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In: Finance

Three “well-known” parity conations in International Finance are presented in textbook and lecture notes.

Three “well-known” parity conations in International Finance are presented in textbook and lecture notes. To answer the questions below, first, write down appropriate formulas and then explain the main ideas. Make sure to clarify the notations used.


a. Interest rate parity (IRP) condition:




b. Relative purchasing power parity (RPPP) condition:




c. International Fisher relation:

Solutions

Expert Solution

ANSWER

A Interest rate parity (IRP) condition:

WHERE

Fo = forward rate

So = spot rate

ic = interest rate in country c

ib =interest rate in country b

IRP is the fundamental equation that governs the relationship between interest rates and currency exchange rates. The basic premise of IRP is that hedged returns from investing in different currencies should be the same, regardless of their interest rates.

IRP is the concept of no-arbitrage in the foreign exchange markets (the simultaneous purchase and sale of an asset to profit from a difference in the price). Investors cannot lock in the current exchange rate in one currency for a lower price and then purchase another currency from a country offering a higher interest rate.

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 IRP, especially as it pertains to arbitrage.

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 more. 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 lower interest rates 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.

B.Relative purchasing power parity (RPPP) condition:

ccording to relative purchasing power parity (RPPP), the difference between the two countries’ rates of inflation and the cost of commodities will drive changes in the exchange rate between the two countries. RPPP expands on the idea of purchasing power parity and complements the theory of absolute purchasing power parity (APPP). The APPP concept declares that the exchange rate between the two nations will be equal to the ratio of the price levels for those two countries.

The relative version of PPP is calculated with the following formula:

S = P1 / P2

S = Exchange rate of currency 1 to currency 2

P1 = cost of good X in currecy 1

P2 = cost of good x in currency 2

Relative Purchasing Power Parity (RPPP) is an expansion of the traditional purchasing power parity (PPP) theory to include changes in inflation over time. Purchasing power is the power of money expressed by the number of goods or services that one unit can buy, and which can be reduced by inflation. RPPP suggests that countries with higher rates of inflation will have a devalued currency.

uppose that over the next year, inflation causes average prices for goods in the U.S. to increase by 3%. In the same period, prices for products in Mexico increased by 6%. We can say that Mexico has had higher inflation than the U.S. since prices there have risen faster by three points.

According to the concept of relative purchase power parity, that three-point difference will drive a three-point change in the exchange rate between the U.S. and Mexico. So we can expect the Mexican peso to depreciate at the rate of 3% per year, or that the U.S. dollar should appreciate at the rate of 3% per year.

c.International Fisher relation:

The IFE is based on the analysis of interest rates associated with present and future risk-free investments, such as Treasuries, and is used to help predict currency movements. This is in contrast to other methods that solely use inflation rates in the prediction of exchange rate shifts, instead functioning as a combined view relating inflation and interest rates to a currency's appreciation or depreciation.

The theory stems from the concept that real interest rates are independent of other monetary variables, such as changes in a nation's monetary policy, and provide a better indication of the health of a particular currency within a global market. The IFE provides for the assumption that countries with lower interest rates will likely also experience lower levels of inflation, which can result in increases in the real value of the associated currency when compared to other nations. By contrast, nations with higher interest rates will experience depreciation in the value of their currency.

This theory was named after U.S. economist Irving Fisher.

Calculating the International Fisher Effect

IFE is calculated as:

For example, if country A's interest rate is 10% and country B's interest rate is 5%, country B's currency should appreciate roughly 5% compared to country A's currency. The rationale for the IFE is that a country with a higher interest rate will also tend to have a higher inflation rate. This increased amount of inflation should cause the currency in the country with a higher interest rate to depreciate against a country with lower interest rates.

Application of the International Fisher Effect

Empirical research testing the IFE has shown mixed results, and it is likely that other factors also influence movements in currency exchange rates. Historically, in times when interest rates were adjusted by more significant magnitudes, the IFE held more validity. However, in recent years inflation expectations and nominal interest rates around the world are generally low, and the size of interest rate changes is correspondingly relatively small. Direct indications of inflation rates, such as consumer price indexes (CPI), are more often used to estimate expected changes in currency exchange rates.


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