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
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Topics
Forward Market in Foreign Currency
Covered Interest Parity
Creating a Synthetic Forward Contract
Foreign Currency Futures
 K.Cuthbertson, D.Nitzsche
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Forward Market in Foreign Currency
 K.Cuthbertson, D.Nitzsche
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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
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Forward Rates (Quotes)
Yen / $
Spot
131.05131.15
Yen / $
spot
spread
0.10
1m forwd 0.01-0.03 spread on
discount
discount
0.02
1m forwd 131.06rate
131.18
0.12
1m forwd
spread
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
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Covered Interest Parity
 K.Cuthbertson, D.Nitzsche
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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
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An Example of CIP
The following set of “prices” are consistent with CIP
rUK = 0.11 (11 %)
rUS = 0.10 (10 %)
S = 0.666666 £ / $
Then F must equal:
F = 0.67272726 £/ $
(I.e. 1.5 $ / £ )
ie. 1.486486 $ / £
 K.Cuthbertson, D.Nitzsche
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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
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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)
At end year $( 100 / 0.6666 )(1.10)
Forward Contract negotiated today
= $150
= $165
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
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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
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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
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Creating a Synthetic Forward
Contract
 K.Cuthbertson, D.Nitzsche
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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
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Actual FX-Forward Contract: Cash Flows
Receive $150
Data: F = 1.5 ($/£)
1
0
Pay out £100
Will receive $150 and pay out £100 at t=1
No “own funds” are used. No cash exchanges hands today ( time t=0)
 K.Cuthbertson, D.Nitzsche
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Synthetic Forward Contract: Cash Flows
Using two money markets and the spot FX rate
Suppose: ruk = 11%, rus =10%, S = 1.513636 ($/£)
Create cash flows equivalent to actual Forward Contract
Begin by “creating” the cash outflow of £100 at t=1
Receive $150
Borrow £90.09 at r(UK) = 11%
1
0
Switch £90.09 in spot market and lend $136.36
£100
in the US at r(US) =10%.
Note : S = 1.513636$/£ and no “own funds” are used
 K.Cuthbertson, D.Nitzsche
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Synthetic FX-Forward Contract
Borrowed £100/(1+ruk)
=£90.09
at t=0
( Pay out £100 at 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)
= $150 at 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
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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
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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
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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
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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
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Foreign Currency Futures
 K.Cuthbertson, D.Nitzsche
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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
3 Japanese Yen Y12,500,000
0.01¢ per 100JY[$12.5] $1,500
4 Canadian Dollar CD100,000
0.001 ($/CD)[$100]
5 Euro
0.01¢ per Euro [$12.50] varies
€125,000
 K.Cuthbertson, D.Nitzsche
$2,000
$900
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Futures: Hedging
S0 = spot rate = 0.6700($/SFr)
F0 = futures price (Oct. delivery) = 0.6738($/SFr)
Contract Size, z = SFr 125,000
Tick size, (value) = 0.0001($/SFr) ($12.50)
US Importer
TVS0 = SFr 500,000
Vulnerable to an appreciation of SFr and hence
takes a long position in SFr futures
Nf = 500,000/125,000 = 4 contracts
 K.Cuthbertson, D.Nitzsche
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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 = TVS0
Hedge “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
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Slides End Here
 K.Cuthbertson, D.Nitzsche
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