The Interest Rate Parity is the basic identity that relates interest rates and exchange rates. The identity is theoretical, and usually follows from assumptions imposed in economics models. There are data evidences that support as well as reject the interest rate parity. An interest rate is the price a borrower pays for the use of money he does not own, and the return a lender receives for deferring his consumption, by lending to the borrower. ...

Two versions of the identity are commonly presented in academic literature: Covered Interest Rate Parity and Uncovered Interest Rate Parity.

Covered Interest Rate Parity

The basic covered interest parity (also called interest parity condition) is:

where: is the domestic interest rate, i_c is the interest rate in the foreign country, F is forward exchange rate between domestic currency ($) and foreign currency (c), i.e. $/c, and S is spot exchange rate between domestic currency ($) and foreign currency (c), i.e. $/c.

The covered interest parity states that the interest rate difference between two countries' currencies is equal to the percentage difference between the forward exchange rate and the spot exchange rate. The parity condition assumes that financial assets are perfectly mobile and similarly risky. If the parity condition does not hold, there exists an arbitrage opportunity. (see covered interest arbitrage below). In economics, arbitrage is the practice of taking advantage of a state of imbalance between two or more markets: a combination of matching deals are struck that exploit the imbalance, the profit being the difference between the market prices. ...

Another way to express the interest rate parity is:

A more approximate version is sometimes given, although it is less correct for countries with high exchange rates:

The chief implication of the interest parity condition is that if a country's interest rates are relatively low compared to other countries, then that country's currency will tend to appreciate. Conversely, if the country's interest rates are relatively high, then the country's currency will tend to depreciate.

Covered Interest Arbitrage Example

In short, assume that

.

This would imply that one dollar invested in the US < one dollar converted into a foreign currency and invested abroad. Such an imbalance would give rise to an arbitrage opportunity, where in one could borrow at the lower effective interest rate in US, convert to the foreign currency and invest abroad.

The following is a rudimentary example to understand Covered Interest Rate Arbitrage (CIA)

Consider the Interest Rate Parity (IRP) equation,

Assume,

the 12-month interest rate in US is 5%, per annum

the 12-month interest rate in UK is 8%, per annum

the current Spot Exchange is 1.5 $/£

the current Forward Exchange is 1.5 $/£

From the given conditions it is clear that UK has a higher interest rate than the US. Thus the basic idea of Covered interest arbitrage is to borrow in the country with lower interest rate and invest in the country with higher interest rate. All else being equal this would help you make money riskless. Thus,

• Per the LHS of the interest rate parity equation above, a dollar invested in the US at the end of the 12-month period will be,

$1 * (1 + 5%) = $1.05

• Per the RHS of the interest rate parity equation above, a dollar invested in the UK (after conversion into £ and back into $ at the end of 12-months) at the end of the 12-month period will be,

$1 * (1.5%/1.5%)(1 + 8%) = $1.08

Thus, one could carry out a Covered Interest Rate (CIA) arbitrage as follows,

1. Borrow $1 from the US bank at 5% interest rate.
2. Convert $ into £ at current spot rate of 1.5$/£ giving 0.67£
3. Invest the 0.67£ in the UK for the 12 month period
4. Purchase a forward contract on the 1.5$/£ (i.e. cover your position against exchange rate fluctuations)

At the end of 12-months

1. 0.67£ becomes 0.67£(1 + 8%) = 0.72£
2. Convert the 0.72£ back to $ at 1.5$/£, giving $1.08
3. Pay off the initially borrowed amount of $1 to the US bank with 5% interest, i.e $1.05

• Making an arbitrage profit of $1.08 - $1.05 = $0.03 or 3 cents per dollar.

Obviously, any such arbitrage opportunities in the market will close out almost immediately.

In the above example, any one or combination of the following may occur to re-establish the equilibrium of the IRP to close out the arbitrage opportunity,

• US interest rates will go up
• Forward exchange rates will go down
• Spot exchange rates will go up
• UK interest rates will go down

Uncovered Interest Rate Parity

The uncovered interest rate parity postulates that

The equality assumes that the risk premium is zero, which is the case if investors are risk-neutral. If investors are not resk-neutral then the forward rate (F_{t,t + 1}) can differ from the expected future spot rate (E_t[S_{t + 1}]), and covered and uncovered interest rate parities cannot both hold. A risk premium is the minimum difference between the expected value of an uncertain bet that a person is willing to take and the certain value that he is indifferent to. ... Risk aversion is a concept in economics and finance theory explaining the behaviour of consumers and investors under uncertainty. ...

The uncovered parity is not directly testable in the absence of market expectations of future exchange rates.

Uncovered Interest Parity Example

An example for the uncovered interest parity condition: Consider an initial situation, where interest rates in the US and a foreign country (e.g. Japan) are equal. Except for exchange rate risk, investing in the US (home) or Japan would yield the same return. If the dollar depreciates against the yen, an investment in Japan would become more profitable than an US-investment: For the same amount of yen, more dollar can be purchased. By investing in Japan and converting back to the dollar at the favorable exchange rate, the return from the investment in Japan, in the dollar term, is higher than the return from the investment in the US. In order to persuade an Investor to invest in the US nonetheless, the dollar interest rate would have to be higher than the yen interest rate by an amount equal to the devaluation (a 20% depreciation of the dollar implies a 20% rise in the dollar interest rate).

Uncovered vs. Covered Interest Parity Example

Let's assume you wanted to pay for something in Yen in a months time. There are two ways to do this.

• (a) You could avoid exchange rate risk by buying some Yen now and selling your Yen forward for 30 days (for example in a Japanese 30 day fixed deposit). This is called covering because you now have covered yourself and have no exchange rate risk.

• (b) You could also invest the money in dollars and change it for Yen in a month.

According to the IPC you would get the same number of Yen as with (a) (but you would still have some exchange rate risk.)

Without going into too much detail, these two methods are similar to what an exchange trader would do to get the 30 day forward rate (method a) and the expected spot rate in 30 days (method b). This links the two rates.

(As an aside, it is only the expected rate in 30 days that method (b) relies on. This may be different to the actual rate on that day, of course).

Cost of carry model

A slightly more general model, used to find the forward price of any commodity, is called the cost of carry model. The cost of carry refers to the lost oppportunity cost of purchasing a particular security rather than an alternative. ...

If the currencies are freely tradeable and there are minimal transactions costs, then a profitable arbitrage is possible if the equation doesn't hold. If the forward price is too high, the arbitrageur sells the forward currency, buys the spot currency and lends it for time period m, and then uses the loan proceeds to deliver on the forward contract. To complete the arbitrage, the home currency is borrowed in the amount needed to buy the spot foreign currency, and paid off with the home currency proceeds of forward contract.

Similarly, if the forward price is too low, the arbitrageur buys the forward currency, borrows the foreign currency for time period m and sells the foreign currency spot. The proceeds of the forward contract are used to pay off the loan. To complete the arbitrage, the home currency from the spot transaction is lent and the proceeds used to pay for the forward contract.

External links

• Disk Lectures MBA level audio lecture with slideshow on Foreign Exchange