Problem 7.1 Amber McClain mber 3lain the urreny speulator 4e met earlier in the haptersells haptersells eight &une futures ontrats for 500000 pesos at the losing prie 6uoted in #'hibit 8.1. a. What is the value of her her position at maturity if the ending ending spot rate is $0.12000/Ps? b. What is the value of her position at maturity if the ending spot rate is $0.09800/Ps? . What is the value of her position at maturity if the ending spot rate is $0.11000/Ps?
Assumptions !umber of pesos per futures ontrat ontrat !umber of ontrats "uy or sell the peso futures?
#nding spot rate $/peso% &une futures settle prie from from #'h8.1 $/peso% (pot ) *utures +alue of total position at maturity ,($% +alue - ) !otional ' (pot ) *utures% ' 8
a. Values 500,000 8.00 Sell
b. Values 500,000 8.00 Sell
c. Values 500,000 8.00 Sell
$0.12000 $0.1077 $0.01227
$0.09800 $0.1077 !$ !$0.0097"
$0.11000 $0.1077 $0.00227
!$#9,080.00"
$8,920.00
!$9,080.00"
nterpretation mber buys at the spot prie and sells at the futures prie. f the futures prie is greater than the ending spot prie she maes a profit.
Problem 7.2 Pele%&s Puts Peleh 4rites a put option on &apanese yen 4ith a strie prie of $0.008000/ 125.00/$% at a premium of 0.0080: per yen and 4ith an e'piration date si' month from no4. ;he option is for 12500000. What is Peleh0/$.
a" Values 12,500,000 180 $0.008000 $0.000080
b" Values 12,500,000 180 $0.008000 $0.000080
c" Values 12,500,000 180 $0.008000 $0.000080
'" Values 12,500,000 180 $0.008000 $0.000080
e" Values 12,500,000 180 $0.008000 $0.000080
(" Values 12,500,000 180 $0.008000 $0.000080
)" Values 12,500,000 180 $0.008000 $0.000080
110.00 $0.009091
115.00 $0.008*9*
120.00 $0.008
125.00 $0.008000
10.00 $0.007*92
15.00 $0.007#07
1#0.00 $0.0071#
7ross profit on option ess premium !et profit ,($/ ¥ ¥%
$0.0 $0.000 000 000 $0.000080 $0.0 $0.000 000 080
$0.00 0.0000 0000 00 $0.000080 $0.00 0.0000 0080 80
$0.0 $0.000 0000 000 0 $0.000080 $0.0 $0.000 0008 080 0
$0. $0.00 0000 0000 00 $0.000080 $0. $0.00 0000 0080 80
!$0. !$0.00 000 008 08"" $0.000080 !$0. !$0.00 0002 0228 28""
!$0. !$0.00 0005 059 9"" $0.000080 !$0. !$0.00 0005 051 1""
!$0. !$0.0 00085 00857" 7" $0.000080 !$0. !$0.0 00077 00777" 7"
!et profit total
$1,000.00
$ 1, 1,000.00
$ 1, 1,000.00
$ 1, 1,000.00
!$2,8#*.15"
!$*,#07.#1"
!$9,71#.29"
Assumptions !otional prinipal ¥ ¥% aturity days% (trie prie ,($/ ¥ ¥% Premium ,($/ ¥ ¥%
#nding spot rate ¥ ¥/,($% in ,($/ ¥ ¥
Problem 7. Ventosa n+estments &amie DodrigueE a urreny trader for 3hiago)based +entosa +entosa nvestments nvestments uses the follo4ing futures 6uotes on the "ritish pound £% to speulate on the value of the pound. ritis% Poun' -utures, S$/poun' !CM" Maturit3 Marc% une
a. b. . d.
pen 1.>2> 1.>1>
4i)% 1.>28 1.>188
o6 1.>21> 1.>1>
Settle 1.>228 1.>12
C%an)e 0.00=2 0.00=0
f &aime buys 5 &une pound futures and the spot rate at maturity is $1.=980/ £ 4hat is the value of her position? f &amie sells 12 arh arh pound futures and the spot rate at maturity is $1.>50/ $1.>50/ £ 4hat is the value of her position? f &amie buys = arh pound futures and the spot rate at maturity is $1.>50/ £ 4hat is the value of her position? f &amie sells 12 &une pound futures and the spot rate at maturity is $1.=980/ £ 4hat is the value of her position? a" Values *2,500 une 5 bu3s
b" Values *2,500 Marc% 12 sells
c" Values *2,500 Marc% bu3s
'" Values *2,500 une 12 sells
$1.980 $1.#1*2 !$0.0182"
$1.#5*0 $1.#228 $0.02
$1.#5*0 $1.#228 $0.02
$1.980 $1.#1*2 !$0.0182"
+alue of position at maturity $% !$5,*87.50" buysC !otional ' (pot (pot ) *utures% ' ontrats sellsC ) !otional ' (pot ) *utures% ' ontrats
!$2#,900.00"
$*,225.00
$1 $ 1,*50.00
Assumptions Pounds A% per futures ontrat aturity month !umber of ontrats Bid she buy or sell the futures?
#nding spot rate $/A% Pound futures ontrat settle prie $ (pot ) *utures
nterpretation
"uys a futuresC &amie buys at the futures prie and sells at the ending spot prie. (he therefore profits 4hen the futures prie is less than the ending spot prie. (ells a futureC &amie buys at the ending spot prie and sells at the futures prie. (he therefore profits 4hen the futures prie is greater than the ending spot prie.
Contract *2,500 poun's pen 4i)% nterest 1.>@00 2505 1.>550 809
Problem 7.# Sallie Sc%nu'el Sc%nu'el (allie (hnudel trades urrenies for Feystone *unds in &aarta. (he fouses nearly all of her time and attention on the ,.(. dollar/(ingapore dollar $/($% ross)rate. ;he urren t spot rate is $0.000/($. fter onsiderable study she has onluded that the (ingapore dollar 4ill appreiat e versus the ,.(. dollar in the oming 90 days probably to about $0.@000/($. (he has the follo4ing options on the (ingapore dollar to hoose fromC ption Put on (ing $ 3all on (ing $
Strie Price $0.500/($ $0.500/($
Premium $0.0000=/($ $0.000>/($
a. (hould (allie buy a put on (ingapore dollars or a all on (ingapore dollars? b. What is (allie
Call on S$ $0.*500 $0.000#*
Put on S$ $0.*500 $0.0000
Values $0.*000 90 $0.7000
a. S%oul' Sallie bu3 a put on Sin)apore 'ollars or a call on Sin)apore Sin)apore 'ollars;
(ine (allie e'pets the (ingapore dollar to appreiate versus the ,( dollar she should buy a all on (ingapore dollars. ;his gives her the right to ",G (ingapore dollars at a future date at $0.5 eah and then immediately resell them in the open maret at $0.@0 eah for a profit. f her e'petation of the future spot rate proves orret.%
Problem 7.9 Vatic Capital 3ahita Haynes 4ors as a urreny speulator for +ati +ati 3apital of os ngeles. Her latest speulative position is to profit from her e'petation that the ,.(. dollar 4ill rise signifiantly against the &apanese yen. ;he urrent spot rate is 120.00/$. (he mu st hoose bet4een the follo4ing 90)day options on the &apanese yenC ption Put on yen 3all on yen
Strie Price 125/$ 125/$
Premium $0.0000=/($ $0.000>/($
a. (hould 3ahita buy a put on yen or a all on yen? yen? b. What is 3ahita0/$? Assumptions 3urrent spot rate &apanese yen/,($% in ,($/yen aturity of option days% #'peted ending spot rate in i n 90 days yen/$% in ,($/yen
(trie prie yen/,($% in ,($/yen Premium ,($/yen% a. S%oul' s%e bu3 a call on 3en or a put on 3en;
Values 120.00 $0.008 90 1#0.00 $0.0071# Call on 3en 125.00 $0.00800 $0.000#*
Put on 3en 125.00 $0.00800 $0.0000
Problem 7.10 Callin) All Pro(its ssume a all option on euros is 4ritten 4ith a strie prie of $1.2500/I at a premium of =.80: per euro $0.0=80/I% and 4ith an e'piration date three months from no4. ;he option is for I100000. 3alulate your profit or loss s hould you e'erise before maturity at a time 4hen the euro is traded spot at ..... !oteC the option premium premium is =.8 ents per euro not =8 ents ents per euro.
Assumptions !otional prinipal euros% aturity days% (trie prie ,($/euro% Premium ,($/euro% #nding spot rate ,($/euro%
7ross profit on option ess premium !et profit ,($/euro% !et profit total
a. Values @ 100,000.00 90 $1.2500 $0.080 $1.1000
b. Values @ 100,000.00 90 $1.2500 $0.080 $1.1500
c. Values @ 100,000.00 90 $1.2500 $0.080 $1.2000
'. Values @ 100,000.00 90 $1.2500 $0.080 $1.2500
e. Values @ 100,000.00 90 $1.2500 $0.080 $1.000
(. Values @ 100,000.00 90 $1.2500 $0.080 $1.500
). Values @ 100,000.00 90 $1.2500 $0.080 $1.#000
$0.0000 !$0.080" !$0.080"
$0.0000 !$0.080" !$0.080"
$0.0000 !$0.080" !$0.080"
$0.0000 !$0.080" !$0.080"
$0.0500 !$0.080" $0.0120
$0.1000 !$0.080" $0.0*20
$0.1500 !$0.080" $0.1120
!$,800.00"
!$,800.00"
!$,800.00"
!$,800.00"
$1,200.00
$*,200.00
$11,200.00
Problem 7.15 C%r3sler C
3hrysler 3 the no4 privately held ompany sold)off by Baimler3hrysler must pay floating rate interest three months from no4. t 4ants to lo in t hese interest payments by buying an interest rate futures ontrat. ontrat. nterest rate futures for for three months from no4 settled at 9=.0@ for a yield of .9=J per annum. a. f the floating interest rate three months from no4 is .00J 4hat did 3hrysler 3hrysler gain or lose? b. f the floating interest rate is 8.00J three months from no4 no4 4hat did 3hrysler gain or lose?
Assumptions nterest rate futures losing prie #ffetive yield on interest rate futures
C%r3sler&s interest rate pa3ments 6it% (utures
nterest payment due in three months (ell a future tae a short positi on% 7ain or loss on position
Values 9.07 *.90 B%ree Mont%s -rom >o6 -loatin) ate is -loatin) ate is *.000 8.000 *.000 ?*.90 ?0.90 oss
8.000 ?*.90 1.070 =ain
Problem 7.17 lu+ia an' Para)uas luvia anufaturing and Paraguas Paraguas Produts both see funding at the lo4est possible ost. luvia 4ould prefer the fle'ibility of floating rate borro4ing borro4ing 4hile Paraguas 4ants the seurity of fi'ed rate rate borro4ing. luvia is the more redit)4orthy ompany. ompany. ;hey fae fae the follo4ing rate struture. luvia 4ith the better redit rating has lo4er borro4ing osts in both types of borro4ing. luvia 4ants floating rate debt so it ould borro4 at "KDL1J. "KDL1J. Ho4ever it ould borro4 borro4 fi'ed at at 8J and s4ap for floating rate debt. Paraguas 4ants fi'ed rate so i t ould borro4 fi'ed at 12J. Ho4ever it ould borro4 floating at "KDL2J and s4ap for fi'ed rate debt. What should they do?
Assumptions 3redit rating Prefers to borro4 *i'ed)rate ost of borro4ing *loating)rate ost of borro4ingC "KD value is unimportant% (pread ;otal floating)rate Comparati+e A'+anta)e in orro6in) luvia
Da+ier AAA -loatin) 8.000
Eulu -iFe' 12.000
5.000 1.000 *.000
5.000 2.000 7.000
Values #.000 1.000 .000
;he =.0J omparative advantage enMoyed by luvia represents the opportunity set for improvement for
Problem 7.18 Bri'ent&s Cross Currenc3 S6ap: S-r (or S$ ;rident 3orporation entered entered into a three)year three)year ross urreny interest rate s4ap to reeive ,.(. dollars and pay (4iss frans. ;rident ho4ever deided to un4ind the s4ap after one year thereby having t4o years left o n the settlement osts of un4inding the s4ap after one year. year. Depeat the alulations for un4inding but assume that the follo4ing rates no4 applyC Assumptions !otional prinipal Kriginal spot e'hange rate (*r./$ !e4 1)year later% spot spot e'hange rate (*r./$ (*r./$ !e4 fi'ed ,( dollar interest !e4 fi'ed (4iss fran interest
$
a. nterest G S6ap Pa3ments
Deeive fi'ed rate dollars at this rateC Kn a notional prinipal ofC ;rident 4ill reeive ash flo4sC
$
Values 10,000,000 1.5000 1.55*0 5.20 2.20
S6ap ates KriginalC ,( dollar KriginalC (4iss fran
? 3ear bi' 5.5* 1.9
Hear 0
Hear 1
Hear 2
Hear
5.5*
5.5*
5.5*
10,000,000 I
;rident 4ill pay ash flo4sC Kn a notional prinipal ofC Pay fi'ed rate (4iss frans at this rateC
I
JJJ
I
JJJ
I
S-r. 01,500 I
S-r. 01,500 I
S-r. 15,01,500
S-r. 15,000,000
b. n6in'in) t%e s6ap a(ter one?3ear
Demaining (4iss fran ash outflo4s P+ fator at no4 urrent fi'ed (* interest P+ of remaining (* ash outflo4s 3umulative P+ of (* ash outflo4s
JJJ
N 1.5000 O
#'hange rate time of s4ap (*r./$ )
Demaining dollar ash inflo4s P+ fator at no4 urrent fi'ed $ interest P+ of remaining dollar ash inflo4s 3umulative P+ of dollar ash infllo4s
?3ear as 5.59 2.01
2.01
2.01
2.01
Hear 1
Hear 2
Hear
$ 5.20 $ $
55*,000 0.950* 528,517
$ $
10,55*,000 0.90* 9,58,22
10,0**,750
2.20 S-r. 1#,9##,827
S-r. 01,500 0.9785 S-r. 295,010
S-r. 15,01,500 0.957# S-r. 1#,*#9,818
Problem 7.20 -alcor *alor is the ,.(.)based automotive parts supplier 4hih 4as spun)off from 7eneral otors in 2000. With annual sales of over $2 billion the ompany has e'panded its marets far beyond the traditional automobile manufaturers in the pursuit of a more diversified sales base. s part of the general diversifiation effort the ompany 4ishes to diversify the urreny of denomination of its debt portfolio as 4ell. ssume *alor enters into a $50 million @)year ross urreny interest rate s4ap to do Must that pay euro and reeive dollars. ,sing the data in #'hibit 8.1= a. 3alulate all prinipal and interest interest payments in both urrenies urrenies for the life of the s4ap. b. ssume that three years years later *alor *alor deides to un4ind the s4ap agreement. agreement. f >)year >)year fi'ed rates of interest interest in euros have no4 risen to 5.=5J and >)year >)year fi'ed rate dollars dollars have fallen to >.>0J and the urrent spot e'hange rate of $1.02/I 4hat is the net present value of the s4 ap agreement? Who pays 4ho 4hat?
Assumptions !otional prinipal (pot e'hange rate $/I
$
Values 50,000,000 1.1*
a. nterest G S6ap Pa3ments
Deeive fi'ed rate dollars at rateC !otional prinipal ofC Deeive ash inflo4s ofC
Hear 0
$
S6ap ates ,( dollar #uros
Hear 1
7? 3ear bi' 5.8* #.01
Hear 2
7?3ear as 5.89 #.05
Hear
Hear #
Hear 5
Hear *
Hear 7
5.8* 50,000,000 $ 2,90,000 $ 2,90,000
$ 2,90,000 $ 2,90,000 $ 2,90,000 $ 2,90,000 $ 52,90,000
N (pot e'hange rate $/I
1.1*
O Pay ash outflo4s ofC !otional prinipal ofC Pay fi'ed rate euros at rateC
@ 1,7#5,*90
@ 1,7#5,*90
@ 1,7#5,*90
@ 1,7#5,*90
@ 1,7#5,*90
@ 1,7#5,*90
@ ##,8#9,18
Hear 1
Hear 2
Hear
Hear #
Hear 5
Hear *
Hear 7
@ #,10,##8 #.05
b. n6in'in)t%e S6ap
Hear 0
f the s4ap is un4ound three years later there are four years of ash flo4s remainingC Demaining dollar ash inflo4s P+ fator at no4 urrent fi'ed $ interest P+ of remaining dollar ash inflo4s 3umulative P+ of $ ash infllo4s
#.#0 $
$ 2,90,000 $ 2,90,000 $ 2,90,000 $ 52,90,000 0.9579 0.9175 0.8788 0.8#18 $ 2,80*,51 $ 2,*88,21 $ 2,57#,9# $ ##,555,5#
52,*25,0
Demaining euro ash outflo4s P+ fator at no4 urrent fi'ed I interest P+ of remaining euro ash outflo4s 3umulative P+ of I cash outflows (pot e'hange rate at un4inding $/I ) 3umulative P+ of I ash outflo4s $
@ #1,12,5#2 1.02 $ #1,955,19
Settlement: 3ash inflo4 3ash outflo4 !et ash settlement settlement of un4inding
$ 52,*25,0 !#1,955,19" $ 10,**9,8#0
5.5
@ 1,7#5,*90 0.9#92 @ 1,*57,08
;his is a net ash payment to *alor from the s4ap dealer. dealer.
@ 1,7#5,*90 0.9010 @ 1,572,889
@ 1,7#5,*90 0.855 @ 1,#9,012
@ ##,8#9,18 0.8118 @ *,#09,*0