Interest Rate Differentials• Tax-free rates typically lower than taxable rates

– People care about after-tax return

– Tax-free bonds “tax expenditure”

• Government rates typically lower than corporate rates

– Default risk• U.S. T-bonds are considered default free

• Risk premium—the spread between the interest rates on bonds with default risk and the interest rates on T-bonds

• Short-term rates typically lower than long-term rates

– Interest rate risk

– Liquidity—the ease with which an asset can be converted into cash

Long-Term Bond Yields, 1919–2008

Sources: Board of Governors of the Federal Reserve System, Banking and Monetary Statistics, 1941–1970; Federal Reserve: www.federalreserve.gov/releases/h15/data.htm.

There are two great powers in the world, the US and Moody’s. The US can destroyyou by dropping bombs. Moody’s can destroy you by dropping your credit rating.

Term Structure of Interest Rates

Yield curve—a plot of the yield on bonds with differing terms to maturity but the same risk, liquidity and tax considerations

Observations

• 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 rates are high, yield curves are more likely to slope downward and be inverted

• Yield curves almost always slope upward

Movements over Time of Interest Rates on U.S. Government Bonds with Different Maturities

Sources: Federal Reserve: www.federalreserve.gov/releases/h15/data.htm.

Segmented Markets Theory• Bonds of different maturities are not substitutes at all

• The interest rate for each bond with a different maturity is determined by the demand for and supply of that bond

• Investors have preferences for bonds of one maturity over another

• If investors have short desired holding periods and generally prefer bonds with shorter maturities that have less interest-rate risk, then this explains why yield curves usually slope upward (fact 3)

Expectations Theory of Term Structure Bonds with same tax, risk and liquidity are substitutes

Explain the yields of bonds of different durations

1

2

For an investment of $1

= today's interest rate on a one-period bond

= interest rate on a one-period bond expected for next period

= today's interest rate on the two-period bond

t

et

t

i

i

i

1

1 1

1 1

1

1

If two one-period bonds are bought with the $1 investment

(1 )(1 ) 1

1 ( ) 1

( )

( ) is extremely small

Simplifying we get

et t

e et t t t

e et t t t

et t

et t

i i

i i i i

i i i i

i i

i i

2 1

12

Both bonds will be held only if the expected returns are equal

2

2The two-period rate must equal the average of the two one-period rates

For bonds with longer maturities

et t t

et t

t

t tnt

i i i

i ii

i ii

1 2 ( 1)...

The -period interest rate equals the average of the one-period

interest rates expected to occur over the -period life of the bond

e e et t ni i

nn

n

Expectations Theory

• Explains why the term structure of interest rates changes at different times

• Explains why interest rates on bonds with different maturities move together over time (fact 1)

• Explains why yield curves tend to slope up when short-term rates are low and slope down when short-term rates are high (fact 2)

• Cannot explain why yield curves usually slope upward (fact 3)

Liquidity Premium and Preferred Habitat Theory

int

it i

t1e i

t2e ... i

t(n 1)e

n l

nt

where lnt

is the liquidity premium for the n-period bond at time t

lnt

is always positive

Rises with the term to maturity

Bonds of different maturities are substitutes but not perfect

• Interest rates on different maturity bonds move together

• Yield curves tend to slope upward when short-term rates are low and to be inverted when short-term rates are high;

• Yield curves typically slope upward -- a larger liquidity premium as the term to maturity lengthens

Reading the tea leaves:

Yield Curves for U.S. Government Bonds

Sources: Federal Reserve Bank of St. Louis; U.S. Financial Data, various issues; Wall Street Journal, various dates.

Some problems6.3 Why are corporate bond yields countercyclical?

6.5 If yield curves on average were flat, what would this say about term premiums? Would this support expectations theory?

6.6 Plot the yield curve when current and expected one-year interest rates are (a) 5%,7%,7%,7%,7%; (b) 5%,4%,4%,4%,4%

Now suppose these are current one-year, two-year, …, rates. What one-year rates are expected in future years?

6.9 Make sense of this yield curve