International Financial Management: INBU 4200 Fall Semester 2004 Lecture 4: Part 1 International Parity Relationships: The Interest Rate Parity Model (Explaining the Forward Rate) (Chapter 5)

Forward Rates: Review Involves contracting today for the future purchase or sale of foreign exchange. –Forward rate is set today! Forward rate can be: –Equal to spot (flat) –Worth more than spot (premium) –Worth less than spot (discount)

Examples of Forward Rates Wednesday, September 8, 2004 American Terms –U.K. (Pound) $ month forward $ European Terms –Japan (yen) month forward Source: orextab.htm orextab.htm

Forward British Pound Question: Is the pound selling at a forward discount or forward premium? –U.K. (Pound) $ month forward $ Answer: –Discount: 1 month forward is less than the spot by $.0049 ($ – = ); the dollar is selling at a premium (less dollars to buy a pound forward than to buy spot).

Forward Yen Question: Is the Japanese yen selling at a forward premium or forward discount? –Japan (yen) month forward Answer: –Convert to American terms ( = $ ; = $ ). Yen 1 month forward is worth more ($ ) than the spot ($ = ). –Premium: Yen is selling at a premium ( ); Dollar is selling at a discount (the 1 month forward less than the spot by.17 yen).

What Determines the Forward Rate? What does NOT determine forward rate: –Market’s expectation about where spot rate will be in the future. What does determine forward rate: –Assuming no capital controls, in equilibrium the rate represents the difference in interest rates between the two currencies in question.

Interest Rate Parity Model What do we mean by parity? –Markets (prices) in equilibrium according to the assumptions of a given model. Interest rate parity theory provides a linkage (and explanation) between international money markets and (forward) foreign exchange markets. The theory states that the forward rate discount or premium on a foreign currency should be equal to, but opposite in sign to, the difference in the national interest rates for securities of similar risk and maturity.

Cross Border Investing: Risk Assume a US dollar-based investor has $1 million to invest for 90 days and can select from two investments: –Invest in the U.S. and earn 4.0% p.a. –Invest in Switzerland and earn 8.0% p.a. What is the risk with Swiss franc investment? –U.S. investor will receive Swiss francs in 90 days. –Risk is the uncertainty about the future Swiss franc spot rate. –If the franc depreciates by 4% or more, this will wipe out the higher interest rate on the Swiss investment

A Solution to Currency Risk Solution for U.S. investor: –How can you manage this risk, or foreign exchange exposure (in the Swiss franc)? –Cover the Swiss franc investment by selling the anticipated Swiss francs forward 90 days. Anticipated amount would be equal to the principal repayment plus earned interest. Issue –What will the forward rate on francs to be delivered in 90 days be? –This will determine the “covered” investment return.

Forward Rate and Interest Rate Parity In equilibrium, the forward rate must settle at a rate to offset the interest rate differential between the two countries (i.e., currencies) in question. –This is the interest rate parity model. This forward rate offset is to insure that the two investments (U.S. and Switzerland) will yield similar returns when covered. –If the forward rate did not offset the interest rate differential, investors could cover and earn higher returns than at home. –Thus, the offset prevents covered interest arbitrage opportunities.

Covered Interest Arbitrage Assume: –90 day Interest rate in U.S. is 4% –90 day Interest rate in Switzerland is 8% Assume the spot rate and the 90 day forward rate are the same. –The Swiss franc is selling flat of its spot. A U.S. investor could invest in Switzerland, and cover (sell francs forward) and obtain a (foreign exchange) riskless return of 8% which is 400 basis points greater than investing in the U.S. This is covered interest arbitrage!

In Equilibrium In equilibrium the forward rate will price the currency’s forward rate to offset the interest rate differential. In the previous example, the “correct,” or equilibrium, 90 day forward Swiss franc rate will be at a discount of 4% of its spot. Thus, when the U.S. investor covers (sells the francs forward), the 8% Swiss return is reduced by the 4% discount, resulting in a covered return of 4%. –This is equal to the return the U.S. investors would get at home.

90 days S = SF /$ SF 1,480,000 Dollar money market $1,000,000$1,010,000  1.01 StartEnd i $ = 4.00 % per annum (1.00 % per 90 days) Swiss franc money market SF 1,509,600  1.02 i SF = 8.00 % per annum (2.00 % per 90 days) Viewing Interest Rate Parity F 90 = SF ?/$ $1,010,000

90 days S = SF /$ SF 1,480,000 Dollar money market $1,000,000$1,010,000  1.01 StartEnd i $ = 4.00 % per annum (1.00 % per 90 days) Swiss franc money market SF 1,509,600  1.02 i SF = 8.00 % per annum (2.00 % per 90 days) Forward Market Equilibrium F 90 = SF /$ $1,010,000

How is the Forward Rate Calculated? The forward rate is calculated from three observable elements: –The (current) spot rate. Use quote in European terms Convert American terms to European terms –Reciprocal of American Terms quote –The foreign currency deposit rate. –The home (U.S.) currency deposit rate. Note: The maturities of the deposit rates should be equal to the calculated forward rate period.

Forward Rate Formula for European Terms Quote Where: F n = forward rate (FC/$), n business days in the future. S = spot rate in European terms (FC/$) N = number of days in forward contract i FC = interest rate on foreign currency deposit i $ = interest rate on U.S. dollar deposit

Example #1 Assume: –Current Yen Spot rate = ¥ –90 day dollar deposit rate = 2.0% –90 day yen deposit rate =.5% Calculate the 90-day yen forward rate

Solution to Example #1

Calculated Yen Forward At ¥ is the 90 day forward yen selling at a discount or premium of its spot (120)? Answer: –At a premium Why? –Premium on the forward yen is offsetting the lower interest rate on yen deposits (relative to U.S. deposits).

Solution to Swiss Franc Example Recall, the following information about the Swiss franc example: –Swiss franc spot rate of Sfr1.4800/$, –a 90-day Swiss franc deposit rate of 8.00% –a 90-day dollar deposit rate of 4.00%.

Swiss Franc Forward At Sfr1.4947is the 90 day forward Swiss franc selling at a discount or premium of its spot (1.4800)? Answer: –At a discount Why? –Discount on the forward franc is offsetting the higher interest rate on Swiss franc deposits (relative to U.S. deposits).

Covered Interest Arbitrage If the forward rate is not correct, the chance of covered interest arbitrage exists. Generally, these situations will not last long. As the market participants take advantage of them, equilibrium will be restored. –Through adjustments in the forward rates.

90 days S = SF /$ SF 1,480,000 Dollar money market $1,000,000$1,010,000  1.01 StartEnd i $ = 4.00 % per annum (1.00 % per 90 days) Swiss franc money market SF 1,509,600  1.02 i SF = 8.00 % per annum (2.00 % per 90 days) Assume the forward rate is Then, the covered Swiss investment yields $1,020,000, $10,000 more than the U.S. investment. Example of Covered Interest Arbitrage F 90 = SF /$ $1,020,000 *

Using the Interest Rate Parity Model to Forecast Future Spot Rates While the forward rate under the assumption of the Interest Rate Parity model assumes: –The forward rate simply represents interest rate differentials –And NOT the market’s view of the future spot rate. Some forecasters do use this model to forecast future spot rates.

Forward Rates as an Unbiased Predictor Some forecasters believe that the forward rate is an “unbiased” predictor of the future spot rate. This is roughly equivalent to saying that the forward rate can act as a prediction of the future spot exchange rate, but – it will generally “miss” the actual future spot rate – and it will miss with equal probabilities (directions) and magnitudes (distances) which offset the errors of the individual forecasts!

Forward Rates: Unbiased Predictor S1S1 Exchange rate Time t 2 t 3 t 4 t 1 S2S2 S3S3 S4S4 Error F2F2 F1F1 F3F3 The forward rate available today (F t,t+ 1), time t, for delivery at future time t+1, is used as a “predictor” of the spot rate that will exist at that day in the future. Therefore, the forecast spot rate for time S t2 is F 1 ; the actual spot rate turns out to be S 2. The vertical distance between the prediction and the actual spot rate is the forecast error. When the forward rate is termed an “unbiased predictor,” it means that the forward rate over or underestimates the future spot rate with relatively equal frequency and amount, therefore it misses the mark in a regular and orderly manner. Over time, the sum of the errors equals zero.