Bond Pricing Term Structure

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Bond Pricing Term Structure

• September 18, 2001

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Ignore for Now / Save for Later

• Floaters and inverse floaters
• Yield for floater
• Bond return
• Factors that affect yield spread
• Types of issuers

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Bonds

• Completely characterized by coupon rate and
  maturity.
• Need
• Cash flows
• Appropriate required yield
• Required yield reflects yields for instruments of
  similar credit quality.
• Bond price changes in opposite direction of
  required yield.

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Changes in Bond Price

• Reasons for a change in bond price
• 1. Change in required yield because issuers
  credit quality changes.
• 2. Change in price because maturity is
  approaching no change in yield.
• 3. Change in required yield because of market
  changes, i.e. happening for other bonds of
  similar credit quality, too.

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Bond Price - example

• Price a two year bond with 10 annual coupons.
  The face value is 100 and the term structure is
  flat at 10 for all maturities.
• What if the interest rate were 12?
• How about 8?

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Pricing Complications

• Day count conventions next coupon is less than
  6 months away.
• Cash flows not known with precision.
• Difficulty in determining appropriate required
  yield.
• Need a discount rate for each cash flow.

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Yield to Maturity

• The average rate of return you would earn on a
  bond investment if you held the bond from the
  current time until its maturity, and if there
  were no defaults on any of the promised payments.
• Bonds of the same credit quality and maturity
  should be priced to yield the same. If they have
  different coupons, their prices will differ.

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Yield to Maturity - example

• A two year bond with a 10 coupon rate that pays
  annual coupons is priced at 103.57.
• What is its yield to maturity?

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Using Yield to Maturity

• Two bonds have the same credit quality and each
  has a 12 year maturity. They pay annual coupons,
  one at 10 and the other at 12.
• The 10 bond has a price of 93.508.
• Estimate the price of the second bond.

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Another Example

• You currently own a 5 year bond with an 8
  coupon. The coupons are semi-annual. If the YTM
  is 10, calculate the current bond price.
• Suppose you expect the YTM to be 8 one year from
  now. If you sell the bond then, what return do
  you expect to have earned?

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YTM and Reinvestment Risk

• Calculation of YTM assumes that the coupons can
  all be reinvested at YTM.
• Degree of reinvestment risk is related to
  maturity and coupon.
• Longer maturity more return is dependent on
  interest-on-interest.

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Yield Curve

• Graphical relation between yields on bonds of
  same credit quality and differing maturities.
• Usually use Treasury securities.
• Do you want to use the yield curve to price bonds?

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The Term Structure

• Coupon bonds are portfolios of zero coupon
  instruments.
• The theoretical spot curve is the term structure.
• Most common method for deriving term structure is
  bootstrapping.

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The Term Structure - cont

• Usually drawn for bonds of uniform credit quality
  and uniform tax exposure.
• At any given time, three possible factors
  influence the shape of the term structure.
• Each corresponds to a major theory of the term
  structure.

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Three Factors Three Theories

• 1. Markets expectations regarding the future
  direction of interest rates.
• 2. Possible existence of liquidity premiums in
  expected bond returns.
• 3. Possible market inefficiences.

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Spot Rates

• The one year spot rate is 8. The two year spot
  rate is 10.
• Price a one year zero coupon bond and a two year
  zero coupon bond.
• Price a two year 5 bond with annual coupons.
• What is the YTM of this last bond?

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Forward Rates

• The one year forward rate from year 1 to year 2
  is determined as if you invest for one year at
  the spot rate and then invest again at the
  forward rate. This forward rate must end you up
  financially equivalent to having invested at the
  two year spot rate.
• Note the forward rate is known at date 0. The
  one year spot rate from year 1 to year 2 is not
  known at date 0.

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Example

• Price these 6 annual coupon Government of Canada
  bonds

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Example - continued

• What are the one-year forward rates?
• What are the expected bond prices one year from
  now for the 2, 3, 4 and 5 year bonds?
• What are the expected yields on year from now for
  the 2, 3, 4 and 5 year bonds?