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Chapter 7. Risk and Term Structure of Interest Rates. Risk Structure Term Structure. Not all interest rates are created equal!. many interest rates at one time But interest rates do move together over time. Interest rate structure. Why do yields differ? Risk structure

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not all interest rates are created equal
Not all interest rates are created equal!
  • many interest rates at one time
  • But interest rates do move together over time
interest rate structure
Interest 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
interest rates a snapshot
Interest 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%
measurement
measurement
  • difference between two interest rates
    • spread
  • measured in
    • percentage points
    • basis points
    • 1 percentage pt. = 100 basis pts.
example 1
example 1
  • 3 mo. Tbill 2.75%
  • 3 mo. Commercial paper 3.25%
  • spread
    • 0.5 percentage pts.
    • 50 basis pts.
example 2
example 2
  • 10 yr Tnote 3.74%
  • 10 BAA corporate 6.54%
  • spread
    • 2.8 percentage pts.
    • 280 basis pts.
i risk structure of interest rates
I. Risk Structure of Interest Rates
  • debt with same maturity,

but different characteristics

    • default risk
    • tax treatment
patterns
Patterns
  • Baa > AAA > U.S. Treasury
    • size of the spread varies
a default risk
A. Default Risk
  • risk of not receiving timely payment of principal and interest
  • depends on
    • creditworthiness of issuer
    • structure of bond
u s government debt
U.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
other issuers
Other issuers
  • private
  • foreign
  • municipal
  • all have some default risk
  • rated for default risk
bond ratings
Bond 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
investment grade
Investment grade

Moodys’ S&P

  • Aaa AAA
  • Aa (Aa1, Aa2, Aa3) AA (AA+, AA, AA-)
  • A A
  • Baa BBB
noninvestment speculative
Noninvestment, speculative
  • Ba BB
  • B B

Highly Speculative (High-yield, “Junk”)

  • Caa CCC
  • Ca CC
  • C C
  • D (in default)
examples
examples
  • 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
slide18
BB
    • GM, Sears
  • B
    • Ford, Clear Channel, Univision
  • CCC
    • Revlon, Sirius, Pep Boys, JoAnn, ToysRUs
  • CC
    • Primus
  • C
    • Wolverine Tube
defaults
Defaults
  • Most likely in industrial sector
  • Defaults over past 10 years:
    • Zenith Delta, Northwest
    • Enron Delphi
    • Daewoo
    • Purina Mills
municipal defaults
Municipal 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)
default risk yield
default risk & yield
  • investors are risk averse

higher

default

risk

lower

credit

rating

higher

yield

slide22
If Treasuries are the benchmark

Bond yield =

Treasury yield + default premium

slide23
so default risk explains

BAA

Corp

yields

AAA

Corp

yields

Treasury

yields

<

<

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%)
b tax treatment
B. 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 interest
municipal bond interest
  • exempt from federal income tax
  • possibly exempt from state income tax
    • if issuer & bondholder are in same state
treasury bond interest
Treasury bond interest
  • exempt from state income tax

Corporate bond interest

  • fully taxable
example federal taxes
example: federal taxes
  • bond where F=$10,000
  • coupon rate = 10%
  • annual coupon pmts = $1000
municipal bond
municipal bond
  • before taxes:
    • $1000 in interest pmts.
  • after taxes:
    • $1000 in interest pmts
corporate bond
Corporate bond
  • before taxes:
    • $1000 interest pmts.
  • after taxes
    • (25% marginal rate)
    • $1000(1-.25)

= $750 interest pmts.

so after taxes
So, 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
tax treatment explains
tax treatment explains

muni

yields

Treasury

yields

Corp

yields

<

<

impact of tax rates
impact of tax rates
  • higher tax brackets derive more benefit from muni’s
  • changing tax rates will affect the corporate-municipal yield spread
ii term structure of interest rates
II. Term structure of interest rates
  • bonds with the same characteristics,

but different maturities

slide36
focus on Treasury yields
    • same default risk, tax treatment
    • many choices of maturity

-- 4 weeks to 10 years

slide38
relationship between yield & maturity is NOT constant
    • sometimes short-term yields are highest,
    • Most of the time, long-term yields are highest
a yield curve
A. Yield curve
  • plot of maturity vs. yield
  • slope of curve indicates relationship between maturity and yield
  • The living yield curve
upward sloping

yield

maturity

upward sloping
  • yields rise w/ maturity (common)
downward sloping inverted

yield

maturity

downward sloping (inverted)
  • yield falls w/ maturity (rare)
slide42

yield

maturity

flat
  • yield varies little with maturity
3 facts about the yield curve
3 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

slide44
2. ST bond yields are more volatile than LT bond yields

3. The yield curve usually slopes up.

understanding the yield curve
Understanding 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
2 theories of term structure
2 theories of term structure
  • assumptions about investor preference
  • implications for maturity and yield
  • check implications against 3 facts about yield curve
b the expectations theory
B. The Expectations Theory
  • Assume:

bond buyers do not have any preference about maturity

i.e.

bonds of different maturities are perfect substitutes

slide48
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
slide49
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

example
example
  • 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

slide51
expected one-year interest rates:

5%, 6%, 7%, 8%, 9%

over next 5 years

so 5-year bond must yield (approx)

yield curve

yield

7%

5%

maturity

1 yr. 5 yrs.

yield curve
  • if ST rates are expected to rise,
  • yield curve slopes up
under exp theory
under exp. theory,
  • slope of yield curve tells us direction of expected future short-term rates
theory vs reality
theory 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)

slide58
2. ST rates are more volatile

YES.

If LT rates are an average of ST rates, then they will be less volatile

slide59
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?
  • 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 theory
B. Liquidity Premium Theory
  • assume:

bonds of different maturities are imperfect substitutes,

and investors PREFER ST bonds

    • Less inflation risk, less interest rate risk
slide62
so if true,

investors hold ST bonds

UNLESS

LT bonds offer higher yield as incentive

higher yield = liquidity premium

slide63
so,

LT yield = average exp. ST yields

+ liquidity premium

example1
example
  • 5 years
  • 1 yr. bond yields:

5%, 6%, 7%, 8%, 9%

  • AND 5yr. bond has 1% liquidity prem.
theory vs reality1
theory vs. reality
  • does the theory explain the 3 facts?

1. & 2?

YES.

LT rates are still based in part on

exp. about ST rates

slide66
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.

problem
Problem
  • 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.
slide68

yield

maturity

yield curve

small liquidity premium

  • if liquidity premium is small,
  • then ST rates are expected to rise
slide69

yield

maturity

yield curve

large liquidity premium

  • if liquidity premium is larger,
  • then ST rates are expected to stay the same
c what does the yield curve tell us
C. What does the yield curve tell us?
  • expected future ST rates?
  • expected inflation?
  • business cycle?
slide71
slope of yield curve is useful in predicting recessions
  • slight upward slope
    • normal GDP growth
  • steep upward slope
    • recovery from recession
slide72
flat curve
    • uncertainty
    • could mean recession,

or slow growth

  • inverted curve
    • exp. lower interest rates
    • followed by slowdown or

recession