Covered interest arbitrage

February 10th, 2010

Covered interest arbitrage is the investment strategy where an investor buys a financial instrument denominated in a foreign currency, and hedges his foreign exchange risk by selling a forward contract in the amount of the proceeds of the investment back into his base currency. The proceeds of the investment are only known exactly if the financial instrument is risk-free and only pays interest once, on the date of the forward sale of foreign currency. Otherwise, some foreign exchange risk remains.

Similar trades using risky foreign currency bonds or even foreign stock may be made, but the hedging trades may actually add risk to the transaction, e.g. if the bond defaults the investor may lose on both the bond and the forward contract.

Example

In this example the investor is based in the United States and assumes the following prices and rates: spot USD/EUR = $1.2000, forward USD/EUR for 1 year delivery = $1.2300, dollar interest rate = 4.0%, euro interest rate = 2.5%.

* Exchange USD 1,200,000 into EUR 1,000,000
* Buy EUR 1,000,000 worth of euro-denominated bonds
* Sell EUR 1,025,000 via a 1 year forward contract, to receive USD 1,260,750, i.e. agree to exchange the euros back into US dollars in 1 year at today’s forward price.
* At the expiry of one year, two transactions occur consecutively. First, the euro-denominated bond delivers EUR 1,025,000. Secondly, the forward contract turns the EUR 1,025,000 into USD 1,260,750. So, the earning is USD 60,750. Had the investment been made in dollar, the return would have been only 4%. But, in this case, the two transactions can be viewed as resulting in an effective dollar interest rate of (1,260,750/1,200,000)-1 = 5.1%
* The above discussion does not consider the cost of capital. Alternatively, if the USD 1,200,000 were borrowed at 4%, USD 1,248,000 would be owed in 1 year, leaving an arbitrage profit of 1,260,750 – 1,248,000 = USD 12,750 in 1 year.

Financial models such as interest rate parity and the cost of carry model assume that no such arbitrage profits could exist in equilibrium, thus the effective dollar interest rate of investing in any currency will equal the effective dollar rate for any other currency, for risk-free instruments.

Triangular arbitrage

February 7th, 2010

Triangular arbitrage (sometimes called triangle arbitrage) refers to taking advantage of a state of imbalance between three foreign exchange markets: a combination of matching deals are struck that exploit the imbalance, the profit being the difference between the market prices.

Triangular arbitrage offers a risk-free profit (in theory), so opportunities for triangular arbitrage usually disappear quickly, as many people are looking for them, or simply never occur as everybody knows the pricing relation.

Example

Consider the three foreign exchange rates among the Canadian dollar, the U.S. dollar, and the Australian dollar. Triangular arbitrage will produce a profit whenever the following relation does not hold:

CD$/US$ * AU$/CD$ = AU$/US$.

For example if you can trade at these exchange rates

* the Canadian Dollar (CD$) against the US dollar (US$) is CD$1.13/US$1.00 (1 US$ gets you CD$1.13)
* the Australian Dollar (AU$) against the US dollar (US$) is AU$1.33/US$1.00 (1 US$ gets you AU$1.33)
* the Australian Dollar (AU$) against the Canadian Dollar (CD$) is AU$1.18/CD$1.00 (1 CD$ gets you AU$1.18)

1.13 * 1.18 = 1.3334 > 1.3300, thus mispricing has occurred.

To take advantage of the mispricing, starting with US$10,000 to invest:

* 1st buy Canadian Dollars with his US Dollars: US$10,000 * (CD$1.13/US$1) = CD$11,300
* 2nd buy Australian Dollars with his Canadian Dollars: CD$11,300 * (AU$1.18/CD$1.00) = AU$13,334
* 3rd buy US Dollars with his Australian Dollars: AU$13,334 / (AU$1.33/US$1.0000) = US$10,025
* Net risk free profit: US$25.00

A profit maximizing trader presented with these prices will trade up to the maximum size possible, or equivalently do the trade as many times as possible, until one of the traders on the other side of one of the deals changes his price. In practice currencies are quoted with a bid ask spread, so a trader should be careful that he is actually buying at the quoted ask price, and selling at the quoted bid price. Other transaction costs, such as commissions often prevent the trade from being profitable.