Covered Interest Arbitrage and Interest Rate Parity
There is a close relationship between the interest rates in two countries and the forward exchange rate premium or discount. Consider a U.S. investor with $1.2 million to invest who notes that the interest rate on 90-day certificates of deposit (CDs) available at German banks is 4 percent for 90 days At the same time, the 90-day CD rate in the U.S. is only 2 percent. The spot rate of the Deutsche mark (DM) is $0.60/DM and the 90-day forward rate is also $0.60. As an investor, you know that you can immediately convert $1.2 million into DM2 million at today's spot rate of $0.60 with no risk. You can also lock in the 4 percent German interest rate for 90 days by purchasing a German CD with your DM2 million. However, there is risk regarding the exchange rate at which you will be able to convert DM back to dollars at the end of 90 days. You can guarantee this rate by selling 2 million DM (plus the interest you will receive on your German CD) in the 90-day forward market at today's forward rate of $0.60. This transaction will guarantee you a risk-free profit. Consider the following steps in this transaction
1. Convert $1.2 million into DM2 million at today's spot rate of $0.60/DM.
2. Buy a 90-day CD at a German bank yielding 4 percent every 90 days.
3. Simultaneously sell DM2.08 million forward (original DM2 million plus DM 80,000 in interest) at $0.60 to net you $1,248,000.
4. This compares favorably with the $1,224,000 ($1.2 million plus interest at 2 percent) you could have received from investing in a U.S. CD.
This risk-free transaction enabled you to earn an additional return of $24,000 over what would be available by investing in the United States. Because there are virtually no barriers to prevent individuals from engaging in this transaction called covered interest arbitrage, it can be expected that opportunities to earn risk-free additional returns such as these will not persist very long. The demand by American investors for DM will put upward pressure on the spot price of DM, to a price greater than $0.60/DM. At the same time, as American investors sell DM forward to cover their position, this will put downward pressure on forward rate of the DM to a price less than $0.60. Furthermore, as funds leave the United States for Germany, the reduced supply of funds will tend to increase U.S. interest rates. The increased supply of funds in Germany, on the other hand, will tend to lower German interest rates.
The net effect of these transactions and market pressures will be an equilibrium condition where covered interest arbitrage transactions are not possible. This relationship is called interest rate parity (IRP). When IRP exists, the forward rate will differ from the spot rate by just enough to offset the interest rate differential between the two currencies. The IRP condition states that the home (or domestic) interest rate must be higher (lower) than the foreign interest rate by an amount equal to the forward discount (premium) on the home currency. In other words, the forward premium or discount for a currency quoted in terms of another currency is approximately equal to the difference in interest rates prevailing between the two countries. Thus, if interest rates in Germany are higher than interest rates in the United States, then the IRP condition indicates that the dollar can be expected to increase in value relative to the DM. The exact IRP relationship is
(3.2)
where ih is the home (U.S.) interest rate, if is the comparable foreign (German) interest rate, F is the direct quote forward rate, and S0 is the direct quote spot rate. (Note that the interest rates in Equation 3.2 are the interest rates for the same period of time as the number of days in the forward price, not necessarily annualized interest rates.) The relationship in Equation 3.2 can be simplified to
(3.3)
An approximation of the IRP relationship is:
(3.4)
Equation 3.4 indicates that when interest rate parity exists, differences in interest rates between two countries will be (approximately) offset by changes in the relative value of the two currencies.
To illustrate, assume that the 90-day interest rate is 1.5 percent in the United States and 2.5 percent in Germany, and the current spot exchange rate between dollars and Deutsche marks is $0.60. If IRP holds, what will the 90-day forward rate be (using the exact relationship in Equation 3.3)?
(F/$0.60) = (1 + 0.015) / (1 +0.025) r= $0.5941
In this case, the dollar has increased in value relative to the DM (i.e. it takes fewer dollars buy each DM) Why do you think this should occur?