Question

In: Finance

Define each of the following theories accompanied by equations. Hypothetical examples are required. a. Interest rate...

Define each of the following theories accompanied by equations. Hypothetical examples are required.

a. Interest rate parity.

b. Expectations theory of forward rates.

c. Purchasing power parity.

d. International capital market equilibrium (relationship of real and nominal interest rates in different countries).

Solutions

Expert Solution

A) Interest Rate Parity : It is the fundamental equation which governs the relationship between interest rate and the exhange rate of currency. Interest rate parity (IRP) plays an important role in foreign exchange markets connecting interest rates, spot exchange rates, and foreign exchange rates. Interest rate parity (IRP) is a theory according to which the interest rate differential between two countries is equal to the differential between the forward exchange rate and the spot exchange rate.

F0​=S0​×(1 +ic /​1+ib​​)

where F0​=Forward Rate S0​=Spot Rate ic​=Interest rate in country C ib​=Interest rate in country B​

Example : Assume JapansesTreasury bills are offering an annual interest rate of 1.95% while U.S. Treasury bills are offering an annual interest rate of 0.5%. If an investor in the United States seeks to take advantage of Japan's interest rates, the investor would have to exchange U.S. dollars to Japanese Yen to purchase the Treasury bill.

Thereafter, the investor would have to sell a one-year forward contract on the Japanese Yen . However, under the covered IRP, the transaction would only have a return of 0.5%; otherwise, the no-arbitrage condition would be violated.

B) Expectations theory try to predict what short-term interest rates will be in the future based on current long-term interest rates. The theory suggests that an investor earns the same interest by investing in two consecutive one-year bond investments versus investing in one two-year bond today. The expectations theory aims to help investors make decisions baed upon a forcast of future interese rates using forward rates.

C) It is a macroeconomic analysis metric to compare economic productivity and standards of living between countries is purchasing power parity (PPP). PPP is an economic theory that compares different countries currencies through a "basket of goods" approach, not to be confused with the Paycheck Protection Program created by the CARES Act. According to this concept, two currencies are in equilibrium when a basket of goods is priced the same in both countries, taking into account the exchange rates for the same.

Equation = S = p1 / p2 where S is the exhange rate of currency one to currency two , P1 is cost of good X in currency one and P2 is cost of good X in currency two.

Example : To better understand how GDP paired with purchase power parity works, suppose it costs $20 to buy a shirt in the U.S., and it costs €16.00 to buy an identical shirt in France. To make an apples-to-apples comparison, we must first convert the €16.00 into U.S. dollars. If the exchange rate was such that the shirt in France costs $30.00, the PPP would, therefore, be 30/10, or 3. In other words, for every $1.00 spent on the shirt in the U.S., it takes $3.00 to obtain the same shirt in France buying it with the euro.

D) International Capital Market Equillibrium is an  economic theory stating that the expected disparity between the exchange rate of two currencies is approximately equal to the difference between their countries nominal interest rates. Real interest rate is the interest when is inflation is added to the nonimal interest rate, so countries with higher real interest rate means higher inflation which leads to depreciation of currency against other currencies. It is based on present and future risk free investment. So, this theories states the combined effect of interest and inflation leading appreciation or depreciation of a countries currency.

E=i1-i2/​1 + i2​​ ≈ i1​−i2​

Where: E= the percent change in the exchange rate i1​=country A’s interest rate i2​=country B’s interest rate​

Example : If country A's interest rate is 15% and country B's interest rate is 7%, country B's currency should appreciate roughly 8% compared to country A's currency. The rationale for the theory 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.


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