Study Notes for Chapter 11: Managing Bond Portfolios

Chapter 11: Managing Bond Portfolios

Basic Relationship: Bond prices and yields exhibit an inverse relationship.
- An increase in a bond's yield to maturity generates a smaller price change compared to the price increase resulting from a yield decrease of equal magnitude.
- Long-term bond prices demonstrate greater sensitivity to changes in interest rates compared to short-term bonds.
- Sensitivity of bond prices to changes in yields increases with maturity; however, this increase occurs at a decreasing rate.

Interest rate risk is inversely correlated with a bond’s coupon rate.
- Low-coupon bonds are generally more sensitive to interest rate fluctuations.
Sensitivity of a bond’s price concerning yield changes is also inversely related to its current yield to maturity.

Bond Yield to Maturity and Price Changes:
- For different maturities (T = 1 year, T = 10 years, T = 20 years) with a coupon rate of 8% and 9%, % change in price will vary.

Bond Yield to Maturity and Price Changes:
- Similar analysis applies as with annual coupon bonds to different maturities (T = 1 year, T = 10 years, T = 20 years) with yield changes of 8% and 9%, resulting in varying % change in price.

Definition: A measure of the effective maturity of a bond.
Formula: D = rac{ ext{CF}_t}{(1+y)^t}
- Where CF represents cash flows, y is the yield, and t is the time.
Duration is calculated as a weighted average of the times until each payment, with weights proportional to the present value of each payment.
Key Insights: Duration serves as an essential tool in managing bond portfolios by immunizing them from interest rate risk and reflects interest rate sensitivity.

Definition: A refined version of duration that accounts for the bond's yield.
Formula:
D^* = rac{ riangle P}{P} = rac{D}{1+y}
Represents how much the price of a bond will change with a change in yield.
The formula can be expressed in the context of price changes as follows:
riangle P = -D^* riangle y P

Zero-Coupon Bond Duration: For zero-coupon bonds, duration is equivalent to the time to maturity.
Holding time/yield constant, a bond's duration increases with declining coupon rates, indicating a higher interest rate sensitivity.
For coupon bonds, duration generally increases with maturity; however, for bonds trading at or above par, duration always increases with maturity.
Furthermore, if other factors are constant, duration and interest rate sensitivity of a coupon bond increase when the bond's yield to maturity is lower.
Duration of level perpetuity can be expressed as:
rac{1}{1+y} = rac{y}{1+y}

A graphical representation that illustrates how duration changes relative to maturity for zero-coupon bonds and various coupon rates with corresponding yields to maturity (YTM).

Example 1: Bond characteristics:
- Maturity: 30 years
- YTM: 9%
- Coupon rate: 8% (annually)
- Price: 897.26
- Duration: 11.37 years
Question posed: What happens to the bond price if the bond's YTM increases to 9.1%?

Definition: A strategy designed to shield net worth from interest rate movements (interest rate risk).
- Involves matching the interest rate exposures of assets and liabilities so that the value of assets tracks the value of liabilities regardless of interest rate fluctuations.
Financial managers aim to immunize funds against interest volatility by achieving a balance between assets and liabilities.
Rebalancing: The process of realigning proportions of assets in a portfolio as required to maintain targeted immunization.

Cash Flow Matching: Involves aligning cash flows from the fixed-income portfolio with corresponding obligations.
Deduction Strategy: A strategy involving matching multi-period cash flows for obligations against expected cash inflows from fixed-income investments.

Definition: The curvature of the price-yield relationship of a bond.
- Its formula is expressed as:
  rac{ riangle P}{P} = -D^* riangle y + rac{1}{2} imes { ext{Convexity}} imes ( riangle y)^2

A graph displaying the actual percentage change in bond price in relation to changes in yield to maturity, illustrating the differences between actual price changes and predictions based on duration.

Investors prefer convex bonds due to the following properties:
- Bonds with greater curvature (higher convexity) result in more significant price gains when yields decline.
- Conversely, they also incur smaller losses when yields rise compared to bonds with lesser convexity.

Substitution Swap: Exchanging one bond for another with similar characteristics but a better price.
Intermarket Swap: Switching between different segments of the bond market based on relative value.
Rate Anticipation Swap: A strategy that responds to forecasts of interest rate changes by adjusting the bond mix in the portfolio.
Pure Yield Pickup Swap: Movement to bonds with higher yields, typically with longer maturities.
Tax Swap: Swapping two similar bonds for tax advantages.
Horizon Analysis: Forecasting bond returns based on expected yield curve movements at the end of the investment horizon.

Students are required to define the following concepts:
- Convexity
- Modified Duration
- Macaulay’s Duration
- Immunization
- Horizon Analysis
Additional questions from the chapter include problem numbers 2, 5, and CFA Problems 10a, 10b, 10c, 10d.