Chapter 6. Risk and Term Chapter 6. Risk and Term Structure of Interest RatesStructure of Interest RatesChapter 6. Risk and Term Chapter 6. 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

• interest rates move together over time

• many interest rates at one time

• interest rates move together over time

January 2004January 2004January 2004January 2004

• 3 mo Tbill 2.33%

• 3 mo Commerical Paper 2.52%

• prime rate 5.25%

• 10 yr. Tnote 4.23%

• 10 yr. AAA corporate 5.46%

• 10 yr. BAA corporate 6.15%

• 30 yr. mortgage 5.71%

• 3 mo Tbill 2.33%

• 3 mo Commerical Paper 2.52%

• prime rate 5.25%

• 10 yr. Tnote 4.23%

• 10 yr. AAA corporate 5.46%

• 10 yr. BAA corporate 6.15%

• 30 yr. mortgage 5.71%

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 2.33%

• 3 mo. Commercial paper 2.52%

• spread .19 percentage pts. 19 basis pts.

• 3 mo. Tbill 2.33%

• 3 mo. Commercial paper 2.52%

• spread .19 percentage pts. 19 basis pts.

example 2example 2example 2example 2

• 10 yr Tnote 4.23%

• 10 BAA corporate 6.15%

• spread 1.92 percentage pts. 192 basis pts.

• 10 yr Tnote 4.23%

• 10 BAA corporate 6.15%

• spread 1.92 percentage pts. 192 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 liquidity tax treatment

• debt with same maturity,

but different characteristics default risk liquidity tax treatment

PatternsPatternsPatternsPatterns

• Baa always the highest yield

• Municipal’s always the lowest (1940)

• Baa > AAA > U.S. > municipal size of the spread varies

• Baa always the highest yield

• Municipal’s always the lowest (1940)

• Baa > AAA > U.S. > municipal 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. 123

• high credit rating low default risk

• bond ratings may change over time

• bond issuer pays rating agency Moody’s, S&P, Fitch p. 123

• high credit rating low default risk

• bond ratings may change over time

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

• 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

• Baa vs. Treasury bond yield 12/99 191 basis pts. 12/01 296 basis pts.

• varies over the business cycle higher in recessions lower in expansions

• Baa vs. Treasury bond yield 12/99 191 basis pts. 12/01 296 basis pts.

B. LiquidityB. LiquidityB. LiquidityB. Liquidity

• how quickly/cheaply can bond be sold for cash?• how quickly/cheaply can bond be

sold for cash?

higher liquidity

lower yield

liquidity is not ratedliquidity is not ratedliquidity is not ratedliquidity is not rated

• Treasuries most liquid

• depends on size of issuer

• related to default risk bonds in default very illiquid higher-rated bonds tend to be

more liquid

• Treasuries most liquid

• depends on size of issuer

• related to default risk bonds in default very illiquid higher-rated bonds tend to be

more liquid

C. Tax treatmentC. Tax treatmentC. Tax treatmentC. 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 (33% marginal rate) $1000(1-.33)

= $670 interest pmts.

• before taxes: $1000 interest pmts.

• after taxes (33% marginal rate) $1000(1-.33)

= $670 interest pmts.

So, after taxesSo, after taxesSo, after taxesSo, after taxes

• muni has 10% coupon rate

• corp has 6.7% coupon rate

• muni can offer a lower yield and still be competitive

• muni has 10% coupon rate

• corp has 6.7% coupon 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 similar liquidity many choices of maturity

-- 4 weeks to 30 years

• focus on Treasury yields same default risk, tax treatment similar liquidity many choices of maturity

-- 4 weeks to 30 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, sometimes long-term yields are

highest

• relationship between yield & maturity is NOT constant sometimes short-term yields are

highest, sometimes 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

• plot of maturity vs. yield

• slope of curve indicates relationship between maturity and yield

upward slopingupward slopingupward slopingupward sloping

• yields rise w/ maturity (common)

• July 1992, currently• yields rise w/ maturity (common)

• July 1992, currently

maturity

yield

downward sloping (inverted)downward sloping (inverted)downward sloping (inverted)downward sloping (inverted)

• yield falls w/ maturity (rare)

• April 1980• yield falls w/ maturity (rare)

• April 1980

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. If short-term rates are low, the yield curve slopes up.

If short-term rates are high, the yield curve slopes down.

3. The yield curve usually slopes up.

2. If short-term rates are low, the yield curve slopes up.

If short-term rates are high, the yield curve slopes down.

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

3 theories of term structure3 theories of term structure3 theories of term structure3 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

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

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. interest rates low, slopes up

interest rates high, slopes down

YES.

ST rates low, must be expected to rise,

so yield curve slopes up

ST rates high, must be expected to fall,

so yield curve slopes down

2. interest rates low, slopes up

interest rates high, slopes down

YES.

ST rates low, must be expected to rise,

so yield curve slopes up

ST rates high, must be expected to fall,

so yield curve slopes down

3. yield curve usually slopes up

NO.

Under expectations theory,

we would expect the yield curve to slope up only about 50% of the time

but it slopes up most of the time

3. yield curve usually slopes up

NO.

Under expectations theory,

we would expect the yield curve to slope up only about 50% of the time

but it slopes up most of the time

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

C. Segmented Markets TheoryC. Segmented Markets TheoryC. Segmented Markets TheoryC. Segmented Markets Theory

• assume:

bonds of different maturities are NOT substitutes at all

• assume:

bonds of different maturities are NOT substitutes at all

• if assumption is true, exp. return of ST bonds does not

affect demand for LT bonds,

and vice versa separate markets for ST and LT

bonds

• if assumption is true, exp. return of ST bonds does not

affect demand for LT bonds,

and vice versa separate markets for ST and LT

bonds

theory vs. realitytheory vs. realitytheory vs. realitytheory vs. reality

• does the theory explain the 3 facts?

1. interest rates move together?

NO.

if they are not related, why would they move together?

• does the theory explain the 3 facts?

1. interest rates move together?

NO.

if they are not related, why would they move together?

2. interest rates low, slopes up

interest rates high, slopes down

NO.

ST yields do not affect LT yields,

so they will not affect the slope

2. interest rates low, slopes up

interest rates high, slopes down

NO.

ST yields do not affect LT yields,

so they will not affect the slope

3. yield curve usually slopes up

YES.

LT bonds have greater interest rate risk. LT bonds have lower demand LT bonds have a higher yield

so LT yield > ST yield,

and yield curve slopes up

3. yield curve usually slopes up

YES.

LT bonds have greater interest rate risk. LT bonds have lower demand LT bonds have a higher yield

so LT yield > ST yield,

and yield curve slopes up

D. Liquidity Premium TheoryD. Liquidity Premium TheoryD. Liquidity Premium TheoryD. Liquidity Premium Theory

• assume:

bonds of different maturities are imperfect substitutes,

and investors PREFER ST bonds

• assume:

bonds of different maturities are imperfect substitutes,

and investors PREFER ST bonds

• 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

E. E. What does the yield curve tell us?What does the yield curve tell us?E. E. 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