Question

You observe the exchange rates from the following 4 currencies(US, EU, UK, and Japan):

a.$1.19/€, $1.30/£, $0.0091/¥

b.€0.84/$, €1.09/£, €0.0076/¥

c.£0.77/$, £.91/€, £0.0055/¥

d.¥110.27/$, ¥130.77/¥, 183.26/£

Suppose that you incur 2% transaction costs. That is, if you attempt to convert one currency to another, you only get 98% of the quoted rate. So with €1, you can get .98*$1.19 = $1.17 There is an arbitrage opportunity in this market. Find it and describe each transaction you would take to exploit it. If a large amount of money went through this process, this would exert pressure on these exchange rates. For each transaction in your arbitrage strategy, explain how that transaction would impact currency values.

Answer 1

Data Provided
Currency	$	Pound	Euro	Yen
$	1.000000	0.840000	0.770000	110.270000
Pound	1.190000	1.000000	0.910000	130.770000
Euro	1.300000	1.090000	1.000000	183.260000
Yen	0.009100	0.007600	0.005500	1.000000
Solution
		Convertion of Pound to $	Conversion of $ to Euro	Conversion of $ to Yen
Convertion of $ to Pound		0.84034	0.76471	109.89076
Conversion of $ to Euro		0.83846	0.76923	140.96923
Conversion of $ to Yen		0.83516	0.60440	109.89011
As can be seen from the highlighted yellow tables above - Conversion of $ to Yen via converting $ to Euro is beneficial
Conversion of Dollar to Eurio				0.769231
Less : Transaction Cost @ 2%				0.015385
Euro available after converting $ to Euro				0.753846
Convert avaiable Euro to Yen				137.062937
If Dollar Directly Converty to Yen (After Transaction Cost of 2%)				108.064600
Benefit of Yen				28.998337