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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

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


Version 1 9 2001

Topics

Forward Market in Foreign CurrencyCovered Interest ParityCreating a Synthetic Forward Contract Foreign Currency Futures

 K.Cuthbertson, D.Nitzsche


Forward market in foreign currency

Forward Market in Foreign Currency

 K.Cuthbertson, D.Nitzsche


Forward market

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


Forward rates quotes

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


Covered interest parity

Covered Interest Parity

 K.Cuthbertson, D.Nitzsche


Covered interest parity1

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


An example of cip

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


Covered interest parity cip

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


Cip return to investment in us or uk are equal

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


Covered interest parity algebra derivation

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


Bank calculates forward quote

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


Creating a synthetic forward contract

Creating a Synthetic Forward Contract

 K.Cuthbertson, D.Nitzsche


Creating a synthetic fx forward contract

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


Actual fx forward contract cash flows

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


Version 1 9 2001

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


Synthetic fx forward contract

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


Bank calculates outright forward quote

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


Bank quotes forward points

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


Risk free arbitrage profits f and sf are different

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


Speculation in forward market

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


Foreign currency futures

Foreign Currency Futures

 K.Cuthbertson, D.Nitzsche


Futures contract specification

Futures: Contract Specification

  • Table 4.1 : Contract Specifications IMM Currency Futures(CME)

  • Size Tick Size [Value] Initial Margin

  • MarginMaintenance Margin

  • 1 Pound Sterling £62,500 0.02¢ per £[$12.50] $2,000

  • 2 Swiss FrancSF125,000 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


Futures hedging

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


Futures hedging1

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


Version 1 9 2001

Slides End Here

 K.Cuthbertson, D.Nitzsche


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