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Chapter 3 Hedging Strategies Using

Futures

Options, Futures, and Other Derivatives, 9th Edition,Copyright © John C. Hull 201 1



Long & Short Hedges

! long "utures hedge is appropriate #henyou $no# you #ill pur%hase an asset inthe "uture and #ant to lo%$ in the pri%e

! short "utures hedge is appropriate#hen you $no# you #ill sell an asset inthe "uture and #ant to lo%$ in the pri%e




Arguments in Favor of Hedging

Options, Futures, and Other Derivatives, 9th Edition,Copyright © John C. Hull 201 &

Co'panies should "o%us on the 'ain(usiness they are in and ta$e steps to

'ini'i)e ris$s arising "ro' interest rates,e*%hange rates, and other 'ar$et varia(les



Arguments against Hedging +hareholders are usually #ell diversi"ied and%an 'a$e their o#n hedging de%isions

t 'ay in%rease ris$ to hedge #hen%o'petitors do not

E*plaining a situation #here there is a loss on

the hedge and a gain on the underlying %an(e di""i%ult

Options, Futures, and Other Derivatives, 9th Edition,Copyright © John C. Hull 201



Basis Risk -asis is usually de"ined as the spotpri%e 'inus the "utures pri%e

-asis ris$ arises (e%ause o" theun%ertainty a(out the (asis #henthe hedge is %losed out




Long Hedge for Purchase of an Asset

De"ine

F 1 : Futures price at time hedge is set up

F 2 : Futures price at time asset is purchased

S 2 : Asset price at time of purchase

b2 : Basis at time of purchase

Options, Futures, and Other Derivatives, 9th Edition,Copyright © John C. Hull 201 /

Cost of asset S 2

Gain on Futures F 2 − F 1

Net amount paid S 2 − ( F 2 − F 1) = F 1 + b2



Short Hedge for Sae of an Asset


e!ne

F 1 : Futures price at time hedge is set up

F 2 : Futures price at time asset is so"dS 2 : Asset price at time of sa"e

b2 : Basis at time of sa"e

#rice of asset S 2

Gain on Futures F 1 − F 2

Net amount recei$ed S 2 + ( F 1 − F 2) = F 1 + b2



Choice of Contract Choose a delivery 'onth that is as %lose aspossi(le to, (ut later than, the end o" the li"e

o" the hedgehen there is no "utures %ontra%t on theasset (eing hedged, %hoose the %ontra%t#hose "utures pri%e is 'ost highly %orrelated#ith the asset pri%e. his is $no#n as %rosshedging.




!ptima Hedge Ratio "page #$%

4roportion o" the e*posure that should opti'ally (ehedged is

#hereσS is the standard deviation o" ∆S , the %hange in the

spot pri%e during the hedging period,

σ F is the standard deviation o" ∆ F , the %hange in the

"utures pri%e during the hedging periodρ is the %oe""i%ient o" %orrelation (et#een ∆S and ∆ F .


F

S h

σ

σρ=*



'ampe "Page ()%

!irline #ill pur%hase 2 'illion gallons o" 5et"uel in one 'onth and hedges using heating

oil "uturesFro' histori%al data σ F 60.0&1&, σS 60.02/&,

and ρ6 0.923


* 0.02630.928 0.780.0313

h = × =



'ampe continued

he si)e o" one heating oil %ontra%t is 2,000 gallons

he spot pri%e is 1.9 and the "utures pri%e is 1.99

7(oth dollars per gallon8 so that

Opti'al nu'(er o" %ontra%ts is

#hi%h rounds to &


0.78 2, 000, 000 42, 000= ×

.303&0002991

000330&000000291

,,.

,,,,.

=×==×=

F

A

V

V



Aternative *efinition of !ptima

Hedge RatioOpti'al hedge ratio is

#here varia(les are de"ined as "ollo#s


Corre"ation %et&een percentage dai"'

changes for spot and futures of percentage dai"' changes in spot

of percentage dai"' changes in futures

ˆˆˆ ˆ

S

F

h σ

ρ σ =

ˆ ρ ˆS

σ

̂F σ



!ptima +um,er of ContractsQ A ie of position %eing hedged (units)

Q F ie of one futures contract (units)

V A

*a"ue of position %eing hedged (=spot price time Q A

)

V F *a"ue of one futures contract (=futures price times Q F )

Options, Futures, and Other Derivatives, 9th Edition,Copyright © John C. Hull 201 1&

Opti'al nu'(er o" %ontra%ts i"ad5ust'ent "or daily settle'ent

Opti'al nu'(er o" %ontra%tsa"ter tailing ad5ust'ent: toallo# or daily settle'ent o"

"utures

F

A

Q

Qh*

=ˆ

A

F

hV

V =



Hedging Using -nde' Futures"Page (.%

o hedge the ris$ in a port"olio the

nu'(er o" %ontra%ts that should (eshorted is

#here V A is the value o" the port"olio, β isits (eta, and V F is the value o" one

"utures %ontra%t


F

A

V

V β



'ampe+;4 00 "utures pri%e is 1,000

<alue o" 4ort"olio is = 'illion

-eta o" port"olio is 1.

hat position in "utures %ontra%ts on the +;4

00 is ne%essary to hedge the port"olio>




Changing Betahat position is ne%essary to redu%ethe (eta o" the port"olio to 0.>

hat position is ne%essary to in%reasethe (eta o" the port"olio to 2.0>

Options, Futures, and Other Derivatives, 9th Edition,Copyright © John C. Hull 201 1/



/h0 Hedge 1uit0 Returns

?ay #ant to (e out o" the 'ar$et "or a #hile.Hedging avoids the %osts o" selling andrepur%hasing the port"olio

+uppose sto%$s in your port"olio have anaverage (eta o" 1.0, (ut you "eel they have(een %hosen #ell and #ill outper"or' the'ar$et in (oth good and (ad ti'es. Hedging

ensures that the return you earn is the ris$@"ree return plus the e*%ess return o" yourport"olio over the 'ar$et.




Stack and Ro "page (2($%

e %an roll "utures %ontra%ts "or#ard tohedge "uture e*posures

nitially #e enter into "utures %ontra%ts tohedge e*posures up to a ti'e hori)on

Just (e"ore 'aturity #e %lose the' out an

repla%e the' #ith ne# %ontra%t re"le%t thene# e*posure

et%




Li1uidit0 -ssues "See Business Snapshot 345%

n any hedging situation there is a danger thatlosses #ill (e reali)ed on the hedge #hile thegains on the underlying e*posure areunreali)ed

his %an %reate liAuidity pro(le's

One e*a'ple is ?etallgesells%ha"t #hi%h sold

long ter' "i*ed@pri%e %ontra%ts on heating oiland gasoline and hedged using sta%$ and roll

he pri%e o" oil "ell.....


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