2015F Investments 02 Forwards, Futures, And Swaps (1)

7/23/2019 2015F Investments 02 Forwards, Futures, And Swaps (1)

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InvestmentsWeek 2: Forwards,

Futures, and Swaps

Fall 2015

Professor Albert Wang王文奇



Page 2

2 Sep 2015 Agenda

►Adm!n!strat!ve "W1 due ne#t week !n $lass

►%e$ture &urrent 'vents (pdate &"22)2*►Pa+o-Pro.t /!agrams►Forwards-Futures►Forwards-Futures e#amples►Swaps



Page *

&urrent 'vents

► AI' Inde#: *0340

►SP500 Inde#: 1,677463

►

8e$ent .nan$!al news (S Federal 8eserve 9 no Sept4 $ange !n

pol!$+

;olkswagen 9 $eated on (S em!ss!ons

tests, .nes $ould be uge4 <ter$ountr!es ma+ follow up4



Page

Pa+o and Pro.t /!agrams

►%!near Pa+osPayof (time T)

Price o underlying

Payof (time T)

Price o underlying



Page 5

Forwards and FuturesIntrodu$t!on

►=ot are $ontra$ts to bu+ - sell anunderl+!ng asset at a spe$!.ed pr!$eand at a spe$!.ed t!me =ot $an oer .nan$!al e#posure to te

same underl+!ng asset

=ot >and all der!vat!ves? are @ero)net)

suppl+►/!eren$es between Forwards and

Futures are !n $ontra$t deta!ls and

log!st!$s of trad!ng



Page 7

Forwards and FuturesAlternat!ves

►Alternat!ve to =u+!ng (nder+!ng &ompl!$at!ons►Ind!$es 9 $ostl+ to adm!n!ster bu+!ng-old!ng ea$

$omponent

►&ommod!t!es 9 storage >were would +ou store porkbell!es and for ow long?

►W+ trade forwards and futures %ower transa$t!on $ost

"!gl+ leveraged pos!t!ons

'as+ to B$loseC pos!t!ons b+ open!ng anoter andBnett!ngC


http://slidepdf.com/reader/full/2015f-investments-02-forwards-futures-and-swaps-1 7/45Page 3

Forwards

►Forwards &ontra$t set toda+ for del!ver+ of a good

at a set date !n te future at a set pr!$e4

Forwards are pr!$ed to ave @ero valuetoda+►Do mone+ $anges ands unt!l matur!t+ wen

del!ver+ !s taken

Str!$tl+ between two pr!vate part!es►'!ter s!de ma+ default4 =ot s!des ave r!sk4

►&ontra$ted between two ent!t!es so ver+

Ee#!ble and spe$!.able


http://slidepdf.com/reader/full/2015f-investments-02-forwards-futures-and-swaps-1 8/45Page

Futures

►Futures Ident!$al !n sp!r!t to forwards

BStandard!@ed, 8egulatedC forwards

&lear!ngouse serves as m!ddle)man►uarantees Bdel!ver+C of $as and underl+!ng to bot

s!des of transa$t!on

►8egulates and evaluates .nan$!al ealt of members

►Prov!des standard!@at!on and a market

►"olds d!vers!.ed portfol!o of default r!sk Garg!n a$$ount to !nsure aga!nst default

► +p!$all+ $as settlement


http://slidepdf.com/reader/full/2015f-investments-02-forwards-futures-and-swaps-1 9/45Page 6

►<pen!ng pos!t!ons &onta$t broker to trade futures &onta$t $ounterpart+ d!re$tl+ >or troug broker?

to trade forwards

►&los!ng pos!t!ons rade !n !dent!$al forward-future !n oppos!te

d!re$t!on w!t ADH $ounterpart+ >not ne$essar!l+or!g!nal?►Gost often pos!t!ons are $losed !n t!s manner►Forward $ounterpart+ rarel+ wants to reverse te trade►Futures $ounterpart+ does not need to be known

ake-make del!ver+ of underl+!ng for $as

=roker or e#$ange arranges nett!ng !f needed

rad!ng Ge$an!$s



Page 10

►Summar+ of ke+ $ara$ter!st!$s futures Standard!@ed $ontra$t un!ts &lear!ngouse warrants performan$e Se$ondar+ trad!ng 9 !ger l!u!d!t+ Garked to market da!l+ >or more often? Garg!n reu!rement

►Forwards or Futures Futures pr!$!ng as !nterest rate $ons!derat!ons due to

marg!n a$$ount balan$e Eu$tuat!ons►Pos!t!on marked to market da!l+ and enoug $as must be !n

marg!n a$$ounts►Garg!n balan$e earns !nterest e$n!$all+ w!ll be us!ng forwards pr!$!ng to s!mpl!f+

$al$ulat!ons, toug !n pra$t!$e futures are mu$ more$ommonl+ traded

8emember, bot ave te same fundamental .nan$!al

e#posure

Don)te$n!$al Summar+



Page 11

Forwards and Futures 8!sks

►Pr!$e 8!sk <nl+ !f used as a spe$ulat!ve !nstrument

8!sk)redu$!ng !f used as a "'/'►

IGG(DIJ'S aga!nst pr!$e r!sk►=as!s 8!sk

Future and Spot >underl+!ng? values d!verge►/epends on !nterest rate so as te same r!sk

$omponents4►/efault 8!sk

From $ounterpart+ !f us!ng forwards

Garg!n $all r!sk !f us!ng futures



Page 12

►Agr!$ultural $ommod!t!es►Getals and m!nerals >!n$lud!ng energ+ $ontra$ts?►Fore!gn $urren$!es►F!nan$!al se$ur!t!es futures

Interest rate >and bond? futures Sto$k !nde# futures Ind!v!dual sto$k futures

►ADH"IDK

Futures are e#$ange)traded and standard!@ed, so wat+ou see !s wat +ou get Forwards for ADH"ID $an be negot!ated b+ an+ !)bank,

t+p!$all+ at ver+ low $ost

Poss!ble (nderl+!ngInstruments



Page 1*

Forwards and Futures'#ample 1

► Hou s!gn a forward $ontra$t to bu+ 100oun$es of gold on Gar$ 2, 2017 atL11*0 L11*0 !s te $ontra$ted forward pr!$e

It does not matter ow mu$ gold !s wortnow, a mont later, or on 10-2-04 be !t

L100, L11*0, or L20004 Hou st!ll ave tobu+ te gold at L11*0 per oun$e or elsedefault on +our $ontra$t >legal fees, et$4?



Page 1

Forwards and Futures'#ample 2

► Hou Must a$$ept +our bo+fr!end-g!rlfr!endNsmarr!age proposal and de$!de to marr+!m-er !n a +ear4

If +ou take +our engagement $omm!tmentser!ousl+, +ou ave to marr+ +our .an$O after a+ear, weter !n te follow!ng +ear +ou .nd oute-se trul+ !s Pr!n$e>ss? &arm!ng or te w!$ked>e)?w!t$4

A ser!ous engagement $omm!tment works l!ke aforward $ontra$t on$e agreed upon te dateand terms are set, regardless of te out$ome

>%u$k!l+? (nl!ke most .nan$!al $ontra$ts, !t !s notlegall+ b!nd!ngK



Page 15

► ere are two wa+s to a$u!re anunderl+!ng asset for some future date 1: Pur$ase !t now and store !t

2: ake a long pos!t!on !n futures► ese two strateg!es must ave te

same $osts to avo!d Barb!trageC

If te $osts are d!erent, ten someonewould BarbC te d!eren$e bu+ te$eap one, sell te e#pens!ve onemak!ng a pro.t but old!ng no r!sk andpa+!ng no $osts

Forward-Futures Pr!$!ng



Page 17

Spot)Futures Par!t+ eorem

►W!t a perfe$t edge te futures pa+o !s$erta!n 9 tere !s no r!sk

►A perfe$tl+ edged pos!t!on sould return

te r!sk)free rate of return %ong te underl+!ng >not!onal value L? and

sort te futures >$ostless to enter? or v!$e versa►<verall return sould be !dent!$al to old!ng L !n te

r!sk)free asset, s!n$e underl+!ng w!ll be del!vered to tefutures bu+er

► !s relat!ons!p $an be used to develop ano)arb!trage futures pr!$!ng relat!ons!p



Page 13

2 Wa+s to et (nderl+!ng'#posure

►=u+ futures !me 0►Do $ost

!me >0,t?►Do $ost

!me t►Pa+ F, re$e!ve

underl+!ng

►=u+ underl+!ng !me 0►Pa+ S

!me >0,t?►Pa+ old!ng $osts,

re$e!ve d!v!dends

!me t►Do $ostQ alread+ave underl+!ng



Page 1

Spot)Futures Par!t+

►'ssent!all+ euates te $as outEow at tematur!t+ date from te 2 wa+s to getunderl+!ng e#posure A? long futures: pa+ F =? bu+ underl+!ng: pa+ F;>S? 9 F;>/!v? R

F;>$osts?

t cd r

t

f

t

f

ccr ccr ccr f Se

cd r S

C Dr S F

)( ,

)1(

)1(

+−

=

+−+=

+−+=



Page 16

Spot)Futures Par!t+: Dotat!on

►Forward pr!$e, F: pr!$e set toda+ to transa$tat matur!t+►Gatur!t+, t: t!me at w!$ $ontra$t e#p!res►Spot pr!$e, S: $urrent pr!$e of te underl+!ng►F;>/!v!dends?, /

/!v!dend +!eld, d►F;>&osts?, &

&ost rate, $

►Det $onven!en$e +!eld, n$+: d)$ BDet $onven!en$e dollar pro.tC /)&

►8!skfree rate, r



Page 20

Arb!trage Poss!b!l!t!es

►If spot)futures par!t+ !s not observed,ten arb!trage !s poss!ble►If te futures pr!$e !s too !g, sort

te futures and a$u!re te sto$k b+borrow!ng te mone+ at te r!skfreerate►

If te futures pr!$e !s too low, go longfutures, sort te sto$k and !nvest tepro$eeds at te r!skfree rate



Page 21

&ow Forward Dumer!$al'#ample

►'#ample: Hou plan to open a lo$al restaurant $all Toann omas Steakouse !n 1 +ear4 If +oua$$uratel+ est!mate te number of $ow forwardsneeded on a regular bas!s, ten +ou $an keep tepr!$es of +our steaks almost $onstant, even !f tepr!$e of $ows !n$reases or de$reases4 Unow!ng +ouw!ll ave to del!ver a $owNs wort of steak !n te.rst week of bus!ness, +ou de$!de to bu+ a kobebeef $ow forward from an !nvestment bank4 epr!$e of tat ual!t+ $ow !s L1000 !n te open

market, te $ont!nuousl+ $ompounded r!sk)free rate!s 5V per +ear, te P; of te m!lk te $ow wouldprodu$e over te +ear !s L*0, and te P; of te a+and water to feed te $ow !s L104 ere are nooter bene.ts or $osts to own!ng su$ a $ow4

►Wat !s te Forward pr!$e



Page 22

$ont!nued

►S L1000, r$$r5V

►P;>/!v!dends? L*0 >m!lk?

►P;>&ost? L10 >a+, water?

25.1030]1030[1000

)(05.05.

=

−−=

−=

ee

CF FV Se F rt



Page 2*

$ont!nued

►'#ample $ont!nued: Instantl+ after go!ng long a s!ngle $ow

forward, te pr!$e of $ows !n$reases to

L11004 Wat !s te ;A%(' of te long pos!t!on

Wat !s te !mpl!ed B$ow e#posureC !n

number of $ows



Page 2

►J'8< !n!t!al $ost to enter a standard forward>marg!n balan$e reu!red for futures? "!g leverage makes for $onven!ent tool to

adMust e#posure to underl+!ng !nstruments

►Spe$ulat!on-%everag!ng 9 !n$rease e#posure long ) bel!eve pr!$e w!ll r!se sort ) bel!eve pr!$e w!ll fall

►

"edg!ng 9 de$rease e#posure long edge ) prote$t!ng aga!nst a r!se !n pr!$e sort edge ) prote$t!ng aga!nst a fall !n pr!$e

Futures rad!ng Strateg!es



Page 25

Pro.t /!agram: Futures =u+er

Profit

Price

0

Futures

Buyer

Fo



Page 27

Pro.t /!agram: Futures Seller

0

Profits

Price

Futures Seller

Fo



Page 23

Futures Pa+o-Pro.t /!agram ougt uest!ons

►Wat !s te d!eren$e between apa+o and pro.t d!agram for a forward$ontra$t Done 9 !n!t!al $ost to enter !s 0

►Wat !s te pa+o d!agram to a olderof an+ underl+!ng wo edges w!t te

appropr!ate not!onal value of futures 8!skfree along #)a#!s >!4e4 pr!$e r!sk of

underl+!ng?



Page 2

"edge '#ample

►Investor owns an !nde# fund tat as a$urrent value of L600►Assume d!v!dends of L20 w!ll be pa!d on te

fund at te end of te +ear►Assume futures $ontra$t tat $alls fordel!ver+ of one !nde# un!t !n one +ear !sava!lable for L625

►Assume te !nvestor edges b+ sell!ng orsort!ng one $ontra$t

►Wat !s te r!skfree rate



Page 26

"edge '#ample Potent!al<ut$omes

Value of ST 885 925 965

Payoff on Short (925 - ST) 40 0 -40

i!i"en" #nco$e 20 20 20

Total 945 945 945



Page *0

8ate of 8eturn for te "edgedPos!t!on

%5

900

900)20925(

)(

0

00

=−+

=

−+

S

S D F



Page *1

ools to AdMust '#posure

►(nderl+!ng <ften d!X$ult or e#pens!ve to obta!n %!ttle leverage allowed

►Forwards-Futures 'as+ and $eap to obta!n >I)=ank for $ustom!@ed

solut!ons, e#$anges for man+? '#treme leverage allowed

►Wen poss!ble, use forwards-futures to

adMust amount of e#posure to underl+!ng %!near $anges !n pa+o d!agram poss!ble '#amples of l!near $anges poss!ble



Page *2

"edge: %o$k In Pro.ts

►I own a w!dget ma$!ne tat produ$esw!dgets at a marg!nal $ost of L* ea$4 G+w!dget ma$!ne w!ll output 1 m!ll!on w!dgets

all at te same t!me, !n * monts4 e$urrent spot pr!$e of w!dgets !s L5, but tere!s no guarantee tat te pr!$e of w!dgets w!llnot Eu$tuate4 ere are no $osts or

d!v!dends to old!ng w!dgets, and ter!skfree rate !s V per +ear4 Wat !s tepresent value of te pro.t $an I lo$k !n !ftere e#!sts a fa!rl+ pr!$ed * mont futures

$ontra$t for w!dgets



Page **

"edge: %o$k In Pro.ts$ont!nued

►If I edge w!t futures, I $an lo$k !n apr!$e of L5407 per w!dget4 /!s$ounted

at te r!skfree rate, tat nets L5 perw!dget4 G+ pro.t !s L2 per w!dget, fora total P; of L2 m!ll!on lo$ked !n4

06.5

)05.1(5

)1(25.

=

+=

+= r S F





Page *5

"edge: 8edu$e '#posure$ont!nued

►Allow "um to sell a $ustom!@ed forward$ontra$t for 600,000 sares of /(G sto$kw!t e#p!rat!on !n 10 +ears4

►&ons!derat!ons for "um 1? &ounterpart+ 8!sk: "um ma+ reasonabl+

reuest tat a spe$!al a$$ount be pla$ed !n !sname for an+ marked ga!ns >!4e4 !f "(G pr!$e

de$reases?, !n $ase G&(bank goes bankruptw!t!n 10 +ears► oug G&(bank !s a better $red!t, "umNs sares are

eld as $ollateral4



Page *7


►Gore $ons!derat!ons for "um 2? &ost for &ustom!@at!on: G&(bank as to make

a pro.t on t!s non)standard forward, so souldoer a pr!$e based on spot)futures par!t+ plus apro.t►In t!s $ase, G&(bank bu+s at a lower pr!$e tan Bfa!rC

►If F 15 a$$ord!ng to spot)futures par!t+, ten forward$ontra$t w!ll spe$!f+ a lower pr!$e ma+be 1450

"um as edged sto$k e#posure on 600U sares w!llre$e!ve 1450-sare on 600U sares regardless of watappens to /(G sto$k pr!$e

G&(bank as lo$ked !n a pro.t above fa!r pr!$e of0450-sare, but !s now e#posed to te sto$k S<



Page *3


►Gore $ons!derat!ons for "um *? 8!sk Sar!ng: G&(bank !s not !n te bus!ness

of old!ng !nd!v!dual sto$k r!sk, and w!ll need tounload tat r!sk►Sell forward to anoter Tbank

=ut onl+ at a Forward pr!$e above 1450 ma+be 1435

►G&(=ank w!ll pa+ 1450-sare on 600U sares to "um

►G&(=ank w!ll re$e!ve 1450-sare on 600U saresfrom Tbank

►Sort sares !n te spot market

►(se opt!ons to $reate sort pos!t!on

►<ter



Page *

Spe$ulate on Garg!n

► Hour t!rd $ous!n Teeesper from !mbu$ktoo as adead)end Mob and no edu$at!on4 "e as managedto save L10000 and !s on te wa+ to te gas stat!onto bu+ lotter+ t!$kets4 Unow!ng tat lotter+ t!$ketsare pr!$ed to return about 50 $ents on te dollar,

+ou suggest spe$ulat!ng !n te $rude o!l marketwere at least te odds are even4 'a$ $rude o!lfutures $ontra$t represents 1000 barrels, and ea$barrel $urrentl+ trades at L74 '#posure to ea$futures $ontra$t reu!res L1000 to be pla$ed !n a

marg!n a$$ount4 "ow mu$ e#posure to o!l $an Teesper obta!n Assum!ng e sells te ma#!mumamount of futures and te pr!$e of o!l de$reases toL5 per barrel, wat !s !s pro.t At wat pr!$ewould e be w!ped out >assum!ng no ma!ntenan$emarg!n?



Page *6

Spe$ulate $ont!nued

►"e $an obta!n e#posure to 10 $ontra$ts:10 $ontra$ts # L7-barrel # 1000 barrels-$ontra$t

L70,000 of spot $rude o!l e#posure►

If e sorts 10 $ontra$ts and te pr!$ede$reases to L5-barrel, ten e makes L2*-barrel # 10 $ontra$ts # 1000 barrels-$ontra$t

L2*0,000►

"e $an lose up to L10,000L10,000 LD-barrel # 10 $ontra$ts # 1000barrels-$ontra$

D 1

If te pr!$e of a barrel of $rude r!ses L1 to L76,

F t d ' t d S t



Page 0

Ti$e

Futures %rices

&ontan'o

or$al Bac*ar"ation

eli!ery "ate

+,%ectations y%othesis

Futures and '#pe$ted SpotPr!$e: eor!es

►F $onverges to S as approa$es If F '>S?, e#pe$tat!ons +potes!s If FY'>S?, $ontango: F de$reases as approa$es If FZ'>S?, normal ba$kwardat!on: F !n$reases as

approa$es



Page 1

F vs '>S?

►Dormal =a$kwardat!on '$onom!sts Ue+nes and "!$k sa!d, !tNs BnormalC

for farmers to edge $ommod!t+ outputs b+sort!ng futures4

'nt!$e non)edgers to bu+ futures: lower F below'>S?

►&ontango

<ppos!te to Dormal =a$kwardat!on ere are more natural bu+ers of te $ommod!t+

tan sellersQ te+ need to bu+ futures

'nt!$e non)edgers to sell futures:!n$rease F

above '>S?



Page 2

Swaps

►A swap !s a pa!r of forwards %ong one forward Sort anoter forward

Wat !s te total $ost to enter a swap►S!n$e swaps are $ompr!sed of full+

$ustom!@able forwards, te+ ma+ be

spe$!.ed for an+t!ng (nspe$!.ed term BswapC often refers to.#ed for Eoat!ng !nterest rate swap >orbond swap?



Page *

Swaps

► <& so tere !s default r!sk4 =ut amount at r!sk !s d!eren$e !n te swapped values, not full

not!onal► otal 8eturn Swaps

Swap te total return on ADH 2 se$ur!t!es, for te same not!onalamount for ea$ se$ur!t!es

<nl+ te d!eren$e b-w te total return of se$ur!t!es a$tuall+$anges ands, D< te not!onal amount

Do forward pr!$!ng ne$essar+ Must e#$ange total return► e fa!r value of L1mm not!onal !n SP500 !s te same as te fa!r

value of L1mm not!onal !n I=G bonds4 ItNs L1mm not!onalK Tuste#$ange te $as Eows to ea$

► Interest 8ate Swap: .#ed for Eoat!ng Swap te $oupon pa+ment of 2 !dent!$al r!sk bonds, one of w!$

!s .#ed rate and one of w!$ !s Eoat!ng rate Pr!n$!pal and .#ed $oupon w!ll alwa+s be !dent!$alQ Eoat!ng rate

w!ll $ange



Page

Swap Pr!$!ng

►Swap pr!$!ng !s based on te fa$t tata swap !s s!mpl+ a ser!es of 2 >ormore? forward $ontra$ts

Appl!$able wen a .#ed amount sould bepa!d ea$ per!od >!4e4 not ne$essar+ !n aswap of !nde# total return swaps?

Start b+ pr!$!ng !nd!v!dual forwards, w!$

leads to Eoat!ng values per per!od Set .#ed amount su$ tat d!s$ounted

value euals d!s$ounted value of separateforwards



Ass!gnment

►8ead &"7►Form ProMe$t roups►'a$ "W group ma+ do te follow!ng:

Sear$ onl!ne or pr!nt news►ADH sour$e►8eal stor!es onl+►Do t!metable >an+ $urrent or !stor!$al e#ample?

=r!ng a pr!nted or $op!ed art!$le about a $ase werefutures-forwards are be!ng used to edge, spe$ulate, orlo$k !n pro.ts►Ident!f+ w!$ of te * strateg!es !s be!ng used►Wr!te a sort summar+ >gu!del!ne 100 words? of te stor+,

!gl!gt!ng te use of futures-forwards !s ass!gnment !s for part!$!pat!on $red!t onl+ /ue ne#t $lass

2015F Investments 02 Forwards, Futures, And Swaps (1)

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