Alabama Bank Is Willing To Buy Or Sell

Do The Following Problemsalabama Bank Is Willing To Buy Or Sell Britis

Do the following problems Alabama Bank is willing to buy or sell British pounds for $1.98. The bank is willing to buy or sell Mexican pesos at an exchange rate of 10 pesos per dollar. The bank is willing to purchase British pounds at an exchange rate of 1 peso = .05 British pounds. Show how you can make a profit from triangular arbitrage and what your profit would be if you had $100,000. You go to a bank and are given these quotes: You can buy a euro for 14 pesos. The bank will pay you 13 pesos for a euro. You can buy a U.S. dollar for .9 euros. The bank will pay you .8 Euros for a U.S. dollar. You can buy a U.S. dollar for 10 pesos. The bank will pay you 9 pesos for a U.S. dollar. You have $1,000. Can you use triangular arbitrage to generate a profit? If so, explain the order of the transactions that you would execute, and the profit that you would earn. If you cannot earn a profit from triangular arbitrage, explain why. Interest rate parity exists between the U.S. and Poland (its currency is the zloty). The one-year risk-free CD (deposit) rate in the U.S. is 7%. The one-year risk-free CD rate in Poland is 5% and denominated in zloty. Assume that there is zero probability of any financial or political problem in either country such as a bank default or government restrictions on bank deposits or currencies. Myron is from Poland and plans to invest in the U.S. What is Myron’s return if he invests in the U.S. and covers the risk of his investment with a forward contract? Assume the following information: Quoted Price Spot rate of Canadian dollar $.80 90‑day forward rate of Canadian dollar $.79 90‑day Canadian interest rate 4% 90â‘day U.S. interest rate 2.5% What would be the yield to a U.S. investor who used covered interest arbitrage? What market forces would occur to eliminate any further possibilities of covered interest arbitrage? The current spot exchange rate is Y190/$ and the 1-year forward rate is Y210/$. The prime rate in the US is 15 percent. What should the Japanese prime rate be? According to the forward parity, by how much should the dollar change in value during the next year?

Paper For Above instruction

The set of financial problems presented explores various aspects of currency markets, including triangular arbitrage, interest rate parity, forward contracts, and exchange rate predictions. This comprehensive analysis demonstrates how investors and banks can exploit discrepancies across currencies to generate profits or understand market expectations. In this paper, I will systematically address each problem, providing detailed explanations, calculations, and insights into the underlying market mechanisms.

Triangular Arbitrage with Currency Quotes and Profits Calculation

The initial scenario involves an American bank willing to buy or sell British pounds at an exchange rate of $1.98 per pound, Mexican pesos at 10 pesos per dollar, and British pounds at 1 peso = 0.05 pounds. To assess whether arbitrage opportunities exist, we must examine the cross-exchange rates and identify potential profit avenues.

Starting with the given rates:

- British pound to USD: 1.98 USD per pound.

- Mexican Peso to USD: 10 pesos per dollar.

- Peso to British pound: 1 peso = 0.05 pounds.

The implied cross-rate between the Mexican peso and the British pound can be derived by combining the given rates:

- Convert pesos to pounds via the peso-pound rate: 1 peso = 0.05 pounds.

- Convert pesos to dollars via the peso-dollar rate: 10 pesos = 1 dollar; therefore, 1 peso = 0.1 dollars.

- Convert dollars to pounds: Using the pound-dollar rate, which can be derived as $1.98 = 1 pound, so 1 dollar = 0.50505 pounds.

Now, check the cross-rate:

- From pesos to pounds directly: 1 peso = 0.05 pounds.

- From pesos to dollars: 1 peso = 0.1 dollars.

- From dollars to pounds: 0.1 dollars = 0.1 * (1/1.98) pounds ≈ 0.0505 pounds.

Since the direct rate (0.05 pounds per peso) versus the implied rate (about 0.0505 pounds per peso) is slightly different, arbitrage is possible.

To profit, an arbitrageur might do the following:

1. Convert USD to pesos at the bank’s USD/ pesos rate.

2. Convert pesos into pounds.

3. Convert pounds to USD at the given rate.

Calculating with an initial capital of $100,000:

- Convert USD to pesos: $100,000 * 10 pesos/USD = 1,000,000 pesos.

- Convert pesos to pounds: 1,000,000 pesos * 0.05 pounds/peso = 50,000 pounds.

- Convert pounds back to USD: 50,000 pounds * $1.98/pound = $99,000.

This indicates a potential loss, but if rates are slightly more favorable or if the rates fluctuate, profit could be achieved. Since the immediate calculation suggests no arbitrage profit unless rates differ, the investor would look for discrepancies in real-time rates.

Triangular Arbitrage with Currency Quotes in the Euro-USD-Peso Market

Given the quotes:

- Buy a euro for 14 pesos.

- Bank pays 13 pesos for a euro.

- Buy USD for 0.9 euros.

- Bank pays 0.8 euros for USD.

- Buy USD for 10 pesos.

- Bank pays 9 pesos for USD.

Starting with $1,000:

- Convert USD to euros at the buy rate: $1,000 / 0.9 euros/USD ≈ 1,111.11 euros.

- Convert euros to pesos: 1,111.11 euros * 14 pesos/euro ≈ 15,555.56 pesos.

- Convert pesos back to USD: 15,555.56 pesos / 10 pesos/USD ≈ $1,555.56.

This suggests a potential profit of approximately $555.56.

However, considering the bank’s selling rates (more unfavorable), the arbitrage opportunity may not exist if transaction costs and bid-ask spreads are considered. Exact profit calculations depend on the rates used for each transaction, but in principle, if the market offers such discrepancies, traders can execute arbitrage sequences for profit.

Interest Rate Parity (IRP) and Myron’s Return Calculation

Interest rate parity suggests that the difference in interest rates between two countries should be offset by the forward exchange rate premium or discount. Given the U.S. rate at 7% and Poland at 5%, the forward rate should reflect this differential.

Myron, from Poland, investing in the U.S., can hedge currency risk with a forward contract. Since the U.S. interest rate exceeds Poland’s, the forward rate should depreciate the dollar relative to the zloty to prevent arbitrage profits.

The forward rate should be:

\[ F = S \times \left( \frac{1 + i_{domestic}}{1 + i_{foreign}} \right) \]

Where:

- \( S \) is the spot rate, assumed given in the problem.

- \( i_{domestic} = 7\% \) in the U.S.

- \( i_{foreign} = 5\% \) in Poland.

Myron’s return from investing in the U.S. and hedging via forward contracts will equal the risk-free rate in the U.S., approximately 7%, adjusted for the forward premium or discount, ensuring no arbitrage.

Covered Interest Arbitrage with Canadian Dollars

The rates:

- Spot rate: $0.80 per CAD.

- Forward rate: $0.79 per CAD.

- Canadian interest rate: 4% over 90 days.

- U.S. interest rate: 2.5% over 90 days.

A U.S. investor could lend USD and convert proceeds into CAD, invest at 4%, and offset exchange rate risk via the forward contract.

Calculating the return:

- Invest USD 1,000 at 2.5% over 90 days: \( 1,000 \times (1 + 0.025) = \$1,025 \).

- Convert USD to CAD at spot: \$1,025 / 0.80 = 1,281.25 CAD.

- Invest CAD at 4%: \( 1,281.25 \times (1 + 0.04) = 1,333.50 CAD \).

- Convert back to USD via forward: 1,333.50 CAD * $0.79 = \$1,053.17.

This yields a profit of approximately \$28.17, above the initial \$1,000, indicating arbitrage profit. Market forces would then adjust forward rates and interest rates, eliminating profitable arbitrage opportunities, tending towards parity conditions.

Exchange Rate and Prime Rate Predictions

The current spot rate is Y190/$, and the year-end forward rate is Y210/$. The forward premium:

\[ \frac{(Y210 - Y190)}{Y190} \approx 10.53\% \]

According to the forward parity, the dollar is expected to depreciate by about 10.5% over the year.

The US prime rate is 15%; by parity, the Japanese prime rate should approximate:

\[ \text{Japanese prime rate} = \text{US prime rate} - \text{forward premium} \approx 15\% - 10.5\% = 4.5\% \]

This aligns with Interest Rate Parity, enforcing equilibrium across currency and interest rate markets.

Conclusion

These problems highlight fundamental principles of international finance, including arbitrage, IRP, and forward exchange rate expectations. They illustrate how discrepancies in rates can be exploited temporarily, but market forces typically restore equilibrium, ensuring that profit opportunities are minimal or nonexistent in efficient markets. Understanding these concepts allows investors and financial institutions to assess risks, hedge exposures, and make informed decisions in the global financial landscape.

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