Download Determinants of Interest Rates

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?
4.9 Which $1000 face value bond currently selling for $800 has higher y-t-m:
•20 year bond with current yield of 15%
or
•1 year bond with current yield of 5%?
4.12 If there is a decline in interest rates, which would you rather be holding,
long-term bonds or short-term bonds? Which type of bond has greater interest
rate risk?
4.19 Interest rates were lower in the mid-1980s than they were in the late 1970s,
Yet many economists say that real interest rates were actually much higher
in the mid-1980s. Does this make sense?
Interest Rate Determination:
Demand and Supply of “Bonds”
Demand for an Asset
• Wealth
• Expected return…relative to alternative
assets
• Risk—uncertainty of return—relative to
alternative assets
• Liquidity—ease and speed an asset can be
turned into cash—relative to alternative assets
Factors That Shift the Demand Curve for Bonds
Factors That Shift the Supply of Bonds
Interest Rate Determination: Bond Market Approach
P down  i up
i = r + πe
Interest rates generally rise when
economy expands
P down
 i up
Interest Rate Determination:
Demand and Supply of Money
Demand for money:
•
•
•
•
Buy stuff
Pay for stuff
Meet payments when they come due
Pick up “bonds” when their price falls
Md = L($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
Shifts in the Supply of Money
• Monetary Base: Controlled by Fed
• Money Multiplier: (1 + c)/(c + r + e)
• We’ll assume Ms controlled by Fed
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 up
Since i = r + πe , if π and πe catches up as it must, i too
Since (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 destroy
you 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
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
For an investment of $1
it = today's interest rate on a one-period bond
ite1 = interest rate on a one-period bond expected for next period
i2t = today's interest rate on the two-period bond
If two one-period bonds are bought with the $1 investment
(1  it )(1  ite1 )  1
1  it  ite1  it (ite1 )  1
it  ite1  it (ite1 )
it (ite1 ) is extremely small
Simplifying we get
it  ite1
Both bonds will be held only if the expected returns are equal
2i2t  it  ite1
it  ite1
i2t 
2
The two-period rate must equal the average of the two one-period rates
For bonds with longer maturities
int 
it  ite1  ite 2  ...  ite ( n 1)
n
The n-period interest rate equals the average of the one-period
interest rates expected to occur over the n-period life of the bond
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 
e
e
e
it  it1
 it2
 ... it(
n1)
 lnt
n
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 problems
6.3 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