Risk and Term Structure of Interest Rates -- Fin 331 1

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 and Term Structure of Interest Rates -- Fin 331 2

Risk Structure of Long Bonds in the US

Risk and Term Structure of Interest Rates -- Fin 331 3

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

Risk and Term Structure of Interest Rates -- Fin 331 4

Increasing Default Risk on Corporate Bonds

Risk and Term Structure of Interest Rates -- Fin 331 5

Bond Ratings

Risk and Term Structure of Interest Rates -- Fin 331 6

Decrease in Liquidity of Corporate Bonds

Risk and Term Structure of Interest Rates -- Fin 331 7

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

Risk and Term Structure of Interest Rates -- Fin 331 8

Tax Advantages of Municipal Bonds

Risk and Term Structure of Interest Rates -- Fin 331 9

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

Risk and Term Structure of Interest Rates -- Fin 331 10

Interest rate

maturities

Risk and Term Structure of Interest Rates -- Fin 331 11

Three Theories of Term Structure

1. Pure Expectations Theory

2. Market Segmentation Theory

3. Liquidity Premium TheoryA. 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

Risk and Term Structure of Interest Rates -- Fin 331 12

Interest Rates on Different Maturity Bonds Move Together

Risk and Term Structure of Interest Rates -- Fin 331 13

Yield Curves

Risk and Term Structure of Interest Rates -- Fin 331 14

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

Risk and Term Structure of Interest Rates -- Fin 331 15

Pure Expectations Theory

21

2

ett

t

iii

See definitions on page 131

Risk and Term Structure of Interest Rates -- Fin 331 16

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

n

iiiii ntnt

121 ...

Risk and Term Structure of Interest Rates -- Fin 331 17

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:

Risk and Term Structure of Interest Rates -- Fin 331 18

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

Risk and Term Structure of Interest Rates -- Fin 331 19

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 = int is 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

Risk and Term Structure of Interest Rates -- Fin 331 20

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, ie

t+2 etc. average of future rates int

3.Therefore: it int , i.e., short and long rates move together

Risk and Term Structure of Interest Rates -- Fin 331 21

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

Risk and Term Structure of Interest Rates -- Fin 331 22

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

Risk and Term Structure of Interest Rates -- Fin 331 23

Market Segmentation TheoryKey Assumption: Bonds of different maturities are

not substitutes at all

Implication: Markets are completely segmented:interest rate at each maturitydetermined 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

Risk and Term Structure of Interest Rates -- Fin 331 24

Liquidity Premium Theory

Key Assumption: Bonds of different maturities aresubstitutes, but are not perfectsubstitutes

Implication: Modifies Pure Expectations Theory

with features of MarketSegmentation Theory

Investors prefer short rather than long bonds must be paid positive liquidity premium, lnt, to hold long term bonds

Risk and Term Structure of Interest Rates -- Fin 331 25

Liquidity Premium Theory

Results in following modification of Pure Expectations Theory

n

iiiili

ent

et

ett

ntnt121 ...

Risk and Term Structure of Interest Rates -- Fin 331 26

Relationship Between the Liquidity Premium and Pure Expectations Theory

Risk and Term Structure of Interest Rates -- Fin 331 27

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

Risk and Term Structure of Interest Rates -- Fin 331 28

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%.

Risk and Term Structure of Interest Rates -- Fin 331 29

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

Risk and Term Structure of Interest Rates -- Fin 331 30

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.

Risk and Term Structure of Interest Rates -- Fin 331 31

Market Predictions of Future Short Rates

Risk and Term Structure of Interest Rates -- Fin 331 32

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)