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
–
–
–
–
Spot:
1 month Forward
3 month Forward
6 month Forward
Rate
Pip Difference (From Spot)
1.5833
1.5829
1.5822
1.5812
- 4
- 11
- 21
83.42
83.39
83.33
83.22
- 3
- 9
-20
• USD/JPY
–
–
–
–
Spot
1 month Forward
3 month Forward
6 month Forward
• Source: Wall Street Journal:
http://online.wsj.com/mdc/public/page/2_3021-forex.html
Forward Discounts and Premiums
GBP/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
$1.5835
0.6326
$1.5833
$1.5830
0.6324
$1.5829
$1.5825
0.6324
0.6322
$1.5822
$1.5820
0.632
$1.5815
0.6318
0.632
0.6318
$1.5812
$1.5810
0.6316
$1.5805
0.6314
$1.5800
0.6316
0.6312
Spot
1-mos forward 3-mos forward 6-mos forward
Spot
1-mos forward 3-mos forward 6-mos forward
Forward Discounts and Premiums
USD/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
83.45
$0.012020
$0.012017
83.42
83.4
$0.012015
83.39
$0.012010
83.35
$0.012005
83.33
$0.012001
$0.012000
83.3
$0.011995
$0.011992
83.25
$0.011990
$0.011988
83.22
$0.011985
83.2
$0.011980
83.15
$0.011975
83.1
$0.011970
Spot
1-mos forward 3-mos forward 6-mos forward
Spot
1-mos forward 3-mos forward 6-mos forward
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
– Spot:
– 6 month Forward
Complete Quote
1.5833 1.5836
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 Hedge
U.S. Firm Paying GBP in 6
Months
U.S. firm Receiving GBP in 6
Months
• U.S. firm has a GBP liability due in
6 months.
• Problem with an “uncovered”
position.
• U.S. firm has a GBP receivable
which will be paid 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.
– 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
•
GBP/USD
– Spot:
– 6 month Forward
1.5800
1.5778
Pip Difference
(From Spot)
Interest Rate
Differential*
- 22
+42
•
AUD/USD
– Spot
– 6 month Forward
.9921
.9691
-230
+422
•
USD/JPY
– Spot
– 6 month Forward
81.85 (0.012217)**
81.67 (0.012245)** -18
-03
–
USD/CAD
– Spot
– 6 month Forward
1.0105 (0.9896)***
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 = 82.00
6 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 .9997
FTet = 81.9795
Example #2 (More than 1 year)
• Assume:
GBP/USD spot = 1.5800
5 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 years
FTat = 1.5800 x ((1 + 0.0107)5/(1 + 0.0105)5)
FTat = 1.5800 x (1.05466/1.05361)
FTat = 1.5800 x 1.001
FTat = 1.5816 (Note: This is the forward 5 year rate)