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Understanding Forward and Futures Markets in Foreign Currency

Learn about forward and futures markets, covered interest parity, creating synthetic forward contracts, and more in foreign currency trading. Explore examples and calculations to enhance your understanding.

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Understanding Forward and Futures Markets in Foreign Currency

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  1. Version 1/9/2001 FINANCIAL ENGINEERING: DERIVATIVES AND RISK MANAGEMENT(J. Wiley, 2001) K. Cuthbertson and D. Nitzsche LECTURE Forward and Futures Markets in Foreign Currency  K.Cuthbertson, D.Nitzsche

  2. Topics Forward Market in Foreign CurrencyCovered Interest ParityCreating a Synthetic Forward Contract Foreign Currency Futures  K.Cuthbertson, D.Nitzsche

  3. Forward Market in Foreign Currency  K.Cuthbertson, D.Nitzsche

  4. Forward Market • Contract made today for delivery in the future • Forward rate is “price” agreed, today • eg. One -year Forward rate = 1.5 $ / £ • Agree to purchase £100 ‘s forward • In 1-year, receive £100 • and pay-out $150  K.Cuthbertson, D.Nitzsche

  5. Forward Rates (Quotes) Rule of thumb. Here discount / premium should be added so that: forward spread > spot spread Premium (discount) % = ( premium / spot rate ) x ( 365 / m )x 100  K.Cuthbertson, D.Nitzsche

  6. Covered Interest Parity  K.Cuthbertson, D.Nitzsche

  7. Covered Interest Parity • CIP determines the forward rate F and CIP holds when: • Interest differential (in favour of the UK) • = forward discount on sterling • (or, forward premium on the $) • ( rUK - rUS) / ( 1 + rUS) = ( F - S ) / S  K.Cuthbertson, D.Nitzsche

  8. An Example of CIP • The following set of “prices” are consistent with CIP • rUK = 0.11 (11 %) rUS = 0.10 (10 %) • S = 0.666666 £ / $ (I.e. 1.5 $ / £ ) • Then F must equal: • F = 0.67272726 £/ $ ie. 1.486486 $ / £  K.Cuthbertson, D.Nitzsche

  9. Covered Interest Parity (CIP) • CHECK: CIP equation holds • Interest differential in favour of UK • ( rUK - rUS) / ( 1 + rUS) = (0.11 -0. 10) / 1.10 • = 0.0091 (= 0.91%) • Forward premium on the dollar (discount on £) • = ( F - S ) / S = 0.91%  K.Cuthbertson, D.Nitzsche

  10. CIP return to investment in US or UK are equal • 1) Invest in UK TVuk = £100 (1. 11) = £111 • = £A ( 1 + rUK ) • 2) Invest in US • £100 to $ ( 100 / 0.6666) = $150 At end year $( 100 / 0.6666 )(1.10) = $165 • Forward Contract negotiated today • Certain TV (in £s) from investing in USA: • TVus = £ [( 100 / 0.666 ) . (1.10) ] 0.6727 = £111 • = £ [ (A / S ) (1 + rUS) ]. F • Hence : TVuk = £111= TVUS = £111  K.Cuthbertson, D.Nitzsche

  11. Covered Interest Parity (Algebra/Derivation) Equate riskless returns ( in £ ) • (1) TVuk = £A ( 1 + rUK ) • (2) TVus = £ [ ( A / S ) ( 1 + rUS ) ]. F F = S ( 1 + rUK ) / ( 1 + rUS ) or F / S = ( 1 + rUK ) / ( 1 + rUS ) Subtract “1” from each side: ( F -S ) / S = ( rUK - rUS ) / ( 1 + rUS ) Forward premium on dollar (discount on sterling) = interest differential in favour of UK eg. If rUK - rUS = minus1%pa then F will be below S, that is you get less £ per $ in the forward market, than in the spot market. - does this make sense for CIP ?  K.Cuthbertson, D.Nitzsche

  12. Bank Calculates Forward Quote • CIP implies, banks quote for F (£/$) is calculated as F(quote) = S [( 1 + rUK ) / ( 1 + rUS ) ] If rUK and rUS are relatively constant then F and S will move together (positive correln) hence: For Hedging with Futures If you are long spot $-assets and fear a fall in the $ then go short (ie.sell) futures on USD  K.Cuthbertson, D.Nitzsche

  13. Creating a Synthetic Forward Contract  K.Cuthbertson, D.Nitzsche

  14. Creating a Synthetic FX-Forward Contract • Suppose the actual quoted forward rate is: F = 1.5 ($/£) • Consider the cash flows in an actual forward contract • Then reproduce these cash flows using “other assets”, that is the money markets in each country and the spot exchange rate. This is the synthetic forward contract • Since the two sets of cash flows are identical then the actual forward contract must have a “value” or “price” equal to the synthetic forward contract. Otherwise riskless arbitrage (buy low, sell high) is possible.  K.Cuthbertson, D.Nitzsche

  15. Actual FX-Forward Contract: Cash Flows • Will receive $150 and pay out £100 at t=1 • No “own funds” are used. No cash exchanges hands today ( time t=0) Receive $150 Data: F = 1.5 ($/£) 1 0 Pay out £100  K.Cuthbertson, D.Nitzsche

  16. Using two money markets and the spot FX rateSuppose: ruk = 11%, rus =10%, S = 1.513636 ($/£)Create cash flows equivalent to actual Forward ContractBegin by “creating” the cash outflow of £100 at t=1 Synthetic Forward Contract: Cash Flows Receive $150 Borrow £90.09 at r(UK) = 11% 1 0 Switch £90.09 in spot market and lend $136.36 in the US at r(US) =10%. Note : S = 1.513636$/£ and no “own funds” are used £100  K.Cuthbertson, D.Nitzsche

  17. Synthetic FX-Forward Contract • Borrowed £100/(1+ruk) =£90.09 at t=0 • ( Pay out£100at t=1) • Convert to USD [100/(1+ruk) ] S = $136.36 at t=0 • Lend in USA and receive [100/(1+ruk) ] S (1+rus) • = $150at t=1 • Synthetic Forward Rate SF: • Rate of exchange ( t=1) = (Receipt of USD) / (Pay out £’s) • = $150 / £100 • SF = [100/(1+ruk) ] S (1+rus) / 100 • = S (1+rus) / /(1+ruk) • The actual forward rate must equal the synthetic forward rate  K.Cuthbertson, D.Nitzsche

  18. Bank Calculates Outright Forward Quote F(quote) = S [ ( 1 + rus ) / ( 1 + ruk ) ] Covered interest parity (CIP) Also Note: If rus and ruk are relatively constant then F and S will move together (positive correln) Hedging Long spot $’s then go short (ie.sell) futures on $  K.Cuthbertson, D.Nitzsche

  19. Bank Quotes “Forward Points” Forward Points = F - S = S [ rus - rUK ) / ( 1 + ruk ) ] • The forward points are calculated from S, and the two money market interest rates Eg. If “forward points” = 10 and S=1.5 then Outright forward rate F = S +Forward Points F = 1.5000 + 10 points = 1.5010  K.Cuthbertson, D.Nitzsche

  20. Risk Free Arbitrage Profits ( F and SF are different) • Actual Forward Contract with F = 1.4 ($/£)Pay out $140 and receive £100 at t=1 • Synthetic Forward(Money Market) • Data: ruk = 11%, rus =10%, S = 1.513636 ($/£) so SF=1.5 ($/£) • Receive $150 and pay out £100 • Strategy: • Sell $140 forward, receive £100 at t=1 (actual forward contract) • Borrow £90.09 in UK money market at t=0 (owe £100 at t=1) • Convert £90.09 into $136.36 in spot market at t=0 • Lend $136 in US money market receive $150 at t=1(synthetic) • Riskless Profit = $150 - $140 = $10  K.Cuthbertson, D.Nitzsche

  21. Speculation in Forward Market • Bank will try and match hedgers in F-mkt to • balance its currency book • Open Position • Suppose bank has forward contract. at F0 = 1.50 $ / £, to • pay out £100,000 and receive $150,000 • One year later : ST = 1.52 $ / £ • Buy £100,000 spot and pay $152,000 • But only receive $150,000 from the f.c. • Loss (or profit) = ST - F0  K.Cuthbertson, D.Nitzsche

  22. Foreign Currency Futures  K.Cuthbertson, D.Nitzsche

  23. Futures: Contract Specification • Table 4.1 : Contract Specifications IMM Currency Futures(CME) • Size Tick Size [Value] Initial Margin • Margin Maintenance Margin • 1 Pound Sterling £62,500 0.02¢ per £[$12.50] $2,000 • 2 Swiss Franc SF125,000 0.01¢ per SFr $2,000 • 3 Japanese Yen Y12,500,000 0.01¢ per 100JY[$12.5] $1,500 • 4 Canadian Dollar CD100,000 0.001 ($/CD)[$100] $900 • 5 Euro € 125,000 0.01¢ per Euro [$12.50] varies  K.Cuthbertson, D.Nitzsche

  24. Futures: Hedging S0 = spot rate = 0.6700($/SFr) F0 = futures price (Oct. delivery) = 0.6738($/SFr)Contract Size, z = SFr 125,000Tick size, (value) = 0.0001($/SFr) ($12.50)US ImporterTVS0 = SFr 500,000 Vulnerable to an appreciation of SFr and hence takes a long position in SFr futuresNf = 500,000/125,000 = 4 contracts  K.Cuthbertson, D.Nitzsche

  25. Futures: Hedging Net $-cost = Cost in spot market - Gain on futures = TVS0 S1 - Nf z (F1 – F0) = TVS0 (S1 - F1 + F0) = TVS0 (b1 + F0) = $ 360,000 - $ 23,300 = $ 336,700 Notes: Nfz = TVS0Hedge “locks in” the futures price at t=0 that is F0, as long as the final basis b1 = S1 - F1 is “small”.Importer pays out $336,700 to receive SFr 500,000 which implies an effective rate of exchange at t=1 of :[4.14] Net Cost/TVS0= b1 + F0 = 0.6734 ($/SFr)~close to the initial futures price of F0 = 0.6738($/SFr) the difference being the final basis b1 = -4 ticks.  K.Cuthbertson, D.Nitzsche

  26. Slides End Here  K.Cuthbertson, D.Nitzsche

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