CFA 2018 Question bank 03 Valuation and Analysis Bonds with Embedded Options

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Test ID: 7441686

Valuation and Analysis: Bonds with Embedded Options

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Sharon Rogner, CFAisevaluating threebondsfor inclusioninfixedincomeportfoliofor oneofher pensionfund clients. All threebondshavea coupon rateof 3%, maturityoffiveyearsandare generallyidenticalinevery respectexceptthatbondAis anoption-freebond, bondBis callableintwoyearsandbondCisputableintwoyears. Rogner computestheOAS ofbondA tobe 50bpsusing abinomialtreewithanassumedinterest rate volatilityof15%.

If Rogner revisesher estimateofinterest rate volatilityto10%, the computedOAS ofBondCwouldmostlikelybe:

lower than 50bps. higher than 50bps. equalto 50bps.

Explanation

TheOAS ofthethreebondsshouldbesameastheyare giventobeidenticalbondsexceptfor theembeddedoptions (OAS is after removing theoptionfeatureandhencewouldnotbeaffectedbyembeddedoptions). HencetheOAS ofbondCwouldbe 50 bpsabsentany changesinassumedlevelof volatility.

Whentheassumedlevelof volatilityinthetreeisdecreased, the valueoftheembeddedputoptionwoulddecreaseandthe computed valueoftheputablebondwouldalsodecrease. The constantspreadthatisnowneededtoforcethe computed valuetobeequaltothemarketpriceisthereforelower thanbefore. Henceadecreaseinthe volatilityestimate reducesthe computedOAS for aputablebond.

Asthe volatilityofinterest ratesincreases, the valueofa callablebondwill:

rise if the interest rate is below the coupon rate, and fall if the interest rate is above the coupon rate.

decline. rise.

Explanation

As volatilityincreases, sowilltheoption value, whichmeansthe valueofa callablebondwilldecline. Remember thatwitha callable bond, theinvestor isshortthe calloption.

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isputableatanytimeatpar. Yield curveis currentlyflatat 3%.

Thebondwiththelowestone-sideddown-durationismostlikelytobe:

Bond C. BondA.

BondB.

Explanation

Whentheunderlying optionisat (or near)money, callablebondswillhavelower one-sideddown-durationthanone-sidedup -duration; theprice changeofa callablewhen ratesfallissmaller thantheprice changefor anequalincreasein rates. Inthis problem, the coupon rateis giventobeequaltothe currentlevelof ratesandhencethebondshouldbeatpar andthe underlying optionisat-the-money.

JosephDentice, CFAisevaluating threebonds. Allthreebondshavea coupon rateof 3%, maturityoffiveyearsandare generallyidenticalinevery respectexceptthatbondAisanoption-freebond, bondBis callableintwoyearsandbondCis putableintwoyears.

Ifinterest ratesdecrease, thedurationofwhichbondismostlikelytodecrease?

Bond A. BondC.

BondB.

Explanation

Decreasein rateswouldincreasethelikelihoodofthe calloptionbeing exercisedand reducetheexpectedlife (andduration) ofthe callablebondthemost.

Ifabondhasseveralkey ratedurationsthatarenegative, itismostlikelythatthebondisa:

Putable bond

Callablebond Zero couponbond.

Explanation

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Supposethemarketpriceofa convertiblesecurityis $1,050 andthe conversion ratiois 26.64. Whatisthemarket conversionprice?

$1,050.00. $39.41. $26.64.

Explanation

Themarket conversionpriceis computedasfollows:

Market conversionprice = marketpriceof convertiblesecurity/conversion ratio = $1,050/26.64 = $39.41

Howdoesthe valueofa callablebond comparetoanoncallablebond? Thebond valueis:

lower. higher. lower or higher.

Explanation

Sincetheissuer hastheoptionto callthebondsbeforematurity, heisableto callthebondswhentheir coupon rateishigh relativetothe marketinterest rateandobtain cheaper financing throughanewbondissue. This, however, isnotintheinterestofthebondholderswho wouldliketo continue receiving thehigh coupon rates. Therefore, theywillonlypayalower pricefor callablebonds.

Whichbondswouldhaveitsmaturity-matched rateasitsmost critical rate?

High coupon callable bonds.

Low coupon callablebonds. Low couponputablebonds.

Explanation

Callablebondswithlow coupon rateareunlikelytobe called; hence, their maturity-matched rateistheir most critical rate (i.e., thehighestkey rateduration correspondstothebond'smaturity). Similarly, putablebondswithhigh coupon ratesareunlikely tobeputandaremostsensitivetotheir maturity-matched rates.

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7.59% 6.35% 5.33%

99.00. 98.75. 97.92.

Explanation

The putable bond price tree is as follows: 100.00

A → 99.00

99.00 100.00

99.84 100.00

As an example, the price at node A is obtained as follows:

Price = max[(prob × (P + coupon / 2) + prob × (P + (coupon / 2)) / (1 + (rate / 2)), put price] = max[(0.5 × (100 + 2.5) + 0.5 × (100 + 2.5)) / (1 + (0.0759 / 2)) ,99] = 99.00. The bond values at the other nodes are obtained in the same way.

The calculated price at node 0 =

[0.5(99.00 + 2.5) + 0.5(99.84 + 2.5)] / (1 + (0.0635 / 2)) = $98.78 but since the put price is $99 the price of the bond will not go below $99.

Which kind of risk remains if the option-adjusted spread is deducted from the nominal spread?

credit risk. liquidity risk. option risk.

Explanation

The OAS captures the amount of credit risk and liquidity risk.

JosephDentice, CFAisevaluating threebonds. Allthreebondshavea coupon rateof 3%, maturityoffiveyearsandare generallyidenticalinevery respectexceptthatbondAisanoption-freebond, bondBis callableintwoyearsandbondCis putableintwoyears.

Thebondwiththelowestdurationisleastlikelytobe:

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Bond A. BondB. BondC.

Explanation

BondAisoption-freeandwouldhaveadurationthatisequaltoor greater thanthedurationofbondsBandC.

A callable bond, a putable bond, and anoption-free bondhave the same coupon, maturity and rating. The call price andput price are 98 and102 respectively. The option-free bond trades at par. Whichof the following lists correctlyorders the values of the three bonds from lowest tohighest?

Option-free bond, putable bond, callable bond.

Putable bond, option-free bond, callable bond.

Callable bond, option-free bond, putable bond.

Explanation

The put feature increases the value of a bond and the call feature lowers the value of a bond, when all other things are equal. Thus, the putable bond generally trades higher than a corresponding option-free bond, and the callable bond trades at a lower price.

Whichof the following statements is most accurate concerning a convertible bond? A convertible bond's value depends:

on both interest rate changes and changes in the market price of the stock. only on changes in the market price of the stock.

only oninterest rate changes.

Explanation

The value of convertible bondincludes the value of a straight bondplus anoption giving the bondholder the right tobuy the common stock of the issuer. Hence, interest rates affect the bond value and the underlying stock price affects the option value.

The value of a callable bondis equal to the:

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$25,000,000

4.75%

du

e 20

1 0 $25,857,300

$

1

05.96 $

11

0.65 $

1

0

1 .

11 $40,000,000 5.85%

du

e 2025 $39,450,000

$98.38

$

1

02.76 $93.53

$65,000,000

B

ond

po

rt

fo

l

i

o

$65,307,300

Ata subsequent meeting withthetrustees ofthefund, Karsteinis askedtoexplainwhatabinomialinterest rate modelis, and howitwas usedtoestimateeffectivedurationandeffective convexity. Karsteinis uncertainoftheexact methodology because theactual calculations weredoneby a junior analyst, but shetries toprovidethetrustees witha reasonably accurate step-b y-stepdescriptionoftheprocess:

Step 1:

Given the bond's current market price, the Treasury yield curve, and an assumption about rate

volatility, create a binomial interest rate tree and calculate the bond's option-adjusted spread (OAS)

using the model.

Step 2: Impose a parallel upward shift in the on-the-run Treasury yield curve of 100 basis points.

Step 3: Build a new binomial interest rate tree using the new Treasury yield curve and the original rate

volatility assumption.

Step 4: Add the OAS from Step 1 to each of the 1-year rates on the tree to derive a "modified" tree.

Step 5: Compute the price of the bond using this new tree.

Step 6:

Repeat Steps 1 through 5 to determine the bond price that results from a 100 basis point decrease in

rates.

Step 7:

Use these two price estimates, along with the original market price, to calculate effective duration and

effective convexity.

JulioCorona, atrusteeanduniversityfinanceprofessor, immediatelyspeaksuptodisagreewith Karstein. He claimsthata moreaccuratedescriptionoftheprocessisasfollows:

Step 1:

Given the bond's current market price, the on-the-run Treasury yield curve, and an assumption about

rate volatility, create a binomial interest rate tree.

Step 2: Add 100 basis points to each of the 1-year rates in the interest rate tree to derive a "modified" tree.

Step 3: Compute the price of the bond if yield increases by 100 basis points using this new tree.

Step 4:

Repeat Steps 1 through 3 to determine the bond price that results from a 100 basis point decrease in

rates.

Step 5:

Use these two price estimates, along with the original market price, to calculate effective duration and

effective convexity.

Coronaisalso concernedabouttheassumptionofa100 basispoint changeinyieldfor estimating effectivedurationand effective convexity. Heasks Karsteinthefollowing question: "Ifweweretousea 50 basispoint changeinyieldinsteadofa 100 basispoint change, howwouldthedurationand convexityestimates changefor eachofthetwobonds?"

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Whichofthefollowing statementsismost accurate?

The two methodologies will result in the same effective duration and convexity estimates only if the same rate volatility assumption is used in each and the bond's OAS is equal to zero.

Corona'sdescriptionisamoreaccuratedepictionoftheappropriatemethodology than Karstein's.

Karstein'sdescriptionisamoreaccuratedepictionoftheappropriatemethodology thanCorona's.

Explanation

Karstein correctlyoutlinedtheappropriatemethodologyfor using abinomialmodeltoestimateeffectivedurationandeffective convexity. Coronafailstoadjustfor theOAS and, instead, simplyadds100 basispointstoevery rateonthetree rather than shifting theyield curveupwardandthen recreating theentiretreeusing thesame rate volatilityassumptionfromthefirststep. Evenifbothusethesame rate volatilityassumption, andtheOAS isequalto zero, thetwomethodologieswill generate significantlydifferentdurationand convexityestimates. (Study Session14, LOS 47.h)

Assumethattheeffective convexityofthe 4.75% 2010 bondis 3.45. Theeffectivedurationofthe 4.75% 2010 bondandthe percentage changeinthepriceofthebondfor an80 basispointdecreaseintheyieldare closest to:

EffectiveDuration % ChangeinBondPrice

4.58 +1.79%

4.50 +3.62%

4.21 +2.09%

Explanation

(Study Session14, LOS 47.h)

The convexityofthe 5.85% 2025 bondfor a100 basispoint changein ratesis closest to: 3.57.

−12.18. &£8722;23.88.

Explanation

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Assumethatthedurationofthe 5.85% 2025 bondis 2.88. Thedurationoftheportfoliois closest to:

3.52.

3.12. 3.01.

Explanation

In regardtotheeffectofa changeinthesizeofthe rateshockonthedurationand convexityestimates, Karsteinis:

incorrect in her analysis of the effect on both bonds. correctinher analysisoftheeffectonbothbonds.

correctonlyinher analysisoftheeffectonthe 4.75% 2010 bond.

Explanation

Durationand convexityestimatesfor bondswithoutembeddedoptionswillnotbesignificantlyaffectedby changing thesizeof the rateshockfrom100 basispointsto 50 basispoints. However, for bondswithembeddedoptions, thesizeofthe rateshock canhaveasignificanteffectontheestimates.

WeknowfromPart 3 thatthe 2025, 5.85% bondexhibitssignificantnegative convexity, whichis consistentwitha callable bond. The 2010, 4.75% bondhaspositive convexity, evenwhenyieldsaresignificantlybelowthe coupon rateandthebondis trading atasubstantialpremium. Thatsuggeststhe 2010, 4.75% bondhasnoembeddedoptions.

Wewouldexpectthat changing thesizeofthe rateshockwouldhaveasignificanteffectonthe 2025, 5.85% callablebond, but notonthe 4.75% 2010 bond. Therefore, Karsteinis correctinher analysisofthe 4.75% bond, butnotthe 5.85% bond. (Study Session14, LOS 47.g)

Theportfolio convexityadjustment, assuming a100 basispointdecreaseinyield, is closest to: +1.77%.

−2.93%. −1.77%.

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Whenisit best for anasset-backedsecurity (ABS)tobe valuedusing the zero-volatilityspreadapproach?

For agency ABS.

To valueABS thathaveaprepaymentoption.

To valueABS thatdonothaveaprepaymentoption.

Explanation

Withthe zero-spreadmethod, the valueofanABS isthepresent valueofits cashflowsdiscountedatthespot ratesplusthe zero -volatilityspread. The Z-spreadtechniquedoesnotincorporateprepayments. Thus, itshouldonlybeusedfor ABSsfor whichtheborrower

either hasnooptiontoprepay, or isunlikelyto.

Alnoor Hudda, CFAis valuing twofloatersissuedby MateoBank. Bothfloatershaveapar valueof $100, threeyear lifeand paybasedonannual LIBOR. Huddahas generatedthefollowing binomialtreefor libor.

1-year forward ratesstarting inyear:

0 1 2

2% 5.7798% 6.0512% 3.8743% 4.0562% 2.7190%

Valueofthe capina cappedfloater witha capof 4% is closestto:

$4.41 $2.18 $1.23

Explanation

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Thespread (k)thatmustbeaddedtoallofthespot ratesalong eachinterest ratepaththatwillforceequalitybetweentheaverage present valueofthepath's cashflowsandthemarketprice (plusaccruedinterest)for themortgage-backedsecurity (MBS)being

evaluatedis calledthe:

PAC spread.

option-adjustedspread (OAS).

k-spread.

Explanation

Thespread (k)thatmustbeaddedtoallofthespot ratesalong eachinterest ratepaththatwillforceequalitybetweentheaverage present valueofthepath's cashflowsandthemarketprice (plusaccruedinterest)for the MBS being evaluatedis calledtheOAS.

Alnoor Hudda, CFAis valuing twofloatersissuedby MateoBank. Bothfloatershaveapar valueof $100, threeyear lifeand paybasedonannual LIBOR. Huddahas generatedthefollowing binomialtreefor libor.

1-year forward ratesstarting inyear:

0 1 2

2% 5.7798% 6.0512% 3.8743% 4.0562% 2.7190%

Valueofa cappedfloater witha capof 4% is closestto:

$98.70 $97.38 $96.71

Explanation

The capwillbeinthemoneyfor nodes 2,UU; 2,UL; and1,U. V = 104/1.060512 = 98.07

V = 104/1.040562 = 99.95 V = 102.7190/1.027190 = 100

2,UU 2,UL

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Generallyspeaking, ananalystwouldliketheoptionadjustedspread (OAS)tobebig controlling for:

Credit and liquidity risk. Option risk.

Credit, liquidityandoption risk.

Explanation

OAS is compensationfor taking creditandliquidity risk. Analystswouldprefer higher OAS after controlling for creditand liquidity risk.

Ifthesimulatedinterest ratesarebasedontheTreasury curve, thenhowistheoption-adjustedspreadobtained (OAS)using the Monte Carlosimulationmodelinterpreted? TheOAS isthe:

average spread over the Treasury spot rate curve. averagespreadover theTreasuryyield.

spreadover theTreasuryspot rate corresponding tothematurityofthemortgage-backed security.

Explanation

Themonthly ratesalong thepaths generatedwiththe MonteCarlosimulationmodelusing theTreasuryyield curveasabenchmarkare Treasuryspot ratesthathavebeenadjustedtobearbitrage-free. Assuch, theOAS measurestheaveragespreadover Treasuryspot

rates, not theTreasuryyield.

Whenshouldanasset-backedsecurity (ABS)be valuedusing theoption-adjustedspread (OAS)approach?

For agency ABS.

To valueABS thatdonothaveaprepaymentoption.

To valueABS thathaveaprepaymentoption.

Explanation

TheOAS method recognizesthat cashflow changesaccompanyinterest rate changes. Thus, itissuitabletouseOAS analysiswith ABSsthathaveaprepaymentoptionthatisfrequentlyexercised, e.g., high qualityhomeequityloans.

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option-freebond, bondBis callableintwoyearsandbondCisputableintwoyears. Theyield curveis currentlyflat.

Iftheyield curveisexpectedtohaveaparalleldownwardshift, thebondwiththehighestpriceappreciationis least likelytobe:

Bond C BondB

BondA

Explanation

BondBhasanembedded calloptionwhichlimitsitsupside resulting innegative convexity. BondsAandCdonothavesuch limits.

Whichofthefollowing correctlyexplainshowtheeffectivedurationis computedusing thebinomialmodel. Inorder to computethe effectivedurationthe:

yield curve has to be shifted upward and downward in a parallel manner and the binomial tree recalculated each time.

binomialtreehastobeshiftedupwardanddownwardbythesameamountfor allnodes.

thenodalprobabilitiesareshiftedupwardanddownwardandthebinomialtree recalculated eachtime.

Explanation

Applyparallelshiftstotheyield curveandusethese curvesto computenewforward ratesintheinterest ratetree. The resulting bond

valuesarethenusedto computetheeffectiveduration.

Ananalysthas constructedaninterest ratetreefor anon-the-runTreasurysecurity. Givenequalmaturityand coupon, whichofthe following wouldhavethe highest option-adjustedspread?

A putable corporate bond with a Aaa rating.

Aputable corporatebondwithaAAA rating.

A callable corporatebondwithaBaa rating.

Explanation

Thebondwiththelowestpricewillhavethehighestoption-adjustedspread. Allother thingsequal, the callablebondwiththelowest rating

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Whatisthemarket conversionpriceofa convertiblesecurity?

The price that an investor pays for the common stock if the convertible bond is purchased and then converted into the stock.

Thepricethataninvestor paysfor the commonstockinthemarket.

The valueofthesecurityifitis convertedimmediately.

Explanation

Themarket conversionprice, or conversionparityprice, isthepricethatthe convertiblebondholder wouldeffectivelypayfor thestockif sheboughtthebondandimmediately convertedit.

market conversionprice = marketpriceof convertiblebond ÷ conversion ratio.

WandaBrunner, CFA, isevaluating twotranchesofasequential-payCMOstructure.

Tranche O

AS

(bps) Z-spread

(bps) Effective

duration

I

95

1

00

4 .25

II

90

1

00

4 .25

HowshouldBrunner tradetheseCMOtranches?

Cannot be determined.

BuyTrancheIIandsellTrancheI. BuyTrancheIandsellTrancheII.

Explanation

TrancheIoption cost = 100 - 95 = 5 basispoints

TrancheIIoption cost = 100 - 90 = 10 basispoints

TrancheIhasahigher OAS andlower option costthanTrancheII, andtheeffectivedurationsofthetwotranchesareequal. Therefore:

TrancheIisundervaluedona relativebasis ("cheap"), andsheshouldbuyit. TrancheIIisovervaluedona relativebasis ("rich"), andsheshouldsellit.

Ona givenday, abondwitha callprovision rosein valueby1%. What canbesaidabouttheleveland volatilityofinterest rates?

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Theonlypossibleexplanationisthatlevelofinterest ratesfell.

Apossibilityisthatthelevelofinterest rates remained constant, butthe volatilityofinterest

ratesfell.

Explanation

As volatilitydeclines, sowilltheoption value, whichmeansthe valueofa callablebondwill rise.

Whichofthefollowing is NOTamajor reasonwhytheeffectivedurations reportedbydealersand vendors canbe verydifferent?

Differences in the assumption how yield volatility changes for shocks to the yield curve. Differencesinthe relationshipbetweenshort-terminterest ratesand refinancing rates. Differentoption-adjustedspreads.

Explanation

Themajor differencesintheeffectivedurationamong analyticalsystemsprovidersareattributabletodifferencesinthefollowing:the incremental changeininterest rate, theprepaymentmodel, theOAS, andtheinterest rate/refinancing ratespreadassumption.

Using thefollowing treeofsemiannualinterest rateswhatisthe valueofa callablebondthathasoneyear remaining to maturity, a callpriceof 99 anda 5% coupon ratethatpayssemiannually?

7.59%

6.35%

5.33%

98.65. 98.26. 99.21.

Explanation

The callablebondpricetreeisasfollows:

100.00

98.75

98.26 100.00

99.00

100.00

Theformulafor thepriceateachnodeis:

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Up Nodeatt = 0.5:min{(0.5 × (100 + 2.5) + 0.5 × (100 + 2.5)) / (1 + 0.0759/2), 99} = 98.75. Down Nodeatt = 0.5:min{(0.5 × (100 + 2.5) + 0.5 × (100 + 2.5)) / (1 + 0.0533/2), 99} = 99.00. Nodeatt = 0.0:min{(0.5 × (98.75 + 2.5) + 0.5 × (99 + 2.5)) / (1 + 0.0635/2), 99} = 98.26.

Supposethatthestockpriceofa commonstockincreasesby10%. Whichofthefollowing ismostaccuratefor thepriceofthe recently issued convertiblebond? The valueofthe convertiblebondwill:

increase by less than 10%. remainunchanged.

increaseby10%.

Explanation

Whentheunderlying stockprice rises, the convertiblebondwillunderperformbecauseofthe conversionpremium. However, buying convertiblebondsinlieuofstockslimitsdownside risk. Thepricefloor setbythestraightbond value causesthisdownsideprotection.

Patrick Wallisanewassociateatalargeinternationalfinancialinstitution. Hisboss, C.D. Johnson, is responsiblefor familiarizing Wallwiththebasicsoffixedincomeinvesting. Johnsonasks Walltoevaluatethetwootherwiseidenticalbonds showninTable1. The callablebondis callableat100 andexercisableonthe coupondatesonly.

Wallistoldtoevaluatethebondswith respecttodurationand convexitywheninterest ratesdeclineby 50 basispointsatall maturitiesover thenextsix months.

Johnsonsupplies Wallwiththe requisiteinterest ratetreeshownin Figure1. Johnsonexplainsto Wallthatthepricesofthe bondsinTable1were computedusing theinterest ratelattice. Johnsoninstructs Walltotryand replicatetheinformationin Table1andusehisanalysistoderiveaninvestmentdecisionfor hisportfolio.

Table1

BondDescriptions

Non-callableBond CallableBond

Price $100.83 $98.79

Timeto Maturity (years) 5 5 Timeto FirstCallDate -- 0

AnnualCoupon $6.25 $6.25

InterestPayment Semi-annual Semi-annual Yieldto Maturity 6.0547% 6.5366% PriceValueper BasisPoint 428.0360 --Figure 1

15.44%

14.10%

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The valueofthe callablebondatnodeAisobtainedasfollows:

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lower riskandlower returnpotential. lower riskandhigher returnpotential.

Explanation

Buying convertiblebondsinlieuofdirectstockinvesting limitsdownside riskduetothepricefloor setbythestraightbond value. The

costofthe riskprotectionisthe reducedupsidepotentialduetothe conversionpremium.

Whichofthefollowing mostaccuratelyexplainshowtheeffective convexityis computedusing thebinomialmodel. Inorder to compute theeffective convexitythe:

yield curve has to be shifted upward and downward in a parallel manner and the binomial tree recalculated each time.

binomialtreehastobeshiftedupwardanddownwardbythesameamountfor allnodes. volatilityhastobeshiftedupwardanddownwardandthebinomialtree recalculatedeachtime.

Explanation

Applyparallelshiftstotheyield curveandusethese curvesto computenewforward ratesintheinterest ratetree. The resulting bond

valuesarethenusedto computetheeffective convexity.

Bill Moxley, CFAisevaluating threebondsfor inclusioninfixedincomeportfoliofor oneofhispensionfund clients. Allthree bondshavea coupon rateof 3%, maturityoffiveyearsandare generallyidenticalinevery respectexceptthatbondAisan option-freebond, bondBis callableintwoyearsandbondCisputableintwoyears. Theyield curveis currentlyflat.

Iftheyield curvebecomesupwardsloping, thebond least likelytohavethehighestpriceimpactwouldbe:

Bond B BondA

BondC

Explanation

BondCisputableandhencehaslimiteddownsidepotentialwhen rates rise. Theother twobondsdonothaveanysuch protection.

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Explanation

Whentheunderlying optionisat (or near)money, callablebondswillhavelower one-sideddown-durationthanone-sidedup -duration; theprice changeofa callablewhen ratesfallissmaller thantheprice changefor anequalincreasein rates. Inthis problem, the coupon rateis giventobeequaltothe currentlevelof ratesandhencethebondshouldbeatpar andthe underlying optionisat-the-money.

Giventhefollowing information, whichbondhasthe greaterinterest rate riskandwhatisthe changeinpriceif ratesincrease by 50 basispoints?

Duration

Convexit

y

BondA

_4.5

_45.8

BondB

_7.8

_125.0

Bond A,change in price = −2.14%. BondB, changeinprice = −27.4%. BondB, changeinprice = −3.59%.

Explanation

BondBhasthe greater interest rate risksincethe changeinpriceislarger thanbondA. Changeinprice = (−D × changeinbp × 100) + (C × changeinbp × 100)

BondA = (−4.5 × 0.005 × 100) + (45.8 × 0.005 × 100) = −2.25 + 0.1145 = −2.14% BondB = (−7.8 × 0.005 × 100) + (125 × 0.005 × 100) = −3.9 + 0.3125 = −3.59%

Howisthe valueoftheembedded calloptionofa callablebonddetermined? The valueoftheembedded calloptionis:

the difference between the value of the option-free bond and the callable bond. equaltotheamountbywhichthe callablebond valueexceedstheoption-freebond value.

determinedusing thestandardBlack-Scholesmodel.

Explanation

The callablebondisequivalenttotheoption-freebondexceptthattheissuer hastheoptionto callthebondatthe callpricebefore maturity. Therefore, for theholder ofthebond, thebondisworththesameastheoption-freebond reducedbythe valueoftheoption.

Eric Romeworksinthebackofficeat Finance Solutions, alimitedliabilityfirmthatspecializesindesigning basic and 2

2

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Question #48 of 88

QuestionID:463849

Question #4

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sophisticatedfinancialsecurities. Mostoftheir clientsare commercialandinvestmentbanks, andthedetection, and controlof

interest rate riskis Financial Solution's competitiveadvantage.

Oneoftheir clientsislooking todesignafairlystraightforwardsecurity:a callablebond. Thebondpaysinterestannuallyover

atwo-year life, hasa7% couponpayment, andhasapar valueof $100. Thebondis callableinoneyear atpar ($100).

Romeusesabinomialtreeapproachto valuethe callablebond. He'salreadydetermined, using asimilar approach, thatthe

valueoftheoption-free counterpartis $102.196. Thisprice camefromdiscounting cashflowsaton-the-run ratesfor the

issuer. Thosediscount ratesare givenbelow:

Romeisalsointerestedinthe 20276% convertiblebondof Stellar Inc. Thebond canbe convertedinto 25 sharesof common

stockandistrading at $1024. Stellar's currentstockpriceis $32. Comparablenonconvertiblebonds currentlyyield6%.

Using thebinomialtreemodel, whatisthe valueofthe callablebond?

$102.196.

$95.521.

$101.735.

Explanation

The valueofthisbondatnode 0 isV = ½ × [($99.391 + $7) ÷ 1.048755 + ($100.000 + $7) ÷ 1.048755] = $101.735, sothe

priceofthe callablebondis $101.735. (LOS 47.d)

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$12.924.

$0.461.

$6.675.

Explanation

Givenintheproblemisthe valueofthebond'soption-free counterpart: $102.196. FromPartAwe'vedeterminedthepriceof

the callablebondtobe $101.735. Fromthe relationship:

V = V - V

We candeterminethatthe valueofthe calloptionis $102.196 - $101.735 = $0.461. (LOS 47.d)

Ifthebondisputableinoneyear atpar, the valueoftheputisclosestto:

$0.291.

$12.487.

$0.461.

Explanation

The valueofthebond'soption-free counterpartis $102.196 (given). We can calculatethepriceoftheputablebondtobe

$102.487. Fromthe relationship:

V = V - V

We candeterminethatthe valueofthe calloptionis $102.487 - $102.196 = $0.291.

Whichofthefollowing stepsthat Romemight gothroughin calculating theeffectivedurationofthis callablebondisleast

accurate?

call option-free callable

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ᅞ A)

ᅞ B)

ᅚ C)

Question #

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QuestionID:463853

ᅚ A)

Given the assumptions about benchmark interest rates, interest rate volatility, and a call and/or put rule,calculate the OAS for the issue, using the binomial model.

Imposeasmallparallelshifttotheinterest ratesusedintheproblembyanamount equalto +∆.

Addthe zero-volatilityspreadtoeachofthe1-year forward ratesintheinterest rate treeto geta "modified" tree.

Explanation

Calculating effectivedurationfor bondswithembeddedoptionsisa complicatedundertaking becauseyoumust calculate valuesofV andV. Giventheinformationintheproblem, this requiresfollowing sevensteps:

Step 1: Giventheassumptionsaboutbenchmarkinterest rates, interest rate volatility, anda calland/or put rule, calculatethe OAS for theissue, using thebinomialmodel.

Step2:Imposeasmallparallelshifttotheinterest ratesusedintheproblembyanamountequalto +D.

Step3:Buildanewbinomialtreeusing thenewyield curve.

Step4:AddtheOAS toeachofthe1-year forward ratesintheinterest ratetreeto geta "modified" tree. (Weassumethatthe OAS doesnot changewhentheinterest rates change.)

Step5:Computethenew valuefor V using thismodifiedinterest ratetree.

Step6: Repeatsteps 2 through 5 using aparallelshiftof -D toobtainthe valuefor V. Step7: Usetheformuladuration = (V + V) / 2V(DI).

If Rome reviseshisestimateofinterest rate volatilityusedin generationoftheinterest ratetreeupwards, thepriceof callable bondwouldmost likely:

Fall.

+

-i

+

I

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ᅞ B) ᅞ C)

Question #

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Increase.

Remainunchanged.

Explanation

Anincreaseininterest rate volatilitywouldincreasethe valueofthe calloptionleaving the valueofoption-freebond unchanged. Thiswouldleadtoadecreaseinthepriceofthe callablebond. (LOS 47.f)

Themarket conversionpremium ratiofor Stellar's convertiblebondisclosestto:

2.4% 28%. 20.6%.

Explanation

Aninvestor whopurchasesthe convertiblebond rather thantheunderlying stockwillpayapremiumover the currentmarket priceofthestock. Thismarket conversionpremiumper shareisequaltothedifferencebetweenthemarket conversionprice andthe currentmarketpriceofthestock.

Market conversionprice = marketpriceofCB ÷ conversion ratio = 1024 / 25 = 40.96 Market conversionpremium = conversionprice−marketprice = 40.96− 32 = 8.96

(LOS 47.j)

For abondwithanembeddedoptionwherethe cashflowisinterest ratepathdependent, whichofthefollowing valuationapproaches shouldbeused?

The option-adjusted spread approach with the binomial model. Theoption-adjustedspreadapproachwiththe MonteCarlosimulationmodel. Thenominalspreadapproachwiththe MonteCarlosimulationmodel.

Explanation

TheOAS method recognizesthat cashflow changesaccompanyinterest rate changes. Thus, itissuitabletouseOAS analysiswith ABSsthathaveaprepaymentoptionthatisfrequentlyexercised, and, ifthe cashflowsaredependentupontheinterest ratepath, OAS

shouldbe computedwiththe MonteCarlosimulationmodel.

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straight bond plus the value of the call option on the stock. callablebondplusthe valueofthe calloptiononthestock.

straightbond.

Explanation

The valueofanoncallable/nonputable convertiblebond canbeexpressedas:

Option-freeconvertiblebondvalue = straight value + valueofthe calloptiononthestock.

Whichofthefollowing scenarioswillleadtoa convertiblebondunderperforming theunderlying stock? The:

stock price rises. stockpriceisstable. stockpricefalls.

Explanation

A convertiblebondunderperformstheunderlying commonstockwhenthatstockincreasesin value. Thisisbecauseofthe conversionpremiumwhichmeansthatthebondwillincreaselessthantheincreaseinstockprice. Ifthestockpricefalls, the convertiblebondshouldoutperformthestockbecauseofthefloor createdbythestraight-value. Ifthestockisstable, thebond islikelytooutperformthestockbecauseofthehigher currentyieldofthebond. Ifthebondisupgraded, thebondshould increasein value. Thereisno reasonthatupgrading thebondshouldleadtothebondunderperforming thestock.

Supposethatthe valueofanoption-freebondisequalto100.16, the valueofthe corresponding callablebondisequalto 99.42, andthe

valueofthe corresponding putablebondis101.72. Whatisthe valueofthe calloption?

0.64. 0.74. 0.21.

Explanation

The calloption valueis justthedifferencebetweenthe valueoftheoption-freebondandthe valueofthe callablebond. Therefore, we have:

Calloption value = 100.16 - 99.42 = 0.74.

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ᅞ A)

Z-spread should be used with the binomial model.

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Question #61 of 88

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Question #6

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ᅞ A) ᅚ B)

ᅞ C)

Whichofthefollowing factorsmustbeincludedinanoption-based valuationapproachtopricea callable convertiblebond?

Interest rates, stock prices and theircorrelation. Interest ratesandstockpricesonly.

Stockpricesonly.

Explanation

The valuationof convertiblebondswithembedded calland/or putoptions requiresamodelthatlinksthemovementofinterest ratesand stockprices.

A collateralizedmortgageobligation (CMO)bondstructureincludesthreetranches, A, B, andC, withthefollowing characteristics:

Tranche OAS(inBP) OptionCost(in

BP)

A 54 73

B 55 94

C 68 71

Using thisinformation, whichofthetranchesappearstobe cheap?

A. C. B.

Explanation

AlargeOAS indicatesawider risk-adjustedspreadandlower relativeprice. Option costmeasuresprepayment risk. In general, the highestOAS andlowestoption costismostattractive. TrancheChasthehighestOAS andthelowestoption costatthesametime.

For anoption-freebondtrading atpar, itis least likelythat:

Its maturity key rate duration is the same as its effective duration.

Thespot ratefor thematurityofthebondisleastimportant rateaffecting the valueof thebond.

The ratedurationsfor allthe ratesother thanthematurity-matched rateare zero.

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Question #64 of 88

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Duetotheembedded calloption, theupsidepotentialof callablebondBislimited.

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ᅞ C)

Question #67 of 88

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Question #68 of 88

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ᅚ A) ᅞ B)

decline.

Explanation

As volatilityincreases, sowilltheoption value, whichmeansthe valueofaputablebondwill rise. Remember thatwithaputablebond, the investor islong theputoption.

Using thefollowing treeofsemiannualinterest rateswhatisthe valueofaputablesemiannualbondthathasoneyear remaining to maturity, aputpriceof 98anda4% coupon rate? Thebondisputabletoday.

7.59% 6.35% 5.33%

97.92. 98.75. 98.00.

Explanation

Theputablebondpricetreeisasfollows:

100.00

A ==> 98.27

98.00 100.00

99.35

100.00

Asanexample, thepriceatnodeAisobtainedasfollows:

Price = max{(prob × (P + coupon/2) + prob × (P + coupon/2))/(1 + rate/2), putlprice} = max{(0.5 × (100 + 2) + 0.5 × (100 + 2))/(1 +

0.0759/2),98} = 98.27. Thebond valuesattheother nodesareobtainedinthesameway.

Thepriceatnode 0 = [0.5 × (98.27+2) + 0.5 × (99.35+2)]/ (1 + 0.0635/2) = $97.71butsincethisislessthantheputpriceof $98thebond

pricewillbe $98.

Whichofthefollowing istheappropriate "nodaldecision" withinthebackwardinductionmethodologyoftheinteresttreeframeworkfor a

callablebond?

Min(call price, discounted value). Max(callprice, discounted value).

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ᅞ C)

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Min(par value, discounted value).

Explanation

When valuing a callablebondusing thebackwardinductionmethodology, the relevant cashflowtouseateachnodalperiodisthe coupon tobe receivedduring thatnodalperiodplusthe computed valueor the callprice, whichever isless.

Patrick Wallisanewassociateatalargeinternationalfinancialinstitution. Wallhas recently completed graduateschoolwitha Master's degreeinfinance, andisalso currentlyaCFA LevelI candidate. Hispreviousworkexperienceincludesthreeyearsasa creditanalystat asmall retailbank. Wall'snewpositionisastheassistanttothefirm'sfixedincomeportfoliomanager. Hisboss, Charles Johnson, is

responsiblefor getting Wallfamiliar withthebasicsoffixedincomeinvesting. Johnsonasks WalltoevaluatethebondsshowninTable1. Thebondsareotherwiseidenticalexceptfor the callfeaturepresentinoneofthebonds. The callablebondis callableatpar and

exercisableonthe coupondatesonly.

Table1

BondDescriptions

Non-Callable CallableBond

Price $100.83 $98.79

Timeto Maturity (years) 5 5

Timeto FirstCallDate -- 0

AnnualCoupon $6.25 $6.25

InterestPayment Semi-annual Semi-annual

Yieldto Maturity 6.0547% 6.5366%

PriceValueper BasisPoint 428.0360

--Wallistoldtoevaluatethebondswith respecttodurationand convexitywheninterest ratesdeclinedby 50 basisatallmaturitiesover

thenextsix months.

Johnsonsupplies Wallwiththe requisiteinterest ratetreeshownin Figure1. Johnsonexplainsto Wallthatthepricesofthebondsin Table1were computedusing thisinterest ratelattice. Johnsoninstructs Walltotryand replicatetheinformationinTable1andusehis analysistoderiveaninvestmentdecisionfor hisportfolio.

15.44%

14.10%

12.69% 12.46%

11.85% 11.38%

9.75% 10.25% 10.05%

8.95% 9.57% 9.19%

7.91% 7.88% 8.28% 8.11%

7.35% 7.23% 7.74% 7.42%

6.62% 6.40% 6.37% 6.69% 6.54%

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Question #77 of 88

QuestionID:463828

ᅚ A)

ᅞ B)

ᅞ C)

Question #78 of 88

QuestionID:463841

ᅞ A)

ᅚ B)

ᅞ C)

Question #7

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ᅞ A)

100.00

Asanexample, thepriceatnodeAisobtainedasfollows:

Price = min[(prob × (P + (coupon / 2)) + prob × (P + (coupon/2)) / (1 + (rate / 2)), callprice] = min[(0.5 × (100 + 2.5) + 0.5 × (100 + 2.5)) / (1 + (0.0776 / 2)), 99} = 98.67. Thebond valuesattheother nodesareobtainedinthesameway.

Ananalysthas constructedaninterest ratetreefor anon-the-runTreasurysecurity. Theanalystnowwishestousethetreeto calculate the convexityofa callable corporatebondwithmaturityand couponequaltothatoftheTreasurysecurity. Theusualwaytodothisisto

calculatetheoption-adjustedspread (OAS):

shift the Treasury yield curve,compute the new forward rates, add the OAS to those forward rates, enter the adjusted values into the interest rate tree, and then use the usual convexity formula.

computethe convexityoftheTreasurysecurity, andaddtheOAS. computethe convexityoftheTreasurysecurity, anddivideby (1+OAS).

Explanation

Theanalystusestheusual convexityformula, wheretheupper andlower valuesofthebondsaredeterminedusing thetree.

For a convertiblebond, whichofthefollowing is leastaccurate?

The conversion ratio times the price per share of common stock is a lower limit on the bond's price.

Theissuer candecidewhento convertthebondstostock.

A convertiblebondmaybeputable.

Explanation

Allofthesearetrueexceptthepossibilityoftheissuer toforce conversion. Thebondholder hastheoptionto convert.

Sharon Rogner, CFAisevaluating threebondsfor inclusioninfixedincomeportfoliofor oneofher pensionfund clients. Allthreebonds havea coupon rateof 3%, maturityoffiveyearsandare generallyidenticalinevery respectexceptthatbondAisanoption-freebond,

bondBis callableintwoyearsandbondCisputableintwoyears. Rogner computestheOAS ofbondAtobe 50bpsusing abinomial treewithanassumedinterest rate volatilityof15%.

If Rogner revisesher estimateofinterest rate volatilityto 20%, the computedOAS ofBondBwouldmost likelybe:

equal to 50bps.

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ᅚ B)

ᅞ C)

Question #8

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ᅚ A)

ᅞ B)

ᅞ C)

Question #81 of 88

QuestionID:463797

ᅞ A)

ᅞ B)

ᅚ C)

lower than 50bps. higher than 50bps.

Explanation

TheOAS ofthethreebondsshouldbesameastheyare giventobeidenticalbondsexceptfor theembeddedoptions (OAS isafter removing theoptionfeatureandhencewouldnotbeaffectedbyembeddedoptions). HencetheOAS ofbondBwouldbe 50 bpsabsent any changesinassumedlevelof volatility.

Whentheassumedlevelof volatilityinthetreeisincreased, the valueoftheembedded calloptionwouldincreaseandthecomputed valueofthe callablebondwoulddecrease. The constantspreadnowneededtoforcethe computed valuetobeequaltothemarketprice isthereforelower thanbefore. Henceanincreasein volatilityestimate reducesthe computedOAS for a callablebond.

A convertiblebondhasa conversion ratioof12 andastraight valueof $1,010. Themarket valueofthebondis $1,055, andthemarket

valueofthestockis $75. Whatisthemarket conversionpriceandpremiumover straight valueofthebond?

Market conversionprice Premiumover straight value

$87.92 0.0446

$75.00 0.1029

$84.17 0.1222

Explanation

Themarket conversionpriceis:

(marketpriceofthebond) / (conversion ratio) = $1,055 / 12 = $87.92. Thepremiumover straightpriceis:

(marketpriceofbond) / (straight value)−1 = ($1,055 / $1,010)−1 = 0.0446.

For a callablebond, the valueofanembeddedoptionisthepriceoftheoption-freebond:

plus the price of a callable bond of the same maturity,coupon and rating.

plusthe risk-free rate.

minusthepriceofa callablebondofthesamematurity, couponand rating.

Explanation

The valueoftheoptionembeddedinabondisthedifferencebetweenthatbondandanoption-freebondofthesamematurity, couponand

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Question #8

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ᅞ A)

ᅚ B)

ᅞ C)

Question #8

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ᅞ A)

ᅚ B)

ᅞ C)

Question #84 of 88

QuestionID:472703

ᅞ A)

ᅞ B)

ᅚ C)

option-freebond'spriceminusthe callablebond'sprice.

Theoptionadjustedspread (OAS)isusedtoanalyze riskbyadjusting for theembeddedoptions. Whichofthefollowing risksdoesthe OAS reflect?

Maturity risk. Credit risk. Prepayment risk.

Explanation

TheOAS reflects credit riskandliquidity risk.

Ananalysthas constructedaninterest ratetreefor anon-the-runTreasurysecurity. Theanalystnowwishestousethetreeto calculate thedurationoftheTreasurysecurity. Theusualwaytodothisistoestimatethe changesinthebond'spriceassociatedwitha:

parallel shift up and down of the forward rates implied by the binomial model. parallelshiftupanddownoftheyield curve.

shiftupanddowninthe currentone-year spot rateallelseheld constant.

Explanation

Theusualmethodistoapplyparallelshiftstotheyield curve, usethose curvesto computenewsetsofforward rates, andthenenter

eachsetof ratesintotheinterest ratetree. The resulting volatilityofthepresent valueofthebondisthemeasureofeffectiveduration.

JosephDentice, CFAisevaluating threebonds. Allthreebondshavea coupon rateof 3%, maturityoffiveyearsandare generally identicalinevery respectexceptthatbondAisanoption-freebond, bondBis callableintwoyearsandbondCisputableintwoyears. Ifinterest ratesincrease, thedurationofwhichbondismost likelytodecrease?

Bond A. BondB. BondC.

Explanation

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Question #8

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ᅞ A)

ᅞ B)

ᅚ C)

Question #86 of 88

QuestionID:463839

ᅞ A)

ᅚ B)

ᅞ C)

Question #87 of 88

QuestionID:463842

ᅞ A)

ᅚ B)

ᅞ C)

Question #88 of 88

QuestionID:463800

Withthe zero volatilityspread (Z-spread)approachthe valueofanasset-backedsecurity (ABS)isthepresent valueof cashflows discountedatthespot ratesplusthe Z-spread. Thismeansthe Z-spreadtechniquedoesnotincorporateprepaymentsandthuswouldbe appropriateto value:

high quality home equity loans.

autoloansor high qualityhomeequityloans.

autoloansor credit cardloans.

Explanation

The Z-spreadwouldbeappropriatefor valuing autoor credit cardbackedsecurities, becauseneither arelikelyto refinance.

Whichofthefollowing correctlydescribesoneofthebasic featuresofa convertiblebond? A convertiblebondisasecuritythat canbe

convertedinto:

another bond at the option of the issuer. commonstockattheoptionoftheinvestor. commonstockattheoptionoftheissuer.

Explanation

Theowner ofa convertiblebond canexchangethebondfor the commonsharesoftheissuer.

For a convertiblebondwitha callprovision, with respecttothebond's convertibilityfeatureandthe callfeature, theBlack-Scholesoption model canapplyto:

neither features. onlyonefeature.

bothfeatures.

Explanation

TheBlack-Scholesmodelappliestothe convertibilityfeature justasitdoestothe commonstock. TheBlack-Scholesmodelisnot appropriatefor the callfeaturebecausethe volatilityofthebond cannotbeassumed constant.

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ᅞ A)

ᅞ B)

ᅚ C)

Embedded call,$0,callable bond, option-free bond.

Embedded call, callablebond, $0, option-freebond.

$0, embedded call, callablebond, option-freebond.

Explanation