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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. Overview of Term Structure. The relationship between yield to maturity and maturity.

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Bond Portfolio Management

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Bond portfolio management

Bond Portfolio Management

  • Term Structure

    • Yield Curve

    • Expected return versus forward rate

    • Term structure theories

  • Managing bond portfolios

    • Duration

    • Convexity

    • Immunization and trading strategy

Overview of term structure

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.

Figure 15 1 treasury yield curves

Figure 15.1 Treasury Yield Curves

1). Pure yield curve; 2). on-the-run yield curve (page 485)

Table 15 1

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%.

Forward rates from observed rates

Forward Rates from Observed Rates

fn = one-year forward rate for period n

yn = yield for a security with a maturity of n

Example page 487

Example: page 487

4 yr = 8.00%3yr = 7.00%f4 = ?

Downward sloping spot yield curve

Downward Sloping Spot Yield Curve

Zero-Coupon RatesBond Maturity






Forward rates downward sloping y c

Forward Rates Downward Sloping Y C

1yr Forward Rates

1yr= =0.115006

2yrs= =0.102567

3yrs= =0.063336

4yrs= =0.063008

Theories of term structure

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

Figure 15 4 yield curves

Figure 15.4 Yield Curves

Figure 15 4 yield curves concluded

Figure 15.4 Yield Curves (Concluded)

Figure 15 6 term spread

Figure 15.6: Term Spread



  • 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.

Bond portfolio management

Figure 16.2 Cash Flows Paid by 9% Coupon, Annual Payment Bond with an 8-Year Maturity and 10% Yield to Maturity

Duration calculation

Duration: Calculation

Example duration

Example: Duration

See page 516-517.

Duration price relationship

Duration/Price Relationship

Price change is proportional to duration and not to maturity.

P/P = -D x [(1+y) / (1+y)

D* = modified duration

D* = D / (1+y)

P/P = - D* x y

Rules for duration

Rules for Duration

Rule 1 The duration of a zero-coupon bond equals its time to maturity.

Rule 2 Holding maturity constant, a bond’s duration is higher when the coupon rate is lower.

Rule 3 Holding the coupon rate constant, a bond’s duration generally increases with its time to maturity.

Rule 4 Holding other factors constant, the duration of a coupon bond is higher when the bond’s yield to maturity is lower.

Rules 5 The duration of a level perpetuity is equal to: (1+y) / y

Figure 16 3 bond duration versus bond maturity

Figure 16.3 Bond Duration versus Bond Maturity

Correction for convexity

Correction for Convexity

Correction for Convexity:

Figure 16 5 convexity of two bonds

Figure 16.5 Convexity of Two Bonds

Which bond does you prefer?

Figure 16 6 price yield of a callable bond

Figure 16.6 Price –Yield of a Callable Bond

Negative convexity: page 526; mortgage has the similar feature (page 526, 528)

Passive management

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



  • Price risk

  • Reinvestment

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

Active management swapping strategies

Active Management: Swapping Strategies

  • The key idea is to predict the interest rate movement

  • Or simply riding on the yield curve

Yield curve ride

Yield Curve Ride

Yield to Maturity %

1.5 1.25 .75


3 mon 6 mon 9 mon

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