The Forward Market and the Forward Exchange Rate
- Slides: 32
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 • USD/JPY – – Spot 1 month Forward 3 month Forward 6 month Forward Rate 1. 5833 1. 5829 1. 5822 1. 5812 83. 42 83. 39 83. 33 83. 22 Pip Difference (From Spot) - 4 - 11 - 21 - 3 - 9 -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/GBP (i. e. , European Terms): USD Selling at a Forward Premium Against the GBP $1. 5840 0. 6326 $1. 5835 0. 6324000001 $1. 5833 $1. 5830 0. 6322 $1. 5829 $1. 5825 0. 6320000004 0. 632 $1. 5820 0. 6318 $1. 5815 0. 6316 0. 6318000004 0. 6316000005 $1. 5812 $1. 5810 0. 6314 $1. 5805 0. 6312 $1. 5800 0. 631 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/USD (i. e. , American Terms): JPY Selling at a Forward Premium Against the USD 83. 45 $0. 012020 83. 42 83. 4 $0. 012017 $0. 012015 83. 39 $0. 012010 83. 35 $0. 012005 83. 33 $0. 012001 $0. 012000 83. 3 $0. 011995 83. 25 $0. 011992 $0. 011990 83. 22 83. 2 $0. 011988 $0. 011985 $0. 011980 83. 15 $0. 011975 83. 1 $0. 011970 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 1 year 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 GBP/USD 1. 5800 1. 5778 - 22 AUD/USD – Spot – 6 month Forward . 9921. 9691 -230 USD/JPY USD/CAD – Spot – 6 month Forward • • • Pip Difference (From Spot) – Spot: – 6 month Forward – Spot – 6 month Forward – F. X. Rate 81. 85 (0. 012217)** 81. 67 (0. 012245)** -18 1. 0105 (0. 9896)*** 1. 0153 (0. 9849)*** *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. +48 Interest Rate Differential* +422 -03 +85
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: 00 am, 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 = S 0 et 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) – S 0 et = 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 = S 0 et 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 = S 0 at 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) – S 0 at = 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 = S 0 at 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 = S 0 et 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) – S 0 et = 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 = S 0 at 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) – S 0 at = 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 = S 0 et 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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