Question

What is the difference between covered and uncovered interest rate parity? What are the formulas?

Answer 1

Covered interest rate parity is a theoretical situation in which the connection between two nations' interest rates and their spot and future currency values is balanced (Chertman, 2020). Due to the covered interest rate parity scenario, there is no possibility for arbitrage between nations with differing interest rates through future contracts, as is often the case. According to the idea of uncovered interest rate parity (UIP), the difference in interest rates between two nations will equal the relative change in currency foreign exchange rates over the same time (Li & Fu, 2020). It is a kind of interest rate parity (IRP) that is often used in conjunction with covered interest rate parity. Covered interest parity is achieved by hedging the currency rate using future contracts.

Meanwhile, uncovered interest rate parity entails predicting rates but not mitigating foreign currency risk—there are no forward rate contracts and the anticipated spot rate is used. The interest rate parities for uncovered and covered debt are fairly comparable. The distinction is that an uncovered IRP refers to a situation in which no-arbitrage is fulfilled without resorting to a forward contract. In the uncovered IRP, the anticipated exchange rate is adjusted in such a way that the IRP remains stable. This notion is a component of determining the anticipated spot exchange rate. The term "covered interest rate parity" refers to a situation in which no-arbitrage is achieved via the use of a forward contract. Investors would be agnostic in the covered IRP as to whether to invest in their home country's interest rate or the foreign country's interest rate since the forward exchange rate maintains currency equilibrium. This notion is included in the methodology for determining forward exchange rates.

 Covered interest parity rates formula;

(1+id)=S/F​∗(1+if​)

Where:

i_d​=The interest rate in the domestic currency or the base currency

i_f=The interest rate in the foreign currency or the quoted currency

S=The current spot exchange rate

F=The forward foreign exchange rate​

Uncovered interest parity rate formula

F₀​=S_0​1+i_b​1+i_c​​

Where:

F₀​=Forward rate

S₀​=Spot rate

i_c​=Interest rate in country _c

i_b​=Interest rate in country _b​
                                                                       

Covered interest rate parity is a theoretical situation in which the connection between two nations' interest rates and their spot and future currency values is balanced.