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Chapter 12. The Term Structure of Interest Rates. The Yield Curve Spot and forward rates Theories of the Term Structure. Term structure. bonds with the same characteristics, but different maturities focus on Treasury yields same default risk, tax treatment similar liquidity

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chapter 12 the term structure of interest rates
Chapter 12. The Term Structureof Interest Rates
  • The Yield Curve
  • Spot and forward rates
  • Theories of the Term Structure
term structure
Term structure
  • bonds with the same characteristics,

but different maturities

  • focus on Treasury yields
    • same default risk, tax treatment
    • similar liquidity
    • many choices of maturity
treasury securities
Treasury securities
  • Tbills:
    • 4, 13, 26, and 52 weeks
    • zero coupon
  • Tnotes:
    • 2, 5, and 10 years
  • Tbonds:
    • 30 years (not since 2001)
  • Tnotes and Tbonds are coupon
slide5
relationship between yield & maturity is NOT constant
    • sometimes short-term yields are highest,
    • most of the time long-term yields are highest
i the yield curve
I. The 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)
  • July 1992, currently
downward sloping inverted
yield

maturity

downward sloping (inverted)
  • yield falls w/ maturity (rare)
  • April 1980
slide9
yield

maturity

flat
  • yields similar for all maturities
  • June 2000
humped
yield

maturity

humped
  • intermediate yields are highest
  • May 2000
theories of the term structure
Theories of the term structure
  • explain relationship between yield and maturity
  • what does the yield curve tell us?
the pure expectations theory
The Pure Expectations Theory
  • Assume:

bond buyers do not have any preference about maturity

i.e.

bonds of different maturities are perfect substitutes

slide13
LT = long-term
  • ST = short-term
slide14
if assumption is true,

then investors care only about expected return

    • if expect better return from ST bonds, only hold ST bonds
    • if expect better return from LT bonds, only hold LT bonds
slide15
but investors hold both ST and LT bonds
  • so,
  • must EXPECT similar return:

LT yields =

average of the expected

ST yields

under exp theory
under exp. theory,
  • slope of yield curve tells us direction of expected future ST rates
slide17
why?
  • if expect ST rates to RISE,

then average of ST rates will be >

current ST rate

    • so LT rates > ST rates
    • so yield curve SLOPES UP
slide19
if expect ST rates to FALL,

then average of ST rates will be <

current ST rate

    • so LT rates < ST rates
    • so yield curve slopes DOWN
slide21
if expect ST rates to STAY THE SAME,

then average of ST rates will be =

current ST rate

    • so LT rates = ST rates
    • so yield curve is FLAT
is this theory true
Is this theory true?
  • not quite.
  • FACT: yield curve usually slopes up
  • but expectations theory would predict this only when ST rates are expected to rise
    • 50% of the time
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
slide26
assumption is too strict
  • so implication is not quite correct
liquidity theory
Liquidity Theory
  • assume:

bonds of different maturities are imperfect substitutes,

and investors PREFER ST bonds

slide28
so if true,

investors hold ST bonds

UNLESS

LT bonds offer higher yield as incentive

higher yield = liquidity premium

slide29
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.
slide31
yield

maturity

yield curve

small liquidity premium

  • if liquidity premium is small,
  • then ST rates are expected to rise
slide32
yield

maturity

yield curve

large liquidity premium

  • if liquidity premium is larger,
  • then ST rates are expected to stay the same
preferred habitat theory
Preferred Habitat Theory
  • assume:

bonds of different maturities are imperfect substitutes,

and investor preference for ST bonds OR LT bonds is not constant

slide34
liquidity premium could be positive or negative
  • yield curve very difficult to interpret
    • do not know size or sign of liquidity premium
segmented markets theory
Segmented Markets Theory
  • assume:

bonds of different maturities are NOT substitutes at all

slide36
if assumption is true,
    • separate markets for ST and LT bonds
    • slope of yield curves tells us nothing about future ST rates
  • unrealistic to assume NO substitution bet. ST and LT bonds
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