the mcgraw-hill companies, inc., 1999 investments fourth edition bodie kane marcus irwin/mcgraw-hill...
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The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 16-3 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 RelationshipsTRANSCRIPT
Irwin/McGraw-Hill
16-16-11 The McGraw-Hill Companies, Inc., 1999
INVESTMENTSFourth Edition
Bodie Kane Marcus
Fixed-IncomeFixed-IncomePortfolio ManagementPortfolio Management
Chapter 16Chapter 16
Irwin/McGraw-Hill
16-16-22 The McGraw-Hill Companies, Inc., 1999
INVESTMENTSFourth Edition
Bodie Kane Marcus
Active strategy- Trade on interest rate predictions- Trade on market inefficiencies
Passive strategy- Control risk- Balance risk and return
Managing Fixed Income Securities: Managing Fixed Income Securities: Basic StrategiesBasic Strategies
Irwin/McGraw-Hill
16-16-33 The McGraw-Hill Companies, Inc., 1999
INVESTMENTSFourth Edition
Bodie Kane Marcus
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 RelationshipsBond Pricing Relationships
Irwin/McGraw-Hill
16-16-44 The McGraw-Hill Companies, Inc., 1999
INVESTMENTSFourth Edition
Bodie Kane Marcus
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
Bond Pricing Relationships (cont’d)Bond Pricing Relationships (cont’d)
Irwin/McGraw-Hill
16-16-55 The McGraw-Hill Companies, Inc., 1999
INVESTMENTSFourth Edition
Bodie Kane Marcus
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
DurationDuration
Irwin/McGraw-Hill
16-16-66 The McGraw-Hill Companies, Inc., 1999
INVESTMENTSFourth Edition
Bodie Kane Marcus
t ttw CF y ice ( )1 Pr
twtDT
t
1
CF Cash Flow for period tt
Duration: CalculationDuration: Calculation
Irwin/McGraw-Hill
16-16-77 The McGraw-Hill Companies, Inc., 1999
INVESTMENTSFourth Edition
Bodie Kane Marcus
8%Bond
Timeyears
Payment PV of CF(10%)
Weight C1 XC4
.5 40 38.095 .0395 .0198
1 40 36.281 .0376 .0376
1.5
2.0
40
1040
sum
34.553
855.611
964.540
.0358
.8871
1.000
.0537
1.7742
1.8853
Duration Calculation: Duration Calculation: Example using Table 16.3Example using Table 16.3
Irwin/McGraw-Hill
16-16-88 The McGraw-Hill Companies, Inc., 1999
INVESTMENTSFourth Edition
Bodie Kane Marcus
Price change is proportional to duration and not to maturity
P/P = -D x [(1+y) / (1+y)D* = modified durationD* = D / (1+y)P/P = - D* x y
Duration/Price RelationshipDuration/Price Relationship
Irwin/McGraw-Hill
16-16-99 The McGraw-Hill Companies, Inc., 1999
INVESTMENTSFourth Edition
Bodie Kane Marcus
Rules for DurationRules 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
Irwin/McGraw-Hill
16-16-1010 The McGraw-Hill Companies, Inc., 1999
INVESTMENTSFourth Edition
Bodie Kane Marcus
Rules for Duration (cont’d)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:
1)1(1
Ty
Ty
y
yy)1(
Irwin/McGraw-Hill
16-16-1111 The McGraw-Hill Companies, Inc., 1999
INVESTMENTSFourth Edition
Bodie Kane Marcus
Rules for Duration (cont’d)Rules for Duration (cont’d)
Rule 7 The duration for a corporate bond is equal to:
yycycTy
yy
T
]1)1[()()1(1
Irwin/McGraw-Hill
16-16-1212 The McGraw-Hill Companies, Inc., 1999
INVESTMENTSFourth Edition
Bodie Kane Marcus
Bond-Index Funds Immunization of interest rate risk
- Net worth immunizationDuration of assets = Duration of liabilities
- Target date immunizationHolding Period matches Duration
Cash flow matching and dedication
Passive ManagementPassive Management
Irwin/McGraw-Hill
16-16-1313 The McGraw-Hill Companies, Inc., 1999
INVESTMENTSFourth Edition
Bodie Kane Marcus
Yield
Price
Duration
Pricing Error from convexity
Duration and ConvexityDuration and Convexity
Irwin/McGraw-Hill
16-16-1414 The McGraw-Hill Companies, Inc., 1999
INVESTMENTSFourth Edition
Bodie Kane Marcus
Correction for ConvexityCorrection for Convexity
n
tt
t tty
CFyP
Convexity1
22 )(
)1()1(1
Correction for Convexity:
])([21 2yConveixityyD
PP
Irwin/McGraw-Hill
16-16-1515 The McGraw-Hill Companies, Inc., 1999
INVESTMENTSFourth Edition
Bodie Kane Marcus
Substitution swap Intermarket swap Rate anticipation swap Pure yield pickup Tax swap
Active Bond Management: Active Bond Management: Swapping StrategiesSwapping Strategies
Irwin/McGraw-Hill
16-16-1616 The McGraw-Hill Companies, Inc., 1999
INVESTMENTSFourth Edition
Bodie Kane Marcus
Maturity
Yield to Maturity %
3 mon 6 mon 9 mon
1.5 1.25 .75
Yield Curve RideYield Curve Ride
Irwin/McGraw-Hill
16-16-1717 The McGraw-Hill Companies, Inc., 1999
INVESTMENTSFourth Edition
Bodie Kane Marcus
Contingent ImmunizationContingent Immunization
Combination of active and passive management
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