Bond Managing Portfolios
2007 The McGrawHill Companies, Inc., All Rights Reserved.
McGrawHill/Irwin
CHAPTER 10
Managing Fixed Income Securities: Basic Strategies
Active strategy
Trade on interest rate predictions Trade on market inefficiencies
Passive strategy
Control risk Balance risk and return
10-2
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
10-3
Bond Pricing Relationships (cont.)
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
10-4
Figure 10.1 Change in Bond Price as a Function of YTM
10-5
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
10-6
Figure 10.2 Cash Flows of 8-yr Bond with 9% annual coupon and 10% YTM
10-7
Duration: Calculation
w t = [CFt (1 + y ) ] Price
t
D=
tw
t= 1
T
t
CF t = Cash Flow
for period
t
10-8
Duration Calculation
8% Time Bond years
1 2 3
Payment PV of CF Weight C1 X (10%) C4
80 80 1080 72.727 66.116 811.420 950.263 .0765 .0690 .8539 1.0000 .0765 .1392 2.5617 2.7774
10-9
Sum
Figure 10.3 Duration as Function a of Maturity
10-10
Duration/Price Relationship
Price change is proportional to duration and not to maturity P/P = -D x [ y / (1+y)] D* = modified duration D* = D / (1+y) P/P = - D* x y
10-11
Uses of Duration
Summary measure of length or effective maturity for a portfolio Immunization of interest rate risk (passive management)
Net worth immunization Target date immunization
Measure of price sensitivity for changes in interest rate
10-12
Figure 10.4 Growth of Invested Funds
10-13
Figure 10.5 Immunization
10-14
Pricing Error from Convexity
Price Pricing Error from Convexity
Duration Yield
10-15
Correction for Convexity
Modify the pricing equation:
P = -D y + 1 Convexity ( y ) 2 2 P
Convexity is Equal to:
1 (1 + y) 2 P
t= 1
N
CF t (t 2 + t ) + y )t (1
Where: CFt is the cash flow (interest and/or principal) at time t.
10-16
Figure 10.6 Bond Price Convexity
10-17
Figure 10.7 Convexity of Two Bonds
10-18
Active Bond Management: Swapping Strategies
Substitution swap Intermarket swap Rate anticipation swap Pure yield pickup Tax swap
10-19
Contingent Immunization
Allow the managers to actively manage until the bond portfolio falls to a threshold level Once the threshold value is hit the manager must then immunize the portfolio Active with a floor loss level
10-20
Figure 10-8 Contingent Immunization
10-21
Interest Rate Swaps
Interest rate swap basic characteristics
One party pays fixed and receives variable Other party pays variable and receives fixed Principal is notional
Growth in market
Started in 1980 Estimated over $60 trillion today
Hedging applications
10-22