International Financial Management: INBU 4200

Fall Semester 2004Lecture 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) $1.7867• 1 month forward $1.7818

• European Terms– Japan (yen) 109.30

• 1 month forward 109.13

• Source: http://online.wsj.com/documents/mktindex.htm?forextab.htm

Forward British Pound

• Question: Is the pound selling at a forward discount or forward premium?– U.K. (Pound) $1.7867

• 1 month forward $1.7818

• Answer:– Discount: 1 month forward is less than the spot by

$.0049 ($1.7818 – 1.7867 = -.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) 109.30

• 1 month forward 109.13

• Answer:– Convert to American terms (109.30 = $.009149;

109.13 = $.009163). Yen 1 month forward is worth more ($.000014) than the spot ($.009163 - .009149 = +.000014).

– Premium: Yen is selling at a premium (.000014); 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 daysS = SF 1.4800/$

SF 1,480,000

Dollar money market

$1,000,000 $1,010,000 1.01Start End

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

F90 = SF ?/$

$1,010,000

90 daysS = SF 1.4800/$

SF 1,480,000

Dollar money market

$1,000,000 $1,010,000 1.01Start End

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

F90 = SF 1.49465/$

$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:Fn = forward rate (FC/$), n business days in the future.S = spot rate in European terms (FC/$)N = number of days in forward contractiFC = interest rate on foreign currency depositi$ = interest rate on U.S. dollar deposit

360N x i 1

360N x i 1

x S F$

FC

FC/$FC/$n

Example #1• Assume:

– Current Yen Spot rate = ¥120.0000– 90 day dollar deposit rate = 2.0%– 90 day yen deposit rate = .5%

• Calculate the 90-day yen forward rate

36090 x i 1

36090 x i 1

x S F$

FC

FC/$FC/$90

Solution to Example #1

1.005 .00125 1 x S F 120/$FC/$

90 119.5522 FFC/$90

36090 x i 1

36090 x i 1

x S F$

FC

FC/$FC/$90

36090 x .020 1

36090.005x 1

x S F 120/$FC/$90

Calculated Yen Forward

• At ¥119.5522 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%.

$Sfr1.4947/ 1.011.02 x Sfr1.4800

36090 x 0.04 1

36090 x 0.08 1

xSfr1.4800 Sfr/$90F

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 daysS = SF 1.4800/$

SF 1,480,000

Dollar money market

$1,000,000 $1,010,000 1.01Start End

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 1.48. Then, the covered Swiss investment yields $1,020,000, $10,000 more than the U.S. investment.

Example of Covered Interest Arbitrage

F90 = SF 1.4800/$

$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 anUnbiased 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

S1

Exchange rate

Time

t 2 t 3 t 4 t 1

S2

S3

S4

Error

F2

F1

Error F3

Error

The forward rate available today (Ft,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 St2 is F1; the actual spot rate turns out to be S2. 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.