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Stephen G. CECCHETTI • Kermit L. SCHOENHOLTZ

The Risk and Term Structure

of Interest Rates

Copyright © 2011 by The McGraw-Hill Companies, Inc. ll rights reser!e". McGraw-Hill#Irwin

Chapter Seven

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Introdution

• Changes in bond prices and the associated

changes in interest rates, can have a pronounced

effect on borrowing costs corporations face.

•In 1998 we saw the simultaneous increase in someinterest rates and decline in others - a rise in what are

called interest rate spreads.

• Changes in the perceived risk of ord!s and "#!s

bonds led to declines in prices.

• $his leads to increases in interest rates and higher

corporate borrowing costs.

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Introdution

• %e must be able to distinguish among man&

different t&pes of bonds that are traded in

financial markets.

$he purpose of this chapter is'

1. $o e(amine how the issuer and time to

maturit& affect the price of a bond, and

). $o use our knowledge to interpret fluctuationsin a broad variet& of bond prices.

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#atin$% and the #i%&Struture o' Intere%t #ate%

• *efault is one of the most important risks a bondholder faces.

• In fact, independent companies +rating

agencies have arisen to evaluate thecreditworthiness of potential borrowers.• $hese companies estimate the likelihood that the

corporate or government borrower will make a

bond!s promised pa&ments.• $he government has acknowledged a few firms asnationall& recognied statistical ratingorganiations/ +023s.

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)ond #atin$%

• $he best known bond rating services are

• #ood&!s

• 2tandard 4 5oor!s

• $he& monitor the status of individual bondissuers and assess the likelihood a lender will

be repaid b& the bond issuer.

• 6 high rating suggests that a bond issuer will

have little problem meeting a bond!s pa&mentobligations.

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)ond #atin$%

• irms or governments with an e(ceptionall&strong financial position carr& the highestratings and are able to issue the highest-rated

bonds, $riple 6.

• 7(' .2. "overnment, 7((on#obil, #icrosoft

• $he top four categories are consideredinvestment-grade bonds.• $hese bonds have a ver& low risk of default.

• eserved for most government issuers andcorporations that are among the most financiall&sound.

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)ond #atin$%

• $he distinction between investment-grade andspeculative, noninvestment-grade is important.

• 6 number of regulated institutional investors are not

allowed to invest in bonds rated below aa on

#ood&!s scale or on 2tandard and 5oor!s

scale.

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)ond #atin$%

• 2peculative grade bonds are bonds issued b&companies and countries that ma& have

difficult& meeting their bond pa&ments but are

not at risk of immediate default.

• :ighl& speculative bonds include debts that are

in serious risk of default.

• oth speculative grades are often referred to as

;unk bonds or high-yield bonds.

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)ond #atin$%

• $&pes of ;unk bonds'• allen angels are bonds that were once investment-

grade, but their issuers fell on hard times.

• onds issued b& issuers about which there is little

known.

• #aterial changes in a firm!s or government!s

financial conditions precipitate changes in its

debt ratings.• atings downgrade - lower an issuer!s bond rating.

• atings upgrade - upgrade an issuer!s bond rating.

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• %hat is a subprime mortgage<• 6 residential mortgage is called subprime when it

does not meet the ke& standards of creditworthiness

that appl& to conventional prime mortgages.

• Conventional mortgages are those that satisf& the

riles for inclusion in a collection or pool of

mortgages to be guaranteed b& a .2. "overnment

agenc&.

• $he standards cover the sie of mortgage, price ofthe home, and the ratio between the two' the loan-

to-value ratio +=$> ratio.

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• 2ubprime loans ma& fail to meet some or all ofthese standards for a ?ualif&ing mortgage.

• =ike other loans, subprime loans can be at a

fi(ed or variable rate +6#s.• 6#s t&picall& provide a low interest rate, or

teaser rate, for a couple of &ears and then the

interest resets to a higher rate.

• $his gives borrowers the abilit& to refinance afterthe introductor& rate is up.

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• 6lthough at their peak subprime mortgagesaccounted for less than 1@ percent of overall

residential mortgages, the& helped trigger the

financial disruptions of )AAB-)AA9.

• $he ke& reason is that some large, highl&

leveraged financial institutions held a siable

volume of #2 backed b& subprime

mortgages.• $hese financial institutions had bet the house/

on subprime mortgage securities.

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• 6s the government sought to reform thefinancial s&stem after the financial crisis of

)AAB-)AA9, the role of ratings agencies

attracted great attention.

• Investors around the world had relied on the

high ratings agencies had awarded to a large

groups of mortgage-backed securities +#2.

• 6s housing prices began to fall, agencies madesharp downgrades.

• *owngrades lowered #2 prices.

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• %hat caused the ratings errors<• *ata didn!t have sufficient information.

• irms hire the agencies to consult on what t&pes of#2 have the highest ratings and then rate them,

which was a conflict of interest.• atings agencies are compensated b& the issuers of

the bonds.

• 6gencies used a single rating scale to represent

default probabilities, independent of othercharacteristics like li?uidit&.

• $his ma& have led investors to underestimateother important risks.

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Commeria/ 0aper

• Commercial paper is a short-term version of a bond.

• $he borrower offers no collateral so the debt is

unsecured .

• Commercial paper is

• Issued on a discount basis, as a ero-coupon bond

specif&ing a single future pa&ment with no

associated coupon pa&ments.

• :as maturit& of less than )BA da&s.

• #ore than one third is held b& mone&-market mutual

funds.

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Commeria/ 0aper

• #ost commercial paper is issued with amaturit& of @ to @ da&s and is used e(clusivel&

for short-term financing.

• $he rating agencies rate the creditworthiness ofcommercial paper issuers in the same wa& the&

do bond issuers.

• 6lmost all carr& #ood&!s 5-1 or 5-) rating

• 5 stands for prime grade commercial paper.

• 2peculative-grade commercial paper does e(ist, but

not because it was issued as such.

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Commeria/ 0aper

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• ond ratings are designed to reflect defaultrisk.

• $he lower the rating

• $he higher the risk of default.• $he lower its price and the higher its &ield.

• $o understand ?uantitative ratings, it is easier

to compare them to a benchmark.

The Impat o' #atin$% on 1ie/d%

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• .2. $reasur& issues are the closet to risk-freeand are commonl& referred to as benchmark

bonds.

• Dields on other bonds are measured in terms ofthe spread over $reasuries.

• ond &ield is the sum of two parts'

E .2. $reasur& &ield F *efault risk premium


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• If bond ratings properl& reflect risk, then thelower the rating if the issuer, the higher the

default-risk premium.

• %hen $reasur& &ields move, all other &ieldsmove with them.

• %e can see this from igure B.) showing a plot

of the risk structure of interest rates.

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• Changes in the .2. $reasur& &ields accountfor most of the movement in the 6aa and aa

bond &ields.

• rom 19B9-)AA9, the 1A-&ear .2. $reasur& bond &ield has averaged almost a full

percentage point below the average &ield on

6aa bonds and two percentage points below

the average &ield on aa bonds.

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• 6 two-percentage point increase in the &ield,from @ to B percent, lowers the value of the

promise of G1AA in 1A &ears b& G1A.@H, or 1B

percent.

• Clearl& ratings are crucial to corporations!

abilit& to raise financing.

• 6 lower rate increases the costs of funds.

• Investors clearl& must be compensated forassuming risk.

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• Companies aren!t the onl& ones with creditratings' &ou have one too.

• $here are companies keeping track of &our

financial information.• 6ll this information is combined into a credit

score, which &ou should care about.

• $he better &our credit score, the lower the

interest rate &ou will pa& on debt.

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i3erene% in Ta4 Statu%and 5uniipa/ )ond%

• $a(es are also an important factor affecting the&ield on a bond.

• ondholders must pa& income ta( on the

interest income the& receive from owning privatel& issued bonds - ta(able bonds.

• $he coupon pa&ments on bonds issued b& state

and local governments, municipal or ta(-

e(empt bonds, are specificall& e(empt fromta(ation.

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• $he general rule in the .2. is that the interestfrom bonds issued b& one government is not

ta(ed b& another government, although the

issuing government ma& ta( it.

• In an effort to make their bonds more attractive

to investors, state and local governments

usuall& choose not to ta( the interest on their

own bonds.• Investors base their decisions on the after-tax

yield .

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• %hat are the ta( implications for bond &ields<

• Consider a one-&ear G1AA face value ta(able

bond with a coupon rate of H percent.

• 5ar is G1AA, and &ield to maturit& is H percent.• "overnment sees this H percent as ta(able income.

• If ta( rate is AJ, the ta( is G1.8A.

• ond &ields G1A.)A after ta(es, e?uivalent of .)

percent.

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$a(-7(empt ond Dield

E +$a(able ond Dield ( +1- $a( ate.

• or an investor with a AJ ta( rate, the ta(-

e(empt &ield on a 1A percent bond is B percent.

• 3verall, the higher the ta( rate, the wider the

gap between the &ields on ta(able and ta(-e(empt bonds.


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• 6sset-backed commercial paper +6C5 is ashort-term liabilit& with a maturit& of up to )BA

da&s.

• 6C5 is collateralied b& assets that financial

institutions place in a special portfolio.

• $hese pla&ed a special role in the housing

boom that preceded the financial crisis of

)AAB-)AA9.

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• $o lower costs and limit asset holding, somelarge banks created firms +a form of shadow bank that issued 6C5 and used the mone& to bu& mortgages and other loans.

• $he pa&ment stream generated b& the loans was usedto compensate the holders of the 6C5.

• $his also allowed banks to boost leverage and takeon more risk.

•%hen mortgage volume surged, these shadow banksissued more 6C5 to finance e(pansion.

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• %hen the 6C5 matures, issues have to borrow +or sell underl&ing assets to be able to

return the principal to the 6C3 holders.

• $he risk was that the issuers would be unableto borrow - the& faced rollover risk.

• If the& were also unable to sell the long-term

assets easil&, the shadow banks would face

failure.

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• $he uncertaint& in the value of mortgages lead6C5 purchasers to realie the risk and 6C5

purchases halted.

• irms that has issued 6C5 faced animmediate threat to their survival.

• Inabilit& to sell assets or obtain other funding

caused man& to fail.

• 2ome banks rescued their shadow banks, facingheightened li?uidit& needs and pressures to sell

assets during the worst time - the middle of a crisis.

T St t '

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Term Struture o'Intere%t #ate%

• %h& do bonds with the same default rate andta( status but different maturit& dates have

different &ields<

• =ong-term bonds are like a composite of a series of

short-term bonds.

• $heir &ield depends on what people e(pect to

happen in the future.

• :ow do we think about future interest rates<

T St t '

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Term Struture o'Intere%t #ate%

• $he relationship among bonds with the samerisk characteristics but different maturities iscalled the term structure of interest rates.

• Comparing -month and 1A-&ear $reasur&

&ields we can see'1. Interest rates of different maturities tend to move

together.

). Dields on short-term bonds are more volatile than

&ields on long-term bonds.. =ong-term &ields tend to be higher than short-term

&ields.

T St t ' I t t

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Term Struture o' Intere%t#ate%

Th E t ti

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The E4petation%H6pothe%i%

• #an& theories have been proposed to e(plainthe term structure of interest rates.

• $he first we will look at is the e(pectations

h&pothesis.• ocuses on the risk-free interest rate.

• $he risk-free interest rate can be computed,

assuming there is not uncertaint& about the

future.

The E petation%

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• If there is no uncertaint&, then an investor will be indifferent between holding a two-&ear bond

or a series of two one-&ear bonds.

• Certaint& means that the bonds of different

maturities are perfect substitutes for each other.

• $he e(pectations h&pothesis implied that the

current two-&ear interest rate should e?ual the

average of current one-&ear rate and the one-&ear interest rate one &ear in the future.

The E4petation%

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• If current interest rate is @ percent and future interestrate is B percent, then the current two-&ear interest rate

will be +@FBK) E HJ.

• %hen interest rates are e(pected to rise, long-term

interest rate will be higher than short-term interestrates.

• $he &ield curve will slope up.

• $his also means'

• If interest rates are e(pected to fall, the &ield curve will slopedown.

• If e(pected to sta& the same, the &ield curve will be flat.

The E4petation%

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The E4petation%

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The E4petation%

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• If bonds of different maturities are perfectsubstitutes for each other, then we can

construct investment strategies that must have

the same &ields.

• 3ptions'

1. Invest in a two-&ear bond and hold it to maturit&

• i2t is interest rate - ) &ear bond bought toda&, t.

• 3ne dollar &ields +1 F i2t +1 F i2t two &earslater.

The E4petation%

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). Invest in two one-&ear bonds, one toda& andone when the first matures.

• 3ne-&ear bond toda& has interest i1t .

• 3ne-&ear bond purchased in &ear ) has interest

ie1t+1, where e is e(pected.

• 3ne dollar invested toda& returns +1 F i1t +1 F

ie1t+1.

The E4petation%

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• $he e(pectations h&pothesis tells us investorswill be indifferent between the two options.

• $his means the& must have the same return'

+1 F i2t +1 F i2t E +1 F i1t +1 F ie

1t+1• %e can now write the two-&ear interest rate as

the average of the current and future e(pected

one-&ear interest rates'

i2t =

i1t + i

1t +1

e

2

The E4petation%

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The E4petation%

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• %e can generalie this' a bond with n &ears tomaturit& is the average of n e(pected future

one-&ear interest rates'

int =

i1t + i

1t +1

e

+ i1t +2

e

+ ...+ i1t +n−1

e

n

The E4petation%

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*oes this h&pothesis e(plain the three observationswe started with<

1. Interest rates of different maturities will move

together.

• %e can see this holds from the previous e?uation.

). Dields on short-term bonds will be more

volatile than &ields on long-term bonds.

• =ong-term rates are averages of short-term rates, sochanging one short-term rate has little effect on the

long term rate.

The E4petation%

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. $his h&pothesis cannot e(plain wh& long-term &ields are normall& higher than short

term &ields.

• It implies that the &ield curve slopes upward onl&

when interest rates are e(pected to rise.

• $his h&pothesis would suggest that interest rates

are normall& e(pected to rise.

•%e need to e(tend the e(pectationsh&pothesis to include risk.

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• $o decode charts and

graphs, use these three

strategies'

1. ead the title of thechart.

). ead the label on the

horiontal a(is.

. ead the label on thevertical a(is.

The Liuidit6 0remium

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The Liuidit6 0remiumTheor6

• isk is the ke& to understanding the slope ofthe &ield curve.

• ondholders face both inflation and interest-

rate risk.

• $he longer the term of the bond, the greater both

t&pes of risk.


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• Computing real return from nominal returnre?uires a forecast of expected future inflation.

• $he further into the future we look, the greater the

uncertaint&.

• A bond’s inflation risk increases with its time to

maturity.


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• Interest-rate risk arises from the mismatch between the investor!s investment horion and

a bond!s time to maturit&.

• If a bondholder plans to sell a bond prior to

maturit&, changes in the interest rate generate

capital gains or losses.

• $he longer the term of the bond, the greater the

price changes for a given change in interest rates

and the larger the potential for capital losses.


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• Investors re?uire compensation for the increasein risk the& take for bu&ing longer term bonds.

• %e can think about bond &ields as having two

parts'

• 3ne that is risk free - e(plained b& the e(pectations

h&pothesis.

• 3ne that is a risk premium - e(plained b& inflation

and interest-rate risk.


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n

iiiirpi

e

nt

e

t

e

t t

nnt

11)1111 ....

−+++ ++++

+=


• $ogether this forms the li?uidit& premiumtheor& of the term structure of interest rates.

• %e can add the risk premium to our previous

e?uation to get'


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• %e can look at the average slope of the termstructure over a long period to get an idea ofthe sie of the risk premium.• rom 198@ to )AA9, the difference between the

interest rate on a 1A-&ear $reasur& bond and that ona -month $reasur& bill has averaged a bit over 1.@

percentage points.

• $his risk premium will var& over time.

• %e have now e(plained all three of ourconclusions about the term structure of interestrates.

The In'ormation Content o'

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The In'ormation Content o'Intere%t #ate%

• isk spreads provide one t&pe of information,

the term structure another.

• %e can appl& what we have ;ust learned to

recent .2. economic histor& to show howforecasters use these tools.

In'ormation in the #i%&

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In'ormation in the #i%&Struture o' Intere%t #ate%

• $he immediate impact of a pending recession isto raise the risk premium on privatel& issued

bonds.

• 0ote that an economic slowdown or recession does

not affect the risk of holding government bonds.

• $he impact of a recession on companies with high

bond ratings is also usuall& ?uite small.

• $he lower the initial grade of the bond, the

more the default-risk premium rises as general

economic conditions deteriorate.

In'ormation in the #i%&

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In'ormation in the #i%&Struture o' Intere%t #ate%

• 5anel 6 of igure B.8 shows the annual "*5

growth over four decades superimposed on

shading that shows the dates of recessions.

• *uring shaded periods growth is usuall& negative.• 5anel of figure B.8 shows "*5 growth

against the spread between &ields on aa-rated

bonds and .2. $reasur& bonds.

• %hen risk spread rises, output falls.

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• *uring financial crises, people take cover.• $he& sell risk& investments 4 bu& safe ones.

• 6n increase in the demand for government

bonds coupled with a decrease in the demandfor virtuall& ever&thing else is called a flight to

?ualit&.

• $his leads to an increase in the risk spread.

• $he 1998 ussian default on its bonds led to aserious flight to ?ualit& causing the financial

markets to cease to function properl&.

In'ormation in the Term

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In'ormation in the TermStruture o' Intere%t #ate%

• Information on the term structure, particularl&

the slope of the &ield curve - helps to forecast

general economic conditions.

• $he &ield curve usually slopes upward.• 3n rare occasions, short-term interest rates e(ceed

long-term &ields leading to an inverted &ield curve.

• $his is a valuable forecasting tool because it

predicts a general economic slowdown.• Indicates polic& is tight because polic&makers are

attempting to slow economic growth and inflation.


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• igure B.9 shows "*5 growth and the slope ofthe &ield curve, measured as the difference

between the 1A-&ear and A month &ields' term

spread.

• 5anel 6 shows "*5 growth together with the

growth and term spread at the same time.

• 5anel shows "*5 growth in the current &ear

against the slope of the &ield curve one &earearlier.

• $he two lines clearl& move together.

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• %hen the term spread falls, "*5 growth tendsto fall one &ear later.

• $his shows that the &ield curve is a valuableforecasting tool.

• :owever, the &ield curve did not predict thedepth or duration of the recession of )AAB-)AA9.• 3ne and two &ear rates did not anticipate the

persistent plunge of overnight rates.

• $he widening risk spread signaled a severe economicdownturn providing a more useful predictor in thiscase.

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• $he slope of the &ield curve can help predictthe direction and speed of economic growth.

• 6t the beginning of )A1A the &ield curve was

usuall& steep - pointing to a strong economic

e(pansion.

• In the aftermath of the financial crisis of )AAB-

)AA9, lenders were especiall& caution about

e(tending credit to risk& borrowers, even withnarrow risk spreads.

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• $he author of this article argues it is onl& amatter of time until the steep &ield curve

encourages lenders to start lending again.

• $he abilit& and willingness will depend on how

?uickl& intermediaries can repair the damage to

their balance sheets and gain confidence about

borrowers.

Stephen G CECCHETTI • Kermit L SCHOENHOLTZ

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Stephen G. CECCHETTI • Kermit L. SCHOENHOLTZ

The Risk and Term Structure

of Interest Rates

End o'

Chapter Seven

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Chap007 (4)