Uncovered Interest Rate Parity – UIP

Uncovered interest rate parity (UIP) theory states that the difference in interest rates between two countries will equal the relative change in currency foreign exchange rates over the same period. It is one form of interest rate parity (IRP) used alongside covered interest rate parity.

If the uncovered interest rate parity relationship does not hold, then there is an opportunity to make a risk-free profit using currency arbitrage or Forex arbitrage.

$\begin{aligned} &F_0=S_0\frac{1+i_c}{1+i_b}\\ &\textbf{where:}\\ &\bullet F_0\text{ is the forward rate}.\\ &\bullet S_0\text{ is the spot rate}.\\ &\bullet i_c\text{ is the interest rate in country }c.\\ &\bullet i_b\text{ is the interest rate in country }b. \end{aligned}$​F0​=S0​1+ib​1+ic​​where:∙F0​ is the forward rate.∙S0​ is the spot rate.∙ic​ is the interest rate in country c.​How to Calculate Interest Rate Parity

Forward exchange rates for currencies are exchange rates at a future point in time, as opposed to spot exchange rates, which are current rates. An understanding of forward rates is fundamental to interest rate parity, especially as it pertains to arbitrage (the simultaneous purchase and sale of an asset in order to profit from a difference in the price).

Forward rates are available from banks and currency dealers for periods ranging from less than a week to as far out as five years and beyond. As with spot currency quotations, forwards are quoted with a bid-ask spread.

The difference between the forward rate and spot rate is known as swap points. If this difference (forward rate minus spot rate) is positive, it is known as a forward premium; a negative difference is termed a forward discount.

A currency with a lower interest rate will trade at a forward premium in relation to a currency with a higher interest rate. For example, the U.S. dollar typically trades at a forward premium against the Canadian dollar; conversely, the Canadian dollar trades at a forward discount versus the U.S. dollar.

Uncovered interest rate parity conditions consist of two return streams, one from the foreign money market interest rate on the investment and one from the change in the foreign currency spot rate. Said another way, uncovered interest rate parity assumes foreign exchange equilibrium, thus implying that the expected return of a domestic asset (i.e., a risk-free rate like a U.S. Treasury Bill or T-Bill) will equal the expected return of a foreign asset after adjusting for the change in foreign currency exchange spot rates.

When uncovered interest rate parity holds, there can be no excess return earned from simultaneously going long a higher-yielding currency investment and shorting a different lower-yielding currency investment or interest rate spread. Uncovered interest rate parity assumes that the country with the higher interest rate or risk-free money market yield will experience a depreciation in its domestic currency relative to the foreign currency.

UIP is related to the so-called "law of one price," which is an economic theory that states the price of an identical security, commodity, or product traded anywhere in the world should have the same price regardless of location when currency exchange rates are taken into consideration – if it is traded in a free market with no trade restrictions.

The "law of one price" exists because differences between asset prices in different locations should eventually be eliminated due to the arbitrage opportunity. The law of one price theory is the underpinning 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 is priced the same in both countries. This relates to a formula that can be applied to compare securities across markets that trade in different currencies. As exchange rates can shift frequently, the formula can be recalculated on a regular basis to identify mispricings across various international markets.

Covered interest parity (CIP) involves using forward or futures contracts to cover exchange rates, which can thus be hedged in the market. Meanwhile, uncovered interest rate parity (UIP) involves forecasting rates and not covering exposure to foreign exchange risk – that is, there are no forward rate contracts, and it uses only the expected spot rate.

There is no theoretical difference between covered and uncovered interest rate parity when the forward and expected spot rates are the same.

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

Empirical evidence has shown that over the short- and medium-term time periods, the level of depreciation of the higher-yielding currency is less than the implications of uncovered interest rate parity. Many times, the higher-yielding currency has strengthened instead of weakened.