# Triangular Arbitrage

1 Triangular Arbitrage

Suppose you are a trader at the foreign exchange desk of Goldman Sachs in London and you observe the following exchange rates of the Euro (EUR) relative to the pound (GBP) and the U.S. Dollar (USD) and the USD relative to GBP:

Quote Currency/Base Currency Rate

EUR/GBP                                                 1.1555

EUR/USD                                                    0.76388

USD/GBP                                                    1.5386

Recall that the base currency is the currency that is being purchased or sold and the quote currency is the price. Thus, if EUR/GBP is equal to 1.1555, then it costs 1.1555 EUR to buy 1 GBP (or I can sell 1 GBP for 1.1555 EUR).

Triangular arbitrage is the act of exploiting an arbitrage opportunity resulting from a pricing discrepancy among three di erent currencies in the foreign exchange market. A triangular arbitrage strategy involves three trades, exchanging the initial currency for a second, the second currency for a third, and the third currency for the initial. During the second trade, the arbitrageur locks in a zero-risk pro t from the discrepancy that exists when the market cross exchange rate is not aligned with the implicit cross exchange rate.

2 Covered Interest Parity

The Euro (EUR) spot exchange rate against the U.S. Dollar (USD) was 1.2834 USD/EUR on March 30, 2010 while the 6-month forward exchange rate was 1.2779 USD/EUR. On the same day, the Wall Street Journal reported the 6-month Eurodollar (USD denominated deposits located in Europe) interest rate as 3.125 % per annum, compounded annually. What was the effective Euro deposit interest rate for 6-months, in percent per annum? Ignore bid/ask spreads. Hint: you will need to convert the compounding frequency from 1-year to 6-months (please look up the compound interest formulas on your own if you forgot).

3 Covered Interest Parity with Bid-Ask Quotes

Below are current quotes on Japanese Yen and U.S. Dollar exchange rates and interest rates. Find and describe the arbitrage opportunity, if any. Recall, the bid and ask prices and rates are from the perspective of the market marker. Bid price is the price the market maker is willing to buy and the ask price is the price the market maker is willing to sell. Similarly, the bid rate is the rate the market maker is willing to borrow and the ask rate is the rate the market maker is willing to lend.

Spot                     113.75               113.95

3-Month            113.60                113.80

3-Month Interest Rate (Compounded Annually) Bid              Ask

JPY                                                                                            1.3125%        1.4375%

USD                                                                                            5.1875%         5.3125%

4 Implied Forward Exchange Rate

Suppose you are a wine maker in Santa Ynez, California (U.S.). You have ordered oak barrels from France for your vineyard. The barrels will arrive in one year, just in time for the Chardonnay from the upcoming 2010 harvest to be transferred from fermentation vats and aged. The barrels cost 122 EUR each, cash on delivery. There is no forward EUR/USD exchange rate beyond six months, but the 1-year EUR deposit rate is 4.75% while the Eurodollar deposit rate is 4.25%. Describe the transaction to lock in a dollar price per barrel and calculate that price (i.e., implied forward exchange rate for EUR/USD). The spot exchange rate is 1.2834 USD/EUR. Hint: Apply the intuition behind the Covered Interest Parity arbitrage proof.