Question

1. Suppose you are a currency speculator trying to forecast what will happen to the value of the dollar over the next year. Suppose all of our usual theories hold (uncovered, covered and real interest rate parities, absolute and relative purchasing power parities, as well as the Fisher effect for nominal interest rates).

For each of the separate cases below, use the information in that case to compute the expected depreciation of the dollar , or state if there is not enough information. State the name of the parity condition(s) you use and show your work.

1. Expected inflation over the next year is expected to be 1% in the U.S. and -1% in Europe.
2. The nominal interest rate in the U.S. for a 1-year dollar deposit is 3%, and that for a euro deposit is 2%.
3. The current spot exchange rate is 1 dollar per euro, and the forward rate for a year from now is 1.1 dollars per euro.

Answer 1

Answers

1. Relative purchasing power parity relates the two countries’ exchange rate with its inflation rate. It is an extension of the Purchasing Power Parity (PPP) and adjusts for the relative changes of inflation over time. PPP compares the price of a fixed basket of goods across the two countries. Relative PPP reduces it by inflation since inflation erodes the value of money and thus decreases the real purchasing power. So, if the inflation rate of a country is r%, then it will be able to purchase r% less the real value of goods.

Here, the inflation rate in US is1% while its-1% in Europe. So, the net difference is = 2%. So, the US dollar is expected to depreciate by 2%.

2. Fisher effect relates to the nominal interest rate, real interest rate, and inflation rate. While making investment decisions, investors consider the real exchange rate. The Fisher equation states that –

Real Interest rate (RRI) = Nominal interest rate (NRI) – inflation rate (dP)

For USA, RRI_USA = 3% - 1% = 2%

For Europe, RRI_EU = 2% - (-1%) = 3%

So, Europe is a better place to invest given that return is higher there. So, the value of the Euro will appreciate and the value of the dollar will depreciate. If we assume free capital mobility,

The extent of the dollar depreciation can be calculated using the uncovered interest parity theory. Let d = expected depreciation of the dollar.

Then, according to UIP, RRI_USA = RRI_EU + d

So, d = 2% - 3% = -1%

So, the dollar’sexpected deprication is1%.

3. Covered interest parity excludes the option for arbitrage by using forward contracts. The formula is given as below.

(1+ RRI_USA) = (F/S) * (1 + RRI_EU), where F =forward exchange rate and S = Spot exchange rate

Using the information given, we get,

(1+ RRI_USA) = (1+2) = 3

(F/S) * (1 + RRI_EU) = (1.11/1) * (1+3) = 4.44

So, (1+ RRI_USA) < (F/S) * (1 + RRI_EU)

The expected depreciation of dollar = F –S = (1.1 -1)/1 * 100 = 10%