In: Finance
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 $10000, what will be your profit after taking an arbitrage opportunity (if it exists)?
1)
USD / GBP = USD 1.4655 / GBP
USD / JPY = USD 0.010854 / JPY
USD / EUR = USD 1.2238 / EUR
UK pound per Japan yen = GBP / JPY
UK pound per Japan yen = (USD / JPY) / (USD / GBP)
UK pound per Japan yen = 0.010854 / USD 1.4655
UK pound per Japan yen = GBP 0.0074063 /GBP
Japan yen per Euro area euro = JPY / EUR
Japan yen per Euro area euro = (USD / EUR) / (USD / JPY)
Japan yen per Euro area euro = 1.2238 / 0.010854
Japan yen per Euro area euro = JPY 112.75106 / EUR
2)
:£/$ = 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