The Risk and Term Structure of Interest Rates

1
The Risk and Term Structure of Interest Rates

• Chapter 5

2
The Term Structure of Rates and the Yield Curve

• Term Structure
• Relationship among yields of different maturities
  of the same type of security.
• Yield Curve
• Graphical relationship between yield and maturity.

3
Empirical Facts

• Interest rates on bonds of different maturities
  move together over time.
• When short-term interest rates are low, yield
  curves are more likely to have an upward slope
  when short-term interest rates are high, yield
  curves are more likely to slope downward and be
  inverted.
• Yield curves almost always slope upward.

4
Different Theories of the Shape of the Yield Curve

• Supply and Demand
• Determined by relative supply/demand of different
  maturities
• Deals with each maturity by itself and ignores
  the interrelationships between different
  maturities of the same security

5
Expectations Hypothesis

• The shape of the yield curve is determined by the
  investors expectations of future interest rate
  movements.
• The interest rate on the long-term bond will
  equal an average of short-term interest rates
  that people expect to occur over the life of the
  long-term bond.
• If the one-year interest rate over the next five
  years is expected to be 5, 6, 7, 8, 9 percent,
• then the interest rate on the two-year bond would
  be 5.5.
• While for the five-year bond it would be 7.
• Investors are indifferent between short and
  long-term securities.

6
Liquidity Premium Modification

• Investors know from experience that short-term
  securities provide greater marketability and have
  smaller price fluctuations than do long-term
  securities.
• The liquidity premium is that premium demanded
  for holding long-term securities.
• Therefore, a two-year security would have to
  yield more than the average of the two one-year
  securities as a reward for bearing more risk.

7
The Preferred Habitat Approach

• The interest rate on a long-term bond will equal
  an average of short-term interest rates expected
  to occur over the life of the long-term bond plus
  a term (liquidity) premium that responds to
  supply and demand conditions for that bond.
• If investors prefer the habitat of short-term
  bonds over long-term bonds, they might be willing
  to hold short-term bonds even though they have a
  lower expected return. This means that investors
  would have to be paid a positive term premium to
  be willing to hold a long-term bond.

8
Real-World Observations

• When interest rates are high relative to past
  rates, investors expect them to decline and the
  price of bonds to rise in the future resulting in
  big capital gains
• Investors would then favor long-term securities,
  which drives up price and lowers yielddownward
  sloping yield curve

9
Real-World Observations

• If interest rates are low relative to
  pastresults in an upward sloping curve
• Historically, over the business cycle short-term
  rates fluctuate more than longer-term rates
• Yield curves tend to be upward sloping more
  often, suggesting the liquidity premium is the
  dominate theory

10
Summary of Term Structure Theory

• Expectations theory forms the foundation of the
  slope of the curve
• Liquidity premium theory makes a long-term
  permanent modification that suggests an upward
  sloping curve
• Over short periods, relative supplies of
  securities have an impact on yields, altering the
  shape of the curve

11
Government Bonds

• Reading the WSJ.
• Current coupon or on the run issue.

12
Marketability

• Recently issued government bonds (current
  couponon the run) are more marketable than
  older issues (off the run)
• Because these newly issued bonds are highly
  marketable, they carry somewhat lower yields to
  maturity as compared to older issues 

13
Default Risk

• Other than US Federal government securities,
  bonds carry a risk of default
• Risk on municipal bonds used to be considered
  very low
• However, experience of New York City (1975),
  Cleveland (1978) and Orange Country, California
  (1995) suggest these bonds are becoming riskier
• Corporate bonds generally have a higher default
  risk than municipal bonds
• Investors will expect higher return to compensate
  for increased default risk

14
Default Risk

• Standard and Poors and Moodys Investors Service
  rate the default risk on bonds which serve as a
  guide to investors
• The introduction of risk in the yield curve will
  cause the curve to shift since another variable
  other than maturity has changed
• The higher the perceived risk, the greater the
  upward shift of the curve for that particular
  security

15
Risk and Tax Structure of Rates

• Investors are concerned about the after tax
  return on bonds
• Although municipal bonds are riskier than federal
  government bonds, tax exempt status of municipal
  bonds will generally result in a lower yield
  (downward shift of the curve)