质量损失率的计算公式固定收益证券的复习计算题

2020年10月13日发(作者：席慕蓉)

Fixed-incometreasury
Ppt3
1、公式：
PracticeQuestion3.1
Supposecurrently,1-yea rspotrateis1%andmarketexpectsthat1-yearspotratenex tyearwou
ldbe2%and1-yearspotratein2yearswouldbe 3%.Computetoday’
s2-yearspotrateand3-yearspotra te.(已做答案）
2、
CurrentYield

Computeth ecurrentyieldfora7%8-yearbondwhosepriceis$$utthecur rentyiel
difpriceis$$100,$$106,respectively?
3、?Case3.1
Considera7%8-yearbondpayingcoup onsemiannuallywhichissoldfor$$
esentvalueusingva riousdiscountrateis:
theYTMforthisbond?
histhetotaldollarreturnonthisbond?
histhet otaldollarreturnifyouputthesameamountofdollarsinto adepositaccoun
twiththesameannualyield?
4、ForwardRates
注：
6-monthbillspotrateis3%是年化利率（3%要除以2）
1-yearbillspotrateis3.3%是年化利率（3.3%要除以2）
Ppt4
1、Fixed‐CouponBonds
?PracticeQuestion4.2
thevalueofa4-year10%c ouponbondthatpaysinterestsemiannuallyassumingthatt heannualdi
scountrateis8%?Whatisthevalueofasimi lar10%couponbondwithaninfinitematurity（无期限）?
thevalueofa5-yearzero-couponbondwithamaturityv alueof$$100discountedatan8%interestr
ate?
et hevaluepar$$100ofparvalueofa4-year10%couponbond,ass umingthepaymentsareannuala
ndthediscountratefor eachyearis6.8%,7.2%,7.6%and8.0%,respectively.
Infinitematurity
Pv=($$100*10%2)(8%2)
(半年付息）
PresentValueProperties
?
PracticeQuestion4.4
ethediscountratef orthe4-year10%couponbondwithaparvalueof$$100is8%.Co mput
eitspresentvalue.
rlater,supposethatth ediscountrateappropriatefora3-year10%couponbondinc r
easesfrom8%to9%.RedoyourcalculationinpartAand decomposethepricechangeattributab
letomovingtom aturityandtotheincreaseinthediscountrate.
（期限与贴现率变化）
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3、PricingaBondbetweenCouponPayments
?PracticeQuestion4.6
Supposethattherearefi vesemiannualcouponpaymentsremainingfora10%couponbo nd.A
lsoassumethefollowing:
①Annualdiscountrateis8%
②78daysbetweenthes ettlementdateandthenextcouponpaymentdate
③182daysinthecouponperiod
thecleanpriceofthisbond?
4、ValuationApproach
?Case4.1
era8%itsfairvalueiftraditionalapproac
his
used,givenyieldforthe10-yearon-the- runTreasuryissueis8%?
thefairvalueofaboveTreas urycouponbondifarbitrage-freeapproachisused,
giventhefollowingannualspotrates?
pproachismoreaccurate（准确）?
C、Arbitrage- FreeApproachismoreaccurate
Ppt5
2、
Convexity

Considera9%20-yearbond sellingat$$134.6722toyield6%.Fora20bpchangeinyield, itspric
ewouldeitherincreaseto$$137.5888ordecrea seto$$131.8439.
etheconvexityforthisbond.
t heconvexityadjustmentforachangeinyieldof200bps? owthatthedurationforthisbondis10.66,whatshouldth etotalestimatedpercenta
gepricechangebefora200b pincreaseintheyield?Howabouta200bpdecreaseintheyie ld?
Ppt6
1、
MeasuringYieldCurveRisk
?
Case6.1:PanelA
Considerthefollowingtw o$$100portfolioscomposedof2-year,16-year,and30-year issues
,allofwhicharezero-couponbonds:
Fors implicity,assumethereareonlythreekeyrates—
2yea rs,atetheportfolio’
skeyratedurationsatthesethr eepointsanditseffectiveduration.
Case6.1:PanelB
Considerthefollowingthreescenarios:
Scenario1:Allspotratesshiftdown10basispoints.
Scenario2:The2-yearkeyrateshiftsup10basispoint santhe
30-yearrateshiftsdown10basispoints.
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Scenario3:The2-yearkeyrateshi ftsdown10basispointsand
the30-yearrateshiftsup10basispoints.
Howwouldtheportfoliovaluechangeineachscenario?
Ppt7
Considera6.5%ppropriatebinom
ialin terestratetreeisshownasbelow,calculatethefairprice ofthisbond.
Ppt8
1、ValuingCallableandPutableBonds
?
Case 8.1
:Valuingacallablebondwithsingle
callprice
Considera6.5%callablebondwith4ye arsremainingtomaturity,callableinoney
earat$$the yieldvolatilityis10%andtheappropriatebinomialinter
atethefairpriceofthiscallablebond.
2、
C ase8.2
:Valuingacallablebondwithcallschedule
Considera6.5%callablebondwith4yearsremainingto
maturity,callableinoneyearatacallscheduleasbel ow:
Assumetheyieldvolatilityis10%andtheappropr iatebinomialinterestratetre
atethefairpriceofth iscallablebond.
3、
Case8.3
:Valuingaputa blebondConsidera6.5%putablebondwith4yearsremainin< br>gtomaturity,putableinoneyearat$$theyield
vol atilityis10%andtheappropriatebinomialinterestratet reeissameasCase6
.atethefairpriceofthisputableb ond.


ConvertibleBonds
?
Case9.1
:
Supposethatthestraightva lueofa5.75%ADCconvertiblebondis$$981.9per$$1,00
0 ofparvalueanditsmarketpriceis$$1,ketpricepershareof commons
tockis$$33andtheconversionratiois25.32sh aresper$$1,
ssumethatthecommonstockdividendis$$0. 90pershare.
公式：
MinimumValue:thegreaterofi tsconversionpriceanditsstraightvalue.
Conversi onPrice=Marketpriceofcommonstock×Conversionratio < br>StraightValueInvestmentValue:presentvalueoftheb ond’scashflowsdiscountedatt
herequiredreturnona comparableoption-freeissue.
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MarketConversionPriceConversionParityPrick
=Marketpriceofconvertiblesecurity÷Conversionratio
MarketConversionPremiumPerShare
=Marketcon versionprice–Marketpriceofcommonstock
MarketConversionPremiumRatio
=Marketconver sionpremiumpershare÷Marketpriceofcommonstock
Premiumoverstraightvalue
=(MarketpriceofconvertiblebondStraightvalue)–1
Thehigherthisratio,thegreaterdownsideriskandth e
lessattractivetheconvertiblebond.
PremiumPaybackPeriod
=Marketconversionprem iumpershare÷Favorableincomedifferentialpershare
FavorableIncomeDifferentialPerShare
=[Coup oninterest–(Conversionratio×Commonstockdividendper share)]÷Conversi
onratio
theminimumvalueofthisconvertiblebond?
atei tsmarketconversionprice,marketconversionpremiumper sharea
ndmarketconversionpremiumratio.
itspremiumpaybackperiod?
ateitspremiumoverstraightvalue.
Marketpriceofcommonstock=$$33,
conversionratio=25.32
StraightValue=$$981.9，
marketpriceofconversiblebond=$$1,065
commonstockdividend=$$0.90
Couponrate=5.75%
A、ConversionPrice=Marketpriceofcommonstock×Con versionratio
=$$33*25.32=$$835.56
theminimum valueofthisconvertiblebond=max{$$835.56,$$981.9}=$$98 1.9
B、MarketConversionPriceConversionParityPrick < br>=Marketpriceofconvertiblesecurity÷Conversionrat io
=$$106525.32
=$$42.06
MarketConversionPremiumPerShare
=Marketcon versionprice–Marketpriceofcommonstock
=$$42.06-$$33
=$$9.06
MarketConversionPremiumRatio
=Marketconver sionpremiumpershare÷Marketpriceofcommonstock
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=$$9.06$$33
=27.5%
C、
PremiumPaybackPeriod
=Marketconversionprem iumpershare÷Favorableincomedifferentialpershare
FavorableIncomeDifferentialPerShare
=[Coup oninterest–(Conversionratio×Commonstockdividendper share)]÷Conversi
onratio
Couponinterestfrombond=5.75%×$$1,000=$$57.50
Favorableincomedifferentialpershare=($$57.50–25.32 ×$$0.90)÷25.32=$$1.37
Premiumpaybackperiod=$$9.06$$1.37=6.6years
D、Premiumoverstraightvalue
=(MarketpriceofconvertiblebondStraightvalue)–1
=$$1,065$$981.5–1=8.5%
Ppt10
No- ArbitragePrinciple:
norisklessprofitsgainedfro mholdingacombinationofaforwardcontractposi
tion aswellaspositionsinotherassets.
FP=Pricethatwo uldnotpermitprofitablerisklessarbitrageinfrictionl essma
rkets,thatis:
Case10.1
Considera3-monthforwardcontractonazero-couponb ondwithafacevalueof$$1,0
00thatiscurrentlyquoted at$$500,andassumearisk-freeannualinterestrateof
6%.Determinethepriceoftheforwardcontractunder
theno-arbitrageprinciple.
Solutions.
Case10.2
Supposetheforwardcontractdescribe dincase10.1isactuallytradingat$$510,whichisgre
t ratehowanarbitrageurcanobtainrisklessarbitragep
rofitfromthisoverpricedforwardcontractandhowmucht hearbitrageprofitwouldbe.
Case10.3
Ifthefo rwardcontractdescribedincase10.1isactuallytradinga t$$502,whichissmallerthanth
tratehowanarbitrageu rcanobtainrisklessarbitrageprofitfrom
thisunder pricedforwardcontractandhowmuchthearbitrageprofitw ouldbe.
Case10.4
:
interest)thathasjust paidacouponandwillmakeanothercouponpaymentin182da< br>ualrisk-freerateis6%.
Solutions.
RememberthatT- bondsmakesemiannualcouponpayments,so
Case10.6
Solutions.
Thesemiannualcoupononasingle,$$1,000face- value7%bondis$$olderw
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illreceiv eonepayment0.5yearsfromnow(0.7yearslefttoexpiratio noffutures
)andonepayment1yearfromnow(0.2years
untilexpiration).Thus,
Ppt11
PayoffsandProfits
Case11.1
ConsideraEu ropeanbondcalloptionwithanexercisepriceof$$lpremium forthis
optionis$$ration,ifthespotpricefortheund erlyingbondis$$1,000,whatisthecallop
tion’
sp ayoffaswellasitsgainloss?Isthisoptioninthemoney,ou tofmoney,oratthemoney?Willy
ouexercisethisoptio n?Howaboutyouranswersifthespotpriceatexpirationis$$ 920,and$$880
,respectively?
Solutions.
p otpriceatexpirationis$$1,000,thepayofftothecallopti onismax{0,$$1
,000-$$900}=$$,thecallisinthemoneyan ditwillbeexercisedwithagaino
f$$50.
potprice atexpirationis$$920,thepayofftothecalloptionis
max{0,$$920-$$900}=$$,thecallisinthemoneyanditwillbee xercisedwith
alossof$$30.(why?)
potpriceis$$8 80atexpiration,thepayofftothecalloptionismax{0,$$88 0
-$$900}=,soccurred
wouldbe$$50.
?
Case11.2
ConsideraEuropeanbondputoptionwit hanexercisepriceof$$pre
miumforthisoptionis$$rati on,ifthespotpricefortheunderlyingbond
is$$1,000, whatistheputoption’spayoffaswellasits
gainloss ?Isthisoptioninthemoney,outofmoney,oratthemoney?Wi llyouexe
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rcisethisoption?Howab outyouranswersifthespotpriceatexpirationis$$920,and$$880,respectively?
Solutions.
potprice atexpirationis$$1,000,thepayofftotheputoptionismax{ 0,$$9
50-$$1,000}=,socc
urredwouldbe$$50.
p otpriceatexpirationis$$920,thepayofftotheputoptioni smax{0,$$950
-$$920}=$$,theputisinthemoneyanditwil lbeexercisedwithalossof$$20.(
why?)
potprice is$$880atexpiration,thepayofftothecalloptionismax{0 ,$$950
-$$880}=$$,theputisinthemoneyanditwillnotbe exercisewithagainof$$20
.

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