Managing Bond Portfolios Chapter 16

Basic Strategies Active strategy Passive strategy Trade on interest rate predictions Trade on market inefficiencies Passive strategy Control risk Balance risk and return

Bond Pricing Relationships Inverse relationship between price and yield. An increase in a bond’s yield to maturity results in a smaller price decline than the gain associated with a decrease in yield. Long-term bonds tend to be more price sensitive than short-term bonds.

Bond Pricing Relationships (cont’d) As maturity increases, price sensitivity increases at a decreasing rate. Price sensitivity is inversely related to a bond’s coupon rate. Price sensitivity is inversely related to the yield to maturity at which the bond is selling.

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.

Duration: Calculation

Duration Calculation: Spreadsheet 16.1 8% Time Payment PV of CF Weight C1 X Bond years (10%) C4 .5 40 38.095 .0395 .0197 1 40 36.281 .0376 .0376 1.5 40 34.553 .0358 .0537 2.0 1040 855.611 . 8871 1.7742 sum 964.540 1.000 1.8852

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 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 for Duration (cont’d) Rules 5 The duration of a level perpetuity is equal to: Rule 6 The duration of a level annuity is equal to:

Rules for Duration (cont’d) Rule 7 The duration for a corporate bond is equal to:

Duration and Convexity Price Pricing Error from convexity Duration Yield

Correction for Convexity

Passive Management Bond-Index Funds 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

Active Management: Swapping Strategies Substitution swap Inter-market swap Rate anticipation swap Pure yield pickup Tax swap

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

Contingent Immunization A combination of active and passive management. The strategy involves active management with a floor rate of return. As long as the rate earned exceeds the floor, the portfolio is actively managed. Once the floor rate or trigger rate is reached, the portfolio is immunized.

Interest Rate Swaps Contract between two parties to exchange a series of cash flows One party pays a fixed rate and receives a variable rate One party pays a variable rate and receives a fixed rate Payments based on notional principal

Swap Example Figure 16-11 6.95% 7.05% 7% Swap Dealer Company A Company B LIBOR LIBOR LIBOR