Introduction

This Chapter discusses two important concepts in foreign exchange markets: covered interest rate parity and uncovered interest rate parity conditions. These conditions are essential in understanding the relationship between interest rates, exchange rates, and the opportunities for arbitrage in the currency markets. In this chapter, we will explore the differences between covered and uncovered interest rate parity, how they relate to forward exchange rates, and their implications for international investors and businesses.

Covered Interest Rate Parity (CIRP)

Covered Interest Rate Parity (CIRP) is a condition that must hold true in a well-functioning foreign exchange market. It describes the relationship between the interest rates in two different currencies and the corresponding forward exchange rate. The covered interest rate parity condition can be mathematically represented as follows:

$$ (1+r_{domestic}) = \dfrac{(1+r_{foreign}) \times (F/S) }{(1+f)} $$

Where:

• $r_{domestic}$ is the domestic interest rate
• $r_{foreign}$ ​is the foreign interest rate
• $F$ is the forward exchange rate between the domestic and foreign currencies
• $S$ is the current spot exchange rate between the domestic and foreign currencies
• $f$ is the cost of entering into the forward contract (transaction cost)

The covered interest rate parity condition implies that an investor can achieve the same return by either investing domestically or converting funds into foreign currency, investing at the foreign interest rate, and then using a forward contract to exchange back to the domestic currency at the forward rate. If CIRP does not hold, arbitrage opportunities may arise.

Example of Covered Interest Rate Parity: Suppose the current spot exchange rate between the US Dollar (USD) and the Euro (EUR) is 1.10 USD/EUR. The US interest rate is 3%, while the Eurozone interest rate is 1.5%. The forward exchange rate for a one-year contract is 1.12 USD/EUR, and the transaction cost (f) is negligible. Let’s check if CIRP holds:

$$ (1+0.03) = \dfrac{(1+0.015) \times (1.12/10) }{(1+0)} $$ $$ 1.03 = \dfrac{1.015 \times 1.01818181818 }{1} $$ $$ 1.03 = 1.03345454545 $$

Since the equation holds true, covered interest rate parity is satisfied, meaning there are no arbitrage opportunities between these two interest rates and exchange rates.

Uncovered Interest Rate Parity (UCIP):

Uncovered Interest Rate Parity (UCIP) is a less restrictive condition compared to CIRP. It suggests that the expected change in the spot exchange rate over a given period equals the difference in interest rates between two currencies for the same period. Mathematically, UCIP can be represented as:

$$ (1+r_{domestic}) = (1+r_{foreign}) \times \dfrac{E(S)}{S} $$

Where:

• $E(S)$ is the expected future spot exchange rate.
• All other variables have the same meaning as in the CIRP equation.

UCIP implies that investors do not cover their foreign exchange exposure using forward contracts. Instead, they rely on their expectations of future exchange rate movements to make investment decisions.

Example of Uncovered Interest Rate Parity: Continuing with the previous example, let’s say that investors expect the Euro to appreciate against the USD, leading to an expected future spot exchange rate of 1.15 USD/EUR in one year. We can check if UCIP holds:

$$ (1+0.03) = (1+0.015) \times \dfrac{1.15}{.10} $$ $$ 1.03 = 1.03260869565 $$

Since the equation holds true, uncovered interest rate parity is satisfied under the given assumptions.