Ch 06 Hull Fundamentals 8 the d
Transcript of Ch 06 Hull Fundamentals 8 the d
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Fundamentals of Futures and Options Markets, 8th Ed, Ch 6, Copyright John C. Hull !"#
Interest Rate Futures
Chapter 6
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Day Count Convention
Defines: the period of time to which the interest rate
applies The period of time used to calculate accrued
interest (relevant when the instrument isbought of sold)
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Fundamentals of Futures and Options Markets, 8th Ed, Ch 6, Copyright John C. Hull !"#
Day Count Conventions
in the U.S. (Page 133-134)
Treasury Bonds: ActualActual (in period)
Corporate Bonds: !"!6"
#oney #ar$et %nstruments: Actual!6"
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Exa!"es
Bond: &' Actual Actual in period ' is earned between coupon payment dates
Accruals on an Actual basis *hen coupons arepaid on #arch + and ,ept +- how much interest is
earned between #arch + and April +. Bond: &' !"!6" Assumes !" days per month and !6" days per
year *hen coupons are paid on #arch + and ,ept
+- how much interest is earned between #arch +and April +.
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Exa!"es #ontinue$
T/Bill: &' Actual!6": &' is earned in !6" days Accrual calculated
by dividing the actual number of days in theperiod by !6" 0ow much interest is earnedbetween #arch + and April +.
Fundamentals of Futures and Options Markets, 8th Ed, Ch 6, Copyright John C. Hull !"#5
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%he Fe&ruary E''e#t (usiness Sna!shot .1*!age 134)
0ow many days of interest are earnedbetween 1ebruary 2&- 2"+! and #arch +-
2"+! when day count is ActualActual in period. day count is !"!6".
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%reasury i"" Pri#es in the US
Fundamentals of Futures and Options Markets, 8th Ed, Ch 6, Copyright John C. Hull !"#7
price3uotedis4+""perpricecashis
+""!6"
P
Y
Y
n
P )( =
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Fundamentals of Futures and Options Markets, 8th Ed, Ch 6, Copyright John C. Hull !"#
%reasury on$ Pri#e +uotes
in the U.S
Cash price 5 uoted price 7Accrued %nterest
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Fundamentals of Futures and Options Markets, 8th Ed, Ch 6, Copyright John C. Hull !"#
%reasury on$ Futures
Pages 13-141
Cash price received by party with shortposition 5
#ost 8ecent ,ettlement 9rice Conversion factor 7 Accrued interest
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Exa!"e
#ost recent settlement price 5 ;"""Conversion factor of bond delivered 5
+!&""Accrued interest on bond 5!""9rice received for bond is
1.380090.00+3.00 = $127.20per 4+"" of principal
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Fundamentals of Futures and Options Markets, 8th Ed, Ch 6, Copyright John C. Hull !"#
C,%
%-on$s %-otes
1actors that affect the futures price:Delivery can be made any time
during the delivery monthAny of a range of eligible bonds
can be delivered
The wild card play
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Euro$o""ar Futures (Page 141-144)
A =urodollar is a dollar deposited in a ban$ outside the>nited ,tates
=urodollar futures are futures on the !/month =urodollar
deposit rate (same as !/month ?%B@8 rate) @ne contract is on the rate earned on 4+ million A change of one basis point or ""+ in a =urodollar
futures 3uote corresponds to a contract price change of
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Fundamentals of Futures and Options Markets, 8th Ed, Ch 6, Copyright John C. Hull !"#
Euro$o""ar Futures #ontinue$
A =urodollar futures contract is settled in cash *hen it e
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Exa!"e
Fundamentals of Futures and Options Markets, 8th Ed, Ch 6, Copyright John C. Hull !"#15
Date uote
ov + ;+2
ov 2 ;2!ov ! ;6;&
Dec 2+ ;2
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Fundamentals of Futures and Options Markets, 8th Ed, Ch 6, Copyright John C. Hull !"#
Exa!"e
,uppose you buy (ta$e a long position in) acontract on ovember +
The contract e
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Fundamentals of Futures and Options Markets, 8th Ed, Ch 6, Copyright John C. Hull !"#
Exa!"e #ontinue$
%f on ov + you $now that you will have 4+million to invest on for three months on Dec 2+-the contract loc$s in a rate of
+"" / ;+2 5 2&&' %n the e
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Foru"a 'or Contra#t /a"ue (!age 140)
Fundamentals of Futures and Options Markets, 8th Ed, Ch 6, Copyright John C. Hull !"#18
%f Qis the 3uoted price of a =urodollarfutures contract- the value of one contractis
10,000[100-0.25(100-Q)]
This corresponds to the 42 per basis
point rule
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Fundamentals of Futures and Options Markets, 8th Ed, Ch 6, Copyright John C. Hull !"#
Forar$ Rates an$ Euro$o""ar
Futures (Page 143-144)
=urodollar futures contracts last as long as+" years
1or =urodollar futures lasting beyond two
years we cannot assume that the forwardrate e3uals the futures rate
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Forar$ Rates an$ Euro$o""ar
Futures #ontinue$
A Gconve
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Fundamentals of Futures and Options Markets, 8th Ed, Ch 6, Copyright John C. Hull !"#
Convexity 2$ustent hen
5.510 (%a&"e .3* !age 146)
#aturity of1utures
Conve
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Fundamentals of Futures and Options Markets, 8th Ed, Ch 6, Copyright John C. Hull !"#
Duration of a bond that provides cash flow ciat time tiis
whereB is its price andyis its yield (continuouslycompounded)
This leads to
Duration (!age 144-147)
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=
B
ect
iyt
in
i
i
1
yDB
B=
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Fundamentals of Futures and Options Markets, 8th Ed, Ch 6, Copyright John C. Hull !"#
Duration Continue$
*hen the yieldyis e
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Fundamentals of Futures and Options Markets, 8th Ed, Ch 6, Copyright John C. Hull !"#
Duration 8at#hing
This involves hedging against interestrate ris$ by matching the durations of
assets and liabilities %t provides protection against small
parallel shifts in the Kero curve
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Use o' Euro$o""ar Futures
@ne contract loc$s in an interest rate on4+ million for a future !/month period
0ow many contracts are necessary to loc$in an interest rate on 4+ million for a futuresi
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Fundamentals of Futures and Options Markets, 8th Ed, Ch 6, Copyright John C. Hull !"#
Duration-ase$ 9e$ge Ratio
VF
Contract 9rice for %nterest 8ate 1utures
DF Duration of Asset >nderlying 1utures at#aturity
P Lalue of portfolio being 0edgedDP Duration of 9ortfolio at 0edge #aturity
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FF
P
DV
PD
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Fundamentals of Futures and Options Markets, 8th Ed, Ch 6, Copyright John C. Hull !"#
Exa!"e (!age 165-161)
Three month hedge is re3uired for a 4+" million portfolioDuration of the portfolio in ! months will be 6& years
!/month T/bond futures price is ;!/"2 so that contract
price is 4;!-"62" Duration of cheapest to deliver bond in ! months is ;2
years umber of contracts for a !/month hedge is
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42.792.950.062,93
8.6000,000,10=
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:iitations o' Duration-ase$
9e$ging
Assumes that only parallel shift in yieldcurve ta$e place
Assumes that yield curve changes aresmall*hen T/Bond futures is used assumes
there will be no change in the cheapest/to/deliver bond
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;2P 8anageent (usiness Sna!shot .3*!age 14