4.2 You have just won $10 million , $1 every year for the next 10 years. Discuss.

4.6 What is the yield to maturity of a $1,000 face value discount bond that matures in 1 year and sells for $800? What if it matured in 2 years?

4.12 If there is a decline in interest rates, which would you rather be holding, long-term bonds or short-term bonds? Which type of bond has greater interest rate risk?

4.19 Interest rates were lower in the mid-1980s than they were in the late 1970s, Yet many economists say that real interest rates were actually much higher in the mid-1980s. Does this make sense?

4.9 Which $1000 face value bond currently selling for $800 has higher y-t-m: • 20 year bond with current yield of 15% or• 1 year bond with current yield of 5%?

Interest Rate Determination: Demand and Supply of “Bonds”

Demand for an Asset• Wealth• Expected return…relative to alternative

assets• Risk—uncertainty of return—relative to

alternative assets• Liquidity—ease and speed an asset can be

turned into cash—relative to alternative assets

Factors That Shift the Demand Curve for Bonds

Factors That Shift the Supply of Bonds

P down i upi = r + πe

Interest Rate Determination: Bond Market Approach

Interest rates generally rise wheneconomy expands

P down i up

Interest Rate Determination:Demand and Supply of Money

Demand for money:

• Buy stuff• Pay for stuff• Meet payments when they come due• Pick up “bonds” when their price falls

Md = L($Y,i) = L(P,Y,i)Supply of money: Monetary Policy

Buy Ease Sell Tighten

Shifts in the Demand for Money• Income Effect:

• Higher income more stuff bought demand for money at each interest rate increases

• Price-Level Effect:• Rise in the price level need more money to buy the

same amount of stuff the demand for money at each interest rate increases

• Monetary Base: Controlled by Fed• Money Multiplier: (1 + c)/(c + r + e)• We’ll assume Ms controlled by Fed

Shifts in the Supply of Money

Interest Rate and the Money Supply• Liquidity effect: Ms up lowers interest rates

But Ms up also increases output and prices• Income effect: Ms up increased output increased

demand for money interest rate up• Price-Level effect: Ms up increased price level

increased demand for money interest rate up• Expected-Inflation effect: Ms growth up expectation

of ongoing inflation (maybe) i upSince i = r + πe , if π and πe catches up as it must, i tooSince (M/P)d = L(Y,i) is stable at each Y, (M/P)s must fall

when π . P must rise faster than M.

Response over time to Increase in the Rate of Growth of the Money Supply

5.6 An important way in which the Fed decreases Ms is by selling bonds to the public. Using a supply and demand analysis for bonds, show the effect on i.Using the liquidity preference framework, show the effect on i.

5.17. The Chairman of the Fed announces that interest rates will fall and stay low next year. What will happen to corporate bond interest rates today? Explain.

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, 1919–2011

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 RatesYield 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

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

ii

2 2

22 2

22 2

22

Expected return over the two periods from investing $1 in thetwo-period bond and holding it for the two periods

(1 + )(1 + ) 1

1 2 ( ) 1

2 ( )

Since ( ) is very smallthe expected re

t t

t t

t t

t

i i

i i

i i

i

2

turn for holding the two-period bond for two periods is2 ti

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 smallSimplifying 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-periodinterest 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 it1

e it2e ... it(n 1)

e

n lnt

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: http://stockcharts.com/charts/YieldCurve.html

Yield Curves for U.S. Government Bonds

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