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

1


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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)

Fundamentals of Futures and Options Markets, 8th Ed, Ch 6, Copyright John C. Hull !"#2


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Day Count Conventions

in the U.S. (Page 133-134)

Treasury Bonds: ActualActual (in period)

Corporate Bonds: !"!6"

#oney #ar$et %nstruments: Actual!6"

3


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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 +.



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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


price3uotedis4+""perpricecashis

+""!6"

P

Y

Y

n

P )( =


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%reasury on$ Pri#e +uotes

in the U.S

Cash price 5 uoted price 7Accrued %nterest

8


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%reasury on$ Futures

Pages 13-141

Cash price received by party with shortposition 5

#ost 8ecent ,ettlement 9rice Conversion factor 7 Accrued interest

9


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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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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

42



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Euro$o""ar Futures #ontinue$

A =urodollar futures contract is settled in cash *hen it e


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Exa!"e


Date uote

ov + ;+2

ov 2 ;2!ov ! ;6;&

Dec 2+ ;2


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Exa!"e

,uppose you buy (ta$e a long position in) acontract on ovember +

The contract e


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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)


%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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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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Convexity 2$ustent hen

5.510 (%a&"e .3* !age 146)

#aturity of1utures

Conve


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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)

23

=

B

ect

iyt

in

i

i

1

yDB

B=


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Duration Continue$

*hen the yieldyis e


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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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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

27

FF

P

DV

PD


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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

28

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

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Ch 06 Hull Fundamentals 8 the d