章節(jié)3-固定收益-任務講義03v

CFA三級培訓項目Fixede講師Topic

Weightings

in

CFA

Level

IIISS

1-2ETHICS

&

PROFESSIONAL

STANDARDSSS

3BEHAVIORAL

FINANCESS

4PRIVATE

WEALTH

MANAGEMENT

(1)SS

5PRIVATE

WEALTH

MANAGEMENT

(2)SS

6PORTFOLIO

MANAGEMENT

FOR

INSTITUTIONAL

INVESTORSSS

7APPLICATIONS

OF

ECONOMIC YSIS

TO

PORTFOLIO

MANAGEMENTSS

8ASSET

ALLOCATION

AND

RELATED

DECISIONS

AND

IN

PORTFOLIO

MANAGEMENT(1)SS

9ASSET

ALLOCATION

AND

RELATED

DECISIONS

AND

IN

PORTFOLIO

MANAGEMENT(2)SS10E

PORTFOLIO

MANAGEMENT

(1)SS

11E

PORTFOLIO

MANAGEMENT

(2)SS

12EQUITY

PORTFOLIO

MANAGEMENTSS

13ALTERNATIVEINVESTMENTS

FOR

PORTFOLIO

MANAGEMENTSS

14RISK

MANAGEMENTSS

15RISK

MANAGEMENT

APPLICATIONS

OF

DERIVATIVESSS

16TRADING,

MONITORING

AND

REBALANCINGSS

17PERFORMANCE

EVALUATIONAND

ATTRIBUTIONSS

18GLOBAL

INVESTMENT

PERFORMANCE

STANDARDS2-126FrameworkeYTMRelationships

between

price

andtimeValuation

withspot

ratesFlat

price,

accrued

interest,

andthe

full

priceMatrix

pricing;Yield

measuresYield

measures

for

floating-ratenotesYield

curveForward

ratesYield

spread3-126YTMFixede4-126Bond

Valuation

ProcessT

eral

procedure

for

valuing e

securities

is

to

take

thepresent

values

of

all

the

expected

cash

flows

and

add

themup

to

get

thevalue

of

the

security.Estimate

the

cash

flowsDeterminate

the

appropriate

discount

rateCalculate

the

present

value

of

the

estimated

cash

flowst1

(1

r)t

B

(1

r)nnP

C

t

5-126Yield

to

Maturity

(YTM)Internal

rate

of

return,

implied

market

discount

rateCritical

assumptions:1.

hold

the

bond

until

maturity2.

full,

timely

coupon,

principal

payments

(no

default)3.

coupons

are

reinvested

at

original

YTMCalculation:

iteration,

back

out6-126RelationshipsBetween

Priceand

YieldFixede7-126Relationships

Between

Price

and

YieldA

bond’s

price

and

YTM

are

inversely

related.A

bond

will

be

pricedat

a

discount

(premium)

to

par

value

if

couponrate

is

less

(more)

than

itsYTM.For

a

given

change

in

yield,percentage

price

increase

is

greaterthan

the

percentage

price

decrease.For

the

same

time

to

maturity,percentage

price

change

is

greaterwith

a

lower-coupon

bond.Generally,

for

the

same

coupon

rate,percentage

price

change

isgreater

with

a

longer-term

bond.8-126Relationships

Between

Price

and

YieldYTMPrice

(%

of

Par)For

an

Option-free

bondthe

price-yield

curve

isconvex

toward

the

originPrice

falls

atrate

as

yieldsa

decreasingincrease110.67100.0090.977%8%9%9-126Example:3-year

bond,

coupon

rate

10%,semi-annual,par

1000,

buyat

8%today,

after

one-year,

the

rate

change

to

7%,

the

value

changeattributable

to

the

passage

of

time?DPt=P1(8%)-

P0(8%)Time

ofMaturityYTM=3%YTM=6%YTM=12%3.0

years$1,085.40$1,000.00$852.482.51,071.741,000.00873.631.51,057.821,000.00896.051.01,029.341,000.00945.000.51,014.781,000.00971.6901,000.001,000.001,000.00Par

value

=

$1000,

Maturity

=

3

years,coupon

rate

=6%,

semi-annualpayment.MaturityPiscountPremiumParRelationships

Between

Price

and

Time10-126Anyst

gathered

the

following

information

about

two

option-freebonds

that

each

have

a

par

value

of

$1,000:If

the

discount

rate

does

not

change

for

either

bond,

one

year

fromtoday,

which

of

the

following

most

likely

describesthe

change

in

pricefor

each

bond?Both

Bond

1

and

Bond

2

willdecrease.Both

Bond

1

and

Bond

2

willincrease.Bond

1

will

increase

and

Bond

2

will

decrease.Correct

answer:

CExampleBond

1Bond

2Time

to

maturity5

years10

yearsAnnual

coupon

rate5.0%7.0%Discount

rate

today6,0%6.5%11-126An

8%

coupon

bond

with

a

par

value

of

$100

matures

in

6

years

and

isselling

at

$95.51

with

a

yield

of

9%.

Exactly

one

year

ago

this

bondsold

at

a

price

of

$90.26

with

a

yield

of

10%.

The

bond

pays

annualinterest.

The

change

in

price

attributable

to

the

change

in

maturityisclosest

to:$0.54.$1.03.$4.22.Correct

answer:BThe

change

in

price

attributable

to

moving

to

maturity

=

$91.29

-$90.26

=

$1.03Example12-126Valuation

withSpot

RatesFixede13-126Valuation

with

Spot

RatesSpot

rates:

are

market

discount

rates

for

single

payments

to

be

made

inthe

future.The

no-arbitrage

price

of

a

bond

is

calculated

using

spot

rates:)N1

2

NCPN2

Parno

-

arbitrage

price

CPN1

CPNN(1

S

)

(1

S

)2(1

SExample:

Treasury

spot

rates

(expressed

as

semiannual-pay)

are

asfollows:

6

months

=

4%,

1

year

=

5%,

1.5

year

=

6%.

A

1.5-year,

4%Treasury

note

is

trading

at

$965.

the

arbitrage

trade

and

arbitrage

profitare:Buy

the

bond,

sell

the

pieces,

earn

$7.09

per

bondSell

the

bond,

buy

the

pieces,

earn

$7.09

perbondSell

the

bond,

buy

the

pieces,

earn

$7.

91

per

bondCorrect

answer:

A14-126Flat

price,

accruedinterest,

and

thefull

priceFixede15-126Accrued

Interest●09/3006/30

12/31Accrued

Interest:

the

interest

received

by

the

seller

when

a

bond

tradesbetween

coupon

dates.Clean(flat)

Price:

the

agreed

upon

price

of

the

bond.Full

Price

(or

dirty

price):

the

amount

that

the

buyer

pays

to

theseller,which

equals

the

clean

price

plus

any

accrued

interest.Full

Price

=

Clean

Price

+Accrued

InterestCoupon

payment

datesSettlement

dateSeller’sinterestAgreed-uponBondPriceAccruedInterestCleanpriceFullprice

Seller’sinterestBuyer’sinterestTotal

interestthat

buyerwill

receive16-126Coupondate2Coupondate1TradingdaytTtAccrued

interest

=Clean

price

=

dirty

price-accrued

interestTCoupon

tAccrued

InterestPV

Full

PMT

PMT

PMT

FV(1

r)1t

/T

(1

r)2t

/T

(1

r)N

t

/T

PMT

FV

]

(1

r)t

/T

PV

(1

r)t

/T

[

PMT

PMT(1

r)1

(1

r)2(1

r)NPV

Full17-126Example:

3-year

bond,

coupon

rate

10%,

par

1000,（semiannual）buy

at

8%,

the

period

between

the

settlement

date

and

the

nextcoupon

period

is

58

days，there

are

183days

in

the

coupon

period,what

is

accrued

interest？AI=（1000*0.1/2）*（1-58/183）=50*（1-0.3169）=34.155Accrued

Interest18-126Example:

A

5%

bond

makes

coupon

payments

on

June

15

andDecember

15

and

is

trading

with

a

YTM

of

4%.

The

bond

is

purchasedand

will

settle

on

August

21

when

there

will

be

four

couponsremaining

until

maturity.

Calculate

the

full

price

of

the

bond

usingactual

days.Correct

answer:Step

1:

Calculate

the

value

of

thebond

on

the

last

coupondate(coupons

are

semiannual,

so

we

use

4%/2

=

2%

for

the

periodicdiscount

rate):N

=

4;

PMT=

25;

FV=

1,000;

I/Y

=2;

CPT PV=

-1,019.04Step

2:

Adjust

for

the

number

of

days

since

the

last

couponpayment:Days

between

June

15

and

December

15

=

183

days.Days

between

June

15

and

settlement

on

August

21

=

67

days.Full

price

1,019.04(1.02)67/183

1,026.46Accrued

Interest19-126Matrix

pricingFixede20-126Matrix

PricingMatrixpricing:a

method

of

estimating

the

required

YTM

ofbonds

that

arecurrently

not

traded

or

infrequently

traded

bonds

according

to

the

yieldsof

traded

bonds

with

the

same

credit

quality.Linear

interpolation

can

be

used

when

the

maturities

between

the

valuedbond

and

the

traded

bond

are

different.21-126Example:

Estimate

the

YTM

of

a

non-traded

4%,

5-year

annual-paybond4-yearannual-pay,

5%

coupon

bond:

YTM=4.738%6-yearannual-pay,

4%

coupon

bond:

YTM=5.232%6-year

annual-pay,

6%coupon

bond:

YTM=5.284%Answer:Average

YTM

of

6-yearbonds=(5.232+5.284)/2=5.258Using

linear

interpolation:YTM

of

the

non-traded

bond=4.738+[(5-4)/(6-4)*(5.258-4.738)=4.998%Matrix

Pricing22-126Consider

the

following

market

yields:5-year,

U.S.

Treasury

bond,

YTM

1.48%5-year,

A

rated

corporate

bond,

YTM

2.64%7-year,

Treasury

bond,

YTM

2.15%7-year,

A

rated

corporate

bond,

YTM

3.55%6-yearTreasury

bond,

YTM

1.74%Estimate

the

required

yield

on

a

newly

issued

6-year,

A

rated

corporatebond.Example23-126Answer:Calculate

the

spreads

to

the

benark(Treasury)

yields.Spread

on

the

5-year

corporate

bond

is

2.64

-1.48

=

1.16%.Spread

on

the

7-year

corporate

bond

is

3.55

-

2.15

=

1.40%.Calculate

the

average

spread

because

the

6-year

bond

is

themidpoint

of

five

and

seven

years.Average

spread

=

(1.16

+

1.40)

/

2

=

1.28%.Add

the

average

spread

to

the

YTM

of

the

6-year

Treasury(benark)

bond.1.74

+

1.28

=

3.02%,

which

is

our

estimate

of

the

YTM

on

thenewly

issued

6-year,

A

rated

bond.Example24-126YieldmeasuresFixede25-126Yield

Measures

for

Fixed-Rate

BondsPeriodicity

of

the

annual

rate:

an

annualized

and

compounded

yield

on

afixed-rate

bond

depends

on

the

assumed

number

of

periods

in

the

year.Typically,

the

periodicity

matches

the

frequency

of

coupon

payments.The

periodicity

of

the

annual

market

discount

rate

for

a

zero-coupon

bond

isarbitrary

because

there

are

nocoupon

payments.26-126Yield

Measures

for

Fixed-Rate

BondsSemiannual

bond

basis

yield(semiannual

bond

equivalent

yield):

anannual

yield

having

a

periodicity

of

two.A

semiannual

bond

basis

yield

is

the

yield

per

semiannual

periodtimes

twoEffective

yield:

Depends

on

its

periodicity,

or

annual

frequency

of

couponpayments.effective

yield

(1

YTM

)m

-1m

nmAn

effective

annual

rate

has

a

periodicity

of

one

because

there

is

justone

compounding

period

in

the

year.For

annual-pay

bond:

effective

yield

equal

toYTMConvert

an

annual

percentage

rate

for

m

periods

per

year

(APRm),

to

anannual

percentagerate

for

n

per

year

(APRn):(1

APRm

)m

(1

APRn

)n27-126Yield

Measures

for

Fixed-Rate

BondsStreet

convention

yield:

Yield

measures

that

neglect

weekends

andholidays

are

quoted

on

what

is

called

street

convention.

The

street

convention

yield-to-maturity

is

the

internal

rate

of

return

onthe

cash

flows

assuming

the

payments

are

made

on

the

scheduleddates.True

yield:

internal

rate

of

return

on

the

cash

flows

using

the

actualcalendar

of

weekends

and

bank

holidays.The

true

yield

is

never

higher

than

the

street

convention

yield

because

weekends

and

holidays

delay

the

time

to

payment.The

difference

is

typically

small,

no

more

than

a

basis

point

or

two.28-126Yield

Measures

for

Fixed-Rate

BondsCurrent

yield

(reinvestmente

or

interest

yield):

not

consider

capital

gains/loss

oresum

of

coupon

payment

received

over

the

yearThe

current

yield

is

a

crude

measure

of

the

rate

of

return

to

an

investorbecause

it

neglects

the

frequency

of

coupon

payments

in

the

numeratorand

any

accrued

interest

in

the

denominator.It

focuses

only

on

interest

e.In

addition

to

collecting

and

reinvesting

coupon

payments,

the

investorhas

a

gain

if

the

bond

is

purchased

at

a

discount

and

is

redeemed

at

parvalue.The

investor

has

a

loss

if

the

bond

is

purchased

at

a

premium

and

isredeemed

at

par

valuecurrent

yield

flat

bond

price29-126Yield

Measures

for

Fixed-Rate

BondsSimple

yield:

It

is

the

sum

of

the

coupon

payments

plus

thestraight-lineamortized

share

of

the

gain

or

loss,

divided

by

the

flat

price.Yield

to

call

(put)

is

calculated

as

a

YTM

but

with

the

number

of

periodsuntil

the

call

(put)

price

substituted

for

the

number

of

periods

to

maturityand

the

maturity

value.Yield

to

Worst:

the

worst

yield e

of

any

that

are

possible

given

thecall

provisions

of

the

bond.Option-adjusted

yield:

the

required

market

discountrate

whereby

the

priceis

adjusted

for

the

value

of

the

embedded

option.For

a

callable

bond:

option-adjusted

yield<YTMFor

a

putable

bond:

option-adjusted

yield>YTMBond

Selling

at:RelationshipParcoupon

rate

=

current

yield

=

yield

to

maturityDiscountcoupon

rate＜current

yield＜yield

to

maturityPremiumcoupon

rate＞current

yield＞yield

to

maturity30-126Tony

Ly

is

a

Treasury

Manager

with

Deeter

Holdings,

a

large

consumerproducts

holding

company.

The

Assistant

Treasurer

has

asked

Lytocalculate

the

current

yield

(CY)

and

the

Yield-to-Call

(YTC)

on

abond

the

company

holds

that

has

the

following

characteristics:7

years

to

maturity$1,000face

value7.0%

semi-annual

couponPriced

to

yield

9.0percentCallable

at

$1,060

in

two

yearsIf

Ly

calculates

correctly,

the

CY

and

YTC

are

approximay:CY

YTC7.80%

15.72%7.80%

15.82%7.78%

15.72%Correct

answer:BExample31-126Yield

measuresfor

floating-ratenotesFixede32-126Yield

measures

for

floating-rate

notesCoupon

rate

=

reference

rate

+

quoted

marginQuoted

margin:

margin

used

to

calculate

the

bond

coupon

paymentsDiscount

rate

=

reference

rate

+

required

margin

(or

discount

margin)Required/discount

margin:

margin

required

to

return

the

FRN

to

itspar

value

at

each

reset

date.Selling

at

par(credit

unchanged):

required

margin

=

quoted

marginSelling

at

discount(downgrade

of

credit):

quoted

margin

<

requiredmarginSelling

at

premium(upgrade

of

credit):

quoted

margin

>

requiredmargin33-126ExampleA

floating-rate

note

has

a

quoted

margin

of

+50

basis

points

and

arequired

margin

of

+75

basis

points.

On

its

nest

reset

date,

the

priceof

note

will:Equal

to

par

valueLess

than

par

valueGreater

than

par

valueCorrect

answer:

BYield

measures

for

floating-rate

notes34-126A

two-year

floating-rate

note

pays

6-month

Libor

plus

80

basis

points.The

floater

is

priced

at

97

per

100

of

par

value.

Current

6-month

Liboris

1.00%.Assume

a

30/360

day-count

convention

and

evenly

spacedperiods.

The

discount

margin

for

the

floater

in

basis

points

(bps)

isclosest

to:180

bps236

bps420

bpsCorrect

answer:BExample35-126Yield

curveFixede36-126Yield

CurveYield

curve

shows

the

term

structure

of

interest

rates

by

displaying

yieldsacross

different

maturities.Spot

curve:

a

yield

curve

for

single

payments

in

the

future,

such

as

zero-coupon

bonds

or

stripped

Treasury

bonds.Spot

curve

for

U.S.

Treasury

bonds

is

calledthe

zero-curve

or

strip

curve.Yield

curve

for

coupon

bonds

shows

the

YTM

for

coupon

bonds

at

variousmaturities,

which

can

be

calculated

by

linear

interpolationPar

bond

yield

curve:

shows

the

coupon

rates

for

bonds

of

variousmaturities

that

would

result

in

bond

prices

equal

to

their

par

values.Forward

yield

curve

shows

the

future

rates

for

bonds

or

money

marketsecurities

for

the

same

maturities

for

annual

periods

in

the

future.37-126Example:

Consider

a

3-year

annual-pay

bond

with

spot

rates

of

1%,

2%，3%

,

the

coupon

payment

satisfies:

PMT

PMT

PMT

100

1001.01

(1.02)2

(1.03)3Correct

answer:

PMT=2.96,

par

bond

coupon

rate=2.96%Yield

Curve38-126Forward

ratesFixede39-126Forward

Rates

vs.

Spot

RatesForward

Rates:

borrowing/lending

rate

for

a

loan

to

be

made

at

somefuture

date.

Marginal

return

for

extending

the

time-to-maturity

for

anadditional

periodE.g.

The

int.

of

a

1-year

loan

that

would

be

made

2

years

from

nowNotation:

2y1y

rate

of

a

1-year

loan

to

be

made

2

years

from

nowRelationship

Between

Forward

Rates

and

Spot

Rates(1+

S

)T

=

(1+

S

)(1+

1y1y) (1+

(T

-

1)y1y)T

1Valuation

Using

Forward

RatesCF1

CF2CFnbond

value

=(1+

S

1)(1+

1y1y)(1+

(T

-

1)y1y)+

+(1+

S

1) (1+

S

1)(1+

1y1y)40-126?$724.$720.$884.Correct

answer:AExampleExample:

Given

the

following

spot

and

forward

rates,

how

muchshould

an

investor

pay

for

a

3-year,

annual

zero-coupon

bond

with

aface

value

of

$1,000?One-year

spot

rate

at

3.5%The1-year

forward

rate

1

year

from

today

is

11.5%The

1-year

forward

rate

2

years

from

today

is

19.75%The

investor

should

pay

approxima

y:41-126Yield

SpreadFixede42-126Yield

Spreadark

bond.Ben ark

spread:

a

yield

spread

relative

to

a

benG-spread:

the

ben arkis ernment

bond

yieldInterpolated

spread

(I-spread):

the

ben ark

is

swap

rateZero-volatility

spread

(Z-spread):

the

spread

that

must

be

added

toeachrate

on

the

ben ark

yield

curve

to

make

the

present

value

of

a

bondequal

to

its

price.43-126Yield

SpreadThe

difference

between

the

GS

and

the

ZSThe

steeper

the

ben ark

spot

rate

curve,

the

greater

the

differencebetween

the

two

spread

measures.There

is

no

difference

between

the

GS

and

ZS

when

the

spot

yieldcurve

is

flat.The

earlier

bond

principal

is

paid,

the

greater

the

difference

between

thetwo

spread

measuresOption-adjusted

spread

(OAS):

used

for

bonds

with

embeddedoptions.Callable

bond:

ZS

>

OASPutable

bond:

ZS

<

OAS44-126Example:

Both

bonds

pay

interest

annually.

The

current

three-year

EURinterest

rate

swap

benark

is

2.12%.

The

G-spread

in

basis

points(bps)

on

the

U.K.

corporate

bond

is

closest

to:264

bps.285

bps.300

bps

.BondCouponrateTime-to-maturityPriceU.K.ernment

Benark2%3years100.25BondU.K.

Corporate

Bond5%3years100.65Correct

answer:AExample45-126Yield

SpreadZTreasury

spotrate

curveZZMaturityGCorporate

bondyield46-126Yield

Spread47-126Yield

SpreadG/Z

spreadOption

riskLiquidity

riskOASCredit

riskTreasury(riskfree)CallableBond48-1261.

The

difference

between

benark

spread

and

Z-spread,

which

oneis

greater?zero-coupon

&

flat

yield

curvezero-coupon

&

increaseyield

curveamortization

&

increase

yield

curveCorrect

answer:

C2.

With

respect

to

callable

bonds,

the

zero-volatility

spread

will

mostlikely

be:less

that

the

option-adjustedspreadgreater

than

the

option-adjusted

spreadequal

to

the

option-adjusted

spread

but

substantially

lessthan

the

nominal

spreadCorrect

answer:

BExample49-126Sources

of

returnFixede50-126Source

of

ReturnThree

sources

ofreturn:Coupon

and

principal

paymentsReinvestment

of

coupon

paymentsCapital

gain

or

loss

if

bond

is

sold

before

maturityTotal

return:

future

value

of

reinvested

coupon

interest

payments

and

thesale

price

(par

value

if

the

bond

is

held

to

maturity)Annualized

holding

period

return:

calculated

as

the

compound

annualreturn

earned

from

the

holding

period

.)

11

ntotal

returnannualzed

holding

period

return

(bond

price51-126Illustration

on

sources

of

returnAssumption:A

bond

makes

all

of

its

promised

coupon

and

principal

payments

on

time

(i.e.,

we

are

not

addressing

credit

risk).The

interest

rate

earned

on

reinvested

coupon

payments

is

the

same

asthe

YTM

on

the

bond.There

are

five

results

to

gain

from

the

ysis

presented

here.An

investor

who

holds

a

fixed-rate

bond

to

maturity

will

earn

anannualized

rate

of

return

equal

to

the

YTM

of

the

bond

when

purchased.An

investor

who

sells

a

bond

prior

to

maturity

will

earn

a

rate

of

returnequal

to

the

YTM

at

purchase

ifthe

YTM

at

sale

has

not

changed

sincepurchase.If

the

market

YTM

for

the

bond,

our

assumed

reinvestment

rate,increases

(decreases)

after

the

bond

is

purchased

but

before

thecoupon

date,

a

buy-and-hold

investor's

realizedreturn

will

be

higher

(lower)

than

the

YTM

of

the

bond

when

purchased.52-126Illustration

on

sources

of

returnThere

are

five

results

to

gain

from

the ysis

presented

here.If

the

market

YTM

for

the

bond,

our

assumed

reinvestment

rate,increases

after

the

bond

is

purchased

but

before

the coupon

date,a

bond

investor

will

earn

a

rate

of

return

that

is

lower

than

the

YTM

atbond

purchase

if

the

bond

is

held

for

a

short

period.If

the

market

YTM

for

the

bond,

our

assumed

reinvestment

rate,decreases

after

the

bond

is

purchased

but

before

the coupon

date,a

bond

investor

will

earn

a

rate

of

return

that

is

lower

than

the

YTM

atbond

purchase

if

the

bond

is

held

for

a

long

period.53-126Illustration

on

sources

of

returnAn

investor

whoholdsa

fixed-rate

bond

to

maturity

will

earn

anannualized

rate

of

return

equal

to

the

YTM

of

the

bond

whenpurchased.We

will

illustrate

this

calculation

(and

the result

listed

earlier)

with

a6%

annual-pay

three-year

bond

purchased

at

a

YTM

of

7%

and

held

tomaturity.With

an

annual

YTM

of

7%

the

bond’s

purchase

price

is

$973.76.At

maturity,

the

investor

will

have

received

coupon e

andreinvestment e

equal

to

the

future

value

of

an

annuity

of

three$60

coupon

payments

calculated

with

an

interest

rate

equal

to

thebond's

YTM.

This

amount

isN=

3;

I/Y

=

7;

PV=

0;

PMT=

60;

CPT:

FV

=

-192.89The

amount

earned

from

reinvestment

of

the

coupons

as

192.89-3(60)

=$12.89annualzed

holding

period

return

（(

1,000

192.89）/

973.76)1

3

-

1

7%54-126Illustration

on

sources

of

returnAn

investor

whosells

a

bond

prior

to

maturity

will

earn

a

rate

of

returnequal

tothe

YTM

at

purchase

iftheYTM

at

sale

has

not

changed

sincepurchase.Using

the

6%

three-year

bond

from

our

earlier

examples,

we

candemonstrate

this

for

an

investor

with

a

two-year

holding

period(investment

horizon).When

the

bond

is

purchased

at

a

YTM

of

7%

(for

$973.76),

we

have:Price

at

sale:

(atend

of

year

2,

YTM

=

7%):1,060/

1.07

=

990.65

orN

=

1;

I/Y

=

7;

FV

=

1,000;

PMT

=

60;

CPT:

PV

=

-990.65Coupon

interest

and

reinvestment e

For

two

years:60(1.07)

+

60

=

$124.20

orN

=

2;

I/Y

=

7;

PV

0;

PMT

=

60;

CPT

FV

=-124.20Investor's

annual

compound

rate

of

return

over

the

two-year

holdingperiod

is:1/2973.76124.20

990.65（

）

1

7%55-126Illustration

on

sources

of

return1000which

is

greater

than

the

6%

YTM

at

purchase.If

the

market

YTM

for

the

bond,

our

assumed

reinvestment

rate,

increases(decreases)

after

the

bond

is

purchased

but

before

the coupon

date,

abuy-and-hold

investor's

realized

return

will

be

higher

(lower)

than

the

YTMof

the

bond

when

purchased.For

a

three-year

6%

bond

purchased

at

par

(YTM

of

6%),

assumethat

the

YTM

and

reinvestment

rate

increases

to

7%

after

purchase

butbefore

the coupon

pay