Bond Portfolio Management

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Bond Portfolio Management

• Term Structure
• Yield Curve
• Expected return versus forward rate
• Term structure theories
• Managing bond portfolios
• Duration
• Convexity
• Immunization and trading strategy

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Overview of Term Structure

• The relationship between yield to maturity and
  maturity.
• Information on expected future short term rates
  can be implied from yield curve.
• The yield curve is a graph that displays the
  relationship between yield and maturity.
• Three major theories are proposed to explain the
  observed yield curve.

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Figure 15.1 Treasury Yield Curves
1). Pure yield curve 2). on-the-run yield curve
(page 485)
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Table 15.1
1-year rate is 5, 2-year rate is 6, 3-year rate
is 7, 4-year rate is 8. Compute the yield to
maturity of a 3-year coupon bond with a coupon
rate of 10.
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Forward Rates from Observed Rates
fn one-year forward rate for period n yn
yield for a security with a maturity of n
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Example page 487
4 yr 8.00 3yr 7.00 f4 ?
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Downward Sloping Spot Yield Curve
Zero-Coupon Rates Bond Maturity 12 1 11.7
5 2 11.25 3 10.00 4 9.25 5
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Forward Rates Downward Sloping Y C

• 1yr Forward Rates
• 1yr 0.115006
• 2yrs 0.102567
• 3yrs 0.063336
• 4yrs 0.063008

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Theories of Term Structure

• Expectation Theory
• Forward rate expected rate (page 494)
• Liquidity Premium Theory
• Upward bias over expectations
• Equation 15.8 on page 499

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Figure 15.4 Yield Curves
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Figure 15.4 Yield Curves (Concluded)
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Figure 15.6 Term Spread
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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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Figure 16.2 Cash Flows Paid by 9 Coupon, Annual
Payment Bond with an 8-Year Maturity and 10
Yield to Maturity
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Duration Calculation
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Example Duration
See page 516-517.
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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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Rules for Duration

• Rule 1 The duration of a zero-coupon bond equals
  its time to maturity.
• Rule 2 Holding maturity constant, a bonds
  duration is higher when the coupon rate is lower.
• Rule 3 Holding the coupon rate constant, a
  bonds duration generally increases with its time
  to maturity.
• Rule 4 Holding other factors constant, the
  duration of a coupon bond is higher when the
  bonds yield to maturity is lower.
• Rules 5 The duration of a level perpetuity is
  equal to (1y) / y

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Figure 16.3 Bond Duration versus Bond Maturity
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Correction for Convexity
Correction for Convexity
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Figure 16.5 Convexity of Two Bonds
Which bond does you prefer?
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Figure 16.6 Price Yield of a Callable Bond
Negative convexity page 526 mortgage has the
similar feature (page 526, 528)
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Passive Management

• Bond-Index Funds
• Lehman Aggregate Bond index
• Salomon Smith Barney Broad Investment Grade (BIG)
  Index
• Merrill Lynch U.S. Broad Market Index
• Immunization of interest rate risk
• Net worth immunization
• Duration of assets Duration of liabilities
• Target date immunization
• Holding Period matches Duration
• Cash flow matching and dedication
• Covered in fixed income class

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Immunization

• Price risk
• Reinvestment
• Immunization is the point that two effects are
  cancelled out.

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Active Management Swapping Strategies

• The key idea is to predict the interest rate
  movement
• Or simply riding on the yield curve

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Yield Curve Ride
Yield to Maturity
1.5 1.25 .75
Maturity
3 mon 6 mon 9 mon