Interest Rate Parity (IRP) Calculator

Interest Rate Parity Formula

The interest rate parity formula relates the spot exchange rate, forward exchange rate, and interest rates of two currencies. It can be expressed in different forms, but here are two common ones:

Standard Formula

F = S * ((1 + i_q) / (1 + i_b))

Where:

• F is the forward foreign exchange rate.
• S is the current spot foreign exchange rate.
• i_b is the interest rate in the base currency.
• i_q is the interest rate in the quoted currency.

Simplified Version

F = S * (i_q - i_b)

Where the meanings of F, S, i_q, and i_b remain the same as in the standard formula.

Forward Premium

Forward Premium = (F/S) - 1 = (F - S) / S

This formula calculates the forward premium, which represents the difference between the forward exchange rate and the spot exchange rate as a percentage of the spot exchange rate.

Interest Rate Parity Condition

The interest rate parity condition is a fundamental principle in international finance that states the relationship between interest rates and exchange rates in two different currencies.

Uncovered Interest Rate Parity (UIP) Condition:

The UIP condition asserts that the expected return on investments denominated in different currencies should be equal when adjusted for the expected changes in exchange rates.

Mathematically, it can be expressed as:

i_b - i_q = (E(S_t+1) - S_t) / S_t

Where:

• i_b is the interest rate in the base currency.
• i_q is the interest rate in the quoted currency.
• E(S_t+1) is the expected future spot exchange rate.
• S_t is the current spot exchange rate.

In simpler terms, the difference between interest rates of two currencies should equal the expected percentage change in the exchange rate over the same period.

Violation of UIP suggests opportunities for arbitrage, where investors can exploit the mispricing of assets to make risk-free profits.

Interest Rate Parity Theory

The interest rate parity (IRP) theory is a fundamental concept in international finance that explains the relationship between interest rates and exchange rates in the global financial markets.

Basic Principle:

IRP theory posits that the difference in interest rates between two countries should equal the difference between the forward exchange rate and the spot exchange rate, adjusted for any expected changes in exchange rates.

Implications:

1. Arbitrage Opportunities: According to IRP theory, if there is a deviation from interest rate parity, it creates arbitrage opportunities for investors to profit by borrowing in one currency, investing in another, and covering the exchange risk through forward contracts.

2. Exchange Rate Expectations: IRP theory suggests that market participants incorporate their expectations of future exchange rate movements into current interest rates. For instance, if investors anticipate a depreciation of a currency, they may demand a higher interest rate to compensate for the expected loss in value.

Forms of Interest Rate Parity:

1. Covered Interest Rate Parity (CIRP): This form holds when the forward exchange rate correctly predicts the future spot exchange rate, considering the interest rate differentials between two currencies.

2. Uncovered Interest Rate Parity (UIP): UIP holds when investors are indifferent between investing in domestic assets versus foreign assets, accounting for expected changes in exchange rates. In UIP, investors are not covered against exchange rate risk.

Real-World Application:

IRP theory serves as a foundation for understanding and analyzing currency markets, influencing investment decisions, international capital flows, and monetary policy formulation by central banks.