Question

Space Arbitrage:

A Paris bank offers to both buy and sell pounds for 1.5581 euros per pound.
A London bank is willing to both buy and sell euros for 0.6323 pounds
per euro. Assume you are a large money center bank who can trade currency
with both the London and Paris banks. Suppose you have 100,000 pounds.
Determine a way to make a profit from this situation by converting the
pounds to euros and then back again.

1. When you convert the pounds to euros, how many euros will you receive?

2. When you convert the euros back to pounds, how many pounds will you
receive?

3. What will be the profit you make in pounds?

Triangular Arbitrage:

A Tokyo bank offers to sell euros at 123.10 yen per euro and buy
123.10 yen per euro. A Berlin bank offers to sell pounds at
1.5939 euros per pound and buy pounds at 1.5939 euros per pound.
A London bank offers to sell pounds at 192.95 yen per pound
and buy pounds at 192.95 yen per pound. Starting with 160,000 euros,
determine some way to make a profit.

4. What will be your profit in euros?

5. Along the way in the above transactions, you had to momentarily hold
pounds. How many pounds did you hold?

6. Along the way in the above transactions, you had to momentarily hold
yen. How many yen did you hold?

Answer 1

Given:

Quote from Paris Bank:

1 pound = euro 1.5581. So 1 euro = 1/1.5581 pounds = 0.6418 pounds

1 euro = pounds 0.6418

Quote from London Bank:

1 euro = pound 0.6323.

i.e; 1 pound = 1/0.6323 euro = euro 1.5815

Have pounds 100,000

1. Convert 100,000 pounds to euro.

Quote of pound from London Bank is more than that of Paris bank for pound. So sell pounds to London bank. For each pound, we receive 1.5815 euros.

For 100,000 pounds we get = 100,000 * 1.5815 = 158,150 euros (answer)

2. Converting euros to pound

• Paris bank quotes 1 euro = 1/1.5581 = pounds 0.6418
• London bank quotes 1 euro = pound 0.6323

Paris bank gives more pounds for each euro. So Sell euros at rate 1 euro = pound 0.6418

Total pounds received = 158,150 * 0.6418 = 101,501.83 pounds (answer)

3. Total profit in pounds = 101,501.83 - 100,000 = 1,501.83 pounds

Triangular arbitrage:

Given rates:

1 euro = yen 123.10

Cross-currency rate for euro and yen:

1 pound = euro 1.5939

1 pound = yen 192.95

1 euro = yen 123.10

Arbitrage steps:

Have 160,000 euros.

1. Sell 160,000 euros and receive Yen 123.10 * 160,000 = 19,696,000 yen
2. Sell 19,696,000 yen and get (19,696,000 yen/ 192.95) = 102,078.30 pounds
3. Sell 102,078.30 pounds at rate, 1 pound = euro 1.5939 and receive euros equal to amount (1.5939 * 102,078.30) = 162702.54 euros
4. Net profit = euros 162702.54 - 160,000 euro = 2702.54 euros

4. Profits in euro = 2702.54

5. Momentary held pounds amounting to = 102078.30

6. Momentarily held yen of amount = 19696000