International Arbitrage and Interest Rate Parity

10 October 2016

There are three forms of international arbitrage: location arbitrage, triangular arbitrage and covered interest arbitrage. Location arbitrage is a process where a participant of the foreign exchange can go to one place, bank in a specified location, to purchase a currency at a lower price and then sell it to another location where the currency is priced higher. The prices of currencies are roughly the same; however, at times currency in one place can sell for more or less than in another place based on the supply and demand for the specified currency.

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This is the window of opportunity where arbitragers can immediately purchase the currency in one place and sell it to another before market forces naturally realign the prices. The act of location arbitrage is a way to readjust prices so that they are once again equal in all places. However, due to the advancement in technology within the exchange market, it is very difficult to use this process since computers are able to detect currency discrepancies.

Triangular arbitrage is used by the discrepancy of prices within cross exchange rates which is the relationship between two currencies that are different from one’s base currency. If the cross exchange rate is less than the actual cross exchange rate of two currencies of the base currency, triangular arbitrage can be used in the spot market to capitalize on the difference. The greater the bid/ask spread the higher the profit from using triangular arbitrage.

The impact of triangular is as follows: (1) When a participant uses their base currency to buy one currency, the bank, of which the currency is bought, increases its ask price of the currency with respect to the base currency, (2) the participant then goes to purchase the other currency with the bought currency which causes the bank, of which the currency is bought, to reduce its bid price of the initial currency bought with respect to the second currency bought and ultimately reduces the number of the second currency to be exchanged for the initial currency, and (3) finally, the participant uses the second currency bought to ult to conduct ecause it is rare to identify arbitrage opportunities due to the technological advancements in the foreign exchange market. Covered interest arbitrage is the process of capitalizing of the difference of interest rates between two countries while hedging the exchange rate risk with a forward contract. How this works is that one will invest a specified amount of money in a different country bank by converting one’s base currency to the other currency. At that same time, one can sell a forward of the amount of the exchanged currency plus the interest of the foreign bank.

Once the deposit matures, one can fulfill the forward contract obligation by converting the amount of the forward into the base currency. This process will reveal a profit only if the foreign bank has a higher interest rate than one’s home bank or else, this would all be a waste of time and effort. What is different about this process as oppose to location arbitrage and triangular arbitrage is that this process requires funds to be held for the length of the contract. The other two forms of arbitrage do not require funds to be held and profits are immediately achieved.

Covered interest arbitrage will, as the other forms do, cause the market to naturally realign itself. Investors capitalizing on this process will cause a downward pressure on forwards that are sold as a means of this form of arbitrage. The realignment of the forward rate might not be completed until several transactions have occurred. However, the realignment does not cause investors who have gained from arbitrage to loss their gains since they had obtained a forward contract on the day they made their investment.

The act to sell the other currency forward would place a downward pressure on the currency but not enough to lessen or completely offset the benefits of the interest rate advantage. In the process of covered interest arbitrage only the forward rate is affected. It is possible for the spot rate to appreciate but the forward rate would not have to decline by as much. Overall, since the forward market is less liquid, the forward rate is more sensitive to market changes and there is likely to experience most or all of the adjustments need to realign the market.

Once there are no opportunities of arbitrage because the prices of currencies have adjusted to where they should be based on the market, there is an equilibrium state referred to as interest rate parity (IRP). In equilibrium, the forward rate differs from the spot rate by a large amount to offset the interest rate difference between the two countries. The relationship between a forward premium for a foreign currency and the interest rates representing these currencies according to IRP can be determined by the following variables:

Ah : The amount of the home currency that is initially invested S : The spot rate in the home currency when the foreign currency is purchased if : The interest rate on the foreign deposit F : The forward rate in the home currency at which the foreign currency will be converted back the home currency. The amount of home currency received at the end of the deposit period due to this strategy (An ) is An = (Ah / S)(1+ if) F This is how the rate of return (R) is calculated from this investment:

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