Chapter 7' Risk and Term Structure of Interest Rates

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Chapter 7. Risk and Term Structure of Interest
Rates

• Risk Structure
• Term Structure

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Not all interest rates are created equal!

• many interest rates at one time
• But interest rates do move together over time

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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

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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

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measurement

• difference between two interest rates
• spread
• measured in
• percentage points
• basis points
• 1 percentage pt. 100 basis pts.

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example 1

• 3 mo. Tbill 2.75
• 3 mo. Commercial paper 3.25
• spread
• 0.5 percentage pts.
• 50 basis pts.

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example 2

• 10 yr Tnote 3.74
• 10 BAA corporate 6.54
• spread
• 2.8 percentage pts.
• 280 basis pts.

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I. Risk Structure of Interest Rates

• debt with same maturity,
• but different characteristics
• default risk
• tax treatment

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Patterns

• Baa gt AAA gt U.S. Treasury
• size of the spread varies

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A. Default Risk

• risk of not receiving timely payment of principal
  and interest
• depends on
• creditworthiness of issuer
• structure of bond

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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

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Other issuers

• private
• foreign
• municipal
• all have some default risk
• rated for default risk

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Bond ratings

• bond issuer pays rating agency
• Moodys, SP, Fitch
• p. 151 or p. 149
• high credit rating
• low default risk
• bond ratings may change over time
• Downgrades or upgrades

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Investment grade

• Moodys SP
• Aaa AAA
• Aa (Aa1, Aa2, Aa3) AA (AA, AA, AA-)
• A A
• Baa BBB

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Noninvestment, speculative

• Ba BB
• B B

Highly Speculative (High-yield, Junk)

• Caa CCC
• Ca CC
• C C
• D (in default)

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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

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• BB
• GM, Sears
• B
• Ford, Clear Channel, Univision
• CCC
• Revlon, Sirius, Pep Boys, JoAnn, ToysRUs
• CC
• Primus
• C
• Wolverine Tube

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Defaults

• Most likely in industrial sector
• Defaults over past 10 years
• Zenith Delta, Northwest
• Enron Delphi
• Daewoo
• Purina Mills

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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)

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default risk yield

• investors are risk averse

higher default risk
lower credit rating
higher yield
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• If Treasuries are the benchmark
• Bond yield
• Treasury yield default premium

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• so default risk explains

BAA Corp yields
AAA Corp yields
Treasury yields
lt
lt
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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)

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B. Tax treatment

• Q. why do municipal bonds have lower yields than
  Tbonds?
• munis less liquid
• munis not default-free
• A. tax treatment

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municipal bond interest

• exempt from federal income tax
• possibly exempt from state income tax
• if issuer bondholder are in same state

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Treasury bond interest

• exempt from state income tax

Corporate bond interest

• fully taxable

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example federal taxes

• bond where F10,000
• coupon rate 10
• annual coupon pmts 1000

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municipal bond

• before taxes
• 1000 in interest pmts.
• after taxes
• 1000 in interest pmts

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Corporate bond

• before taxes
• 1000 interest pmts.
• after taxes
• (25 marginal rate)
• 1000(1-.25)
• 750 interest pmts.

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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

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tax treatment explains
muni yields
Treasury yields
Corp yields
lt
lt
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impact of tax rates

• higher tax brackets derive more benefit from
  munis
• changing tax rates will affect the
  corporate-municipal yield spread

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II. Term structure of interest rates

• bonds with the same characteristics,
• but different maturities

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• focus on Treasury yields
• same default risk, tax treatment
• many choices of maturity
• -- 4 weeks to 10 years

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Treasury yields over time
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• relationship between yield maturity is NOT
  constant
• sometimes short-term yields are highest,
• Most of the time, long-term yields are highest

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A. Yield curve

• plot of maturity vs. yield
• slope of curve indicates relationship between
  maturity and yield
• The living yield curve

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upward sloping

• yields rise w/ maturity (common)

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downward sloping (inverted)

• yield falls w/ maturity (rare)

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flat

• yield varies little with maturity

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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

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• 2. ST bond yields are more volatile than LT bond
  yields
• 3. The yield curve usually slopes up.

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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

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2 theories of term structure

• assumptions about investor preference
• implications for maturity and yield
• check implications against 3 facts about yield
  curve

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B. The Expectations Theory

• Assume
• bond buyers do not have any preference about
  maturity
• i.e.
• bonds of different maturities are perfect
  substitutes

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• 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

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• 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

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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

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• expected one-year interest rates
• 5, 6, 7, 8, 9
• over next 5 years
• so 5-year bond must yield (approx)

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yield curve

• if ST rates are expected to rise,
• yield curve slopes up

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under exp. theory,

• slope of yield curve tells us direction of
  expected future short-term rates

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ST rates expected to fall
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ST rates expected to stay the same
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ST rates expected to rise, then fall
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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)

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• 2. ST rates are more volatile
• YES.
• If LT rates are an average of ST rates, then they
  will be less volatile

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• 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 dont
• (rates have trended down for 20 yrs.)

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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

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B. Liquidity Premium Theory

• assume
• bonds of different maturities are imperfect
  substitutes,
• and investors PREFER ST bonds
• Less inflation risk, less interest rate risk

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• so if true,
• investors hold ST bonds
• UNLESS
• LT bonds offer higher yield as incentive
• higher yield liquidity premium

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• so,
• LT yield average exp. ST yields
• liquidity premium

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example

• 5 years
• 1 yr. bond yields
• 5, 6, 7, 8, 9
• AND 5yr. bond has 1 liquidity prem.

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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

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• 3. yield curve usually slopes up
• YES.
• IF LT bond yields have a liquidity premium,
• then usually LT yields gt ST yields
• or yield curve slopes up.

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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.

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yield curve
small liquidity premium

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

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yield curve
large liquidity premium

• if liquidity premium is larger,
• then ST rates are expected to stay the same

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C. What does the yield curve tell us?

• expected future ST rates?
• expected inflation?
• business cycle?

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• slope of yield curve is useful in predicting
  recessions
• slight upward slope
• normal GDP growth
• steep upward slope
• recovery from recession

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• flat curve
• uncertainty
• could mean recession,
• or slow growth
• inverted curve
• exp. lower interest rates
• followed by slowdown or
• recession