Basis risk. When speaking about forward or futures contracts, basis risk is the market


 Francine Lynch
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1 Basis risk Whn spaking about forward or futurs contracts, basis risk is th markt risk mismatch btwn a position in th spot asst and th corrsponding futurs contract. Mor broadly spaking, basis risk (also calld sprad risk) is th markt risk rlatd to diffrncs in th markt prformanc of two similar positions. Th mor th instrumnt to hdgd and th undrlying usd ar imprfct substituts, th biggr th basis risk is. For xampl, a forign xchang tradr who is hdging a long spot position with a short forward position is taking th basis risk. Whil th spot position is snsitiv only to changs in th xchang rat, th forward position is also affctd by yild curv shifts. Accordingly, th two positions do not prfctly hdg on anothr, and th tradr is taking basis risk. A portfolio managr who wants to tmporarily liminat th markt xposur of a divrsifid stock portfolio might short &P 500 futurs. If th composition of th portfolio dos not xactly mirror th &P 500, th hdg will not b prfct, and th portfolio managr will b taking basis risk. A swap tradr who hdgs hrslf/himslf with bonds is also taking a basis risk. Complx risks ar somtims dscribd as consisting of svral simplr risks, on or mor of which ar sprad risks. For xampl, th markt risk of corporat bonds can b dscribd as comprising Trasury yild curv risk as wll as th sprad risk btwn Trasury yilds and corporat yilds.
2 Th basis is traditionally dfind as th diffrnc btwn th futurs pric and th cash or strt pric. Th basis is mad up of a numbr of componnts: storag, intrst, handling and transportation costs btwn th location and th futurs dlivry point, local supply and dmand conditions, profit margins including opportunity costs, quanto and convxity corrction (th latr is particularly rlvant for intrst rats futurs). Th narby futurs month is normally usd to calculat th basis. Basis = Futurs pot (1) Factors that incras th basis ar: Intrst costs, storag costs, positiv handling and transportation costs btwn th location and th futurs dlivry point Positiv convxity corrction as for Eurodollar futurs. Th convxity is positiv in th cas of ngativ corrlation btwn th undrlying of th futurs contract and th intrst rats. Positiv quanto corrction, in th cas of positiv corrlation btwn th Forign xchang rat usd to comput th valu of th undrlying of th futurs and th undrlying of th futurs itslf. Whil factors that dcrass th basis ar: hortag of local supply on th spot markt Positiv dividnds paid by th undrlying asst of th futurs contract
3 Known positiv cash flows gnratd by th undrlying asst of th futurs contract Th basis may b consistnt ovr tim but in crtain situations it may fluctuat considrably. Th basis risk concrns th risk associatd with unxpctd changs in th basis btwn th tim a hdg is placd and th tim that it is liftd. Unfortunatly, hdging cannot liminat basis risk. Entring in a trad that spculats on th cost of carry is rfrrd to as basis trading. It consists in taking th sprad btwn th futurs contract and th spot asst. Futurs Pric in contango: F> Positiv basis pot Pric Convrgnc to spot At xpiry F T = T. Futurs Pric in backwardation: F< Ngativ basis Tim Figur 1: Contingo and backwardation for futurs markts Whn comparing th forward/futurs prics with th spot pric, on may find:
4 A positiv cost of carry, maning that forward/futurs prics F ar highr than spot prics. Th basis F is positiv. Futurs markts ar said to b in contingo. A ngativ cost of carry, implying a ngativ basis. Futurs markts ar said to b in backwardation. This situation is also rfrrd to as invrtd markt. Figur 1 summariss th two situations and shows that at maturity futurs convrg to spot. At maturity, th basis convrgs to zro. (Nglcting som tchnical problm such as th wild card ffct for bond futurs) In ordr to do basis trading, it is important to know how to comput th fair valu of th basis. Long th basis mans long futurs and short th spot whil short th basis is xactly th opposit trad. Tabl 1, blow givs xampl of th computation of th fair valu of th futurs contract. Th notations usd for th tabl ar r is th rat usd to comput th cost of financing, clos to th risk fr rat as rad from th standard intrst rat curv and adjustd by th funding cost of th trading dsk q is th continuous yild dividnd of th undrlying asst of th futurs contract g is th yild of th storag and transportation costs also calld th convninc yild for commodity futurs
5 I is th prsnt valu of th diffrnt cash flows gnratd by th undrlying asst of th futurs contract forign r is th forign funding rat whil r dom = r is th domstic on σ HL is th yarly Ho&L volatility (typical valus ar around 1%) T is th tim to maturity of th futurs contract T U is th tim to maturity of th rat undrlying th futurs contract ρ ( FX,U ) is th corrlation btwn th FX rat X and th undrlying asst U of th futurs contract ρ ( IR,U ) is th corrlation btwn th spot intrst rat IR and th undrlying asst U of th futurs contract X is th rat usd to comput th quanto futurs. Th futurs pays forign in domstic currncy and X is domstic/forign σ X is th yarly volatility of th forign rat σ forign is th volatility of th forign asst undrlying th futurs contract W thn hav th following tabl to comput th fair valu of th futurs. Ral lif xampls oftn includ a combination of th simpl cas dscrib in th tabl 1. (s Quantityadjusting options (quantos))
6 Cas Valu of th Futurs Cash Flow(s) with prsnt valu I ( ) rt / 0 Know continuous dividnd yild q ( r q )T 0 torag cost g ( r+ g )T Forign currncy forward dom forign ( r r )T 0 0 Convxity corrction (this is addd on top of th normal valu of th forward) Quanto corrction (this is addd on top of th normal valu of th forward) Exp 1 σ ρ 2 ( IR, U ) TT ) ( U ( X, U ) σ X σ ) Exp( ρ T U Tabl 1: Exampl of computation of Futurs in ordr to comput th fair valu of th basis Eric Bnhamou 1 waps tratgy, London, FICC Goldman achs Intrnational 1 Th viws and opinions xprssd hrin ar th ons of th author s and do not ncssarily rflct thos of Goldman achs
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