 K.Cuthbertson, D.Nitzsche 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 Forward Market in Foreign Currency Covered Interest Parity Creating a Synthetic Forward Contract Foreign Currency Futures Topics

 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 $) ( r UK - r US ) / ( 1 + r US ) = ( F - S ) / S

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

 K.Cuthbertson, D.Nitzsche 9 Covered Interest Parity (CIP) CHECK: CIP equation holds Interest differential in favour of UK ( r UK - r US ) / ( 1 + r US ) = ( ) / 1.10 = (= 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 TV uk = £100 (1. 11) = £111 = £A ( 1 + r UK ) 2) Invest in US £100 to $ ( 100 / ) = $150 At end year $( 100 / )(1.10) = $165 Forward Contract negotiated today Certain TV (in £s) from investing in USA: TV us = £ [( 100 / ). (1.10) ] = £111 = £ [ (A / S ) (1 + r US ) ]. F Hence : TV uk = £111= TV US = £111

 K.Cuthbertson, D.Nitzsche 11 Covered Interest Parity (Algebra/Derivation) Equate riskless returns ( in £ ) (1) TV uk = £A ( 1 + r UK ) (2) TV us = £ [ ( A / S ) ( 1 + r US ) ]. F F = S ( 1 + r UK ) / ( 1 + r US ) or F / S = ( 1 + r UK ) / ( 1 + r US ) Subtract “1” from each side: ( F -S ) / S = ( r UK - r US ) / ( 1 + r US ) Forward premium on dollar (discount on sterling) = interest differential in favour of UK eg. If r UK - r US = 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 + r UK ) / ( 1 + r US ) ] If r UK and r US 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) 1 0 Pay out £100 Receive $150 Data: F = 1.5 ($/£)

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

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

 K.Cuthbertson, D.Nitzsche 18 Bank Calculates Outright Forward Quote F(quote) = S [ ( 1 + r us ) / ( 1 + r uk ) ] Covered interest parity (CIP) Also Note: If r us and r uk 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 [ r us - r UK ) / ( 1 + r uk ) ] 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 = points =

 K.Cuthbertson, D.Nitzsche 20 Risk Free Arbitrage Profits ( F and SF are different) Actual Forward Contract with F = 1.4 ($/£) Pay out $140 and receive £100 at t=1 Synthetic Forward(Money Market) Data: r uk = 11%, r us =10%, S = ($/£) 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 $ 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 F 0 = 1.50 $ / £, to pay out £100,000 and receive $150,000 One year later : S T = 1.52 $ / £ Buy £100,000 spot and pay $152,000 But only receive $150,000 from the f.c. Loss (or profit) = S T - F 0

 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 MarginMaintenance Margin 1 Pound Sterling £62, ¢ per £[$12.50] $2,000 2 Swiss FrancSF125, ¢ per SFr $2,000 3 Japanese Yen Y12,500, ¢ per 100JY[$12.5] $1,500 4 Canadian Dollar CD100, ($/CD)[$100] $900 5 Euro € 125, ¢ per Euro [$12.50] varies

 K.Cuthbertson, D.Nitzsche 24 Futures: Hedging S 0 = spot rate = ($/SFr) F 0 = futures price (Oct. delivery) = ($/SFr) Contract Size, z = SFr 125,000 Tick size, (value) = ($/SFr) ($12.50) US Importer TVS 0 = SFr 500,000 Vulnerable to an appreciation of SFr and hence takes a long position in SFr futures N f = 500,000/125,000 = 4 contracts

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

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