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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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3 mo 6 mo 1 yr 2 yr 3 yr 5 yr 7 yr 10 yr 30 yr

The Yield Curve and Monetary Policy

September 7, 2001

Percent, weekly average

December 29, 2000

January 4, 2002

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Recent Treasury Yield Curves

March 14, 2011

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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?

• Example:

• FACT: bond markets are very sensitive to economic news!

News Surprises=

Realized inflationin year 2000 = 6%=> Surprise = 0%

No NEWS! No Market Reaction!

Realized inflationin year 2000 = 8%

=> Surprise = +2%NEWS! Market Reacts!

market expects inflation in year 2000 to equal 6%.

Realized - Expected=

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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.

•All of these price changes took place within 15 minutes of the macro news.

Time period from August 22, 1993 to August 19, 1994

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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