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# International arbitrage and interest rate parity

session 7

by

Tweet## Pratik Singhi

on 13 January 2016#### Transcript of International arbitrage and interest rate parity

International Arbitrage and Interest Rate Parity Arbitrage is the act of capitalizing on a discrepancy in quoted prices by making a risk-less profit

Theoretically, it causes prices to realign Process of buying a currency at the location where it is priced cheap and immediately selling it at another location where it is priced higher

If the demand and supply conditions for a particular currency vary among banks, the banks may price that currency at different rates, and market forces will force realignment

with tech advancements, such opportunities are disappearing Locational Arbitrage Locational Arbitrage Cross exchange rates represent the relationship b/w two currencies different from home currency

Triangular arbitrage when currency transactions are conducted to capitalize on a discrepancy in the cross exchange rate between two currencies

If any two of these three exchange rates are known, the exchange rate of the third pair can be determined by cross calculation Triangular Arbitrage Triangular Arbitrage Interest arbitrage – process of capitalizing on difference between interest rates between two countries

Covered – Hedging your position against exchange rate risk with a forward contract Covered Interest Arbitrage Comparing arbitrage

strategies The forward rate differs from the spot rate by a sufficient amount to offset the interest rate differential between two currencies Interest Rate Parity

Where

Ah = Amount of home currency

S = Spot rate

if = Interest rate on foreign deposit

F = Forward rate

An = Amount of home currency received at the end of the deposit period Interest Rate Parity Rate of return

Forward Premium

Relationship between forward premium and interest rate differential Interest Rate Parity Interest Rate Parity If you have $10,000, how many dollars will you end up with if you implement this triangular arbitrage strategy Example

You have $800,000 to invest

Current GBP spot rate is $1.60

90-day forward rate of GBP is $1.60

90-day interest rate in US is 2%

90-day interest rate in UK is 4% You have $1,000,000 to invest

The current spot rate of the pound is $1.60

The 90-day forward rate of the pound is $1.60

The 90-day interest rate in the United States is 2%

The 90-day interest rate in the United Kingdom is 4%

What strategy would you follow? How much would you gain? Assume that as a result of covered interest arbitrage, the market forces caused the following

Spot rate of the pound to rise to $1.62 and

the 90-day forward rate of the pound declined to $1.5888

Consider the results from using $1,000,000 to engage in covered interest arbitrage Assume the following information:

Spot rate of £ /$1.60

180-day forward rate of £ /$1.56

180-day British interest rate 4%

180-day U.S. interest rate 3%

Based on this information, is covered interest arbitrage by U.S. investors feasible (assuming that U.S. investors use their own funds)? Explain.

Does interest rate parity exist? Explain.

Assume that the British pound’s one-year forward rate exhibits a discount. Assume that interest rate parity continually exists. In such a case, explain how the discount on the British pound’s one-year forward discount would change if British one-year interest rates rose by 3 percentage points while U.S. one-year interest rates rose by 2 percentage points The one-year interest rate in Singapore is 11 percent. The one-year interest rate in the United States is 6 percent. The spot rate of the Singapore dollar (S$) is $.50 and the forward rate of the S$ is $.46. Assume zero transaction costs.a. Does interest rate parity exist? b. Can a U.S. firm benefit from investing funds in Singapore using covered interest arbitrage? Interest Rate Parity Triangular Arbitrage You go to a bank and are given these quotes:

You can buy 1 euro for 14 pesos or sell them for 13

You can buy 1 USD for 0.9 euros, or sell it for 0.8

You can buy 1 USD for 10 pesos, or sell it for 9

You have $1,000. Can you use triangular arbitrage to generate a profit? If so, explain the order of transactions that you would execute and the profit that you would earn Triangular arbitrage As an employee of the foreign exchange department for a large company, you have been given the following information at the beginning of the year:

Spot rate of £ $1.596

Spot rate of Australian dollar (A$) $.70

Cross exchange rate: £1 A$2.28

One-year forward rate of A$ $.71

One-year forward rate of £ $1.58004

One-year U.S. interest rate 8.00%

One-year British interest rate 9.09%

One-year Australian interest rate 7.00%

Is triangular arbitrage feasible? If yes, how it should be conducted to make a profit Assume that the Mexican peso exhibits a 6-month interest rate of 6%, while the USD exhibits a 6-month interest rate of 5%. The peso’s spot rate is $0.10. Determine a U.S. investor’s return from using covered interest arbitrage.

Full transcriptTheoretically, it causes prices to realign Process of buying a currency at the location where it is priced cheap and immediately selling it at another location where it is priced higher

If the demand and supply conditions for a particular currency vary among banks, the banks may price that currency at different rates, and market forces will force realignment

with tech advancements, such opportunities are disappearing Locational Arbitrage Locational Arbitrage Cross exchange rates represent the relationship b/w two currencies different from home currency

Triangular arbitrage when currency transactions are conducted to capitalize on a discrepancy in the cross exchange rate between two currencies

If any two of these three exchange rates are known, the exchange rate of the third pair can be determined by cross calculation Triangular Arbitrage Triangular Arbitrage Interest arbitrage – process of capitalizing on difference between interest rates between two countries

Covered – Hedging your position against exchange rate risk with a forward contract Covered Interest Arbitrage Comparing arbitrage

strategies The forward rate differs from the spot rate by a sufficient amount to offset the interest rate differential between two currencies Interest Rate Parity

Where

Ah = Amount of home currency

S = Spot rate

if = Interest rate on foreign deposit

F = Forward rate

An = Amount of home currency received at the end of the deposit period Interest Rate Parity Rate of return

Forward Premium

Relationship between forward premium and interest rate differential Interest Rate Parity Interest Rate Parity If you have $10,000, how many dollars will you end up with if you implement this triangular arbitrage strategy Example

You have $800,000 to invest

Current GBP spot rate is $1.60

90-day forward rate of GBP is $1.60

90-day interest rate in US is 2%

90-day interest rate in UK is 4% You have $1,000,000 to invest

The current spot rate of the pound is $1.60

The 90-day forward rate of the pound is $1.60

The 90-day interest rate in the United States is 2%

The 90-day interest rate in the United Kingdom is 4%

What strategy would you follow? How much would you gain? Assume that as a result of covered interest arbitrage, the market forces caused the following

Spot rate of the pound to rise to $1.62 and

the 90-day forward rate of the pound declined to $1.5888

Consider the results from using $1,000,000 to engage in covered interest arbitrage Assume the following information:

Spot rate of £ /$1.60

180-day forward rate of £ /$1.56

180-day British interest rate 4%

180-day U.S. interest rate 3%

Based on this information, is covered interest arbitrage by U.S. investors feasible (assuming that U.S. investors use their own funds)? Explain.

Does interest rate parity exist? Explain.

Assume that the British pound’s one-year forward rate exhibits a discount. Assume that interest rate parity continually exists. In such a case, explain how the discount on the British pound’s one-year forward discount would change if British one-year interest rates rose by 3 percentage points while U.S. one-year interest rates rose by 2 percentage points The one-year interest rate in Singapore is 11 percent. The one-year interest rate in the United States is 6 percent. The spot rate of the Singapore dollar (S$) is $.50 and the forward rate of the S$ is $.46. Assume zero transaction costs.a. Does interest rate parity exist? b. Can a U.S. firm benefit from investing funds in Singapore using covered interest arbitrage? Interest Rate Parity Triangular Arbitrage You go to a bank and are given these quotes:

You can buy 1 euro for 14 pesos or sell them for 13

You can buy 1 USD for 0.9 euros, or sell it for 0.8

You can buy 1 USD for 10 pesos, or sell it for 9

You have $1,000. Can you use triangular arbitrage to generate a profit? If so, explain the order of transactions that you would execute and the profit that you would earn Triangular arbitrage As an employee of the foreign exchange department for a large company, you have been given the following information at the beginning of the year:

Spot rate of £ $1.596

Spot rate of Australian dollar (A$) $.70

Cross exchange rate: £1 A$2.28

One-year forward rate of A$ $.71

One-year forward rate of £ $1.58004

One-year U.S. interest rate 8.00%

One-year British interest rate 9.09%

One-year Australian interest rate 7.00%

Is triangular arbitrage feasible? If yes, how it should be conducted to make a profit Assume that the Mexican peso exhibits a 6-month interest rate of 6%, while the USD exhibits a 6-month interest rate of 5%. The peso’s spot rate is $0.10. Determine a U.S. investor’s return from using covered interest arbitrage.