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Lecture 7: The Forward Exchange Market

Lecture 7: The Forward Exchange Market. Determining the Appropriate Forward Exchange Quote: The Interest Rate Parity Model. Where is this Financial Center?. How do Market Makers Determine the Forward Exchange Rate?.

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Lecture 7: The Forward Exchange Market

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  1. Lecture 7: The Forward Exchange Market Determining the Appropriate Forward Exchange Quote: The Interest Rate Parity Model

  2. Where is this Financial Center?

  3. How do Market Makers Determine the Forward Exchange Rate? • The quoted forward rate is not a reflection of where market makers think the spot exchange rate will be on that forward date . • 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. • To develop this concept, and the Interest Rate Parity Model, we will work through the following example.

  4. Consider Cross Border Investing • Assume a U.S. investor has $1 million to invest for 1 year and can select from either of the following 1 year investments: • (1) Invest in a U.S. government bond and earn 2.0% p.a. • (2) Invest in an Australian government bond and earn 5.5% 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.

  5. Risk of Investing Cross Border • Question: Using the previous example, what is the risk for the U.S. investor if he/she buys the 1 year Australian government bond? • Answer: The risk associated with foreign exchange exposure in AUD. • 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 (spot) weakens, the U.S. investor will receive fewer U.S. dollars at maturity: • Example: If the Australian dollar weakened by 2% by the end of the year, this reduces the return on the Australian investment (from 5.5 % to 3.5%).

  6. Solution to The Currency Risk for the U.S. Investor • Question: Using the previous example, how could the U.S. investor manage the risk associated with this Australian dollar exposure? • Solution: The US investor can cover the Australian dollar investment by selling Australian dollars 1 year forward. • Australian dollar amount which the investor will sell forward would be equal to the principal repayment plus earned interest (Note: this was the known amount of AUD to be received in 1 year).

  7. Calculating the U.S. Dollar Equivalent of the Maturing AUD Government Bond when Covered • Assume: • A 1 year Australian Government Bond with a par value of 1,000AUD (assume you purchased 100 of these at par) • Assume an annual coupon of 5.5% (payable at the end of the year) • Assume the following market maker bank quoted exchange rates: • AUD/USD spot 1.0005/1.0009 • AUD/USD 1 year forward 0.9650/0.9657 • Calculate the USD covered amount when the bond matures: ______________________

  8. Concept of Covered Return • The covered return (i.e., hedged return) on a cross border investment is the return after the investment’s foreign exchange risk has been covered with the appropriate forward contract. • The forward exchange rate will determine the “covered” investment return for the U.S. investor. • In the previous example, how would you determine the covered return to the U.S. investor?

  9. Calculating the Covered Return • Answer: Calculate the yield to maturity on the investment when covered. • Note: Yield to Maturity is the internal rate of return (IRR), or the discount rate that sets the present value of the future cash inflow to the price of the investment. • USD Purchase Price = AUD100,000 x 1.0009 = USD100,090 • USD Hedged Equivalent Cash Inflow in 1 year = USD101,807.50 • Solve for the IRR (k): -100,090 = 101,807.50/(1+k) • http://www.datadynamica.com/IRR.asp • k = 1.72% (Why is this different from the 5.5%) • Answer: Because AUD is selling at a 1 year forward discount.

  10. Another Example of a Covered Return • Assume the following: • A 1 year Japanese Government Bond with a coupon of 1%. • Par value of 100,000 yen and selling at par. • Exchange Rates: • USD/JPY spot: 76.61/76.65 • 1 year forward: 73.50/73.55 • Calculate the covered return for a U.S. investor on the above JGB

  11. Answer to JGB Covered Return • Step 1: Calculate the USD purchasing price of the JGB: • 100,000/76.61 (note this is spot bid) = 1305.31 • Step 2: Calculate the yen inflow expected in 1 year: • 100,000 x 1.01 = 101,000 (note: coupon rate is 1%) • Step 3: Calculate the USD equivalent of the 1 year yen inflow using a forward contract. • 101,000/73.55 = 1373.22 (note this is 1 year ask) • Step 4: Calculate the IRR (using the web site) • -1305.31= 1373.22/(1+k); k = 5.21% (Why is this different from the 1%)

  12. Covered Interest Arbitrage • Covered interest “arbitrage” is a situation that occurs when a covered return offers a higher return than that 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% • AUD 1 year forward rate is quoted at a discount of 2%. • In this case, a U.S. investor could invest in Australia and • Cover (sell Australian dollars forward) and earn a covered return of 5% (7% - 2%) which is 100 basis points greater than the U.S. return • This is covered interest arbitrage: earning more (when covering) than the rate at home.

  13. Explanation for Covered Interest Arbitrage Opportunities • Covered interest arbitrage will exist whenever the quoted forward exchange rate is not priced correctly. • If the forward rate is priced correctly, covered interest arbitrage should not exist. • Going back to our original example: • (1) Invest in a U.S. government bond and earn 2.0%. • (2) Invest in an Australian government bond and earn 5.5% • If the AUD 1 year forward were quoted at a discount of 3.5%, then the covered return (2%) and the home return (2%) would be equal.

  14. The Appropriate Forward Exchange Rate and the Interest Rate Parity Model • The Interest Rate Parity Model (IRP) offers an explanation of the market’s correctly priced (i.e., “equilibrium”) forward exchange rate. • This equilibrium rate is the forward rate that precludes covered interest arbitrage • 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.” • Thus, the equilibriumforward rate is whatever forward exchange rate willinsure that the two cross border investments will yield similar returns when covered.

  15. Test of the Interest Rate Parity Model: 1974-1992

  16. Interest Rate Parity Model, 2004

  17. IRP: October 16, 2012

  18. How is the Forward Rate Calculated? • Market maker banks calculate their quoted forward rate is calculated from three observable elements: • The (current) spot rate. • A foreign currency interest rate. • A home currency interest rate (assume to be the U.S.). • Note: The maturities of the interest rates used should be approximately equal to the calculated forward rate period (i.e., maturity of the forward contract). • What interest rates are used? • Interbank market (wholesale) interest rates for currencies (euro-deposit rates). Large global banks continuously quote each other and clients market interest rates in a range of currencies.

  19. Example: October 11, 2012 • http://www.forexpros.com/rates-bonds/forward-rates

  20. Forward Rate Pips off of Spot EUR Selling at a Forward Premium CAD Selling at a Forward Discount

  21. 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 = Set x [(1 + INTf) / (1 + INTus)] • Where: • FTet = forward foreign exchange rate at time period T, expressed as units of foreign currency per 1 U.S. dollar; thus European terms, i.e., “et” • Set = today's European terms spot foreign exchange rate, • INTf = foreign interest rate for a maturity of time period T (expressed as a percent, e.g., 1% = 0.01) • INTus = U.S. interest rate for a maturity of time period T

  22. Example: Solving for the Forward European Terms Exchange Rate • Assume the following data: • USD/JPY spot = ¥120.00 • Japanese yen 1 year interest rate = 1% • US dollar 1 year interest rate = 4% • Calculate the 1 year yen forward exchange rate: • Set up the formula and insert data.

  23. Example: Solving for the Forward European Terms Exchange Rate • Assume the following data: • USD/JPY spot = ¥120.00 • Japanese yen 1 year interest rate = 1% • US dollar 1 year interest rate = 4% • Calculate the 1 year yen forward exchange rate: • FTet = Set x [(1 + INTf) / (1 + INTus)] • FTet = ¥120 x [(1 + .01) / (1 + .04)] • FTet = ¥120 x .971153846 • FTet = ¥116.5384615

  24. 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 = Sat x [(1 + INTus) / (1 + INTf)] • Where: • FTat = forward foreign exchange rate at time period T, expressed as the amount of 1 U.S. dollars per 1 unit of the foreign currency; thus American terms, or at) • Sat = today's American terms spot foreign exchange rate. • INTus = U.S. interest rate for a maturity of time period T (expressed as a percent, e.g., 4% = 0.04) • INTf = Foreign interest rate for a maturity of time period T

  25. Example: Solving for the American Terms Forward Exchange Rate • Assume the following data: • GPB/USD spot = $1.9800 • UK 1 year interest rate = 6% • US dollar 1 year interest rate = 4% • Calculate the 1 year pound forward exchange rate: • Set up the formula and insert data:

  26. Example: Solving for the American Terms Forward Exchange Rate • Assume the following data: • GPB/USD spot = $1.9800 • UK 1 year interest rate = 6% • US dollar 1 year interest rate = 4% • Calculate the 1 year pound forward exchange rate: • FTat = Sat x [(1 + INTus) / (1 + INTf)] • FTat = $1.9800 x [(1 + .04) / (1 + .06)] • FTat= $1.9800 x .9811 • FTat = $1.9426

  27. Appendix A Calculating the forward rate for periods less than and greater than one year

  28. Formulas and Interest Rates • The formulas used in the previous slides show you how to calculate the forward exchange rate 1 year forward. • The following slides illustrate how to adjust the forward rate formula for periods other than 1 year. • Important: • All interest rates quoted in financial markets are on an annual basis, thus and adjustment must be made to allow for other than annual interest periods.

  29. Forwards Less Than 1 Year: European Terms • FTet = Set x [(1 + ((INTf) x n/360)) / (1 + ((INTus) x n/360))] • Where: • FT = forward foreign exchange rate at time period T, expressed as units of foreign currency per 1 U.S. dollar; • Set = today's European terms spot foreign exchange rate. • INTf = foreign interest rate for a maturity of time period T • INTus = U.S. interest rate for a maturity of time period T • n = number of days in the forward contract (note: we use a 360 day year in this formula). • Note: What we have added to the original formula is an adjustment for the time period (n/360)

  30. European Terms Example: Less than 1 year • Assume: USD/JPY spot = 82.00 6 month Japanese interest rate = 0.12%* 6 month U.S. interest interest rate= 0.17%* *These are interest rates expressed on an annual basis. • Calculate the 6 month forward yen • FTet = Set x [(1 + ((INTf) x n/360))/ (1 + ((INTus) 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

  31. Forwards More Than 1 Year: American Terms • FTat = Sat x [(1 + (INTus)n / (1 + (INTf)n] • Where: • FT = forward foreign exchange rate at time period T, expressed as the amount of 1 U.S. dollars per 1 unit of the foreign currency. • Sat = today's American terms spot foreign exchange rate. • INTus = U.S. interest rate for a maturity of time period T • INTf = Foreign interest rate for a maturity of time period T • n = number of years in the forward contract.

  32. American Terms Example: More than 1 Year • Assume: GBP/USD spot = 1.5800 5 year United Kingdom interest rate = 1.05%* 5 year United States interest rate = 1.07%* *These are interest rates expressed on an annual basis. • Calculate the 5 year forward pound: FTat = Sat x ((1 + INTus)n/(1 + INTf)n) 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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