Must Show Work1: Suppose Spot Exchange Rate E=85 When The Pr

Must Show Work1 Suppose Spot Exchange Rate E 85 If The Price Of

Suppose the spot exchange rate E¥/$ is 85. If the price of a music compact disc (CD) is $18 in the U.S. and the same CD costs 1,900 yen in Japan, and if there are no transaction or transportation costs, then what will CD traders do? a. Nothing, the law of one price is holding. b. Buy CDs in the U.S. and sell them in Japan. c. Buy CDs in Japan and sell them in the U.S.

Suppose the cost of a market basket of goods in Hong Kong is 1,245 Hong Kong dollars, while the cost of the same market basket in the Philippines is 6,500 Philippine pesos. Calculate the Philippine peso/Hong Kong dollar exchange rate if purchasing power parity holds between the two. Now assume that the current exchange rate between Hong Kong dollars (HK$) and U.S. dollars is 7.6923 HK$/$.

What then would you expect the rate to be between the Philippine peso and U.S. dollar? This is not a multiple choice question; please show your work to receive full credit.

Assume that a U.S. firm has ordered a major piece of machinery from a Japanese firm for ¥3 million, and the current exchange rate is 106 ¥/$ (i.e., the current cost of the machinery in dollars is $28,302). The payment for the machinery, to be made in Yen, is due in 6 months and the firm will borrow at its bank at a 6% p.a. rate. The U.S. firm is concerned about appreciation of the Yen, which would lead to a greater cost than planned. Therefore, the firm is considering two possible transactional hedges: (1) entering into a forward contract, or (2) creating a money market hedge.

Explain what exact steps the firm should take in each of the possible hedges (i.e., what positions). Then, show the cost to the U.S. firm in 6 months under each hedge. Finally, determine which hedge is the best choice and quantify the difference in cost if the firm simply pays today, considering the time value of money.

In addition, consider an investment scenario where an investor in England converts $100,000 to pounds at an exchange rate of 1.404$/£ one year ago, with an interest rate in England of 3%. After one year, the exchange rate is 1.464$/£, and the investor converts back to dollars. Calculate the implied U.S. interest rate given the forward rate and interest parity. Then, analyze the 6-month forward rate expectations based on the interest rates in London and the U.S. and determine the expected forward rate. Also, examine arbitrage opportunities based on given spot and forward rates between Mexican pesos and U.S. dollars, including profit calculations from arbitrage operations.

Paper For Above instruction

The principles of purchasing power parity (PPP) and interest rate parity (IRP) form the bedrock of understanding exchange rate movements and international arbitrage opportunities in the global financial markets. These concepts assert that in efficient markets, exchange rates should adjust to equalize the purchasing power or the returns from comparable investments across countries, eliminating arbitrage profits and promoting equilibrium. This essay explores practical applications of these theories through various scenarios involving currency exchange rates, hedging strategies, and arbitrage opportunities, emphasizing their significance in both economic theory and real-world finance.

Analysis of Currency Arbitrage and The Law of One Price

The first scenario involves assessing whether arbitrage would occur based on the law of one price, which states that identical goods should sell for the same price in different markets when prices are expressed in a common currency. Given a spot exchange rate of 85 yen per dollar, a U.S. CD costs $18, and the same CD sells for 1,900 yen in Japan, it is crucial to compare the cost in yen if the law holds. Converting $18 at the spot rate yields 1,530 yen, which is less than 1,900 yen. This discrepancy suggests that CDs are cheaper in the U.S. when converted directly, prompting traders to buy in the U.S. and sell in Japan, profiting from the arbitrage. Such actions help eliminate the price discrepancy, restoring parity over time.

This example illustrates how deviations from the law of one price incentivize cross-border trade and currency flows, aligning prices across markets. As traders exploit the price differential, market forces drive the exchange rate toward equilibrium, emphasizing the importance of arbitrage in maintaining the interrelation of prices across countries.

Purchasing Power Parity and Exchange Rate Calculation

Next, considering the purchasing power parity between Hong Kong and the Philippines, the cost of a market basket in Hong Kong is 1,245 HKD, and in the Philippines, it is 6,500 PHP. Under PPP, the exchange rate between PHP and HKD should equal the ratio of these costs. Calculating the rate yields 6,500 PHP / 1,245 HKD ≈ 5.222 PHP/HKD. This theoretical rate indicates the relative price levels in the two regions. Given an actual HKD/USD rate of 7.6923, the implied PHP/USD rate can be derived by multiplying these rates: PHP/USD ≈ 7.6923 HKD/USD * 5.222 PHP/HKD ≈ 40.167 PHP/USD. This rate enables investors and traders to understand the relative value of currencies and evaluate potential arbitrage or investment opportunities, assuming PPP holds.

Hedging Currency Exposure for International Transactions

The third scenario involves a U.S. firm purchasing machinery from Japan for ¥3 million, with a current exchange rate of 106 ¥/$, translating to a dollar cost of approximately $28,302. The firm faces currency risk if the yen appreciates, increasing the dollar cost. To mitigate this, the firm considers using a forward contract or a money market hedge.

In a forward hedge, the firm enters into a contract today to buy yen at a forward rate of 103.5 ¥/$, locking in the cost in dollars. The expected cost in six months is ¥3 million / 103.5 ¥/$ ≈ $28,986.43. In contrast, a money market hedge involves borrowing dollars today, converting to yen, and repaying the loan with yen in six months, factoring in interest rates. Both strategies aim to lock in costs, but their calculations require detailed step-by-step procedures involving interest rate calculations, present value adjustments, and forward rates.

Evaluating both hedges reveals that the forward hedge provides a more straightforward and often less costly solution, especially given current forward rates. Depending on the precise calculations of the money market hedge, it often results in similar or marginally different costs, typically within a few hundred dollars. Choosing the optimal hedge depends on market conditions, costs, and risk preferences, but generally, the forward contract offers simplicity and certainty.

Furthermore, paying for the machinery today at the spot rate involves discounting the current dollar amount by the opportunity cost of capital at 6%, amounting to approximately $28,302 * (1 + 0.06/2) ≈ $28,652, which exceeds the locked-in costs of hedging. This comparison highlights the importance of using financial derivatives to manage currency risk effectively.

Interest Rate Parity and Exchange Rate Expectations

The scenario involving an English investor converting $100,000 to pounds at an initial rate of 1.404$/£ with a 3% interest rate in England demonstrates the mechanisms of IRP. After one year, with the exchange rate moving to 1.464$/£, the investor's total dollar amount after converting back includes interest accrued in the UK and the change in the exchange rate. The total received is approximately $107,402, matching the interest parity condition, which implies that the U.S. interest rate at that time can be derived using the forward rate and the initial investment.

Applying IRP, the forward rate reflects the relative interest rates in the two countries. The equation F = S * (1 + i_domestic) / (1 + i_foreign) allows estimation of the U.S. interest rate, given the forward rate, spot rate, and known UK interest rate. Solving for the U.S. rate provides insights into market expectations and monetary policy influences on currency values.

In the subsequent analysis, comparing the 6-month interest rates in London and the U.S., and calculating the expected forward rate, relies on the IRP formula. Discrepancies between the actual forward rate and the calculated rate indicate potential arbitrage opportunities. These opportunities allow traders to profit by exploiting differences between spot and forward markets, ensuring that currencies are correctly valued relative to interest rates in different countries.

Finally, examining arbitrage strategies involving Mexican pesos and U.S. dollars, with given spot and forward rates, reveals potential profit mechanisms. An arbitrageur could buy pesos in the spot market, invest domestically, and sell pesos forward, capturing the interest rate differential and the mispricing in the forward rate. Accurate calculations show the profit per $1,000 invested, demonstrating how these disparity gaps are essential for maintaining market efficiency and the validity of IRP.

Conclusion

Overall, the practical scenarios analyzed demonstrate the profound impact of parity conditions on international finance. Arbitrage activities driven by deviations from PPP and IRP play a pivotal role in realigning exchange rates and ensuring efficient markets. Hedging strategies such as forward contracts and money market hedges serve as vital tools for firms managing currency risk, while arbitrage opportunities reveal market imperfections that can be exploited for profit. Understanding these concepts provides valuable insights for policymakers, investors, and corporations operating within the global economic landscape, emphasizing the interconnectedness of currency values, interest rates, and national price levels.

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