International Parity Conditions Overview
What are international parity conditions?
International parity conditions show how expected inflation differentials, interest rate differentials, forward exchange rates, current spot rates, and expected future spot rates are related to one another in an ideal world.
What is the main purpose of these international parity conditions?
The primary purpose of these conditions is to explain and predict movements in exchange rates and to ensure that there are no arbitrage opportunities in international markets.
Main international parity conditions
1. Covered Interest Rate Parity (CIRP)
Covered Interest Rate Parity (CIRP) is an economic theory that explains the relationship between interest rates and exchange rates for two countries. CIRP suggests that the difference in interest rates between two countries is equal to the difference between the forward exchange rate and the spot exchange rate, thus preventing arbitrage opportunities.
Formula
From the formula, we can see that:
Note: Since the exchange rate risk is completely hedged, an investment in a foreign money market instrument should yield the exact same return as an otherwise identical domestic money market investment. (i.e., There is no arbitrage opportunity.)
2. Uncovered interest rate party (UIRP)
Unlike Covered Interest Rate Parity (CIRP), UIRP does not involve the use of forward contracts to hedge against exchange rate risk. Instead, UIRP relies on the expectation that the exchange rate will adjust to reflect interest rate differentials between two countries.
Formula
Note: UIRP can't prevent arbitrage because of the unpredictable nature of currency markets, practical market constraints, and varying investor preferences. These factors create an environment where perfect arbitrage is challenging to achieve.
3. Forward rate parity (FRP)
Forward Rate Parity (FRP) is a financial theory that posits a relationship between the spot exchange rate, the forward exchange rate, and the interest rate differential between two countries. It asserts that the forward exchange rate should be an unbiased predictor of the future spot exchange rate. This means that, on average, the forward rate will equal the future spot rate. The concept is closely related to the Covered Interest Rate Parity (CIRP) but focuses on the idea of the forward rate as an unbiased predictor.
Note: For FRP to hold, both CIRP and UIRP need to hold.
Formula
Remarks: If UIRP holds, then FRP holds. However, UIRP is often violated in the real world because:
4. Purchasing power parity (PPP)
Purchasing power parity (PPP) is an economic theory used to compare the relative value of currencies. It measures the purchasing power of different countries' currencies over the same types of goods and services. The principle behind PPP is that, in the absence of transaction costs and other frictions, identical goods should have the same price when expressed in a common currency (i.e., Law of one price).
Different types of PPP
4.1. Absolute PPP states that the exchange rate will be determined entirely by the ratio of the foreign and domestic broad price indexes.
Formula
The absolute PPP assumes that: (Note that these assumptions rarely hold in the real world.)
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4.2. Relative PPP states that the percentage change in the spot exchange rate will be completely determined by the difference between the foreign and domestic inflation rates.
Formula
For instance, if the foreign inflation rate is 10% and the domestic inflation rate is 2%, the domestic currency must appreciate by 8% to maintain the relative competitiveness of both regions.
4.3. Ex ante version of PPP states that the “expected” changes in spot exchange rates are driven by “expected” inflation differentials. (i.e., The only major difference between Relative PPP and Ex ante PPP is whether they focus on Actual or Expectation.)
Formula
Over short time horizons, nominal exchange rate movements appear random. However, over longer time horizons, nominal exchange rates tend to gravitate toward their long-run PPP equilibrium values.
5. International Fisher Effect (IFE)
Real Interest Rate Parity: If UIRP and Ex ante PPP hold, the real interest rate in the domestic country should be equal to the real interest rate in the foreign country. (i.e., Real interest rate should converge to the same level across different markets).
International Fisher Effect states that, given that the Real Interest Rate Parity holds, the difference in nominal interest rates between two countries is an indicator of the expected change in exchange rates between their currencies. Specifically, a country with a higher nominal interest rate will experience depreciation in its currency compared to a country with a lower nominal interest rate.
Formula
The summary of main international parity conditions is as follows:
1. According to covered interest rate parity, arbitrage ensures that nominal interest rate
spreads equal the percentage forward premium or discount.
2. According to uncovered interest rate parity, the expected percentage change in the
spot exchange rate should, on average, be equal to the nominal interest rate spread.
3. If both covered and uncovered interest rate parity hold, then the forward exchange
rate will be an unbiased predictor of the future spot exchange rate.
4. According to the ex-ante PPP the expected change in the spot exchange rate should
equal the expected difference between domestic and foreign inflation rates.
5. According to the International Fisher effect, the nominal yield spread between
domestic and foreign markets will equal the domestic-foreign expected inflation
differential.
If all the main international parity conditions held at all times, then the expected percentage change in the spot exchange rate would equal:
? the forward premium or discount (i.e., Forward rate - Spot rate expressed in percentage terms)
? the nominal yield spread between countries
? the difference between expected national inflation rates
Note: If all the main international parity conditions held at all times, then it would be impossible for a global investor to earn consistent profits on currency movements.