Question

Suppose you are a U.S.-based investor with $1,000,000 to invest. The dollar-euro exchange rate is quoted as $1.60 = €1.00 and the dollar-pound exchange rate is quoted at $2.00 = £1.00. If a bank quotes you a cross rate of £1.00 = €1.20. Is there any arbitrage opportunities? What transactions will you carry out? How much money can you make

Answer 1

The Rate of Dollar to Euro is

$1.60 = €1.00

and the rate of Dollar to pound is

$2 = £1.00

so to bring all three in one equation, we have to convert Dollar to Euro rate as per $2 rate (because Dollar to pound is given as per $2 rate) and for that we have to multiply Dollar to Euro rate by 1.25, so

$1.60 * 1.25 = €1.00 *1.25

$2 = €1.25

Now we can put both rate in one equation, so

$2 = €1.25 = £1.00

so as per that,€1.25 = £1.00

and inter bank quotes

£1.00 = €1.20 or €1.20 = £1.00

so arbitrage opportunity exist as the rate for 1 pound is different in both case

Transactions will be carried out in the below mentioned ways

First we exchange Dollar to Euro

$1.60 = €1.00

so $ 1000000 = €( 1000000 / 1.6)

$ 1000000 = € 625000

Now we will convert Euro to pound

€1.20 = £1.00 (as per inter-bank quotes )

€ 625000 = £ ( 625000 / 1.2)

€ 625000 = £ 520833.33

Finally we will convert Pound to dollar

$2 = £1.00

So ( 520833.33 * 2) = £ 520833.33

$1041664 =£ 520833.33

Total gain = End value - Initial value

  = $1041664 - $1000000

= $ 41664