Question

2. Triangular Currency Arbitrage

A)   Given $1.5271 / £ in NY, $0.9250 / € in Frankfurt, and €1.6645 / £ in London.

Identify if there exists a triangular arbitrage opportunity. What is your strategy to achieve your profit? How much is your triangular arbitrage profit starting with $1,000,000.

B) Assuming no transaction cost,

A:   You can buy a U.S. dollar for 10 pesos;     The bank will pay you 9 pesos for a U.S. dollar.

B:   You can buy a U.S. dollar for .9 euros;     The bank will pay you .8 Euros for a U.S. dollar.

C:   You can buy a euro for 14 pesos.              The bank will pay you 13 pesos for a euro.

Reorganize the above into $/peso (A), $/euro (B) and euro/peso (C) and identify if triangular arbitrage is possible. What is your trading strategy? Compute the triangular arbitrage profit starting with $1,000,000.

Answer 1

A)	Calculate $/£ Rate using Exchange Rate at London and
	Frankfurt and such rate should be compared with rate
	in NY.
	$/£ = €/£*$/€ = 1.6645 * 0.9250 = 1.5397
	Rate qoted in NY is $1.5271/£
	So, Arbitrage Opportunity is available as follows
1)	Convert $1,000,000 in NY @ $1.5271/£
	We will Receive £654,835.9636 ($1,000,000 / $1.5271)
2)	Convert £654,835.9636 in London @ €1.6645/£.
	We will receive €1,089,974.4614 (£654,835.9636* €1.6645)
3)	Convert €1,089,974.4614 in Frankfurt @ $0.9250/€.
	We will receive $1,008,226.5420 (€1,089,974.4614*$0.9250)
	Arbitrage Gain
	= $1,008,226.5420 - $1,000,000
	= $8226.5420
B)	Convert Peso/$ into $/Peso
	Bid = Rate which bank will pay = 1/10 Peso = $0.10/Peso
	Ask = Rate at which we will buy = 1/9Peso = $0.11/Peso
	Convert €/$ into $/€
	Bid = Rate which bank will pay = 1/€0.9 = $1.11/€
	Ask = Rate at which we will buy = 1/€0.8 = $1.25/€
	Convert Peso/€ into €/Peso
	Bid = Rate which bank will pay = 1/14 Pesos = €0.0714/Pesos
	Ask = Rate at which we will buy = 1/13 Pesos = €0.0769/Pesos
1)	Convert $1,000,000 into euros using Ask Rate of $/€ i.e. $1.25/€
	We will receive €800,000 ($1,000,000 / $1.25)
2)	Convert €800,000 into Pesos using Ask Rate of €/Peso i.e. €0.0769/Peso
	We will receive 10,403,120.9362 Pesos (€800000 / €0.0769)
3)	Convert 10,403,120.9362 Pesos in $ using Bid Rate $/Peso i.e. $0.10/Peso
	We will Receive $1,040,312.0936 (10,403,120.9362 Pesos*$0.10)
	Arbitrage Profit
	= $1,040,312.0936 - $1,000,000
	= $40,312.0936