be $7,200 ($107,200 - $100,000)