Question

Part II: Triangular Arbitrage

The quotations of exchange rates of US dollars, British pound, and the New Zealand dollar in National Bank is as below. ​

	Quoted Bid Price	Quoted Ask Price
USD/GBP	0.65	0.66
NZD/USD	0.50	0.52
GBP/NZD	​2.72	​2.75

Is the triangular arbitrage feasible? If yes, how much is the triangular arbitrage profit when you have $500,000 to invest. If no, please explain why (20 points)

Answer 1

Theoritical USD/GBP = USD/NZD * NZD/GBP

USD/GBP (Bid rate) = 1/{NZD/USD (Ask rate) * GBP/NZD (Ask rate)}

= 1/(0.52*2.75) = 1/1.43 = 0.6993

USD/GBP (Ask rate) = 1/{NZD/USD (Bid rate) * GBP/NZD (Bid rate)}

= 1/(0.50*2.72) = 1/1.36 = 0.7353

USD per GBP is underpriced hence there is an arbitrage possibility exist.

Part II

If an investor Convert USD into GBP by using USD 500,000 at Ask rate i.e 0.66 = GBP 757,575.76 ($500,000/0.66)

Convert GBP into NZD by using ask rate i.e 2.75 = NZD 275,482.09 (GBP 757,575.76/2.75)

Again convert back NZD into USD by using ask ratei. 0.52 = USD 529,773.26 (NZD 275,482.09/0.52)

Arbitrage Profit = $ 529,773.26 - $ 500,000 = $ 29,773.26