Exercise Set 5.1
ARBITRAGE

I. Objectives

1. To understand how arbitrage profits can be made
2. To compute cross exchange rates
3. To see how triangular arbitrage works

II. Data

a. Arbitrage with 2 currencies

Consider the dollar/pound exchange rate (E_$/pound).

• Given: The spot rate in New York is: E_NY = $1.60/pound
• Select a different value for the spot rate in London, E_London.
• You have $100,000 to play with. Carry out an arbitrage transaction that delivers profits.
  [Assume there are zero transaction costs.]

Consider the pairwise exchange rates among three currencies - the dollar, euro and yen.

• The exchange rate between the $ and euro is: E_$/euro = $1.05/euro
• The exchange rate between the yen and the euro is: E_yen/euro = 120 yen/euro

• Select a value for the exchange rate between the yen and the dollar.

• You have $100,000 to play with. Carry out an arbitrage transaction that delivers profits. [Assume zero transaction costs.]

III. Questions

a. Arbitrage with 2 currencies

1. Choose a value for the London spot rate (in $/pound) that is higher than the New York rate. Then, in order to make arbitrage profits, what should you do?

   Step 1: Sell $100,000 and buy ____________ pounds in [ New York / London ].

   Step 2: Sell ______________ pounds and buy _____________ dollars in [ New York / London ].

   Step 3: You make an arbitrage profit of $ _____________.

   • As more currency traders begin to carry out Step 1, the pound will [ depreciate / appreciate ] in [ New York / London ]. Explain.

   • As more currency traders begin to carry out Step 2, the pound will [ depreciate / appreciate ] in [ New York / London ]. Explain.

2. Choose a value for the London spot rate (in $/pound) that is lower than the New York rate. Then, in order to make arbitrage profits, what should you do?

   Step 1: Sell $100,000 and buy ____________ pounds in [ New York / London ].

   Step 2: Sell ______________ pounds and buy _____________ dollars in [ New York / London ].

   Step 3: You make an arbitrage profit of $ _____________.

   • As more currency traders begin to carry out Step 1, the pound will [ depreciate / appreciate ] in [ New York / London ]. Explain.

   • As more currency traders begin to carry out Step 2, the pound will [ depreciate / appreciate ] in [ New York / London ]. Explain.

1. The cross rate between the yen and the dollar (E_yen/$) is ___________ yen/$. Show your calculations.

2. Select a value for the yen/dollar exchange rate that is higher than the cross rate. Discuss the series of transactions that will result in arbitrage profits. The maximum possible profit is $ __________. Explain.

3. Select a value for the yen/dollar exchange rate that is lower than the cross rate. Discuss the series of transactions that will result in arbitrage profits. The maximum possible profit is $ __________. Explain.