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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
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

12% 1

11.75% 2

11.25% 3

10.00% 4

9.25% 5


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





Duration
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.


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 Bond with an 8-Year Maturity and 10% Yield to Maturity


Example duration
Example: Duration Bond with an 8-Year Maturity and 10% Yield to Maturity

See page 516-517.


Duration price relationship
Duration/Price Relationship Bond with an 8-Year Maturity and 10% Yield to Maturity

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 Bond with an 8-Year Maturity and 10% Yield to Maturity

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 Bond with an 8-Year Maturity and 10% Yield to Maturity


Correction for convexity
Correction for Convexity Bond with an 8-Year Maturity and 10% Yield to Maturity

Correction for Convexity:


Figure 16 5 convexity of two bonds
Figure 16.5 Convexity of Two Bonds Bond with an 8-Year Maturity and 10% Yield to Maturity

Which bond does you prefer?


Figure 16 6 price yield of a callable bond
Figure 16.6 Price –Yield of a Callable Bond Bond with an 8-Year Maturity and 10% Yield to Maturity

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


Passive management
Passive Management Bond with an 8-Year Maturity and 10% Yield to Maturity

  • 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


Immunization
Immunization Bond with an 8-Year Maturity and 10% Yield to Maturity

  • Price risk

  • Reinvestment

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


Active management swapping strategies
Active Management: Swapping Strategies Bond with an 8-Year Maturity and 10% Yield to Maturity

  • The key idea is to predict the interest rate movement

  • Or simply riding on the yield curve


Yield curve ride
Yield Curve Ride Bond with an 8-Year Maturity and 10% Yield to Maturity

Yield to Maturity %

1.5 1.25 .75

Maturity

3 mon 6 mon 9 mon


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