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2. Currency Forwards and Futures
 

2. Currency Forwards and Futures

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    2. Currency Forwards and Futures 2. Currency Forwards and Futures Document Transcript

    • FOREIGN CURRENCY FUTURES First, we review some aspects of the currencies cash markets with emphasis on the: Interest Rates Parity. We then review the currency futures markets with quasi-arbitrage and hedging examples.
      • FOREIGN CURRENCY: THE CASH MARKET
      • EXCHANGE RATES:
      • THE VALUE (PRICE) OF ONE CURRENCY IN TERMS OF ANOTHER CURRENCY IS THE EXCHANGE RATE BETWEEN THE TWO CURRENCIES.
      • THERE ARE TWO QUOTE FORMATS FOR QUOTATIONS:
      • S($/FC)
      • THE NUMBER OF U.S. DOLLARS IN ONE UNIT OF THE FOREIGN CURRENCY.
      • S(FC/$)
      • THE NUMBER OF THE FOREIGN CURRENCY UNITS IN ONE U.S. DOLLAR.
    • NOT TAKING INTO ACCOUNT BID-ASK SPREAD:
    • CURRENCY CROSS RATES LET FC1, FC2 AND FC3 DENOTE 3 DIFFERENT CURRENCIES. THEN IN THE ABSENCE OF ARBITRAGE OPPORTUNITIES, THE FOLLOWING EQUALITY MUST HOLD: KEY CURRENCY CROSS RATE NOV 12,1998
    • CURRENCY CROSS RATES EXAMPLE
    • AN EXAMPLE OF CROSS SPOT RATES ARBITRAGE DOLLAR POUND CHF SWITZERLAND 1.7920 2.8200 1.0000 U.K. 0.6394 1.0000 0.3546 U.S. 1.0000 1.5640 0.5580 THE CROSS RATE EQUALITIES DO NOT HOLD:
    • THE CASH ARBITRAGE ACTIVITIES: $1,000,000 $1,006,134.26 .6394 .5580 BP639,400 2.8200 CHF1,803,108
    • DETERMINANTS OF FOREIGN EXCHANGE RATES Most foreign currencies today, are determined in free exchange markets, I.e., by supply and demand without any Government intervention. In other words, the exchange rates of most countries are floating rates. Exchange rates are quoted for cash transactions as well as for forward transactions.
      • Freely floating exchange rates.
      • No central bank intervention
      • Managed floating exchange rate.
      •  The central bank takes part in the market to influence the exchange rate value.
      • Pegged exchange rate systems.
      • The value of one currency is fixed in terms of another currency, that itself floats.
      •  Again, the central bank must operate in the market to ensure the pegged rate.
    • WSJ
    • THE INTEREST RATES PARITY Wherever financial flows are unrestricted, goods’ prices, the forward prices of these goods and the interest rates in any two countries must maintain a NO- ARBITRAGE relationship. This relationship is called the Interest Rates Parity. Next, we derive the parity, using the cash-and-carry and the reverse cash-and-carry strategies.
    • NO ARBITRAGE: CASH-AND-CARRY TIME CASH FUTURES t (1) BORROW $A. r DOM (4) SHORT FOREIGN (2) BUY FOREIGN CURRENCY CURRENCY FORWARD F t,T ($/FC) A/S($/FC) [=AS(FC/$)] AMOUNT: (3) INVEST IN BONDS DENOMINATED IN THE FOREIGN CURRENCY r FOR T (3) REDEEM THE BONDS (4) DELIVER THE CURRENCY TO EARN CLOSE THE SHORT POSITION (1) PAY BACK THE LOAN RECEIVE: IN THE ABSENCE OF ARBITRAGE:
    • NO ARBITRAGE: REVERSE CASH – AND - CARRY TIME CASH FUTURES t (1) BORROW FC A. r FOR (4) LONG FOREIGN (2) BUY DOLLARS CURRENCY FORWARD F t,T ($/FC) AS($/FC) AMOUNT IN DOLLARS: (3) INVEST IN T-BILLS FOR R DOM T REDEEM THE T-BILLS TAKE DELIVERY TO CLOSE EARN THE LONG POSITION PAY BACK THE LOAN RECEIVE IN THE ABSENCE OF ARBITRAGE:
    • FROM THE CASH-AND-CARRY STRATEGY: FROM THE REVERSE CASH-AND-CARRY STRATEGY: THE ONLY WAY THE TWO INEQUALITIES HOLD SIMULTANEOUSLY IS BY BEING AN EQUALITY:
    • ON MAY 25 AN ARBITRAGER OBSERVES THE FOLLOWING MARKET PRICES: S($/BP) = 1.5640 <=> S(BP/$) = .6393 F($/BP) = 1.5328 <=> F(BP/$) = .6524 R US = 7.85% ; R GB = 12% THE THEORETICAL FORWARD PRICE IS LESS THAN THE MARKET PRICE CASH AND CARRY TIME CASH FUTURES MAY 25 (1) BORROW $100M AT 7. 85% SHORT BP 68,477,215 FORWARD FOR 209 DAYS FOR DEC. 20, FOR $1.5328/BP (2) BUY BP63,930,000 (3) INVEST THE BP63,930,000 IN BRITISH BONDS DEC 20 RECEIVE BP68,477,215 DELIVER BP68,477,215 FOR $104,961,875.2 REPAY YOUR LOAN: ARBITRAGE PROFIT: 104,961,875.2 - 104,597,484.3 = $364,390.90 NOTICE THAT : 104,597,484/68,477,215 = 1,5275, BUT THIS EXCHANGE RATE CANNOT BE GUARANTEED ON MAY 25.
    • THE INTEREST RATES PARITY So far, we derived the interest rates parity in a theoretical market. In the real markets, buyers pay the ask price while sellers receive the bid price. Moreover, borrowers pay the ask interest rate while lenders only receive the bid interest rate. Therefore, in the real markets, it is possible for the forward exchange rate to fluctuate within a band of rates without presenting arbitrage opportunities.Only when the market forward exchange rate diverges from this band of rates arbitrage exists.
    • NO ARBITRAGE: CASH - AND - CARRY TIME CASH FUTURES t (1) BORROW $A. r D,ASK (4) SHORT FOREIGN (2) BUY FOREIGN CURRENCY CURRENCY FORWARD A/S ASK ($/FC) F BID ($/FC) (3) INVEST IN BONDS DENOMINATED IN THE FOREIGN CURRENCY r F,BID T REDEEM THE BONDS DELIVER THE CURRENCY TO EARN CLOSE THE SHORT POSITION PAY BACK THE LOAN RECEIVE IN THE ABSENCE OF ARBITRAGE:
    • NO ARBITRAGE: REVERSE CASH - AND - CARRY TIME CASH FUTURES t (1) BORROW FCA . r F,ASK (4) LONG FOREIGN (2) EXCHANGE FOR CURRENCY FORWARD AS BID ($/FC) (3) INVEST IN T-BILLS FOR r D,BID FOR F ASK ($/FC) T REDEEM THE T-BILLS TAKE DELIVERY TO CLOSE EARN THE LONG POSITION PAY BACK THE LOAN RECEIVE in foreign currency. IN THE ABSENCE OF ARBITRAGE:
    • IN SUMMARY: INEQUALITY 1: INEQUALITY 2: NOTICE THAT: RHS(1) > RHS(2) RHS(2) RHS(1) . . F BID F ASK F ASK ($/FC) > F BID ($/FC). CONCLUSION: ARBITRAGE EXISTS ONLY WHEN BOTH FUTURES PRICES ARE ABOVE RHS(1) OR BOTH ARE BELOW RHS(2)
    • EXAMPLE: The following are market prices on a given day: S($/NZ) F($/NZ) R(NZ) R(US) ASK $0.4438 $0.4480 6.000% 10.8125% BID $0.4428 $0.4450 5.875% 10.6875% Clearly, F(ask) > F(bid). What remains to be checked is whether the inequalities are satisfied or not.
    • EXAMPLE: INEQUALITY 1: .4450 < (.4438)e (.108125 - .05875)/12 = .4456 RHS(2)=.4445 RHS(1)=.4456 . . . . F BID = .4450 F ASK =.4480 .4480 > (.4428)e (.106875 - .06000)/12 = .4445  NO ARBITRAGE OPPORTUNITY EXISTS. INEQUALITY 2:
    • EXAMPLE: The following are market prices on a given day: S($/NZ) F($/NZ) R(NZ) R(US) ASK $0.4431 $0.4480 6.000% 10.7025% BID $0.4428 $0.4450 5.888% 10.6875% Clearly, F(ask) > F(bid). What remains to be checked is whether the inequalities are satisfied or not.
    • EXAMPLE: INEQUALITY 1: .4450 < (.4431)e (.107025 - .05888)/12 = .4449 RHS(2)=.4445 RHS(1)=.4449 . . . F BID = .4450 F ASK =.4480 .4480 > (.4428)e (.106875 - .06000)/12 = .4445  ARBITRAGE OPPORTUNITY EXISTS. INEQUALITY 2:
    • FOREIGN CURRENCY CONTRACT SPECIFICATIONS CURRENCY SIZE MIN. MIN.F. CHANGE CHANGE JAPAN YEN 12.5M .000001 $12.50 CAN. DOLLAR 100,000 .0001 $10.00 BRITISH POUND 62,500 .0002 $12.50 SWISS FRANC 125,000 .0001 $12.50 AUSTRALIAN DOLLAR 100,000 .0001 $10.00 MEXIAN PESO 500,000 .000025 $12.50 BRAZILIAN REAL 100,000 .0001 $10.00 EURO FX 125,000 .0001 $12.50 * THERE ARE NO DAILY PRICE LIMITS * CONTRACT MONTHS FOR ALL CURRENCIES: MARCH, JUNE, SEPTEMBER, DECEMBER LAST TRADING DAY: FUTURES TRADING TERMINATES AT 9:16 AM ON THE SECOND BUSINESS DAY IMMEDIATELY PRECEEDING THE THIRD WEDNESDAY OF THE CONTRACT MONTH. DELIVERY BY WIRED TRASFER. 3RD WEDNESDAY OF CONTRACT MONTH
    • SPECULATION: TAKE RISK FOR EXPECTED PROFIT AN OUTRIGHT NAKED POSITION k - MARCH 1. S($/CD) = .6345 <=> S(CD/$) = 1.5760 t- SEPTEMBER F($/CD) = .6270 <=> F(CD/$) = 1.5949 SPECULATOR: “THE CD WILL NOT DEPRECIATE TO THE EXTENT IMPLIED BY THE SEP. FUTURES. INSTEAD, IT WILL DEPRECIATE TO A PRICE HIGHER THAN $.6270/CD.” TIME CASH FUTURES MAR 1 DO NOTHING LONG N, CD FUTURES AT $.6270/CD AUG 20 DO NOTHING SHORT N, CD FUTURES AT $.6300/CD PROFIT = ($.6300/CD - $.6270/CD)(CD100,000)(N) = $300(N).
    • INTERCURRENCY FUTURES SPREAD A FUTURES CROSS-CURRENCY SPREAD IS THE PURCHASE OF ONE CURRENCY FUTURES AND THE SIMULTANEOUS SALE OF ANOTHER CURRENCY FUTURES; BOTH FUTURES ARE FOR THE SAME DELIVERY MONTH. A POSITION TRADER OBSERVES THE FOLLOWING RATES: CROSS RATES MARCH 1: $1.7225/BP $.6369/CHF  BP.3698/CHF JUNE Fs $1.7076/BP $.6448/CHF  BP.3776/CHF (Currently: 1BP = 2.7042CHF. JUN Fs: 1BP = 2.6483CHF) SPECULATOR: “THE BRITISH POUND WILL DEPRECIATE RELATIVE TO THE SWISS FRANK BY LESS THAN WHAT IS EXPECTED ACCORDING TO THE JUNE FUTURES CROSS RATE. IN FACT, I BELIEVE THAT THE BRITISH POUND WILL APPRECIATE AGAINST THE SWISS FRANC BETWEEN NOW AND THE END OF MAY TO AROUND BP.3600/CHF OR, BP2,7778/CHF.” IN OTHER WORDS, THE SPREAD $1.7076/BP - $.6448/CHF = $1.0628 WILL INCREASE!!!! BUY THIS SPREAD! LONG THE BP JUNE FUTURES AND SIMULTANEOUSLY, SHORT THE SF JUNE FUTURES
    • TIME CASH FUTURES MAR 1 DO NOTHING SHORT 1 JUNE CHF FUTURES FOR $.6448/CHF SF Fs = 125,000CHF LONG 2 JUNE BP BP Fs = 62,5000BP FUTURES FOR $1.7076/BP SPREAD COST = $1.7076 - $.6448 = $1.0628 MAY 20 DO NOTHING CLOSE YOUR SPREAD: LONG 1 JUNE CHF FUTURES FOR $.630/CHF SHORT 2 JUNE BP FUTURES FOR $1.730/BP SPREAD REVENUE = $1.730 - $.6300 = $1.1000 PROFIT = ($1.1000 - $1.0628)(125,000) = $4,650/CONTRACT NOTICE THAT THE BP HAS APPRECIATED FROM BP.3698/CHF ( 1BP = 2.7042CHF) IN MARCH TO $.6300/CHF/$1.730/BP = BP.3642/CHF (1BP = 2.7457CHF) IN JUNE
    • BORROWING U.S. DOLLARS SYNTHETICALLY ABROAD OR HOW TO BEAT THE DOMESTIC BORROWING RATE – A CASE OF QUASI-ARBITRAGE A FIRM NEEDS TO BORROW $200M FROM MAY 25,2001 TO DECEMBER 20, 2001, FACES THE FOLLOWING DATA: SPOT: BID $.4960/NZ NZ2.0125/$ ASK $.4968/NZ NZ2.0161/$ DEC. FUTURES BID $.5024/NZ NZ1.9889/$ ASK $.5028/NZ NZ1.9904/$ INTERST RATE BID ASK r(NZ) 6.75% 6.8634% (365-DAY YEAR) r(USA) 8.50% 9.90% (360-DAY YEAR)
    • IN THE SPIRIT OF REVERSE CASH-AND-CARRY TIME CASH FUTURES MAY 25 (1) BORROW NZ403,220,000 LONG 3,355 DEC. NZ AT AN ANNUAL RATE OF FUTURES FOR F = .5028 6.8634% FOR 209 DAYS (2) EXCHANGE THE NZ403,220,000 INTO LOAN VALUE ON DEC. 20 403,220,000e (.068634)209/365 = NZ419,382,000 DEC 20 TAKE DELIVERY OF NZ419,382,000 BY PAYING REPAY THE LOAN  $419,382,000(.5028) = $210,865,000 compared with: THE IMPLIED REVERSE REPO RATE FOR 209 DAYS =
    • EXAMPLES OF FOREIGN CURRENCY LONG HEDGES EXAMPLE 1. ON JULY 1, AN AMERICAN AUTOMOBIL DEALER ENTERS INTO A CONTRACT TO IMPORT 100 BRITISH SPORT CARS FOR BP28,000 EACH. PAYMENT AND DELIVERY WILL BE MADE IN BRITISH POUNDS ON NOVEMBER 1. RISK EXPOSURE: IF THE BP APPRECIATES RELATIVE TO THE $ THE IMPORTER’S COST WILL RISE. TIME CASH FUTURES JUL. 1 S($/BP) = 1.3060 BUY 46 DEC BP FUTURES CURRENT COST = $3,656,800 FOR F = $1.2780/BP DO NOTHING NOV. 1 S($/BP) = 1.4420 SELL 46 DEC BP FUTURES COST = 28,000(1.4420) FOR F = $1.4375/BP = $40,376/CAR, OR PROFIT $4,037,600 FOR THE (1.4375 - 1.2780)62,500(46) 100 CARS = $458,562.50 ACTUAL COST = $3,579,037.50
    • A LONG HEDGE EXAMPLE 2. ON MARCH 1, AN AMERICAN WATCH RETAILER AGREES TO PURCHASE 10,000 SWISS WATCHES FOR CHF375 EACH. THE SHIPMENT AND THE PURCHASE WILL TAKE PLACE ON AUGUST 26. TIME CASH FUTURES MAR. 1 S($/CHF) = .6369 LONG 30 SEP CHF FUTURES CURRENT COST 10,000 (375)(.6369) F(SEP) = $.6514/CHF = $2,388,375 CONTRACT = (.6514)125,000 DO NOTHING = $81,425. AUG. 25 S=$.6600/CHF SHORT 30 SEP CHF FUTURES WATCHES FOR F(SEP) = $.6750/CHF BUY 10,000 WATCHES PROFIT: AT 375(.6600) = $247.50/WATCH (.6750 - .6514)125,000(30) TOTAL $2,475,000. = $88,500. ACTUAL COST $2,386,500
    • LONG HEDGE: PROTECT AGAINST DEPRECIATING DOLLAR EXAMPLE 3. AN AMERICAN FIRM AGREES TO BUY 100,000 MOTORCYCLES FROM A JAPANESE FIRM FOR ¥ 202,350 . CURRENT PRICE DATA: SPOT: S(ask) = $.007020/ ¥ ¥ 142.30/$ S(bid) = $.007027/ ¥ ¥ 142.45/$ DEC FUTURES: F(ask) = $.007190/ ¥ ¥ 139.08/$ F(bid) = $.007185/ ¥ ¥ 139.19/$ ON DECEMBER 20 THE FIRM NEEDS ¥ 20,235,000,000 THIS SUM IS 20,235,000,000(.007027) = = $142,191,345 IF PURCHESED TODAY. N = $142,191,345/( ¥ 12,500,000)($.007190/JY) = 1,582.
    • TIME CASH FUTURES MAY 23 DO NOTHING LONG 1,582 JY FUTURES FOR CURRENT VALUE = $142,191,345 F(ask) = $.007190/ ¥ CASE I: DEC 20 S = $.0080/ ¥ SHORT 1,582JY Fs. BUY MOTORCYCLES FOR $.0080/ ¥ FOR $161,880,000 PROFIT:(.0080-.00719)12,500,000(1,582) = $16,017,750 NET COST: $161,880,000 - $16,017,750 = $145,862,250. CASE II: DEC 20 S = $.0065/ ¥ SHORT 1,582 JY Fs. PURFHASE PRICE FOR $.0065/ ¥ $131,527,500 LOSS: (.00719-.0065)12,500,000(1,582) = $13,644,750 NET COST: $145,172,250.
    • A SHORT HEDGE A U.S. BASED MULTINATIONAL COMPANY’S MEXICAN SUBSIDIARY WILL GENERATE EARNINGS OF MP100M AT THE END OF THE QUARTER - MARCH 31. THE MONEY WILL BE DEPOSITED IN THE NEW YORK BANK ACCOUNT OF THE FIRM IN U.S. DOLLARS. RISK EXPOSURE: IF THE DOLLAR APRECIATES RELATIVE TO THE MEXICAN PESO THERE WILL BE LESS DOLLARS TO DEPOSIT. TIME CASH FUTURES FEB. 21 S($/MP) = .I000 F(JUN) = $.1250/DM CURRENT SPOT VALUE F = 500,000($.1250MP) = $62,500 = $10M. DO NOTHING SHORT 160 JUN MP FUTURES MAR 31 S($/MP) = .0925 LONG 160 JUN MP FUTURES DEPOSIT F(JUN) = $.1165/DM 100,000,000(.0925) PROFIT: = $9,250,000 (.1250 - .1165)500,000(160) = $680,000 TOTAL AMOUNT TO DEPOSIT $9,930,000