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### The Forward Market and the Forward Exchange Rate

### Appendix A

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 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

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

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 Hedge

U.S. Firm Paying GBP 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.

- 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.

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 ArbitrageOpportunities

- 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 differencein the interest rates associated with the two currencies in the forward transaction.”
- This equilibriumforward rate is whatever forward exchange rate willinsure 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 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%

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)

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