Final answer:
Yes, there is an arbitrage opportunity. An investor can buy EUR with USD, convert EUR to GBP and convert GBP back to USD, resulting in a profit. The sequence of buys and sales is explained in detail. To profit 100,000 USD, the initial investment amount in EUR and GBP needs to be calculated.
Step-by-step explanation:
Arbitrage opportunity refers to the possibility of taking advantage of price differences in different markets. In this case, we can analyze the given exchange rates to determine if there is an arbitrage opportunity.
To determine if there is an arbitrage opportunity, we can use cross rates to check if they are in line with the given rates. Cross rates involve calculating the implied rate using the given rates and comparing it with the actual rate. If there is a difference, it indicates a possible arbitrage opportunity.
If we consider the given exchange rates,
- EUR/USD = 0.8784
- EUR/GBP = 1.4654
- USD/GBP = 1.6724
We can calculate the implied rate for EUR/USD using the formula (EUR/USD) = (EUR/GBP) * (GBP/USD). If the calculated rate is significantly different from the actual rate, it indicates a potential arbitrage opportunity.
To calculate the implied rate, (EUR/USD) = (1.4654) * (1.6724) = 2.4482. However, the actual rate is 0.8784.
Since the calculated rate is different from the actual rate, there is an arbitrage opportunity. To take advantage of this opportunity, an investor can:
- Buy EUR with USD at the rate of 0.8784.
- Convert EUR to GBP at the rate of 1.4654.
- Convert GBP back to USD at the rate of 1.6724.
The investor will end up with more USD than the initial investment, realizing a profit from the arbitrage opportunity.
To profit 100,000 USD, the investor needs to calculate the required investment amount in EUR and GBP. This can be done by following the same steps as mentioned before and calculating the required initial investment that will yield a profit of 100,000 USD.