# Assume the following information: Beal Bank Yardley Bank Bid price of New Zealand dollar $.401 $.398 Ask price of New Zealand dollar $.404 $.400 Given this information, is locational arbitrage possible? If so, explain the steps involved in locational arbitrage, and compute the profit from this arbitrage if you had $1,000,000 to use. What market forces would occur to eliminate any further possibilities of locational arbitrage?

**QUESTION**

1. Assume the following information:

Beal Bank Yardley Bank

Bid price of New Zealand dollar $.401 $.398

Ask price of New Zealand dollar $.404 $.400

Given this information, is locational arbitrage possible? If so, explain the steps involved in locational arbitrage, and compute the profit from this arbitrage if you had $1,000,000 to use. What market forces would occur to eliminate any further possibilities of locational arbitrage?

2. Assume the following information:

Quoted Price

Value of Canadian dollar in U.S. dollars $.90

Value of New Zealand dollar in U.S. dollars $.30

Value of Canadian dollar in New Zealand dollars NZ$3.02

Given this information, is triangular arbitrage possible? If so, explain the steps that would reflect triangular arbitrage, and compute the profit from this strategy if you had $1,000,000 to use. What market forces would occur to eliminate any further possibilities of triangular arbitrage?

3. **Covered Interest Arbitrage. **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%

90‑day U.S. interest rate 2.5%

Given this information, what would be the yield (percentage return) to a U.S. investor who used covered interest arbitrage? (Assume the investor invests $1,000,000.) What market forces would occur to eliminate any further possibilities of covered interest arbitrage?

4. Explain the concept of interest rate parity. Provide the rationale for its possible existence.

5. Assume that annual interest rates in the U.S. are 4 percent, while interest rates in France are 6 percent.

a. According to IRP, what should the forward rate premium or discount of the euro be?

b. If the euro’s spot rate is $1.10, what should the one-year forward rate of the euro be?

6. Explain how you could determine whether PPP exists. Describe a limitation in testing whether PPP holds.

7. Explain the international Fisher effect (IFE). What is the rationale for the existence of the IFE? What are the implications of the IFE for firms with excess cash that consistently invest in foreign Treasury bills? Explain why the IFE may not hold.

8. Compare and contrast interest rate parity (discussed in the previous chapter), purchasing power parity (PPP), and the international Fisher effect (IFE).

9. Assume that the spot exchange rate of the British pound is $1.73. How will this spot rate adjust according to PPP if the United Kingdom experiences an inflation rate of 7 percent while the United States experiences an inflation rate of 2 percent?

10. Assume that the spot exchange rate of the Singapore dollar is $.70. The one‑year interest rate is 11 percent in the United States and 7 percent in Singapore. What will the spot rate be in one year according to the IFE? What is the force that causes the spot rate to change according to the IFE?

**ANSWER**

In locational arbitrage, traders take advantage of price discrepancies between different locations in the foreign exchange market. In this case, there is a potential for locational arbitrage because the bid price of the New Zealand dollar is higher at Beal Bank ($.401) compared to Yardley Bank ($.398), while the ask price of the New Zealand dollar is also higher at Beal Bank ($.404) compared to Yardley Bank ($.400).

**To perform locational arbitrage, the following steps can be taken**

Convert the $1,000,000 into New Zealand dollars at Yardley Bank using the ask price of $.400, resulting in NZ$2,500,000.

Transfer the NZ$2,500,000 to Beal Bank.

Convert the NZ$2,500,000 back into U.S. dollars at Beal Bank using the bid price of $.401, resulting in $1,002,500.

The profit from this locational arbitrage would be $2,500 (=$1,002,500 – $1,000,000).

Market forces, such as increased demand for the New Zealand dollar at Yardley Bank and increased supply at Beal Bank, would occur due to the arbitrage activity. These market forces would lead to the equalization of bid and ask prices between the two banks, eliminating further possibilities of locational arbitrage.

Triangular arbitrage involves exploiting exchange rate discrepancies between three currencies. In this case, triangular arbitrage is possible given the provided information.

**To perform triangular arbitrage, the following steps can be taken**

Convert $1,000,000 into Canadian dollars at a rate of $.90, resulting in CAD$1,111,111.

Convert CAD$1,111,111 into New Zealand dollars at a rate of NZ$3.02, resulting in NZ$3,359,873.

Convert NZ$3,359,873 into U.S. dollars at a rate of $.30, resulting in $1,007,962.

The profit from this triangular arbitrage would be $7,962 (=$1,007,962 – $1,000,000).

Market forces, such as increased demand for the Canadian dollar and the New Zealand dollar and increased supply of U.S. dollars, would occur due to the arbitrage activity. These market forces would lead to the adjustment of exchange rates, eliminating further possibilities of triangular arbitrage.

Covered interest arbitrage involves taking advantage of interest rate differentials between two countries while hedging against exchange rate risk using forward contracts. In this case, a U.S. investor can use covered interest arbitrage to profit from the interest rate differential between Canada and the U.S.

**To calculate the yield from covered interest arbitrage, the following steps can be taken**

1. Convert $1,000,000 into Canadian dollars at the spot rate of $.80, resulting in CAD$1,250,000.

2. Invest CAD$1,250,000 in a Canadian investment with a 90-day interest rate of 4%.

3. Enter into a 90-day forward contract to sell CAD$1,250,000 at the forward rate of $.79.

4. At the end of 90 days, the investment will grow to CAD$1,250,000 * (1 + 4%) = CAD$1,300,000.

5. Convert CAD$1,300,000 into U.S. dollars at the forward rate of $.79, resulting in $1,027,273.

The yield from covered interest arbitrage would be $27,273 (=$1,027,273 – $1,000,000), representing a 2.73% return on the investment.

Market forces, such as increased demand for the Canadian dollar and decreased demand for the U.S. dollar, would occur due to the covered interest arbitrage activity. These market forces would lead to the equalization of interest rates and exchange rates, eliminating further possibilities of covered interest arbitrage.

Interest rate parity is a theory that suggests that the difference in interest rates between two countries should be equal to the percentage difference between the spot and forward exchange rates. In other words, it states that the forward exchange rate should be adjusted based on the interest rate differential to prevent arbitrage opportunities.

The rationale for interest rate parity is based on the principle of covered interest arbitrage. If the interest rate differential between two countries is higher than the expected depreciation of the higher interest rate currency, investors can take advantage of the arbitrage opportunity by borrowing in the low-interest rate currency, converting it to the high-interest rate currency, investing it, and using a forward contract to hedge against exchange rate risk. This arbitrage activity will lead to the adjustment of exchange rates and interest rates, aligning with interest rate parity.

According to interest rate parity (IRP), the forward rate premium or discount of the euro would be equal to the interest rate differential between the U.S. and France. In this case, the interest rate in the U.S. is 4% while the interest rate in France is 6%. Therefore, the forward rate premium of the euro would be 2%.

If the euro’s spot rate is $1.10, the one-year forward rate of the euro can be calculated as follows:

Forward rate = Spot rate × (1 + Interest rate differential)

Forward rate = $1.10 × (1 + 2%) = $1.122

Purchasing Power Parity (PPP) is a theory that suggests that the exchange rates between two currencies should adjust to equalize the prices of a basket of goods and services in different countries. To determine whether PPP exists, researchers often compare the price levels of identical goods in different countries using a common currency.

One common method is to use the Big Mac Index, which compares the prices of Big Macs in different countries. If the prices of Big Macs in different countries are significantly different from the exchange rate implied by PPP, it suggests a deviation from PPP.

However, there is a limitation in testing whether PPP holds. PPP assumes that goods are identical across countries and that there are no trade barriers or transportation costs. In reality, various factors such as product differentiation, tariffs, and non-tariff barriers can influence price differences. Additionally, PPP does not account for factors like market imperfections, taxes, and non-tradable goods, which can lead to deviations from the theory.

The International Fisher Effect (IFE) suggests that the nominal interest rate differentials between two countries should reflect the expected inflation differential. The rationale behind the IFE is based on the concept that investors require compensation for the expected loss in purchasing power of a currency due to inflation.

The implications of the IFE for firms with excess cash that consistently invest in foreign Treasury bills are as follows:

– If a firm consistently invests in foreign Treasury bills with higher interest rates, it can earn higher nominal returns.

– However, if the IFE holds, the higher nominal returns should be offset by an equivalent depreciation of the foreign currency due to higher inflation expectations.

The IFE may not hold in practice due to several reasons, including:

– Imperfect expectations: Investors may not accurately predict future inflation rates, leading to deviations from the IFE.

– Capital controls and transaction costs: Barriers to capital mobility and transaction costs can limit the ability of investors to take advantage of interest rate differentials and prevent the IFE from fully materializing.

– Risk premium: Investors may

require a risk premium to compensate for risks associated with foreign investments, which can affect the relationship between interest rate differentials and exchange rate movements.

Interest rate parity (IRP), purchasing power parity (PPP), and the international Fisher effect (IFE) are economic theories that explain different aspects of the relationship between interest rates and exchange rates:

– Interest rate parity (IRP): It states that the difference in interest rates between two countries should be equal to the percentage difference between the spot and forward exchange rates. IRP is based on the principle of covered interest arbitrage, where investors can exploit interest rate differentials and exchange rate movements to generate risk-free profits.

– Purchasing power parity (PPP): It suggests that exchange rates should adjust to equalize the prices of a basket of goods and services in different countries. PPP is based on the idea that in the long run, currencies should have the same purchasing power across countries. PPP is often used to compare price levels and assess currency valuation.

– International Fisher effect (IFE): It proposes that the nominal interest rate differentials between two countries should reflect the expected inflation differential. The IFE is based on the concept that investors require compensation for the expected loss in purchasing power due to inflation. It implies a relationship between interest rates and exchange rate movements.

According to the purchasing power parity (PPP) theory, the spot exchange rate should adjust to reflect the inflation differential between two countries. In this case, the United Kingdom has an inflation rate of 7%, while the United States has an inflation rate of 2%.

To calculate the expected spot rate adjustment, we can use the formula:

Percentage change in exchange rate = Difference in inflation rates

Percentage change in exchange rate = 7% – 2% = 5%

If the spot exchange rate of the British pound is $1.73, it would depreciate by 5% according to PPP:

Spot rate adjustment = $1.73 × 5% = $0.0865

The adjusted spot rate would be $1.73 – $0.0865 = $1.6435.

The International Fisher Effect (IFE) can be used to estimate the spot rate in one year based on the interest rate differential between two countries. According to the IFE, the spot rate will change by the percentage difference in interest rates.

In this case, the interest rate in the United States is 11% and in Singapore is 7%. The interest rate differential is 11% – 7% = 4%.

The spot rate adjustment according to the IFE can be calculated as follows:

Percentage change in exchange rate = Difference in interest rates

Percentage change in exchange rate = 4%

If the spot exchange rate of the Singapore dollar is $0.70, the one-year forward rate according to the IFE would be:

Forward rate = Spot rate × (1 + Percentage change in exchange rate)

Forward rate = $0.70 × (1 + 4%) = $0.728

The force that causes the spot rate to change according to the IFE is the expectation of differential inflation rates between the two countries. Investors demand higher interest rates in a country with higher expected inflation to compensate for the loss of purchasing power, leading to a depreciation of the currency in the foreign exchange market.

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