FNCE 4103 Week 3 Interest Rate Parity Brief Example

Does Covered Interest Rate Parity Hold for Lakeland's 90-Day Euro Payable? Two Interest Rates, the Implied Forward Rate, the Quoted Forward and What a Gap of a Few Hundredths of a Percent Means

Student Name

Walden University

FNCE 4103: International Finance

Instructor Name

Month Day, Year

Does Covered Interest Rate Parity Hold for Lakeland's 90-Day Euro Payable? Two Interest Rates, the Implied Forward Rate, the Quoted Forward and What a Gap of a Few Hundredths of a Percent Means

The Relationship

Under covered interest rate parity, the gap between a forward rate and today's spot rate mirrors the gap between the two currencies' interest rates for the same term. In symbols, F = S x (1 + i_US x t) / (1 + i_EUR x t), where F is the forward rate in dollars per euro, S is the spot rate, i_US and i_EUR are annual interest rates on comparable dollar and euro deposits and t is the fraction of a year, here 90 / 360 (Madura, 2021). Were it to fail, a trader could fund a position in dollars, switch into euros, earn euro interest and sell the proceeds forward, pocketing a gain with no currency risk.

The Data

The inputs are illustrative but consistent with conditions when U.S. short-term rates were well above euro-area rates:

The comparison only works if the two rates are for the same maturity and comparable credit quality. Comparing a 3-month dollar rate with a 1-year euro rate, or a government rate with a bank deposit rate, would produce a meaningless gap.

Table 1

Inputs for the 90-Day Parity Calculation

Illustrative figures for the case; both rates are for the same 90-day maturity, which the comparison requires.

The Implied Forward Rate

F = 1.0850 x (1 + 0.0500 x 0.25) / (1 + 0.0360 x 0.25)

F = 1.0850 x 1.012500 / 1.009000

F = 1.0850 x 1.003469

F = $1.0888 per euro

With dollar interest above euro interest, the euro sells forward at a premium: the forward rate is above the spot rate by about 0.35 percent for 90 days. Parity says the higher interest an investor earns on dollars is offset by paying more, in dollars, for euros delivered later.

Why Parity Should Hold

The logic is an arbitrage argument. Suppose the forward rate were well above $1.0888, say $1.0950. A trader could borrow dollars at 5 percent, buy euros at $1.0850, invest them at 3.6 percent and sell the euros forward at $1.0950. At the end of 90 days the trader would receive more dollars from the forward sale than needed to repay the dollar loan, with no exposure to the exchange rate, because every rate was fixed at the start. Traders doing this at scale would push the spot rate up, the forward rate down and the interest rates toward each other until the profit disappeared. Levich (2001) describes covered parity as one of the most reliable relationships in international finance precisely because the trades that enforce it carry no currency risk.

The Quoted Rate Beside It

The bank's quoted forward is $1.0890, against the implied $1.0888. The difference is $0.0002 per euro, or about 0.02 percent. On Lakeland's €2,000,000 payable, that is about $400.

What the Gap Means

A gap this small does not signal an arbitrage opportunity. Bid-ask spreads on the spot and forward rates, on the deposit rates and on the transactions needed to exploit the gap would each cost more than 0.02 percent, so no trader could profit from it. For practical purposes, covered interest rate parity holds here. Research has found, however, that since 2008 small but persistent deviations from covered parity have appeared in major currency pairs, especially at quarter ends, because regulation has made it more costly for banks to use their balance sheets for arbitrage (Du et al., 2018). The deviation in this example is within the range those studies report for the euro.

What It Means for Lakeland

For Lakeland's treasurer, the result has a simple meaning. A forward contract at $1.0890 locks in a dollar cost of $2,178,000 for the €2,000,000 payable, about $8,000 more than paying at today's spot rate. That $8,000 is not a fee or a forecast of the euro rising; it reflects the interest rate difference. Lakeland could obtain essentially the same result by borrowing dollars today, buying euros at spot and investing them in a euro deposit for 90 days, a money market hedge, because parity links the two. The choice between those methods, and whether to hedge at all, is the subject of later weeks.

References

Du, W., Tepper, A., & Verdelhan, A. (2018). Deviations from covered interest rate parity. The Journal of Finance, 73(3), 915-957. https://doi.org/10.1111/jofi.12620

Levich, R. M. (2001). International financial markets: Prices and policies (2nd ed.). McGraw-Hill.

Madura, J. (2021). International financial management (14th ed.). Cengage Learning.