Question

Write a report to your company’s treasurer in which you:

• List the current spot exchange rates between the:

o US dollar and the British pound

? 1 USD = .7614 GBP ? 1 GBP = 1.31 USD

o Japanese yen and the European Union Euro

? 1 JPY = 0.0077 E ? 1 E = 130.69 JPY

o Swiss franc and the Mexican peso.

? 1 CHF = 19.15 MXN ? 1 MXN = .0521 CHF

• Explain how you would use arbitrage to earn an instant, risk–free profit between each of these currency pairs.

Answer 1

(a)

1 USD = 0.7614 GBP

1 GBP = 1.31 USD

Suppose in the begining, 1,000,000 GBP are available.

1,000,000 GBP will be used to buy USD

Hence, number of USD to be bought = 1,000,000 x 1.31

= 1,310,000 USD

Now, USD will be used to buy GBP

Number of GBP to be bought = 1,310,000 X 0.7614

= 997,434 GBP

Hence, loss in the arbitrage = 997,434 - 1,000,000

= 2,566 GBP

Suppose, reverse strategy is chosen.

Suppose in the begining, 1,000,000 USD are available.

1,000,000 USD will be used to buy GBP

Hence, number of GBP to be bought = 1,000,000 x 0.7614

= 761,400 GBP

Now, GBP will be used to buy USD

Number of USD to be bought = 761,400 X 1.31

= 997,434 USD

Hence, loss in the arbitrage = 997,434 - 1,000,000

= 2,566 USD

Hence, arbitraging is not profiable in this case

(b)

1JPY = 0.0077E

1E = 130.69 JPY

Suppose in the begining, 1,000,000 JPY are available.

1,000,000 JPY will be used to buy European Union Euro (E)

Hence, number of Euro to be bought = 1,000,000 x 0.0077

= 7,700

Now, Euros will be used to buy JPY.

Number of JPY to be bought = 7,700 x 130.69

= 1,006,313

Hence, profit to be earned = 1,006,313 - 1,000,000

= 6,313 JPY

(c)

1 CHF = 19.15 MXN

1 MXN = 0.0521 CHF

Suppose in the begining, 1,000,000 CHF are available.

1,000,000 CHF will be used to buy MXN

Hence, number of MXN to be bought = 1,000,000 x 19.15

= 19,150,000 MXN

Now, MXN will be used to buy CHF

Number of CHF to be bought = 19,150,000 x 0.0521

= 997,715

Hence, loss in the arbitrage = 997,715 - 1,000,000

= 2,285 CHF

Same will be the result, when reverse arbitrage is used.

Hence, in this case arbitraging is not profitable.

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