Bond Portfolio Management

1
Bond Portfolio Management

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

2
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.

3
Figure 15.1 Treasury Yield Curves
1). Pure yield curve 2). on-the-run yield curve
(page 485)
4
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.
5
Forward Rates from Observed Rates
fn one-year forward rate for period n yn
yield for a security with a maturity of n
6
Example page 491
4 yr 8.00 3yr 7.00 f4 ?
7
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
8
Forward Rates Downward Sloping Y C

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

9
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

10
Figure 15.4 Yield Curves
11
Figure 15.4 Yield Curves (Concluded)
12
Figure 15.6 Term Spread
13
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.

14
Figure 16.2 Cash Flows Paid by 9 Coupon, Annual
Payment Bond with an 8-Year Maturity and 10
Yield to Maturity
15
Duration Calculation
16
Example Duration
See page 516-517.
17
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

18
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

19
Figure 16.3 Bond Duration versus Bond Maturity
20
Correction for Convexity
Correction for Convexity
21
Figure 16.5 Convexity of Two Bonds
Which bond does you prefer?
22
Figure 16.6 Price Yield of a Callable Bond
Negative convexity page 526 mortgage has the
similar feature (page 526, 528)
23
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

24
Immunization

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

25
Active Management Swapping Strategies

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

26
Yield Curve Ride
Yield to Maturity
1.5 1.25 .75
Maturity
3 mon 6 mon 9 mon