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# Unhedged Interest Rate Parity – UIP Definition

## What is Unhedged Interest Rate Parity (UIP)?

The Unhedged Interest Rate Parity (UIP) theory states that the difference in interest rates between two countries will be equal to the relative change in currency exchange rates during the same period. This is a form of interest rate parity (IRP) used alongside the hedged interest rate parity.

If the unhedged interest rate parity relationship does not hold, then it is possible to make a risk-free profit using currency arbitrage or Forex arbitrage.

Key points to remember

• Uncovered Interest Rate Parity (UIP) is a fundamental equation in economics that governs the relationship between foreign and domestic interest rates and exchange rates.
• The basic principle of interest rate parity is that, in a global economy, the price of goods should be the same everywhere (the law of one price) once interest rates and exchange rates are taken into account.
• The IPU can be compared to the hedged interest rate parity, which involves the use of futures contracts to hedge exchange rates for forex traders.

Unhedged interest rate parity

## The formula for the uncovered interest rate parity is:



F

0

=

S

0

1

+

I

vs

1

+

I

b

or:

F

0

=

Forward rate

S

0

=

Spot rate

I

vs

=

Interest rate in the country

vs

I

b

=

Interest rate in the country

b

begin {aligned} & F_0 = S_0 frac {1 + i_c} {1 + i_b} & textbf {where:} & F_0 = text {Forward Rate} & S_0 = text {Spot Rate} & i_c = text {Interest rate in the country} c & i_b = text {Interest rate in the country} b end {aligned}

F0=S01+Ib1+Ivsor:F0=Forward rateS0=Spot rateIvs=Interest rate in the country vsIb=Interest rate in the country b??

### How to calculate interest rate parity

Forward exchange rates for currencies are exchange rates at a future time, as opposed to spot exchange rates, which are current rates. Understanding forward rates is fundamental to interest rate parity, especially with regard to arbitrage (simultaneous buying and selling of an asset in order to take advantage of a price difference).

Forward rates are available from banks and currency brokers for periods ranging from less than a week to five years and beyond. As with spot currency quotes, futures contracts are quoted with a bid-ask spread.

The difference between the forward rate and the spot rate is called swap points. If this difference (forward rate minus spot rate) is positive, we speak of term premium; a negative difference is called a term.

A currency with a lower interest rate will trade with a forward premium compared to a currency with a higher interest rate. For example, the US dollar typically trades at a term premium to the Canadian dollar; conversely, the Canadian dollar trades at a forward discount to the US dollar.

## What does the uncovered interest rate parity tell you?

The parity conditions for unhedged interest rates consist of two streams of return, one from the foreign money market interest rate on the investment and the other from the change in the spot rate of the currency. foreign. In other words, the unhedged interest rate parity assumes an exchange rate equilibrium, which implies that the expected return on a domestic asset (i.e. a risk-free rate such as a US Treasury bill or a Treasury bill) will be equal to the expected return on a foreign asset. after adjustment for changes in spot currency exchange rates.

When the unhedged interest rate parity is maintained, there can be no excess return by simultaneously going long in one higher yielding currency investment and short selling another low yielding currency investment or an interest rate differential. Unhedged interest rate parity assumes that the country with the highest interest rate or risk-free money market yield will experience a depreciation of its domestic currency against the foreign currency.

UIP is related to the so-called “law of one price,” which is an economic theory that states that the price of an identical security, commodity or product traded anywhere in the world should have the same price regardless of where exchange rates are taken into account, if it is traded in an open market without trade restrictions.

The “law of one price” exists because the differences between the prices of assets in different places should ultimately be eliminated due to the opportunity for arbitrage. The law of a price theory is the basis of the concept of purchasing power parity (PPP). Purchasing power parity states that the value of two currencies is equal when a basket of identical goods has the same price in both countries. This is a formula that can be applied to compare securities in markets that trade in different currencies. As exchange rates can change frequently, the formula can be recalculated periodically to identify pricing errors in various international markets.

## The difference between the hedged interest rate parity and the unhedged interest rate parity

Hedged Interest Parity (CIP) is the use of futures or futures contracts to hedge exchange rates, which can thus be hedged in the market. Meanwhile, Unhedged Interest Rate Parity (UIP) involves rate forecasting and does not hedge currency risk exposure i.e. there are no contracts forward rate and uses only the expected spot rate.

There is no theoretical difference between the parity of hedged and unhedged interest rates when the expected forward and spot rates are the same.

## Limits of uncovered interest parity

There is only limited evidence to support the IPU, but economists, academics and analysts still use it as a theoretical and conceptual framework to represent rational expectation models. The IPU requires the assumption that capital markets are efficient.

Empirical evidence has shown that in the short to medium term, the level of depreciation of higher yielding money is less than the implications of unhedged interest rate parity. Many times the high yielding currency has strengthened instead of weakened. 