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Version 1/9/2001

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. Topics.

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Version 1/9/2001

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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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