Managing Fixed-Income Investments

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Chapter 11

• Managing Fixed-Income Investments

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Managing Fixed Income Securities Basic Strategies

• Active strategy
• Trade on interest rate predictions
• Trade on market inefficiencies
• Passive strategy
• Control risk
• Balance risk and return

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Bond Pricing Relationships

• Inverse relationship between price and yield
• An increase in a bonds yield to maturity results
  in a smaller price decline than the gain
  associated with a decrease in yield
• Long-term bonds tend to be more price sensitive
  than short-term bonds

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Bond Pricing Relationships (cont.)

• As maturity increases, price sensitivity
  increases at a decreasing rate
• Price sensitivity is inversely related to a
  bonds coupon rate
• Price sensitivity is inversely related to the
  yield to maturity at which the bond is selling

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Duration

• A measure of the effective maturity of a bond
• The weighted average of the times until each
  payment is received, with the weights
  proportional to the present value of the payment
• Duration is shorter than maturity for all bonds
  except zero coupon bonds
• Duration is equal to maturity for zero coupon
  bonds

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Other duration rules

• A bonds duration (and interest sensitivity) are
  higher the lower is the coupon rate (all else the
  same)
• Duration and interest rate sensitivity usually
  increase with maturity (all else the same)
• Duration and interest rate sensitivity are higher
  when yields are lower (all else the same)
• Duration for perpetuity 1/(1y)

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Duration Calculation
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Duration Calculation
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Consider a 5-year, 10 coupon bond. Yield 14.
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Duration/Price Relationship

• Price change is proportional to duration and not
  to maturity
• ?P/P -D x ?(1y) / (1y)
• D modified duration
• D D / (1y)
• ?P/P - D x ?y

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Approximating price changes

• Consider our 10, 5-year bond. Yields are
  initially at 14 and the duration of the bond is
  4.1.
• Suppose rates fall by 200 basis points. Estimate
  the percentage change in the bonds price.
  Estimate the price ( compare to actual price).

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Estimating price sensitivity
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Using duration and convexity to estimate price
changes.
Correction for convexity
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Convexity
Estimate of percentage price change
0.074997 Estimate of price 927.3751
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Uses of Duration

• Summary measure of length or effective maturity
  for a portfolio
• Immunization of interest rate risk (passive
  management)
• Net worth immunization
• Target date immunization
• Measure of price sensitivity for changes in
  interest rate

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Target date immunization

• Consider the two components of interest rate risk
• price risk
• reinvestment rate risk
• Suppose rates are at 14 and you have a 4.1 year
  horizon.
• Consider the bond with a 10 annual coupon, 5
  years, and duration of 4.1 years

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Target date immunization
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Target or Horizon Date Immunization

• Set Dp Horizon Date or Target date
• then price risk (sale price of the bond) and
  reinvestment risk (accumulated value of the
  coupon payments) offset one another
• Rebalancing (must monitor update)
• Changing interest rates
• The passage of time

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Other approaches

• Cash flow matching
• dedication strategy
• horizon matching (not analysis)
• contingent immunization

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Active Bond Management Swapping Strategies

• Substitution swap
• Intermarket swap
• Rate anticipation swap
• D HD gt immunized
• D gt HD gt net price risk
• D lt HD gt net reinvestment rate risk
• Pure yield pickup
• Tax swap

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Rate anticipation

• Consider a bond with 10 years to maturity, 8
  coupon (paid annually), priced at 877.11.
  Current interest rates 10
• Duration 7.04
• Suppose your HD 4 years
• You expect interest rates will decline
• Since D gt HD gt net price risk

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Rate anticipation
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Interest rate swap

• Contract between two parties to trade the cash
  flows corresponding to different securities
  without actually exchanging the securities
  directly.
• Plain vanilla convert interest payments based on
  a floating rate into payments based on a fixed
  rate (or vice versa)
• Notional