Question

In: Finance

1. Using the information given below, calculate a cross-rate matrix for the UK pound, Japanese Yen,...

1. Using the information given below, calculate a cross-rate matrix for the UK pound, Japanese Yen, and European Euro in a triangular matrix. Currency in US$UK pound 1.4655 Japan yen 0.010854 Euro area euro 1.2238

Calculate: a) UK pound per Japan yen

b) Japan yen per Euro area euro

2. A bank is quoting the following exchange rates against the dollar for the pound and the Canadian dollar:£/$ = 0.6850C$/$ = 0.9629A Canadian firm asks the bank for an £/C$ quote. What cross-rate would the bank quote?

C). The British pound is trading for $1.9724 in New York and the Euro is trading for $1.3450 in Frankfort, while the British pound is trading for €1.4510 in London.

a. Does an arbitrate opportunity exist? Why?

b. Let us say you start with $10000, what will be your profit after taking an arbitrage opportunity (if it exists)?

Expert Solution

1)

USD / GBP = USD 1.4655 / GBP

USD / JPY = USD 0.010854 / JPY

USD / EUR = USD 1.2238 / EUR

UK pound per Japan yen = GBP / JPY

UK pound per Japan yen = (USD / JPY) / (USD / GBP)

UK pound per Japan yen = 0.010854 / USD 1.4655

UK pound per Japan yen = GBP 0.0074063 /GBP

Japan yen per Euro area euro = JPY / EUR

Japan yen per Euro area euro = (USD / EUR) / (USD / JPY)

Japan yen per Euro area euro = 1.2238 / 0.010854

Japan yen per Euro area euro = JPY 112.75106 / EUR

2)

:£/$ = 0.6850

C$/$ = 0.9629

£/C$ = (£/$) / (C$/$)

£/C$ = 0.6850 / 0.9629

£/C$ = £ 0.71139 / C$

3)

USD / GBP = $1.9724 / £

USD / EUR = $1.3450 / €

EUR / GBP = €1.4510 / £

a) To take advantage of the arbitrage opportunity we need to convert $1 into Euros

Amount in Euros = (1 / (USD / EUR)

Amount in Euros = 1 / $1.3450 / €

Amount in Euros = €0.7435

We then convert this amount to British pounds

Amount in British pounds = Amount in Euros * (1 / (EUR / GBP)

Amount in British pounds = €0.7435 * (1 / €1.4510 / £)

Amount in British pounds = £0.5124

We then convert this amount to US Dollars

Amount in US Dollars = British pounds * (USD / GBP)

Amount in US Dollars = €0.7435 * $1.9724 / £

Amount in US Dollars = $1.01066

There is exists an arbitrage opportunity with a arbitrage profit of ($1.01066 - $1) = 0.01066 per dollar

b)

To take advantage of the arbitrage opportunity with $10000

Amount in Euros = Amount in US Dollars * (1 / (USD / EUR)

Amount in Euros = $10,000 * (1 / $1.3450 / €)

Amount in Euros = €7,434.94

We then convert this amount to British pounds

Amount in British pounds = Amount in Euros * (1 / (EUR / GBP)

Amount in British pounds = €7434.94 * (1 / €1.4510 / £)

Amount in British pounds = £5,124.01

We then convert this amount to US Dollars

Amount in US Dollars = British pounds * (USD / GBP)

Amount in US Dollars = £5124.01 * $1.9724 / £

Amount in US Dollars = $10,106.60511

Arbitrage profit = Amount in US Dollars - Initial amount in US Dollars

Arbitrage profit = $10,106.60511 - $10,000

Arbitrage profit = $106.60511 or $106.61

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