Chp04 Currency Forwards and Futures

8/13/2019 Chp04 Currency Forwards and Futures

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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 Marketsin Foreign Currency


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Forward Market in Foreign Currency

Covered Interest Parity

Creating a Synthetic Forward Contract

Foreign Currency Futures

Topics


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Forward Market in Foreign Currency


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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


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Forward Rates (Quotes)

Yen / $ Yen / $

Spot 131.05-131.15

spotspread

0.10

1m forwd

discount

0.01-0.03 spread on

discount

0.02

1m forwdrate

131.06-131.18

1m forwdspread

0.12

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


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7/26K.Cuthbertson, D.Nitzsche 7


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



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 $ /



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%



CIPreturn 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) = $165Forward 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



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, thatis you get less per $ in the forward market, than in the

spot market. - does this make sense for CIP ?



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



Creating a Synthetic ForwardContract



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 spotexchange 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 priceequal to the synthetic forward contract. Otherwiseriskless arbitrage (buy low, sell high) is possible.


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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

Borrow 90.09 at r(UK) = 11%

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

Receive $150

100

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Synthetic Forward Contract: Cash Flows



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)

= $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



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)

HedgingLong spot $s then go short (ie.sell) futures on $



Bank Quotes Forward Points

Forward Points = F - S

= S [ rus- rUK) / ( 1 + ruk) ]

The forward points are calculated from S, and the twomoney market interest rates

Eg. If forward points = 10 and S=1.5 then

Outright forward rate F = S +Forward PointsF = 1.5000 + 10 points = 1.5010



Risk Free Arbitrage Profits ( F and SF are different)

Actual Forward Contractwith 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



Speculation in Forward Market

Bank will try and match hedgers in F-mkt to

balance its currency bookOpen 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



Foreign Currency Futures



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



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 hencetakes a long position in SFr futuresNf= 500,000/125,000 = 4 contracts



Futures: Hedging

Net $-cost = Cost in spot market - Gain on futures= TVS0S1- Nfz (F1F0)

= 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 longas the final basis b1= S1- F1is small.Importer pays out $336,700 to receive SFr 500,000 whichimplies 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.


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Chp04 Currency Forwards and Futures