Example of Currency Arbitrage

So at a party recently, I hijacked an otherwise pleasant conversation to explain currency arbitrage.  I created this blog to provide a venue for this sort of thing so I wouldn't do it at parties.  I failed, clearly.  The example I used was a good one, though, so I'll repeat and refine here.

Imagine a big multinational company like Toyota needs to make payroll on Friday.  They have to make a $500 million dollar payment to the US bank that pays their US employees on Thursday night.  The cash that they have to make this payment is in their Japanese bank, though, in Yen.  They arrange to use Yen to buy the $500 million that they need.

Now, suppose that before this trade, anyone engaging in relatively small amounts can trade 1 US Dollar for 90 Yen.  They can also trade 1 Euro for 109.8 Yen, and 1.22 US Dollar for 1 Euro.

When Toyota executes this large trade, though, it pushes the price of dollars up in relation to the price of Yen (it takes more Yen to buy a Dollar).  I touched on the reasoning behind this in the liquidity miniseries.  If an asset is suddenly desired more (less) than it was a moment ago, it's price will go up (down).  Dollars and Yen are simply assets being bought and sold.  So, instead of getting their $500 million Dollars for 45 billion Yen, the exchange rate changes, and Toyota has to pay 45.25 billion Yen.

Meanwhile, Euros are trading with Dollars and Yen at the same rates they were before.  This is where an arbitrageur makes some money.  A trader in Boston sees the Toyota trade go through the market, and she does the following:

• Borrows $100,000 from her firm's trading account.
• Sells 100,000 Dollars to Buy 9,050,000 Yen (moving the opposite direction as Toyota).
• Sells 9,050,000 Yen to Buy 82,423 Euro.
• Sells 82,423 Euro to Buy 100,556 Dollars.
• Pays back the $100,000 to her firm's trading account.
• Takes her husband out on a hot $556 date.

Arbitrageurs do this until the three currencies move back into equilibrium.