Foreign Exchange Determination and Parity Conditions: II

1. Foreign Exchange Determination and Parity Conditions: II

2. The relative purchasing power parity: states that the exchange rate between the home currency and any foreign currency will adjust to reflect changes in the price levels of the two countries. For example, if inflation is 5% in the USA and 1% in Japan, then the dollar value of the Japanese yen must rise by about 4% to equalize the dollar price of goods in the two countries.

3. Formally, if ih and if are the periodic price level increases (rates of inflation) for the home country and foreign country, respectively; e0 is the dollar (HC) value of one unit of foreign currency at the beginning of the period; and et is the spot exchange rate in period t, then et / e0 = (1 + ih)t / (1 + if)t Or, et = e0 × (1 + ih)t / (1 + if)t Let us assume that the exchange rate between US dollars and UK pound is $2 per £. Further accept that the US will have inflation rate of 10% for the coming year and the UK will have inflation rate of 20% over the same period. What is the new exchange rate?

4. et = $2 × (1 + 0.10)1 / (1 + 0.20)1 = 1.83 / £ The new exchange rate is $1.83 per pound sterling. This indicates that the US dollar price of the pound should decrease in value by about 10% from $2 per pound to $1.83 per pound to equalise the dollar price of goods in two countries. Appraisal of PPP: • The theory explains how relative inflation rates between two countries can influence their exchange rates • It can be used to forecast exchange rates • Only work well under a freely floating exchange rate system.

5. The Fisher Effect: The generalized version of the Fisher effect asserts that real returns are equalized across countries through arbitrage – that is, ah = af, where the subscripts h and f refer to home and foreign real rates, respectively. Therefore, if there is any difference in interest rate between two countries, this is due to inflation differential because the nominal interest rate is the sum of real interest rate and inflation rate.

6. The equation for generalized Fisher Effect is: (1 + rh) / (1 + rf) = (1 + ih) / (1 + if) Where rh is the home nominal interest rate rf is the foreign nominal interest rate ih is the home inflation rate if is the foreign inflation rate For example, if inflation rates in the USA and UK are 4% and 7% respectively, the Fisher effect says that nominal interest rates should be about 3% higher in the UK than in the USA.

7. The International Fisher Effect: International Fisher effect is the combination of PPP and generalized Fisher effect. Where et is the expected exchange rate in period t. The single period analogue to this equation is: The equation indicates that the expected return from investing at home (1 + rh), should equal the expected home currency return from investing abroad (1 + rf) * e1/e0

8. Now, if home interest is relatively small, then International Fisher Effect can be written as:

9. Interest Rate Parity: Interest rate parity ensures that the return on a hedged (or covered) foreign investment will just equal the domestic interest rate on investments of identical risk, thereby eliminating the possibility of having a money machine. When this condition hold, the covered interest differential – the difference between the domestic interest rate and the hedged foreign rate – is zero. Suppose an investor with$1000,000 to invest for 90 days is trying to decide between investing in US dollars at 8% per annum (2% for 90 days) or in euros at 6% per annum (1.5% for 90 days). The current spot rate is €1.13110/$, and the 90-day forward rate is €1.12556/$. Now if the investor chooses to invest in euros on a hedged basis, he will,

10. Convert the $1000,000 to euros at the spot rate of €1.13110/$. This yields €1,131,100 available for investment. • Invest the principal of €1,131,100 at 1.5% for 90 days. At the end of 90 days, the investor will have €1,148,066.50. • Simultaneously with the other transactions, sell the €1,148,066.50 in principal plus interest forward at a rate of €1.12556/$ for delivery in 90 days. This transaction will yield €1,148,066.50 / 1.12556 = $1,020,000 in 90 days. If the covered interest differential between two money markets is nonzero, there is an arbitrage incentive to move money from one market to the other. This movement of money to take advantage of a covered interest differential is known as covered interest arbitrage.

11. Interest rate parity holds when there are no covered interest arbitrage opportunities. On the basis of the previous discussion, this no-arbitrage condition can be stated as follows: Or, interest rate parity is often approximated by the following equation: Where in both the equations, rh is the interest in home country rf is the interest in foreign country f1 is the forward rate in terms of home currency price of foreign currency e0 is the spot rate in terms of home currency price of foreign currency

12. Example: Assume four things: the Swiss interest rate is 9% and the US interest rate is 7%. The spot rate for Swiss franc is $0.4000 and the 180 day forward rate for the Swiss franc is $0.3960. In this case the percentage discount on the 180-day forward rate is equal to the interest rate differential:

13. The forward rate and the future spot rate: • If speculators think that a forward rate is higher than their prediction of a future spot rate, they will sell the foreign currency forward. This speculative transaction will bid down the forward rate until it equals the expected future spot rate. By the same token, if speculators believe that a forward rate is lower than an expected future spot rate, they will buy a foreign currency forward.

14. Synthesis of International Parity Conditions: Let us assume the followings: • The current spot rate for the Swiss franc: SF1 = $0.5000 • The one year forward rate for the Swiss franc: SF1 = $0.4750 • The expected spot rate in one year for the Swiss franc: SF1 = $0.4750 • The expected inflation for one year: in Switzerland = 10%, in US = 5% • Interest rates on one year govt. securities: Switzerland = 12%, in US = 7% Using the above information, discuss international parity relationship among spot rate, forward rate, inflation rate and interest rate using four assumptions: (a) PPP theory (b) the Fisher effect (c) the International Fisher effect and (d) the interest rate parity theory.

15. PPP Theory: • Holds that any change in the differential rate of inflation between two countries tends to be offset by an equal but opposite change in the spot rate. A 5% higher rate in Switzerland is offset by a 5% depreciation in the spot rate in the franc. This 5% depreciation in the spot rate for the franc is computed as follows: • Percentage change = (ending rate – beginning rate) / beginning rate • (0.4750 – 0.5000) / 0.5000 = - 0.05 or – 5%

16. The Fisher Effect: • The Fisher effect suggests that real interest rates are identical everywhere and that nominal interest rates will vary by the difference in expected rates of inflation. The real inflation adjusted interest rate in both countries is computed by equation: • Nominal rate = real rate + inflation • For US: 7% = Real rate + 5%; So, Real rate = 2% • For Switzerland: 12% = Real rate + 10%; So, Real rate = 2%

17. The international Fisher effect states that a future spot rate should move in an amount equal to, but in the opposite direction from, the difference in the interest rate between two countries. The 5% interest differential in favour of Switzerland is equal to the 5% depreciation in the future spot rate for the franc.

18. Interest Rate Parity: According to the interest rate parity theory, the spread (difference) between a forward rate and a spot rate should be equal to the difference between domestic interest rate and a foreign interest rate