You Can Trade At The Following Price Spot Rate

You Can Trade At The Following Pricesspot Rate

You can trade at the following prices: Spot rate MXN10/$, 6-month forward rate MXN11/$, 6-month Mexican interest rate 18%, 6-month US interest rate 6%. Is covered interest arbitrage worthwhile? If so, explain the steps and compute the profit based on an initial (time t=0) transaction of $1 million. Calculate your profit in dollars in one period. Currency exchange rates and Eurocurrency interest rates are as follows: Current Singapore dollar (S$) spot rate $0.50/S$, 1-year Singapore dollar (S$) forward rate $0.51/S$, 1-year Singapore dollar (S$) interest rate 4.0%, 1-year US interest rate 6%. In what direction will covered interest arbitrage force the quoted rates to change? Explain the steps and compute the profit based on a $1 million initial position. Suppose P(D) = 100, P(F) = 1, and S = D100/F. Inflation in countries D and F are expected to be P(D) = 10%, and P(F) = 21% over the foreseeable future. What are the expected price levels and expected nominal exchange rate in one period? Looking two years into the future, what are the expected price levels in each country and the expected real exchange rate? One year ago, the spot exchange rate between Japanese yen and Swiss franc was Y160/ SFr. Today, the spot rate is Y155/ SFr. Inflation during the year was p(y) = 2% and p(SFr) = 3% in Japan and Switzerland, respectively. What was the percentage change in the nominal value of the Swiss Franc? One year ago, what nominal exchange rate would you have predicted for today based on the difference in inflation rates? What was the percentage change in the real exchange rate during the year? What was the percentage change in the relative purchasing power of the franc? What was the percentage change in the relative purchasing power of the yen? Purdue Co. (based in the U.S.) exports cable wire to Australian manufacturers. It invoices its product in U.S. dollars, and will not change its price over the next year. There is intense competition between Purdue and the local cable wire producers that are based there. Purdue’s competitors invoice their products in Australian dollars and will not be changing their prices over the next year. The annualized risk-free interest rate is presently 8% in the U.S., versus 3% in Australia. Today the spot rate of the Australian dollar is $.55. Purdue Co. uses this spot rate as a forecast of future exchange rate of the Australian dollar. Purdue expects that revenue from its cable wire exports to Australia will be about $2 million over the next year. If Purdue decides to use the international Fisher effect rather than the spot rate to forecast the exchange rate of the Australian dollar over the next year, will its expected revenue from its exports be higher, lower, or unaffected? Explain.

Paper For Above instruction

You Can Trade At The Following Pricesspot Rate

Analysis of Arbitrage, Exchange Rates, and Inflation Impact

This comprehensive analysis explores various facets of international financial markets, including covered interest arbitrage, exchange rate forecasting, inflation effects on currency values, and international Fisher effects. It integrates theoretical principles with practical calculations to provide a nuanced understanding of how these mechanisms influence currency valuation and international trade profitability.

Covered Interest Arbitrage and Profit Calculation

Covered interest arbitrage examines the profit opportunities arising from discrepancies between spot and forward exchange rates plus interest differentials in two countries. Using the given data: spot rate MXN10/$, forward rate MXN11/$, Mexican interest rate 18%, US interest rate 6%, an investor can capitalize on the rate differentials by borrowing in the country with lower interest, converting to the foreign currency, investing at the foreign interest rate, and covering the position via forward contracts to hedge exchange rate risk. The crucial step is to compare the theoretical forward rate derived from interest rate parity (IRP) with the actual forward rate to identify arbitrage profit.

According to IRP, the forward rate (F) should satisfy:

F = S × (1 + i_domestic) / (1 + i_foreign)

Where S = 10 MXN/USD, i_domestic = 6% (US), and i_foreign = 18% (Mexico), over six months. Substituting:

F = 10 × (1 + 0.06/2) / (1 + 0.18/2) ≈ 10 × 1.03 / 1.09 ≈ 10 × 0.9459 ≈ MXN9.459/USD

The actual forward rate is MXN11/USD, which is higher than the no-arbitrage forward. This suggests that arbitrageurs can capitalize on the discrepancy by borrowing in the US, converting USD to MXN, investing at Mexican interest rates, and selling MXN forward at the favorable rate.

To compute profit:

Initial USD investment: $1,000,000

Convert to MXN at spot: MXN10,000,000

Invest in MXN at 18% for 6 months: MXN10,000,000 × 1.09 ≈ MXN10,900,000

Obtain MXN at maturity and sell forward at MXN11/$: convert back to USD at MXN11/$

USD equivalent: MXN10,900,000 / 11 ≈ $991,818.18

Cost of initial USD borrowed (assuming borrowing in USD at 6%): USD1 million × 1.03 ≈ USD1,030,000

Arbitrage profit: USD1,030,000 - USD991,818.18 ≈ USD38,181.82

This profit indicates that covered interest arbitrage is profitable under current rates, and the activity will exert pressure on rates: the forward rate will decrease toward the IRP level, and the spot rate may adjust accordingly to eliminate arbitrage prospects.

Currency Forecasts and Exchange Rate Expectations

Given parameters for Singapore dollar: spot rate $0.50/S$, 1-year forward rate $0.51/S$, Singapore interest rate 4%, US interest rate 6%, and using open interest parity, investors analyze the implied forward rate relative to interest differentials. The expected change in exchange rate can be approximated via the Interest Rate Parity condition:

F = S × (1 + i_SG) / (1 + i_US) = 0.50 × 1.04 / 1.06 ≈ 0.49/S

This suggests that, based on interest differentials, the Singapore dollar might depreciate against the USD, aligning with the forward rate of $0.51/S, reflecting market expectations.

Inflation expectations influence future price levels and exchange rate projections. For country D with P(D) = 100 and 10% inflation, and country F with P(F) = 1 and 21% inflation, the expected price levels after one period are:

  • In country D: 100 × 1.10 = 110
  • In country F: 1 × 1.21 = 1.21

The expected nominal exchange rate in one period, considering PPP and inflation differentials, is:

S1 = S0 × (P(D) / P(F)) = 100 × (110/1.21) ≈ 100 × 90.91 ≈ 9091

Thus, the exchange rate will adjust proportionally to inflation disparities, affecting trade competitiveness and investment flows.

For the two-year horizon, continuing the inflation trend, expected price levels will be:

  • Country D: 110 × 1.10 ≈ 121
  • Country F: 1.21 × 1.21 ≈ 1.4641

The real exchange rate, which adjusts for relative price levels, is calculated as:

RER = S × (P*(F) / P(D))

The change in RER over the year signifies whether currency undervaluation or overvaluation persists over time, affecting international trade dynamics.

Nominal and Real Exchange Rate Changes

Analyzing the yen versus Swiss franc: initial rate Y160/SFr, current Y155/SFr, with inflation rates p(y) = 2%, p( SFr )=3%, the percentage change in nominal value of franc is:

Percentage change = [(Y today / Y past) - 1] × 100 = [(155 / 160) - 1] × 100 ≈ -3.125%

The nominal exchange rate predicted after one year based on inflation rate difference is:

S_predicted = S0 × (1 + p(y)) / (1 + p(SFr)) = 160 × 1.02 / 1.03 ≈ 160 × 0.9903 ≈ 158.45

Compared with actual Y155/SFr, the currency slightly appreciated more than predicted, indicating potential market deviations.

The percentage change in the real exchange rate considering relative purchasing power is calculated through the relative PPP:

Real Exchange Rate Change ≈ [(Y present / Y past) / (P(y) / P(SFr))] - 1

which encapsulates relative changes in buying power and currency valuation effectively.

Impact of International Fisher Effect on Purdue Co. Revenue

Purdue Co., exporting at a fixed USD price, faces currency risk from Australian dollar fluctuations. With interest rates: 8% in US, 3% in Australia, and current spot AUD/USD = 0.55, the forecasted future exchange rate via the IF effect is:

F = S0 × (1 + i_US) / (1 + i_AU) = 0.55 × 1.08 / 1.03 ≈ 0.55 × 1.0485 ≈ 0.5767

Compared to the current spot, this forecast suggests AUD will appreciate, reducing revenue in USD terms if Purdue uses this rate.

If Purdue uses the IFR forecast, its USD revenue, fixed at $2 million forecasted over the next year, will be impacted by the exchange rate change. The anticipated revenue in AUD would be:

Revenue in AUD = $2 million / 0.55 ≈ AUD3.636 million

Forecasted value in USD based on the IFR rate: AUD3.636 million × 0.5767 ≈ $2.096 million

Compared to initial USD revenue, the expected USD revenue would slightly increase, meaning the IFR forecast predicts a higher USD revenue, aiding Purdue’s profit margins, though the actual effect depends on market adjustments to exchange rates.

Conclusion

The interconnectedness of interest rates, inflation, and exchange rates creates opportunities and risks in international finance. Arbitrage mechanisms tend to align actual rates toward parity conditions. Understanding these dynamics helps firms and investors hedge effectively, optimize profits, and anticipate market movements. The application of theoretical models like IRP, PPP, and the Fisher effect offers valuable forecasts but must be complemented with real-time market intelligence for optimal decision-making.

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