Suppose You Have The Following Spot Exchange Rates

Suppose You Have The Following Spot Exchange Rates

Suppose You Have The Following Spot Exchange Rates

1. Suppose you have the following spot exchange rates: £1 = $1.57, euro 1 = $1.23, and £1 = euro 1.25. i) Please check if the cross rate between the euro and the UK pound (£) is consistent or not. ii) How much profit (in $ terms) could you make from trading $1,000? Describe your trading process to get your profit.

2. You purchased a European foreign exchange option contract to buy 5000 UK pounds at the price of $1.66/£ which expires today. You have paid $250 for the contract. Suppose the spot rate on the expiration date, today, is $1.69/£, what will be your optimal decision for the contract (exercise or not exercise)?

3. The recent market data on the U.S. and UK are shown as: the spot rate of the UK pound $1.55/£, the 90-day forward rate $1.57/£, the 180-day forward rate $1.58/£, your expected future spot rate in 3 months $1.56/£, your expected future spot rate in 6 months $1.59/£, interest rate (TB) in the U.S.: 4% (per year), interest rate (TB) in the UK.: 2% (per year). If you have $1 million available for 3 months, where do you want to invest (assume no transaction costs)?

Paper For Above instruction

The given assignment involves analyzing exchange rates, currency arbitrage opportunities, options trading decisions, and investment strategies based on forward rates and interest rates. This comprehensive financial analysis aims to assess market efficiency, profit opportunities, and optimal investment decisions in the context of foreign exchange markets and international finance.

Introduction

Foreign exchange markets are pivotal in facilitating international trade, investment, and finance. They operate under complex mechanisms governed by principles of parity conditions, arbitrage, and hedging strategies. By examining exchange rates, cross rates, options, and forward rates, financial analysts can identify profitable trades and make informed investment choices. This paper explores these aspects through specific scenarios involving exchange rate consistency, arbitrage profit potential, currency option evaluation, and investment decision-making based on interest and forward rate differentials.

Analysis of Currency Cross Rate Consistency

The first task involves verifying the consistency of the cross rate between the euro and pound (£). Given the rates: £1 = $1.57, euro 1 = $1.23, and £1 = euro 1.25, the cross rate between euro and pounds can be calculated in two ways. Primarily, the cross rate between euro and pound can be derived from the given rates by dividing the dollar rate of the euro by the dollar rate of the pound: (1.23 / 1.57) ≈ 0.783. Alternatively, the direct rate can be obtained from the reciprocal of the pound-to-euro rate, which is 1 / 1.25 ≈ 0.8. Since these two figures (0.783 and 0.8) are not equal, the cross rates are inconsistent, indicating potential arbitrage opportunities or market inefficiencies.

Currency Arbitrage and Profit Calculation

To illustrate potential arbitrage profits, consider trading $1,000. Using the given rates, the process involves converting dollars into euros, then euros into pounds, and finally back into dollars at the spot rate. First, convert $1,000 into euros at the rate of $1.23 per euro, yielding approximately 813.01 euros ($1,000 / 1.23). Next, convert euros into pounds using the rate of £1 = euro 1.25, so the amount in pounds is 813.01 / 1.25 ≈ 650.41 pounds. Finally, convert pounds back into dollars at the rate of £1 = $1.57, resulting in 650.41 * 1.57 ≈ $1,020.46. The profit from this arbitrage is approximately $20.46, providing a relatively riskless profit if these rates held simultaneously.

Options Trading Decision

Regarding the European foreign exchange option to buy 5,000 pounds at $1.66/£, the question is whether to exercise or not when the spot rate at expiration is $1.69/£. Since the spot price exceeds the strike price ($1.69 > $1.66), it is profitable to exercise the option, purchasing pounds at the lower strike price and selling them at the higher market rate, yielding a profit per pound of $0.03. Total profit before considering the premium paid would be 5,000 * ($1.69 - $1.66) = $150. Subtracting the premium ($250), the net outcome is a loss of $100. Therefore, the optimal decision is not to exercise the option, as it would result in a net loss.

Investment Decision Based on Forward Rates and Interest Rates

The final scenario involves deciding where to invest $1 million for three months, considering spot, forward rates, expected future rates, and interest rates in the US and UK. The US interest rate is 4%, and the UK rate is 2%, both annualized. The forward rate for 90 days ($1.57/£) is compared against the expected future spot rate ($1.56/£). If investing in the US, the future value after three months, considering US interest, is $1,000,000 (1 + 0.04/4) = $1,010,000. When converting in the future at the forward rate, the amount of pounds obtained would be $1,010,000 / 1.57 ≈ 643,312 pounds. Conversely, investing in the UK, with a 2% interest rate on pounds, would result in 1,000,000 pounds (1 + 0.02/4) ≈ 1,005,000 pounds. Converting this back to dollars at the forward rate implies 1,005,000 * 1.57 ≈ $1,577,850, which is significantly higher than the US-based investment. Therefore, considering interest rates, forward rates, and the expected spot rate, investing in the UK appears more advantageous in this scenario.

Conclusion

Analyzing differences in exchange rates and their implications reveals opportunities for arbitrage, optimal hedging strategies via options, and strategic investment decisions in international markets. The inconsistencies in cross rates highlight market inefficiencies, while profit calculations demonstrate potential arbitrage gains. The choice to exercise options depends on spot prices relative to strike prices, considering premiums paid. Lastly, interest rate differentials and forward exchange rates influence where investors should allocate their funds to maximize returns, with current data favoring UK investments based on the provided information. These principles are fundamental in international finance, providing insights into market dynamics and strategic planning for investors and traders.

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