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Taylor Rule and the Term Structure
Objectives:
1. To understand the relation between central bank policy
and long term interest rates.
2. Understand “news” and its impact on financial markets
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The Yield Curve and Monetary Policy
6.0
Percent, weekly average
December 29, 2000
5.5
5.0
4.5
4.0
3.5
September 7, 2001
3.0
2.5
2.0
January 4, 2002
1.5
1.0
3 mo
6 mo
1 yr
2 yr
3 yr
5 yr
7 yr
10 yr
30 yr
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Recent Treasury Yield Curves
Date
1 mo
3 mo
6 mo
1 yr
2 yr
3 yr
5 yr
7 yr
10 yr
20 yr
30 yr
10/01/08
0.66
0.85
1.49
1.72
1.82
2.12
2.87
3.29
3.77
4.33
4.22
10/02/08
0.21
0.63
1.21
1.45
1.62
1.91
2.68
3.13
3.66
4.28
4.16
10/03/08
0.15
0.51
1.14
1.41
1.60
1.86
2.64
3.09
3.63
4.26
4.11
10/06/08
0.19
0.54
1.12
1.23
1.43
1.69
2.45
2.92
3.48
4.12
3.99
10/07/08
0.39
0.82
1.14
1.27
1.47
1.69
2.45
2.91
3.50
4.15
4.01
10/08/08
0.23
0.68
1.07
1.28
1.65
1.88
2.70
3.15
3.72
4.31
4.09
10/09/08
0.19
0.60
1.07
1.33
1.65
1.93
2.79
3.25
3.84
4.41
4.14
10/10/08
0.07
0.25
0.84
1.08
1.62
1.87
2.77
3.27
3.89
4.41
4.15
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Current Treasury Yield Curves
December 2, 2009
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Issues
• What is the term structure of interest rates?
• Relation between central bank policy and the term
structure?
• How does economic information affect bond
markets?
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Term Structure
• Relationship between yield to maturity for zero coupon bond
and bond price is:
q(n,t) = 100/(1+y(n,t))n
• A bond that matures in n years at date t has an yield to
maturity of y(n,t)
• The current price (i.e., at date t) is q(n,t)
• The bond delivers 100 dollars at date t+n (in years)
• This is the annual yield on a bond that delivers 100 dollar after
n years
• 100*y(n,t) annual percentage yield that you see in the
newspapers and the graphs
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Example
• Suppose a bond that matures in 6 months (n, in years
is 1/2) and has current price of 96 dollars.
• Then its annual percentage yield is calculated as:
(100/96)2 –1 = 0.085 (or 8.5%)
• This can be done for each maturity, that is n
• The relation between n and y(n,t) is the yield curve
or the term structure at date t
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Yield to Maturity and Interest Rates
• The yield to maturity on a pure-discount bond is also
the rate of return on the bond
• The yield to maturity is equal to the interest rate of
similar maturity:
R(n,t) = y(n,t)
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The Term Structure: Why Do We Care?
• The central bank manages the short term interest rates,
overnight Fed funds rate
– How does the central bank control the long term nominal
interest rate?
• Answer provided by the expectations theory
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The Expectations Theory
• The expectations theory provides a relationship between short-term interest
and long term yields
• The expectations theory says that long term yields are averages of expected
one period (e.g., one year) yields
• For example:
y(2,t) = ( y(1,t) + y(1,t+1)e )/2
• As the next year’s one-year yield is not known today, we use its expectation
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The Expectations Theory
• This can be generalized as:
y(n,t) = ( y(1,t) + y(1,t+1)e +…+ y(1,t+n-1)e)/n
• Yield on an n period bond at time t is equal to the average of the
expected one period interest rates between t and t+n
• The above statement is called the expectations theory of term
structure of interest rates
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The Expectations Theory
• The expectations theory implies
– Case 1: If investors expect the future one period interest rates to rise
then the current yield curve upward sloping
– Case 2: If investors expect no change in the future one period
interest then the current yield is flat
– Case 3: If investors expect the future one period interest rates to fall
then the current yield curve downward sloping
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The Central Bank
and the Term Structure
• The Fed manages the one period interest rate (fed funds rate)
• Expectations theory  today’s yield curve reflects the markets
expectations of future Fed actions regarding the Fed Funds rate
• There is an important link between the yield curve and Federal
Reserve’s monetary policy
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Fed’s Reaction Function
• In the US, the Fed seems to set the Fed funds rate using the following
rule (Taylor rule)
R = 1.5*pi + 0.5*d + 1.0
– R is the Fed funds rate
– d is the percentage deviation of output from the trend real GDP
– pi is the rate of inflation over the preceding four quarters
• If the real GDP is below the trend line (d less than zero) then the Fed
will lower the Fed funds rate
• If pi continues to rise, then the Fed will increase the Fed funds rate
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The Slope of the Yield Curve Predicts Recessions
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Yield Spread:Leading Indicator
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Policy Rule and Expectations Theory
• The policy rule provides a sharp link between the inflation,
real GDP and the Fed funds rate
• The expectations theory links all bond yields to the
dynamics of the Fed funds rate
• This implies that yields and changes in yields are
determined by key economic variables
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What Moves Financial Markets?
Macroeconomic News!
• What is news?
News
=
Surprises
=
Realized - Expected
• Example: market expects inflation in year 2000 to equal 6%.
Realized inflation
in year 2000 = 6%
=> Surprise = 0%
No NEWS!
No Market Reaction!
Realized inflation
in year 2000 = 8%
=> Surprise = +2%
NEWS!
Market Reacts!
• FACT: bond markets are very sensitive to economic news!
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Macroeconomic Announcements
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Price Volatility
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Macro-Announcements and Prices
•The 25 largest
price changes
coincide with days
when
macroeconomic
news is released.
Time period from August 22, 1993 to August 19,
1994
•All of these price
changes took
place within 15
minutes of the
macro news.
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Announcement Surprises
•
•
•
The bond prices fall (or yields rise) in
reaction to
– a positive employment surprise
– a positive inflation surprise
– a positive Fed funds target rate
surprise
The market understands that these
positive surprises will likely lead to a rise
in the future Fed funds rate
Implication: current yields should rise
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Effect of Economic News on Bond Prices
• WSJ, 03/02/2000: “Long Bond Falls…”
“…a broad gauge of manufacturing sector activity
- rose”
“On balance, the report bolstered the market’s
view Federal reserve policy makers will have to
push short term interest rates higher to contain
inflation...”
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Key Message
• Always interpret the impact of economic news on Bond
markets 
Thinking about the Taylor Rule + The expectations hypothesis
• You will always arrive at the right conclusion regarding
the impact on bond prices
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