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Lecture 7: The Forward Exchange Market. Determining the Appropriate Forward Exchange Quote: The Interest Rate Parity Model. Where is this Financial Center?. Pudong , Shanghai: The Bund and the Oriental Pearl Tower. Shanghai Foreign Exchange Trade Center (1901).

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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



Pudong shanghai the bund and the oriental pearl tower
Pudong, Shanghai: The Bund and the Oriental Pearl Tower



China s foreign exchange trade system
China’s Foreign Exchange Trade System

  • China’s Foreign Exchange Trade System (CFETS) was founded in April 1994 as part of China’s FX reforms. Today CFETS plays a significant role in managing the Yuan exchange rate.

  • CFETS is a sub-institution of the People's Bank of China (PBC). Its main foreign exchange functions include: providing a system for foreign exchange trading; organizing interbank FX trading, providing information on the FX, market; and engaging in other businesses authorized by the PBC.

  • CFETS is headquartered in Shanghai.



How do market makers determine the forward exchange rate
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.


  • Consider cross border investing
    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.


    Risk of investing cross border
    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 (open position).

      • 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%).


    Solution to the currency risk for the u s investor
    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 (a short position).

      • 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).


    Calculating the u s dollar equivalent of the maturing aud government bond when covered
    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:

      ______________________


    Answer u s dollar equivalent of the maturing aud government bond
    Answer: U.S. Dollar Equivalent of the Maturing AUD Government Bond

    • Amount of AUD to be received in 1 year from maturing bonds:

      • Par value = AUD1,000 x 100 = AUD100,000

      • Interest (5.5% coupon) = 100,000 x 0.055 = AUD5,500

      • Total received = AUD105,500 (to be sold forward)

        • Exchange rates:

        • AUD/USD spot 1.0005/1.0009

        • AUD/USD 1 year forward 0.9650/0.9657

    • USD covered amount (to be received in 1 year) = AUD105,500 x 0.9650 = USD101,807.50


    Concept of covered return
    Concept of Covered Return Government Bond

    • 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 (as a %) to the U.S. investor?


    Calculating the covered return
    Calculating the Covered Return Government Bond

    • 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,

      • So given:

      • AUD/USD spot 1.0005/1.0009

      • AUD/USD 1 year forward 0.9650/0.9657

    • USD Purchase Price = AUD100,000 x 1.0009 = USD100,090

    • USD Hedged Equivalent Cash Inflow in 1 year = AUD105,500 x 0.9650 = 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.


    Another example of a covered return
    Another Example of a Covered Return Government Bond

    • 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


    Answer to jgb covered return
    Answer to JGB Covered Return Government Bond

    • 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)

        • Ask is the price at which the bank will sell you dollars.

    • 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%)


    Covered interest arbitrage
    Covered Interest Arbitrage Government Bond

    • 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.


    Explanation for covered interest arbitrage opportunities
    Explanation for Covered Interest Arbitrage Opportunities Government Bond

    • 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.


    The appropriate forward exchange rate and the interest rate parity model
    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.




    Irp october 16 2012
    IRP: October 16, 2012 Parity Model


    Irp october 16 20121
    IRP: October 16, 2012 Parity Model


    Irp october 16 20122
    IRP: October 16, 2012 Parity Model


    How is the forward rate calculated
    How is the Forward Rate Calculated? Parity Model

    • Market maker banks calculate their quoted forward rate is calculated from three observable numbers:

      • 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 (sometimes called euro-deposit rates). Large global banks quote each other and clients market interest rates in a range of currencies.


    Example october 11 2012
    Example: October 11, 2012 Parity Model

    • http://www.forexpros.com/rates-bonds/forward-rates


    Forward rate pips off of spot
    Forward Rate Pips off of Spot Parity Model

    EUR Selling at a Forward Premium

    CAD Selling at a Forward Discount


    Forward rate formula for european terms quote currencies
    Forward Rate Formula for European Terms Quote Currencies Parity Model

    • 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


    Example solving for the forward european terms exchange rate
    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.

      • FTet = Set x [(1 + INTf) / (1 + INTus)]


    Example solving for the forward european terms exchange rate1
    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


    Forward rate formula for american terms quote currencies
    Forward Rate Formula for American Terms Quote Currencies Rate

    • 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


    Example solving for the american terms forward exchange rate
    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:

      • FTat = Sat x [(1 + INTus) / (1 + INTf)]


    Example solving for the american terms forward exchange rate1
    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


    Appendix a

    Appendix A Rate

    Calculating the forward rate for periods less than and greater than one year


    Formulas and interest rates
    Formulas and Interest Rates Rate

    • 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.


    Forwards less than 1 year european terms
    Forwards Less Than 1 Year: European Terms Rate

    • 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)


    European terms example less than 1 year
    European Terms Example: Less than 1 year Rate

    • 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


    Forwards more than 1 year american terms
    Forwards More Than 1 Year: American Terms Rate

    • 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.


    American terms example more than 1 year
    American Terms Example: More than 1 Year Rate

    • 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)