Introduction to Forwards

8/9/2019 Introduction to Forwards

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L E C T U R E 2

Introduction to Forwards



Ove r v ie w

y Both futur es and forwards sp ecify a committ ed trad e betw ee n two count er-parti es:

T here is a commitm ent to deliver an ass et (this is th e seller , or th e sh o r t ), at a sp ecified forward pric e.

T here is a commitm ent to tak e delivery of an ass et (this is th e buyer , or th e long ), at a sp ecified forward pric e.A t d el i very, cash is exchang ed for th e ass et .

y M any tim es, futur es contracts and forward contracts ar e substitut es. How eve r, at oth er tim es, th e relati ve costs,liquidity, and con

veni

enc

eof using on

emark

et ve

rsus the oth er wi ll diff er .



Futur es and Forwards: A Comparison T ab le

Futur es ForwardsDefault Risk: Borne by Clearinghouse Borne by Counter-Parties

What to Trade: Standardized Negotiable

The Forward/Futures Agreed on at Time Agreed on at TimePrice of Trade Then, of Trade. Payment at

Marked-to-Market Contract Termination

Where to Trade: Standardized Negotiable

When to Trade: Standardized Negotiable

Liquidity Risk: Clearinghouse Makes it Cannot Exit as Easily:Easy to Exit Commitment Must Make an Entire

New Contrtact

How Much to Trade: Standardized Negotiable

What Type to T rade: Standardized Negotiable

Margin Required Collateral is negotiable

Typical Holding Pd. Offset prior to delivery Delivery takes place



Forward Contracts:Payoff Profi les

profitprofit

S(T) S(T)

Th e f ts f t h e s t ce ate e y ( T), excee s t h e a

f a ce , F (0 ,T).

Th e s hor t ro f ts if th e pri ce ate ive r y, S (T), i s b e ow th e

origin a f orw a rd pri ce , F (0 ,T).

Long f orw a rdShor t f orw a rd

F (0,T) F (0,T)



E xamp le

y J ohn shorts £20m forward at a forward pric e £/$=1 .75. A t expiration, th e spot pric e £/$=1 .7

-- Did J ohn profit or did h e lose?

-- How much ?



Defau lt Risk for Forwards

y If th e forward pric e is ³fair´ at initiation:T he contract is v aluele ss .T here is no imm ediat e defau lt risk .

y A s tim e goes by, th e forward pric e (for d el i very on th e sam e dat e as th e origina l contract ) can chang e:

E xisting forward contracts acquir e v alue: T he y becom e anass et for on e party and a liabi lity for th e oth er .Defau lt risk app ears . (Q: Which party fac es d efau lt risk ?)



Defau lt Risk for Forwards

y E xamp le : On 4 th M ay, J ohn bought 100,000 bb l of oi l forward at a forward pric e of £2 7/bb l. T he del i very dat e is A ugust 4th . On J un e 4th, th e forward pric e for d el i very on A ugust 4th is £23/bb l.

Who has th e inc enti ve to d efau lt?

If th e int erest rat e on M ay 4th for 2-month d e bt instrum ents is 5% , what is th e amount expos ed to d efau lt risk ?



Forward Rat e A gree m ents (FR A s)

y A FR A is a forward contract on an interest rate(not on a bond, or a loan)

y T he buy er effectively has agr ee d to borrow an

amount of mon e y in th e futur e at th e stat edforward (contract) rat e. T he selle r has eff ecti vel y lock ed in a lending rat e.

y T he buyer of a FR A pr of it s from an inc re a se inint erest rat es. T he seller of a FR A pr of it s from ade cli n e in rat es.

y FR A s ar e cash s ett led .




y On l y th e diff erenc e in int erest rat es is paid . T he principa l is not exchang ed .

0 t1 t2

Loan periodorigination date

settlement date, or delivery date

end of forwardperiod



FR A s

y A FR A¶s v alue is initia ll y zero, wh en th e contract rat e is th e th eor etica l forward rat e. Subs equ ent l y,forward rat es will chang e, so th e FR A will ha ve

positi ve v alue for on e party (and equa ll y negati ve v alue for th e oth er) .




y Let r(t1,t2) = s ett lem ent rat e (spot rat e at d el i very)y Let fr(0,t1,t2) = contract rat e = origina l forward

rat ey

Let D = days in contract p

eriod = t2 - t1

y Let P = notiona l principa ly Let B = 360, (or 36 5 som etim es)y Cash s ett lem ent paym ent equa ls:

P[ r(t ,t ) - fr( ,t ,t )](D/B)+ [r(t ,t )(D/B)]



FR A ³ J argon´

y A t1 X t2 FR A : T he start dat e, or d el i very dat e, is t1months h ence. T he end of th e forward p eriod is t2months h ence. T he loan p eriod is t1-t2 months

long .

y E .g., a 9 X 12 FR A has a contract p eriod b eginningnin e months h ence, ending 12 months h enc e.



A n E xamp le of an FR A

y A firm s ells a 5X8 FR A , with a NP of £300 MM , anda contract rat e of 5.8% (3-month forward LIB OR) .

y

On th e sett lem ent dat e (fi ve months h enc e), 3month spot LIB OR is 5.1%.

y T here ar e 91 days in th e contract p eriod (8- 5=3months), and a y ear is d efined to b e 360 days .

y Fi ve months h enc e, th e firm r ecei ves:





FR A s and Int erest Rat e Swaps

y A FR A is essentia ll y equi v alent to a on e-p eriodp lain v ani lla int erest rat e swap:

FR A SwapBuy er pay fi xed (fr(0,t1,t2), and

recei ve f loating (r(t1,t2))

Selle r r ecei ve fixed and pay f loating



Forward For eign E xchang e

y For eign exchang e rat e: th e pric e of on e curr ency in t erms of th e oth er curr ency

y T here ar e spot exchang e rat es and forward exchang e rat es.

y See h tt p://www.bl oom ber g.com / ma r k e t s/ fxc .h tm l forspot rat es.



Curr ency Quotation

y A pp ear in Pair, th e first on e is bas e curr ency, th e second on e is quot e curr ency (count er curr ency)

y T he bas e curr ency a l ways has th e v alue of 1 and th e

count er curr ency has th e v alue of quot ey Usua ll y a fi ve-figur ed quotation and th e last numb er

is ca lled pip (or point)y T he quot es ris e, th e bas e curr ency str ength ens and

v ice versay Cross curr enci es: quot es do not inc lud e US do llar



Curr ency Quotation

y Bid/ A sk ar e th e pric es to S ell/Buy th e bas e curr ency (short/ long th e pair); or Buy/ S ell th e count er curr ency

y Bid ±ask spr ead is usua ll y 4- 5 pips for th e M ajors and 5-20pips for cross or exotics (th e pairs less trad ed)

y Dir ect quot e: th e amount of loca l curr ency requir ed/r ecei ved to purchas e/s ell on e unit of for eigncurr ency

y Indir ect quot e: th e amount of for eign curr ency requir ed/r ecei ved to purchas e/s ell on e unit of loca l curr ency



A Forward FX Contract is aPair of Z ero Coupon Bonds, I .

O ne is an asset, and the other is a liability denominated in a differentcurrency.

Consider the forward contract to buy £100,000 for the forward price of ¥70/ £.

R ece ive £1 00 ,000 , at the forwardprice of ¥70/ £.

p ay ¥7 m illion for the £100,000.today





Som e E qui librium R elations

y T he T erm Structur e

where s is spot rat e and f is forward rat e

y Co vered Int erest Parity

Wh ere se is spot X-rat e and f e is forward X-rat e.

t t t t

t t s f s )1(),1()1( 1

)1(1 !

t at

at

t bt

a s fe s se )1()1( ,0/

,0,0/

0,0!

bb

b/0,0

ae



E xamp le

y T he spot X-rat e for th e pair E UR/GBP is 0 .9249 .

y T he 3-month forward rat e for th e pair E UR/GBP is0 .9199

y T he spot int erest rat e for E UR is 0 .45%y T he spot int erest rat e for GBP is 0 .39 %y Q: Is th ere arbitrag e opportunity ?

O ptions, Futures, and O ther erivatives 6 th

Edition, Copyright © John C. Hull 2005



Profits and Loss es forForward FX Contracts

y Defin e F(0, T ) as th e forward exchang e rat e at origination

y S(T ) = th e spot exchang e rat e at d el i very .

y If S( T ) > F(0, T ), th e long (in bas e curr ency) profits by: N [S( T ) -F(0, T )] .

y If S( T ) < F(0, T ), th e short (in bas e curr ency) profits by: N [F(0, T ) -S(T )] .



Profits and Loss es for Forward FX Contracts: A nE xamp le

y Not e th e WSJ reprint on th e nex t s lide. O bs er ve th e spot rat e, and th e forward exchang e rat e for th e y en fordel i very 3 months h enc e.

y If th e spot rat e remains unchang ed from today unti l th e

del i very dat e, what is th e profit/ loss for a party whogoes long a forward contract on ¥10,000,000 ?(R eut er: $/¥ quot e bid =9 7.14)



E xamp le



Curr ency Carry T rad e

y A strat egy in which an in vestor s ells a certaincurr ency with a r elati vel y low int erest rat e and us esth e funds to purchas e a diff erent curr ency yi elding

a high er int erest rat e. y M ajor risk: th e unc ertainty of exchang e rat e. y Carry spot trad e



E xamp le

y T he int erest rat es for HK$ and GBP£ ar e resp ecti vel y 5.25% and 0 .5%.

y Carry trad e strat egy:

borrowing GBP100000Con verting into HK$Buying a bond for th e equi v alent amount paying5.25%



E xamp le Cont .

y T he spot exchang e rat e GBP/HKD is 12 .586 5y A ssum e th e futur e spot exchang e rat e at th e end of

on e y ear is on e of th e followings, 12 .7230 and

13.2134y What is th e payoff of this carry trad e?

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Introduction to Forwards