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Chapter 7. Risk and Term Chapter 7. Risk and Term Structure of Interest RatesStructure of Interest RatesChapter 7. Risk and Term Chapter 7. Risk and Term Structure of Interest RatesStructure of Interest Rates
• Risk Structure
• Term Structure• Risk Structure
• Term Structure
Not all interest rates are created Not all interest rates are created equal!equal!Not all interest rates are created Not all interest rates are created equal!equal!
• many interest rates at one time
• But interest rates do move together over time
• many interest rates at one time
• But interest rates do move together over time
Interest rate structureInterest rate structureInterest rate structureInterest rate structure
• Why do yields differ?
• Risk structure bonds/debt with same maturity but
different characteristics
• Term structure Bond with same characteristics
but different maturities
• Why do yields differ?
• Risk structure bonds/debt with same maturity but
different characteristics
• Term structure Bond with same characteristics
but different maturities
Interest rates: a snapshotInterest rates: a snapshotInterest rates: a snapshotInterest rates: a snapshot
1/07 1/08 • 3 mo Tbill 4.98% 2.75%
• 3 mo Com Paper 5.17% 3.25%
• 10 yr. Tnote 4.76% 3.74%
• 10 yr. AAA corp 5.4% 5.33%
• 10 yr. BAA corp 6.34% 6.54%
• 30 yr. mortgage 6.22% 5.76%
1/07 1/08 • 3 mo Tbill 4.98% 2.75%
• 3 mo Com Paper 5.17% 3.25%
• 10 yr. Tnote 4.76% 3.74%
• 10 yr. AAA corp 5.4% 5.33%
• 10 yr. BAA corp 6.34% 6.54%
• 30 yr. mortgage 6.22% 5.76%
measurementmeasurementmeasurementmeasurement
• difference between two interest rates spread
• measured in percentage points basis points 1 percentage pt. = 100 basis pts.
• difference between two interest rates spread
• measured in percentage points basis points 1 percentage pt. = 100 basis pts.
example 1example 1example 1example 1
• 3 mo. Tbill 2.75%
• 3 mo. Commercial paper 3.25%
• spread 0.5 percentage pts. 50 basis pts.
• 3 mo. Tbill 2.75%
• 3 mo. Commercial paper 3.25%
• spread 0.5 percentage pts. 50 basis pts.
example 2example 2example 2example 2
• 10 yr Tnote 3.74%
• 10 BAA corporate 6.54%
• spread 2.8 percentage pts. 280 basis pts.
• 10 yr Tnote 3.74%
• 10 BAA corporate 6.54%
• spread 2.8 percentage pts. 280 basis pts.
I. Risk Structure of Interest RatesI. Risk Structure of Interest RatesI. Risk Structure of Interest RatesI. Risk Structure of Interest Rates
• debt with same maturity,
but different characteristics default risk tax treatment
• debt with same maturity,
but different characteristics default risk tax treatment
PatternsPatternsPatternsPatterns
• Baa > AAA > U.S. Treasury size of the spread varies
• Baa > AAA > U.S. Treasury size of the spread varies
A. Default RiskA. Default RiskA. Default RiskA. Default Risk
• risk of not receiving timely payment of principal and interest
• depends on creditworthiness of issuer structure of bond
• risk of not receiving timely payment of principal and interest
• depends on creditworthiness of issuer structure of bond
U.S. government debtU.S. government debtU.S. government debtU.S. government debt
• zero default risk
• backed by “full faith and credit”
of U.S. government
• why? power to tax largest economy power to issue stable currency
• zero default risk
• backed by “full faith and credit”
of U.S. government
• why? power to tax largest economy power to issue stable currency
Other issuersOther issuersOther issuersOther issuers
• private
• foreign
• municipal
• all have some default risk
• rated for default risk
• private
• foreign
• municipal
• all have some default risk
• rated for default risk
Bond ratingsBond ratingsBond ratingsBond ratings
• bond issuer pays rating agency Moody’s, S&P, Fitch p. 151 or p. 149
• high credit rating = low default risk
• bond ratings may change over time Downgrades or upgrades
• bond issuer pays rating agency Moody’s, S&P, Fitch p. 151 or p. 149
• high credit rating = low default risk
• bond ratings may change over time Downgrades or upgrades
Investment gradeInvestment gradeInvestment gradeInvestment grade
Moodys’ S&P
• Aaa AAA
• Aa (Aa1, Aa2, Aa3) AA (AA+, AA, AA-)
• A A
• Baa BBB
Moodys’ S&P
• Aaa AAA
• Aa (Aa1, Aa2, Aa3) AA (AA+, AA, AA-)
• A A
• Baa BBB
Noninvestment, speculativeNoninvestment, speculativeNoninvestment, speculativeNoninvestment, speculative
• Ba BB
• B B• Ba BB
• B B
Highly Speculative (High-yield, “Junk”)Highly Speculative (High-yield, “Junk”)Highly Speculative (High-yield, “Junk”)Highly Speculative (High-yield, “Junk”)
• Caa CCC
• Ca CC
• C C
• D (in default)
• Caa CCC
• Ca CC
• C C
• D (in default)
examplesexamplesexamplesexamples
• AAA GE, Toyota, Berkshire Hathaway, Pfizer
• AA Wells Fargo, Merck, Merrill Lynch, Gillette, NYC GO
bonds, Rochester, Syracuse, Onondaga Co.
• A Caterpillar, Boeing, Dow Chemical, Coca Cola,
California GO bonds,
• BBB DaimlerChrysler, Union Pacific, Mattel, Home Depot
• AAA GE, Toyota, Berkshire Hathaway, Pfizer
• AA Wells Fargo, Merck, Merrill Lynch, Gillette, NYC GO
bonds, Rochester, Syracuse, Onondaga Co.
• A Caterpillar, Boeing, Dow Chemical, Coca Cola,
California GO bonds,
• BBB DaimlerChrysler, Union Pacific, Mattel, Home Depot
• BB GM, Sears
• B Ford, Clear Channel, Univision
• CCC Revlon, Sirius, Pep Boys, JoAnn, ToysRUs
• CC Primus
• C Wolverine Tube
• BB GM, Sears
• B Ford, Clear Channel, Univision
• CCC Revlon, Sirius, Pep Boys, JoAnn, ToysRUs
• CC Primus
• C Wolverine Tube
DefaultsDefaultsDefaultsDefaults
• Most likely in industrial sector
• Defaults over past 10 years: Zenith Delta, Northwest Enron Delphi Daewoo Purina Mills
• Most likely in industrial sector
• Defaults over past 10 years: Zenith Delta, Northwest Enron Delphi Daewoo Purina Mills
Municipal defaultsMunicipal defaultsMunicipal defaultsMunicipal defaults
• NYC 1975, Cleveland 1978
• Largest: Washington Power SS Over $2 billion (failed nuclear plants in 1970s)
• The Cicero Commons (2003)
• Wilkes-Barre, PA (2002)
• NYC 1975, Cleveland 1978
• Largest: Washington Power SS Over $2 billion (failed nuclear plants in 1970s)
• The Cicero Commons (2003)
• Wilkes-Barre, PA (2002)
default risk & yielddefault risk & yielddefault risk & yielddefault risk & yield
• investors are risk averse• investors are risk averse
higher default risk
lower credit rating
higher yield
• If Treasuries are the benchmark
Bond yield =
Treasury yield + default premium
• If Treasuries are the benchmark
Bond yield =
Treasury yield + default premium
• so default risk explains• so default risk explains
Treasuryyields
AAACorpyields
BAACorpyields
< <
default risk is not constant!default risk is not constant!default risk is not constant!default risk is not constant!
• varies over the business cycle higher in recessions lower in expansions
• Tnote vs. BAA yield 1/07 158 basis pts. (6.34% vs. 4.76%) 1/08 280 basis pts. (6.54% vs. 3.74%)
• varies over the business cycle higher in recessions lower in expansions
• Tnote vs. BAA yield 1/07 158 basis pts. (6.34% vs. 4.76%) 1/08 280 basis pts. (6.54% vs. 3.74%)
B. Tax treatmentB. Tax treatmentB. Tax treatmentB. Tax treatment
Q. why do municipal bonds have lower yields than Tbonds? muni’s less liquid muni’s not default-free
A. tax treatment
Q. why do municipal bonds have lower yields than Tbonds? muni’s less liquid muni’s not default-free
A. tax treatment
municipal bond interestmunicipal bond interestmunicipal bond interestmunicipal bond interest
• exempt from federal income tax
• possibly exempt from state income tax if issuer & bondholder are in same
state
• exempt from federal income tax
• possibly exempt from state income tax if issuer & bondholder are in same
state
Treasury bond interestTreasury bond interestTreasury bond interestTreasury bond interest
• exempt from state income tax• exempt from state income tax
Corporate bond interestCorporate bond interestCorporate bond interestCorporate bond interest
• fully taxable• fully taxable
example: federal taxesexample: federal taxesexample: federal taxesexample: federal taxes
• bond where F=$10,000
• coupon rate = 10%
• annual coupon pmts = $1000
• bond where F=$10,000
• coupon rate = 10%
• annual coupon pmts = $1000
municipal bondmunicipal bondmunicipal bondmunicipal bond
• before taxes: $1000 in interest pmts.
• after taxes: $1000 in interest pmts
• before taxes: $1000 in interest pmts.
• after taxes: $1000 in interest pmts
Corporate bondCorporate bondCorporate bondCorporate bond
• before taxes: $1000 interest pmts.
• after taxes (25% marginal rate) $1000(1-.25)
= $750 interest pmts.
• before taxes: $1000 interest pmts.
• after taxes (25% marginal rate) $1000(1-.25)
= $750 interest pmts.
So, after taxesSo, after taxesSo, after taxesSo, after taxes
• muni has 10% coupon rate
• corp has 7.5% coupon rate
• After tax yield = i(1- tax rate)
• muni can offer a lower yield and still be competitive
• muni has 10% coupon rate
• corp has 7.5% coupon rate
• After tax yield = i(1- tax rate)
• muni can offer a lower yield and still be competitive
tax treatment explainstax treatment explainstax treatment explainstax treatment explains
Treasuryyields
muniyields
Corpyields< <
impact of tax ratesimpact of tax ratesimpact of tax ratesimpact of tax rates
• higher tax brackets derive more benefit from muni’s
• changing tax rates will affect the corporate-municipal yield spread
• higher tax brackets derive more benefit from muni’s
• changing tax rates will affect the corporate-municipal yield spread
II. Term structure of interest ratesII. Term structure of interest ratesII. Term structure of interest ratesII. Term structure of interest rates
• bonds with the same characteristics,
but different maturities• bonds with the same characteristics,
but different maturities
• focus on Treasury yields same default risk, tax treatment many choices of maturity
-- 4 weeks to 10 years
• focus on Treasury yields same default risk, tax treatment many choices of maturity
-- 4 weeks to 10 years
Treasury yields over timeTreasury yields over timeTreasury yields over timeTreasury yields over time
• relationship between yield & maturity is NOT constant sometimes short-term yields are
highest, Most of the time, long-term yields
are highest
• relationship between yield & maturity is NOT constant sometimes short-term yields are
highest, Most of the time, long-term yields
are highest
A. Yield curveA. Yield curveA. Yield curveA. Yield curve
• plot of maturity vs. yield
• slope of curve indicates relationship between maturity and yield
• The living yield curve
• plot of maturity vs. yield
• slope of curve indicates relationship between maturity and yield
• The living yield curve
upward slopingupward slopingupward slopingupward sloping
• yields rise w/ maturity (common)• yields rise w/ maturity (common)
maturity
yield
downward sloping (inverted)downward sloping (inverted)downward sloping (inverted)downward sloping (inverted)
• yield falls w/ maturity (rare)• yield falls w/ maturity (rare)
maturity
yield
flatflatflatflat
• yield varies little with maturity• yield varies little with maturity
maturity
yield
3 facts about the yield curve3 facts about the yield curve3 facts about the yield curve3 facts about the yield curve
• based on historical data on U.S. Treasury yields
1. interest rates on bonds of different maturities generally move together
• based on historical data on U.S. Treasury yields
1. interest rates on bonds of different maturities generally move together
2. ST bond yields are more volatile than LT bond yields
3. The yield curve usually slopes up.
2. ST bond yields are more volatile than LT bond yields
3. The yield curve usually slopes up.
Understanding the yield curveUnderstanding the yield curveUnderstanding the yield curveUnderstanding the yield curve
• what causes the 3 facts?
• what does the shape of the yield curve tell us?
• must understand why/how maturity affects yield
• what causes the 3 facts?
• what does the shape of the yield curve tell us?
• must understand why/how maturity affects yield
2 theories of term structure2 theories of term structure2 theories of term structure2 theories of term structure
• assumptions about investor preference
• implications for maturity and yield
• check implications against 3 facts about yield curve
• assumptions about investor preference
• implications for maturity and yield
• check implications against 3 facts about yield curve
B. The Expectations TheoryB. The Expectations TheoryB. The Expectations TheoryB. The Expectations Theory
• Assume:
bond buyers do not have any preference about maturity
i.e.
bonds of different maturities are perfect substitutes
• Assume:
bond buyers do not have any preference about maturity
i.e.
bonds of different maturities are perfect substitutes
• if assumption is true,
then investors care only about expected return for example, if expect better return from short-
term bonds, only hold short-term bonds
• if assumption is true,
then investors care only about expected return for example, if expect better return from short-
term bonds, only hold short-term bonds
• but investors hold both short-term an long-term bonds
• so,
• must EXPECT similar return:
long-term yields =
average of the expected
future short-term yields
• but investors hold both short-term an long-term bonds
• so,
• must EXPECT similar return:
long-term yields =
average of the expected
future short-term yields
exampleexampleexampleexample
• 5 year time horizon
• investors indifferent between
(1) holding 5-year bond
(2) holding 1year bonds, 5 yrs. in a row
as long as expected return is same
• 5 year time horizon
• investors indifferent between
(1) holding 5-year bond
(2) holding 1year bonds, 5 yrs. in a row
as long as expected return is same
• expected one-year interest rates:
5%, 6%, 7%, 8%, 9%
over next 5 years
so 5-year bond must yield (approx)
• expected one-year interest rates:
5%, 6%, 7%, 8%, 9%
over next 5 years
so 5-year bond must yield (approx)
maturity
yield
1 yr. 5 yrs.
5%
7%
yield curveyield curveyield curveyield curve
• if ST rates are expected to rise,
• yield curve slopes up• if ST rates are expected to rise,
• yield curve slopes up
under exp. theory,under exp. theory,under exp. theory,under exp. theory,
• slope of yield curve tells us direction of expected future short-term rates• slope of yield curve tells us direction
of expected future short-term rates
ST rates expected to fallST rates expected to fallST rates expected to fallST rates expected to fall
maturity
yield
ST rates expected to stay the ST rates expected to stay the samesameST rates expected to stay the ST rates expected to stay the samesame
maturity
yield
ST rates expected to rise, then fallST rates expected to rise, then fallST rates expected to rise, then fallST rates expected to rise, then fall
maturity
yield
theory vs. realitytheory vs. realitytheory vs. realitytheory vs. reality
• does the theory explain the 3 facts?
1. interest rates move together?
YES.
If ST rates rise, then average will rise (LT rate)
• does the theory explain the 3 facts?
1. interest rates move together?
YES.
If ST rates rise, then average will rise (LT rate)
2. ST rates are more volatile
YES.
If LT rates are an average of ST rates, then they will be less volatile
2. ST rates are more volatile
YES.
If LT rates are an average of ST rates, then they will be less volatile
3. yield curve usually slopes up
NO.
Under expectations theory,
this means we would expect interest rates to rise most of the time
BUT we don’t
(rates have trended down for 20 yrs.)
3. yield curve usually slopes up
NO.
Under expectations theory,
this means we would expect interest rates to rise most of the time
BUT we don’t
(rates have trended down for 20 yrs.)
what went wrong?what went wrong?what went wrong?what went wrong?
• back to assumption:
bonds of different maturities are perfect substitutes
• but this is not likely long term bonds have greater price
volatility short term bonds have reinvestment
risk
• back to assumption:
bonds of different maturities are perfect substitutes
• but this is not likely long term bonds have greater price
volatility short term bonds have reinvestment
risk
B. Liquidity Premium TheoryB. Liquidity Premium TheoryB. Liquidity Premium TheoryB. Liquidity Premium Theory
• assume:
bonds of different maturities are imperfect substitutes,
and investors PREFER ST bonds Less inflation risk, less interest rate risk
• assume:
bonds of different maturities are imperfect substitutes,
and investors PREFER ST bonds Less inflation risk, less interest rate risk
• so if true,
investors hold ST bonds
UNLESS
LT bonds offer higher yield as incentive
higher yield = liquidity premium
• so if true,
investors hold ST bonds
UNLESS
LT bonds offer higher yield as incentive
higher yield = liquidity premium
• so,
LT yield = average exp. ST yields
+ liquidity premium
• so,
LT yield = average exp. ST yields
+ liquidity premium
exampleexampleexampleexample
• 5 years
• 1 yr. bond yields:
5%, 6%, 7%, 8%, 9%
• AND 5yr. bond has 1% liquidity prem.
• 5 years
• 1 yr. bond yields:
5%, 6%, 7%, 8%, 9%
• AND 5yr. bond has 1% liquidity prem.
theory vs. realitytheory vs. realitytheory vs. realitytheory vs. reality
• does the theory explain the 3 facts?
1. & 2?
YES.
LT rates are still based in part on
exp. about ST rates
• does the theory explain the 3 facts?
1. & 2?
YES.
LT rates are still based in part on
exp. about ST rates
3. yield curve usually slopes up
YES.
IF LT bond yields have a liquidity premium,
then usually LT yields > ST yields
or yield curve slopes up.
3. yield curve usually slopes up
YES.
IF LT bond yields have a liquidity premium,
then usually LT yields > ST yields
or yield curve slopes up.
ProblemProblemProblemProblem
• How do we interpret yield curve?
• slope due to 2 things:
(1) exp. about future ST rates
(2) size of liquidity premium
• do not know size of liq. prem.
• How do we interpret yield curve?
• slope due to 2 things:
(1) exp. about future ST rates
(2) size of liquidity premium
• do not know size of liq. prem.
• if liquidity premium is small,
• then ST rates are expected to rise• if liquidity premium is small,
• then ST rates are expected to rise
maturity
yield yield curve
small liquidity premium
• if liquidity premium is larger,
• then ST rates are expected to stay the same
• if liquidity premium is larger,
• then ST rates are expected to stay the same
maturity
yield yield curve
large liquidity premium
C. C. What does the yield curve tell us?What does the yield curve tell us?C. C. What does the yield curve tell us?What does the yield curve tell us?
• expected future ST rates?
• expected inflation?
• business cycle?
• expected future ST rates?
• expected inflation?
• business cycle?
slope of yield curve is useful in predicting recessions
• slight upward slope normal GDP growth
• steep upward slope recovery from recession
slope of yield curve is useful in predicting recessions
• slight upward slope normal GDP growth
• steep upward slope recovery from recession
• flat curve uncertainty could mean recession,
or slow growth
• inverted curve exp. lower interest rates followed by slowdown or
recession
• flat curve uncertainty could mean recession,
or slow growth
• inverted curve exp. lower interest rates followed by slowdown or
recession
