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THE RISK AND TERM STRUCTURE OF INTEREST RATES. Risk Structure of Interest Rates Default risk Liquidity Income Tax Consideration Term Structure of Interest Rates Pure Expectation Theory Market Segmentation Theory Liquidity Premium Theory. Risk Structure of Long Bonds in the US.

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slide1

THE RISK AND TERM STRUCTURE OF INTEREST RATES

  • Risk Structure of Interest Rates
    • Default risk
    • Liquidity
    • Income Tax Consideration
  • Term Structure of Interest Rates
    • Pure Expectation Theory
    • Market Segmentation Theory
    • Liquidity Premium Theory
slide3

Puzzling Phenomenon

1. Riskfree bonds have a lower return than risky bonds

2. High risk bonds have a higher return than low risk bonds

3. Municipal bonds have a lower return than US Government long term bonds

why bonds have different liquidity
Why bonds have different liquidity
  • US Treasury bonds are the most liquid because they are widely traded
  • Corporate bond are less liquid because fewer bonds are traded and it’s costly to sell bonds in an emergency
term structure facts to be explained
Term Structure Facts to Be Explained
  • 1. Interest rates for different maturities move together
  • 2. Yield curves tend to have steep upward slope when short rates are low and downward slope when short rates are high
  • 3. Yield curve is typically upward sloping
slide10

Interest rate

maturities

three theories of term structure
Three Theories of Term Structure
  • 1. Pure Expectations Theory
  • 2. Market Segmentation Theory
  • 3. Liquidity Premium Theory

A. Pure Expectations Theory explains 1 and 2, but not 3.

B. Market Segmentation Theory explains 3, but not 1 and 2

C. Solution: Combine features of both Pure Expectations Theory and Market Segmentation Theory to get Liquidity Premium Theory and explain all facts

pure expectations theory
Pure Expectations Theory
  • Key Assumption: Bonds of different maturities are perfect
  • substitutes
  • Implication: RETe on bonds of different maturities are
  • equal
  • Investment strategies for two-period horizon
    • 1. Buy $1 of one-year bond and when matures buy another one-year bond
    • 2. Buy $1 of two-year bond and hold it
pure expectations theory15
Pure Expectations Theory

See definitions on page 131

more generally for n period bond
More generally for n-period bond:
  • In words: Interest rate on long bond = average of short rates expected to occur over life of long bond
more generally for n period bond17
More generally for n-period bond:
  • Numerical example:
    • One-year interest rate over the next five years 5%, 6%, 7%, 8% and 9%,
  • Interest rate on two-year bond:
  • Interest rate for five-year bond:
  • Interest rate for one to five year bonds:
slide18
Another example (on future short-term rate):
    • The interest rates for 1-year through 5-year bonds are 5%, 6%, 7%, 8% and 9%,
  • Expected interest rate of a 1-year bond in year 2:
  • Expected interest rate of a 1-year bond in years 3, 4, and 5
pure expectations theory and term structure facts
Pure Expectations Theory and Term Structure Facts
  • Explains why yield curve has different slopes:
  • 1. When short rates expected to rise in future, average of future short rates = intis above today's short rate: therefore yield curve is upward sloping
  • 2. When short rates expected to stay same in future, average of future short rates same as today's, and yield curve is flat
  • 3. Only when short rates expected to fall will yield curve be downward sloping
pure expectations theory and term structure facts20
Pure Expectations Theory and Term Structure Facts
  • Pure Expectations Theory explains Fact 1 that short and long rates move together
  • 1. Short rate rises are persistent
  • 2. If it today, iet+1, iet+2 etc.  average of future rates int
  • 3.Therefore: itint, i.e., short and long rates move together
pure expectations theory and term structure facts21
Pure Expectations Theory and Term Structure Facts
  • Explains Fact 2 that yield curves tend to have steep slope when short rates are low and downward slope when short rates are high
  • 1. When short rates are low, they are expected to rise to normal level, and long rate = average of future short rates will be well above today's short rate: yield curve will have steep upward slope
  • 2. When short rates are high, they will be expected to fall in future, and long rate will be below current short rate: yield curve will have downward slope
pure expectations theory and term structure facts22
Pure Expectations Theory and Term Structure Facts
  • Doesn't explain Fact 3 that yield curve usually has upward slope
  • Short rates as likely to fall in future as rise, so average of expected future short rates will not usually be higher than current short rate: therefore, yield curve will not usually slope upward
market segmentation theory
Market Segmentation Theory
  • Key Assumption: Bonds of different maturities are
  • not substitutes at all
  • Implication: Markets are completely segmented:
  • interest rate at each maturity
  • determined separately
  • Explains Fact 3 that yield curve is usually upward sloping

People typically prefer short holding periods and thus have higher demand for short-term bonds, which have higher prices and lower interest rates than long bonds

  • Does not explain Fact 1 or Fact 2 because assumes long and short rates determined independently
liquidity premium theory
Liquidity Premium Theory

Key Assumption: Bonds of different maturities are

substitutes, but are not perfect

substitutes

Implication: Modifies Pure Expectations Theory

with features of Market

Segmentation Theory

  • Investors prefer short rather than long bonds  must be paid positive liquidity premium, lnt, to hold long term bonds
liquidity premium theory25
Liquidity Premium Theory
  • Results in following modification of Pure Expectations Theory
slide27

Liquidity Premium Theory:

  • Explains all 3 Facts
    • Explains Fact 3 of usual upward sloped yield curve by liquidity premium for long-term bonds
    • Explains Fact 1 and Fact 2 using same explanations as pure expectations theory because it has average of future short rates as determinant of long rate
numerical example
Numerical Example:
  • 1. One-year interest rate over the next five years:5%, 6%, 7%, 8% and 9%
  • 2. Investors' preferences for holding short-term bonds so liquidity premium for one to five-year bonds: 0%, 0.25%, 0.5%, 0.75% and 1.0%.
numerical example29
Numerical Example:
  • Interest rate on the two-year bond:
  • Interest rate on the five-year bond:
  • Interest rates on one to five-year bonds:
  • Comparing with those for the pure expectations theory, liquidity premium theory produces yield curves more steeply upward sloped
calculate future short term rate
Calculate future short term rate
  • 1. Interest rates for one- to five-year bonds are:5%, 6%, 7%, 8% and 9%
  • 2. Investors' preferences for holding short-term bonds so liquidity premium for one to five-year bonds: 0%, 0.25%, 0.5%, 0.75% and 1.0%.
  • 3. Calculate 1-year short-term rate over the next five years.
forward rate
Forward Rate
  • The expected future short-term rate is also known as forward rate, as opposed to the current short-term rate, known as the spot rate.
  • Two ways to compute forward rates:
  • (1) Using the formula covered in the class
  • (2) Formula in the text book (page 123-126, not required)