投资学10版习题答案15Word文档下载推荐.docx
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2
5.50%
2/1.06）–1=5.0%
3
5.67%
32）–1=6.0%
4
43）–1=7.0%
8.Theexpectedpricepathofthe4-yearzerocouponbondisshownbelow.（Notethatwediscountthefacevaluebytheappropriatesequenceofforwardratesimpliedbythisyear’syieldcurve.）
BeginningofYear
ExpectedPrice
ExpectedRateofReturn
（$839.69/$792.16）–1=6.00%
（$881.68/$839.69）–1=5.00%
（$934.58/$881.68）–1=6.00%
（$1,000.00/$934.58）–1=7.00%
9.Ifexpectationstheoryholds,thentheforwardrateequalstheshortrate,andtheone-yearinterestratethreeyearsfromnowwouldbe
10.a.A3-yearzerocouponbondwithfacevalue$100willselltodayatayieldof6%andapriceof:
Nextyear,thebondwillhaveatwo-yearmaturity,andthereforeayieldof6%（fromnextyear’sforecastedyieldcurve）.Thepricewillbe$89,resultinginaholdingperiodreturnof6%.
b.Theforwardratesbasedontoday’syieldcurveareasfollows:
Year
2/1.04）–1=6.01%
32）–1=8.03%
Usingtheforwardrates,theforecastfortheyieldcurvenextyearis:
6.01%
（1.0601×
1.0803）1/2–1=7.02%
ThemarketforecastisforahigherYTMon2-yearbondsthanyourforecast.Thus,themarketpredictsalowerpriceandhigherrateofreturn.
11.a.
b.Theyieldtomaturityisthesolutionforyinthefollowingequation:
[Usingafinancialcalculator,entern=2;
FV=100;
PMT=9;
PV=–101.86;
Computei]YTM=7.958%
c.Theforwardratefornextyear,derivedfromthezero-couponyieldcurve,isthesolutionforf2inthefollowingequation:
⇒f2=0.0901=9.01%.
Therefore,usinganexpectedratefornextyearofr2=9.01%,wefindthattheforecastbondpriceis:
d.Iftheliquiditypremiumis1%thentheforecastinterestrateis:
E（r2）=f2–liquiditypremium=9.01%–1.00%=8.01%
Theforecastofthebondpriceis:
12.a.Thecurrentbondpriceis:
（$85×
0.94340）+（$85×
0.87352）+（$1,085×
Thispriceimpliesayieldtomaturityof6.97%,asshownbythefollowing:
[$85×
Annuityfactor（6.97%,3）]+[$1,000×
b.Ifoneyearfromnowy=8%,thenthebondpricewillbe:
Annuityfactor（8%,2）]+[$1,000×
PVfactor（8%,
Theholdingperiodrateofreturnis:
[$85+（$1,008.92–$1,040.20）]/$1,040.20=0.0516=5.16%
13.
PVof$1receivedatperiodend
1
5%
2
7
⨯
3
8
⨯⨯
a.Price=（$60×
0.9524）+（$60×
0.8901）+（$1,060×
0.8241）=$984.14
b.Tofindtheyieldtomaturity,solveforyinthefollowingequation:
$984.10=[$60×
Annuityfactor（y,3）]+[$1,000×
PVfactor（y,3）]
Thiscanbesolvedusingafinancialcalculatortoshowthaty=6.60%:
PV=-$984.10;
N=3;
FV=$1,000;
PMT=$60.SolveforI=6.60%.
c.
Period
PaymentReceivedatEndofPeriod:
WillGrowby
aFactorof:
ToaFuture
Valueof:
1.07⨯
$984.10⨯（1+yrealized）3
1+yrealized=
⇒yrealized=6.66%
Alternatively,PV=-$984.10;
FV=$1,194.14;
PMT=$0.SolveforI=6.66%.
d.Nextyear,thepriceofthebondwillbe:
[$60×
Annuityfactor（7%,2）]+[$1,000×
PVfactor（7%,
Theholdingperiodreturnis:
14.a.Thereturnontheone-yearzero-couponbondwillbe6.1%.
Thepriceofthe4-yearzerotodayis:
Nextyear,iftheyieldcurveisunchanged,today’s4-yearzerocouponbondwillhavea3-yearmaturity,aYTMof6.3%,andthereforethepricewillbe:
Theresultingone-yearrateofreturnwillbe:
6.70%
Therefore,inthiscase,thelonger-termbondisexpectedtoprovidethehigherreturnbecauseitsYTMisexpectedtodeclineduringtheholdingperiod.
b.Ifyoubelieveintheexpectationshypothesis,youwouldnotexpectthattheyieldcurvenextyearwillbethesameastoday’scurve.Theupwardslopeintoday'
scurvewouldbeevidencethatexpectedshortratesarerisingandthattheyieldcurvewillshiftupward,reducingtheholdingperiodreturnonthefour-yearbond.Undertheexpectationshypothesis,allbondshaveequalexpectedholdingperiodreturns.Therefore,youwouldpredictthattheHPRforthe4-yearbondwouldbe6.1%,thesameasforthe1-yearbond.
15.Thepriceofthecouponbond,basedonitsyieldtomaturity,is:
[$120×
Annuityfactor（5.8%,2）]+[$1,000×
Ifthecouponswerestrippedandsoldseparatelyaszeros,then,basedontheyieldtomaturityofzeroswithmaturitiesofoneandtwoyears,respectively,thecouponpaymentscouldbesoldseparatelyfor:
Thearbitragestrategyistobuyzeroswithfacevaluesof$120and$1,120,andrespectivematuritiesofoneyearandtwoyears,andsimultaneouslysellthecouponbond.Theprofitequals$2.91oneachbond.
16.a.Theone-yearzero-couponbondhasayieldtomaturityof6%,asshownbelow:
y1=0.06000=6.000%
Theyieldonthetwo-yearzerois8.472%,asshownbelow:
y2=0.08472=8.472%
Thepriceofthecouponbondis:
Therefore:
yieldtomaturityforthecouponbond=8.333%
[Onafinancialcalculator,enter:
n=2;
PV=–106.51;
PMT=12]
b.
c.Expectedprice
（Notethatnextyear,thecouponbondwillhaveonepaymentleft.）
Expectedholdingperiodreturn=
Thisholdingperiodreturnisthesameasthereturnontheone-yearzero.
d.Ifthereisaliquiditypremium,then:
E（r2）<
f2
E（Price）=
E（HPR）>
6%
17.a.Weobtainforwardratesfromthefollowingtable:
Price（forpartsc,d）
1year
10%
2years
11%
2/1.10）–1=12.01%
3years
12%
32）–1=14.03%
b.Weobtainnextyear’spricesandyieldsbydiscountingeachzero’sfacevalueattheforwardratesfornextyearthatwederivedinpart（a）:
12.01%
13.02%
Notethatthisyear’supwardslopingyieldcurveimplies,accordingtotheexpectationshypothesis,ashiftupwardinnextyear’scurve.
Similarly,thecurrent3-yearzerowillbea2-yearzeroandwillsellfor:
Expectedtotalrateofreturn:
2-yearbond:
3-yearbond:
d.Thecurrentpriceofthebondshouldequalthevalueofeachpaymenttimesthepresentvalueof$1tobereceivedatthe“maturity”ofthatpayment.Thepresentvalueschedulecanbetakendirectlyfromthepricesofzero-couponbondscalculatedabove.
Currentprice=（$120×
0.90909）+（$120×
0.81162）+（$1,120×
0.71178）
Similarly,theexpectedpricesofzerosoneyearfromnowcanbeusedtocalculatetheexpectedbondvalueatthattime:
Expectedprice1yearfromnow=（$120×
0.89278）+（$1,120×
0.78293）
Totalexpectedrateofreturn=
18.a.
Maturity（years）
8.00%
8.50%
5
b.Foreach3-yearzeroissuedtoday,usetheproceedstobuy:
$782.92/$715.00=1.095four-yearzeros
Yourcashflowsarethusasfollows:
Time
CashFlow
$0
-$1,000
The3-yearzeroissuedattime0matures;
theissuerpaysout$1,000facevalue
+$1,095
The4-yearzerospurchasedattime0mature;
receivefacevalue
Thisisasyntheticone-yearloanoriginatingattime3.Therateonthesyntheticloanis0.095=9.5%,preciselytheforwardrateforyear4.
c
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