Session 2 Derivatives & Risk Management Prof. Aparna BhatForwards & FuturesForward ontra!tsDefnition an agreement between two parties that calls for the delivery of an asset at a future point in time with a price agreed upon todayFeaturesExistence of two partiesOTC contractPrice determination takes place todayMutual obligation to performCounterparty riskMutual consent for cancellationNo upfront paymentNormally settled by delivery of the underlying assetForward ontra!ts v"s Spot !ontra!tsSpot !ontra!ts re#uire immediate pa$ment % forward &u$er gains in terms of interestSpot !ontra!ts re#uire immediate de'iver$% forward se''er earns in!ome on asset and in!urs storage !ost% short(se''ing possi&'eSpot !ontra!t possi&'e &etween unknown persons% forward !ontra!ts possi&'e on'$ &etween known !ounterparties or re#uire me!hanisms to prote!t against defau'tFutures !ontra!ts )h$ futures !ontra!ts*Forwards invo've !redit risk hen!e unsuita&'e for sma'' investors+a!k of widespread investor parti!ipation 'eads to 'ow 'i#uidit$ and poor pri!e dis!over$,rading through an e-!hange !an mitigate !redit risk whi!h however re#uires standardi.ation of !ontra!tsFutures !ontra!t is /a forward contract with standardized terms traded on an organized exchange and follows a daily settlement procedure whereby losses of one party to the contract are paid to the other partySpe!i0!ations of a futures !ontra!tontra!t Si.e1uotation unitMinimum pri!e 2u!tuation 3ti!k si.e4ontra!t grade,rading hoursSett'ement Pri!eDe'iver$ termsDai'$ pri!e 'imits and trading ha'tsSett'ement of a futures !ontra!t56setting or 7S#uaring o68 the positionDe'iver$(&ased or 7ph$si!a'8 sett'ementash(&ased sett'ementForwards and futures ( distin!tion Forwards Futures,raded 5ver the !ounterustom(made !ontra!tsredit risk &orne &$ parties9o marginsSett'ed &$ de'iver$% !'ose(out di6i!u't9o pu&'ished pri!e(vo'ume information:-!hange tradedStandardi.ed !ontra!tsredit risk &orne &$ the P;nitia' margin and dai'$ M,M marginsDe'iver$ rare% !'ose(out eas$Pu&'ished pri!e(vo'ume dataSnapshot of a futures #uote5pen ;nterest ?D 2@>? a trader takes a 'ong position in >@ !ontra!ts of 9ift$ futures e-piring on =u'$ A@D 2@>? at F@G?. a'!u'ate his dai'$ M,M pa$(in"pa$(out on the &asis of the fo''owing dataompute the gain or 'oss for the trader if the position is !'osed on =une 2A at FB>@.>@ Date Settlement Price!"#$"%#! '#('!$"#$"%#! )$(%!)"#$"%#! *(*!&"#$"%#! &))(!!+"#$"%#! &%!&('#%%"#$"%#! &*)!($#%*"#$"%#! &'#%(#App'i!ations of Forwards and FuturesTrading or speculation taking a position in a forward or futures !ontra!t without an$ under'$ing e-posure and tr$ing to pro0t from a directional viewHedging taking an opposite position in a forward"futures !ontra!t in order to mitigate risks to the under'$ing Arbitrage taking a !om&ined position in the forward"futures and the under'$ing in order to proft from the mispricing of the forward"futures,rading in forwards and futuresPart$ entering into a &u$ !ontra!t H /'ongEPart$ entering into a se'' !ontra!t H /shortEA 'ong position &ene0ts from a rise in pri!e of the under'$ingPro0t to 'ong H Spot pri!e at maturit$ 5rigina' futures pri!eA short position &ene0ts from a fa'' in pri!e of under'$ingPro0t to short H 5rigina' futures pri!e Spot pri!e at maturit$ Forwards and futures have linear! pa$o6sPri!ing of a forward !ontra!t79o ar&itrage8 is the main assumption ,he prin!ip'e of 7rep'i!ation8ost of the 7rep'i!ating portfo'io8 H !ost of the derivative :-amp'e Forward pri!e of a paintingost of !arr$ mode'Spot pri!e of go'd is S and !urrent interest rate is denoted &$ r)hat shou'd &e the pri!e for &u$ing or se''ing go'd at the end of si- months from toda$*,he forward pri!e 7F8 wi'' &e re!eived on'$ on the maturit$ dateD i.e. at the end of si- months;f the se''er se''s at the spot pri!e S and invests the pro!eeds at the !urrent interest rate rD he wi'' re!eive SI3> J rIt4,he minimum pri!e F is therefore S I3> J rIt4 ,his is the pri!e at whi!h there wi'' &e no ar&itrage opportunit$Assumptions of !ost(of(!arr$ mode'9o transa!tion !osts9o restri!tions on short sa'esSame risk(free rate for &orrowing and 'ending2@D risk(free rateH?LD periodH > $earAs FH SI3>Jrt4 D F H >2M;f a!tua' F H >2F cash"carr# arbitrage possi&'eBu$ sto!k toda$ at >2@ &$ &orrowing at ?LSe'' sto!k one($ear forward at >2FCo'd sto!k for > $earAt maturit$D se'' sto!k at >2FRepa$ &orrowing with interest at >2M9et gain is Rs.2 3free 'un!h *4Hence F cannot be greater than $%&'(rt)2@D risk(free rateH?LD periodH > $earAs FH SI3>Jrt4 D F H >2M;f a!tua' F H >2A reverse cash"carr# arbitrage possi&'eSe'' sto!k toda$ at >2@ and 'end pro!eeds at ?LBu$ sto!k one($ear forward at >2AAt maturit$D get &a!k 'oan with interest at >2MRe!eive de'iver$ of sto!k at >2A9et gain is Rs.A3free 'un!h *4Hence F cannot be less than $%&'(rt) Pri!ing with !ontinuous !ompounding;nvestment assets with no interim !ash 2ows;nvestment assets with known interim !ash 2ows;nvestment assets with known dividend $ie'donsumption assets)here FH forward pri!eD SHspot pri!eD rH!ontinuous'$ !ompounded interest rateD #H dividend $ie'dD ;H P< of known !ash 2owD uHstorage !osts per unit of timeD $H !onvenien!e $ie'd($ear TSD('i&or H ?LD >($ear ;9R rate H>@LD >($ear TSD";9R forward rate H BU.>@)hat is the ar&itrage imp'ied*Forwards on !onsumption assetsFair va'ue of forward H )here u H storage !osts as a L of va'ue of asset and $ H !onvenien!e $ie'donvenien!e $ie'd measures &ene0t of ho'ding ph$si!a' inventor$ of !onsumption asset instead of forward !ontra!t on that asset;s not o&serva&'e or measura&'e dire!t'$an &e estimated from past dataSophisti!ated mode's to determine it)h$ ar&itrage not a'wa$s feasi&'e*;mp'ementing !ash(!arr$ ar&itrage re#uires a&i'it$ to &orrow at risk(free rate5n'$ 'arge institutiona' p'a$ers have that a&i'it$Reverse !ash(!arr$ ar&itrage re#uires a&i'it$ to &orrow the se!urit$5wners ma$ &e unwi''ing to se'' or 'end espe!ia''$ in !ase of !onsumption assetsRegu'ator$ restri!tions on short se''ingontango and Ba!kwardation9orma''$ futures pri!e P spot pri!eVnown as /ontangoE market9on(in!ome earning 0nan!ia' assets norma''$ in !ontangoSometimes spot pri!e P futures pri!eVnown as /&a!kwardationE or inverted market onsumption assets in &a!kwardation when /!onvenien!e $ie'dE e-!eeds !ost of !arr$Ma$ &e due to anti!ipated disruption in supp'$ou'd &e due to /short s#uee.eE;mp'ied repo rate 3;RR4;t is 7that interest rate whi!h wou'd make the o&served forward or futures pri!e e#ua' to the theoreti!a' pri!e predi!ted under !onditions of no(ar&itrage using given va'ues of the spot pri!e and other varia&'es8 ;mp'ied repo rate is the rate at whi!h an investor !an 7&orrow s$ntheti!a''$8 &$ going short spot and 'ong forward7invest s$ntheti!a''$8 &$ going 'ong spot and short forward,here wi'' &e no ar&itrage when+ending rate R ;RR R Borrowing rateForward pri!e and va'ue@ $ears at pri!es 0-ed in >GG2Due to 'ong(term short forward !ontra!ts the !ompan$ fa!ed the risk of a rise in oi' pri!esCedged the a&ove risk &$ a /sta!k and ro'' hedgeE:ntered into a 'ong position in near(month oi' futures !ontra!ts for the entire #uantit$ to &e supp'ied over the >@ $ear period5n e-pir$ of near(month !ontra!t the position was ro''ed over to the ne-t near(month !ontra!t for the remaining #uantit$ of e-posurease stud$ !ontd..5i' pri!es were in norma' &a!kwardation when strateg$ was adopted &a!kwardation was e-pe!ted to !ontinueTnder !onditions of &a!kwardation futures pri!e is &e'ow the /e-pe!ted future spot pri!eE and hen!e futures pri!es rise to !onverge with the spot at e-pir$Cen!e MO e-pe!ted to make M,M gains on its 'ong futures positions even as it 'ost on its forward sa'e !ommitmentsCowever oi' market !hanged to !ontangoD i.e. spot pri!es started de!'ining and fe'' &e'ow the futures pri!esCen!e as MO8s 'ong futures !ontra!ts approa!hed e-pir$D the futures pri!es were de!'ining and MO in!urred huge M,M 'ossesase stud$ !ontdDue to its huge 'ong position in the futures marketD MO fa!ed margin !a''s and ran into funding pro&'emsA'though MO was making pro0ts on its a!tua' sa'es under the forward !ontra!tsD these gains !ou'd not &e re!ogni.ed in P&+ under the Oerman a!!ounting ru'es whi'e M,M 'osses on the 'ong futures position had to &e re!ogni.edAs a resu't MO8s P&+ was in a mess and adverse !onse#uen!es in the market:ventua' 'osses Y>.? &i''ionRisks fa!ed &$ MO &asis riskD 'i#uidit$ risk and operationa' risk