The Forward Market and the Forward Exchange Rate

Understanding the use of the forward market and what determines the

“equilibrium” forward exchange rate

Foreign Exchange Rate Quotes

• Recall that exchange rates can be quoted for two possible settlement dates:– Immediate settlement (actually 1 or 2 business

days): Call the Spot Rate.– Settlement at some date in the future: Call the

Forward Rate.

Examples of Spot and Forward Quotes

• Monday, October 4, 2010

• GBP/USD Rate Pip Difference (From Spot)– Spot: 1.5833– 1 month Forward 1.5829 - 4– 3 month Forward 1.5822 - 11– 6 month Forward 1.5812 - 21

• USD/JPY– Spot 83.42– 1 month Forward 83.39 - 3– 3 month Forward 83.33 - 9– 6 month Forward 83.22 -20

• Source: Wall Street Journal: http://online.wsj.com/mdc/public/page/2_3021-forex.html

Forward Discounts and PremiumsGBP/USD (i.e., American Terms): GBP Selling at a Forward Discount Against the USD

USD/GBP (i.e., European Terms): USD Selling at a Forward Premium Against the GBP

Forward Discounts and PremiumsUSD/JPY (i.e., European Terms): USD Selling at a Forward Discount Against the JPY

JPY/USD (i.e., American Terms): JPY Selling at a Forward Premium Against the USD

The Forward Exchange Market• The forward exchange market is a commercial bank

provided over-the-counter market.– Large market maker banks quote bid and ask prices for

various currencies as they receive requests.• Bid at which they will buy “base” currency (against the “quote”

currency) and ask at which they will sell the “base” currency (against the “quote” currency).

– Quotes given are specific to time periods as requested by bank customers.• Thus, forward contracts (i.e., forward time period) are “tailored”

to the specific needs of bank clients– Popular journal newspapers publish forward quotes for set

time periods.• For Example: Wall Street Journal: 1, 3 and 6 months forward.

Forward Quote Example• GBP/USD Complete Quote– Spot: 1.5833 1.5836– 6 month Forward 1.5812 1.5816

• Thus the market maker will:– Buy 1 GPB spot at $1.5833 and sell 1 GPB spot at

$1.5836.– Or:– Buy 1 GBP 6 months from now at $1.5812 and sell 1

GBP 6 month from now at $1.5816.• Recall: The GBP is selling at a 6 month forward

discount.

Using the Forward Market to HedgeU.S. Firm Paying GBP in 6 Months• U.S. firm has a GBP liability due in

6 months.• Problem with an “uncovered”

position.– If the GBP strengthens in 6

months, it will cost more in USD to pay the liability.

• U.S. company “locks” in the USD cost of the GBP liability by buying GBP 6 months forward at the forward rate quoted.– $1.5816 in previous example

• The U.S. firm has “covered” (i.e., hedged) its GBP liability due in 6 months.

U.S. firm Receiving GBP in 6 Months• U.S. firm has a GBP receivable

which will be paid in 6 months.• Problem with an “uncovered”

position:– If the GBP weakens in 6 months,

the U.S. firm will receive less USD.• U.S. company “locks” in the USD

return of the GBP receivable by selling GBP 6 months forward at the forward rate quoted.– $1.5812 in the previous example

• The U.S. firm has “covered” (i.e., hedged) its GBP 6 month receivable.

So What Determines the Forward Exchange Rate?

• First: What does NOT determine the forward exchange rate?– Where market makers think the exchange rate will be

in the future.• Lloyds Bank, UK (Corporate Banking and Treasury Training

Publication) : “Forward rates .. are not the dealer's [i.e., market maker bank’s] opinion of where the spot rate will be at the end of the period quoted.”

• So what determines the forward rate?– Quick answer: Interest rate differentials between

currencies being quoted, or the Interest Rate Parity Model.

But Why do Interest Rate Differentials Determine the Forward Rate?

• To answer this question, we need to work our way through the following example:

• Assume a U.S. investor has $1 million to invest for 1 year and can select from either of the following 1 year investments:– Invest in a U.S. government bond and earn 4.0% p.a.– Invest in an Australian government bond and earn 7.0% p.a.

• If the U.S. investor invests in Australian government bonds, he/she will receive a known amount of Australian dollars in 1 year when the bond matures.– Principal repayment and interest payment both in AUD.

Risk of Investing Cross Border• Question: What is the risk for the U.S. investor if

he/she buys the 1 year Australian government bond?• Answer: Risk comes about because the U.S. investor

has taken on a foreign exchange exposure in Australian dollars.– The U.S. investor will be paid a specified amount of

Australian dollars 1 year from now:• The risk is the uncertainty about the Australian dollar spot rate 1year

from now.– If the Australian dollar weakens, the U.S. investor will receive

fewer U.S. dollars at maturity:• In the example, if the Australian dollar depreciates by 3% or more, this

will offset the relatively higher interest rate on the Australian investment (7% versus 4%).

The Solution to The Currency Risk for the U.S. Investor

• Question: How can the U.S. investor manage the risk associated with this Australian dollar transaction exposure?

• Solution:– The US investor can cover the Australian dollar investment by selling

Australian dollars 1 year forward.• Australian dollar amount to be sold forward would be equal to the principal

repayment plus earned interest (this is a known amount to be received in 1 year).

• Thus, the forward exchange rate will determine the “covered” (i.e.., hedged) investment return for the U.S. investor.

• Question: What will the market maker quote as the forward rate on Australian dollars? – This will determine what the U.S. investor receive in US dollars 1 year

from now?

Concept of a Covered Return• The covered return is what an investor will earn after the

foreign exchange risk has been hedged (i.e., covered).• The covered return is equal to:

– The local currency return on an investment adjusted by the cost of covering (with a forward contract).

• Examples:– (1) If a 1 year investment in the United Kingdom is 7% in local currency

terms and– The British pound is selling at a 1 year discount of 3%, then– The investment’s covered 1 year return would be equal to 4% (i.e., 7% –

3%) for a U.S. dollar based investor.– (2) Or if a Japanese yen 1 year investment return is 2% and the yen is

selling at a 1 year premium of 5%, then:– The investment’s covered 1 year return would be 7% (i.e., 2%+5%) for a

U.S. dollar based investor.

Concept of Covered Interest Arbitrage • Covered interest “arbitrage” results when an investor can

secure a higher covered return on a foreign investment compared to the return in the investor’s home market.

• As an example assume: – 1 year interest rate in U.S. is 4%– 1 year interest rate in Australia is 7%– Assume the Australian dollar 1 year forward rate is trading at

a discount of 2%.• In this case, a U.S. investor could invest in Australia, – And cover (sell Australian dollars forward) and– Obtain a riskless return of 5% (7% - 2%) – Which is 100 basis points greater than investing at home in

the U.S. (covered return of 5% versus U.S. return of 4%)• This is covered interest arbitrage: earning more (when

covering) than the rate at home.

Market Makers Responding to Covered Interest Arbitrage Opportunities

• If the forward rate is not priced correctly, the chance of covered interest arbitrage exists.

• As the market participants take advantage of covered interest arbitrage opportunities, market maker banks will respond and restore equilibrium through adjustments in their forward rate quotes.– In the previous example, market makers will adjust the 1 year

forward discount on Australian dollars to 3%, thus– Producing a covered Australian dollar investment equal to the

U.S. investment (i.e., both at 4%):• US rate = 4%; Australian covered = 4% = 7% - 3%• Note: The cost of the forward is equal, but opposite in sign,

to the interest rate differential.• The adjustment of the forward exchange rate to the interest

rate differential is referred to as interest rate parity.

The Forward Exchange Rate and the Interest Rate Parity Model

• The “equilibrium” forward exchange rate is explained by the Interest Rate Parity (IRP) model.

• The Interest Rate Parity Model states:– “That in equilibrium the forward rate on a currency

will be equal to, but opposite in sign to, the difference in the interest rates associated with the two currencies in the forward transaction.”

• This equilibrium forward rate is whatever forward exchange rate will insure that the two cross border investments will yield similar returns when covered.

• Question: If interest rate parity does exists, why do global investors ever invest overseas?

Forwards and Interest Rate Differentials• Wednesday, October 13, 2010• Wall Street Journal and FXStreet.com

F.X. Rate Pip Difference Interest Rate• GBP/USD (From Spot) Differential*

– Spot: 1.5800– 6 month Forward 1.5778 - 22

+42• AUD/USD

– Spot .9921– 6 month Forward .9691 -230 +422

• USD/JPY– Spot 81.85 (0.012217)**– 6 month Forward 81.67 (0.012245)** -18 -03

– USD/CAD– Spot 1.0105 (0.9896)***– 6 month Forward 1.0153 (0.9849)*** +48 +85

• *Foreign T-Bill Rate – U.S. T-Bill Rate (in basis points.• **JPY/USD = Exchange rate in American Terms.• ***CAD/USD = Exchange rate in American Terms.

Test of the Interest Rate Parity Model: 1974-1992, 3-month rates

Test of Interest Rate Parity, 2004 Data: Forward Premium or Discount of Foreign Currency Against USD

How is the Forward Rate Calculated?• The forward rate is calculated from three observable

numbers:– The (current) spot rate.– The foreign currency interest rate.– The home currency interest rate.

• Note: The maturities of the interest rates must be equal to the calculated forward rate period (i.e., maturity of the forward contract).– What interest rates are used? – The international money market rates known as LIBOR, or

“borrowing” rates for currency deposits in the London interbank market are used.

– LIBOR is the deposit rate (interest rate) for offshore currencies as set in London.

LIBOR Market• LIBOR rate (or offer or ask rate) : Interbank market in London where

large global banks quote interest rates at which they will sell (called the offer rate).

• LIBID: Interbank market in London where large global banks quote interest rates at which they will also a buy (called the bid rate) foreign currency deposits.– Of the two, the LIBOR is regarded as the more important, as this

represents the costs of funds for banks in need of foreign currency deposits.

• LIBOR rates are “set” each day in London by 8 to 16 global banks for 10 different currencies shortly after 11:00am, London time.– For a list of banks see:

http://www.bba.org.uk/bba/jsp/polopoly.jsp?d=141– And link to LIBOR panel (note: 16 banks are involved in setting US

dollar Libor)

Forward Rate Formula for European Terms Quote Currencies

• The formula for the calculation of the equilibrium European terms forward foreign exchange rate is as follows:

• FTet = S0et x [(1 + IRf) / (1 + IRus)] – Where: – FT = forward foreign exchange rate at time period T (expressed

as units of foreign currency per 1 U.S. dollar; thus European terms, or et)

– S0et = today's European terms spot foreign exchange rate (i.e., number of units of the foreign currency per 1 U.S. dollar)

– IRf = foreign interest rate (LIBOR) for a maturity of time period T – IRus = U.S. interest rate (LIBOR) for a maturity of time period T

Example: Solving for the Forward European Terms Exchange Rate

• Assume the following data:– USD/JPY spot = ¥120.00– Japanese yen 1 year (LIBOR) interest rate = 1%– US dollar 1 year (LIBOR) interest rate = 4%

• Calculate the 1 year yen forward exchange rate:– FTet = S0et x [(1 + INf) / (1 + INus)]– FTet = ¥120 x [(1 + .01) / (1 + .04)]– FTet = ¥120 x .971153846– FTet = ¥116.5384615

Evaluating the Forward Yen Example• Question: – At ¥116.5385 is the 1 year forward yen selling at a

discount or premium of its spot (¥120)?• Answer:– At a premium

• Question: Why is there a premium on the 1 year forward yen?– A premium on the forward yen occurs to offset the

lower interest rate on Japanese yen investments (measured by LIBOR).

– Japan = 1.0% and the U.S. 4.0%

Forward Rate Formula for American Terms Quote Currencies

• The formula for the calculation of the equilibrium American terms forward foreign exchange rate is as follows:

• FTat = S0at x [(1 + IRus) / (1 + IRf)] – Where:– FT = forward foreign exchange rate at time period T (expressed

as the amount of 1 U.S. dollar per 1 unit of the foreign currency; thus American terms, or at)

– S0at = today's American terms spot foreign exchange rate (i.e., USD per 1 unit of the foreign currency)

– IRus = U.S. interest rate for a maturity of time period T – IRf = Foreign interest rate for a maturity of time period T

Example: Solving for the American Terms Forward Exchange Rate

• Assume the following data:– GPB/USD spot = $1.9800– UK 1 year (LIBOR) interest rate = 6%– US dollar 1 year (LIBOR) interest rate = 4%

• Calculate the 1 year pound forward exchange rate:– FTat = S0at x [(1 + IRus) / (1 + IRf)]– FTat = $1.9800 x [(1 + .04) / (1 + .06)]– FTat= $1.9800 x .9811– FTat = $1.9436

Evaluating the Forward Pound Example• Question: – At $1.9436 is the 1 year forward pound selling at a

discount or premium of its spot ($1.9800)?• Answer:– At a discount

• Question: Why is there a discount on the 1 year pound forward?– A discount on the forward pound occurs to offset the

higher interest rate on British pound investments (measured by LIBOR).

– U.K. = 6.0% and the U.S. 4.0%

Appendix A

Calculating the forward rate for periods less than and greater than

one year

Background• The formulas used to date, calculate the forward

exchange rate 1 year forward.• The following slides illustrate how to adjust the

formula and data for periods other than 1 year.• Important:– All interest rates quoted in financial markets

(including LIBOR) are on an annual basis, thus and adjustment must be made to allow for other than annual interest periods.

– Most forward contracts are for 1 year or less.• LIBOR rates are only set for 1 year maturities.

Forwards Less Than 1 year• FTet = S0et x [(1 + ((IRf) x n/360)) / (1 + ((IRus) x n/360))]

– Where: – FT = forward foreign exchange rate at time period T (expressed as

units of foreign currency per 1 U.S. dollar; thus European terms, or et) – S0et = today's European terms spot foreign exchange rate (i.e.,

number of units of the foreign currency per 1 U.S. dollar) – IRf = foreign interest rate (LIBOR) for a maturity of time period T – IRus = U.S. interest rate (LIBOR) for a maturity of time period T– n = number of days in the forward contract.

• FTat = S0at x [(1 + ((IRus x n/360)) / (1 + ((IRf x n/360))] – Where:– FT = forward foreign exchange rate at time period T (expressed as the

amount of 1 U.S. dollar per 1 unit of the foreign currency; thus American terms, or at)

– S0at = today's American terms spot foreign exchange rate (i.e., USD per 1 unit of the foreign currency)

– IRus = U.S. interest rate for a maturity of time period T – IRf = Foreign interest rate for a maturity of time period T– n = number of days in the forward contract.

Example #1 (Less than 1 year)• Assume:

USD/JPY spot = 82.006 month JYP LIBOR = 0.12%*6 month USD LIBOR = 0.17%**Annualized interest rates

• Calculate the 6 month forward yen:• FTet = S0et x [(1 + ((IRf) x n/360))/ (1 + ((IRus) x n/360))]

Ftet = 82.00 x [(1 + ((0.0012 x 180/360))/((1 + ((0.0017 x 180/360))] FTet = 82.00 x (1.0006/1.00085)FTet = 82.00 x .9997FTet = 81.9795

Example #2 (More than 1 year)• Assume:

GBP/USD spot = 1.58005 year GBP interest rate = 1.05%*5 year USD interest rate = 1.07%**Annualized interest rates on Government securities.Calculate the 5 year forward pound:FTat = Soat x ((1 + IRus)n/(1 + IRf)n)Where: n = number of yearsFTat = 1.5800 x ((1 + 0.0107)5/(1 + 0.0105)5) FTat = 1.5800 x (1.05466/1.05361) FTat = 1.5800 x 1.001FTat = 1.5816 (Note: This is the forward 5 year rate)