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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

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

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

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

fn = one-year forward rate for period n

yn = yield for a security with a maturity of n

Example: page 487

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

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

1yr Forward Rates

1yr= = 0.115006

2yrs= = 0.102567

3yrs= = 0.063336

4yrs= = 0.063008

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

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

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

See page 516-517.

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

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

Correction for Convexity:

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 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 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

- Net worth immunization
- Cash flow matching and dedication
- Covered in fixed income class

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 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 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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