1® 1999 South-Western College Publishing

Chapter 17Bonds-Analysis And

Management

2® 1999 South-Western College Publishing

Bond Pricing Principles

• Bond Prices and the Passage of TimeBond Prices and the Passage of Time

• Bond Prices and Changes in Yield to MaturityBond Prices and Changes in Yield to Maturity

• Bond Price Sensitivity and MaturityBond Price Sensitivity and Maturity

• Changes in Bond Price Sensitivity and Changes in Bond Price Sensitivity and Changes in Time to Maturity for Various Changes in Time to Maturity for Various MaturitiesMaturities

• Bond Price and CouponBond Price and Coupon

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Bond Prices And The Passage Of Time

• Price and Value Change Price and Value Change with the Passage of Timewith the Passage of Time

• PremiumPremium

• ParPar

• DiscountDiscount

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Bond Prices And Changes In Yield To Maturity

• Prices are Inversely Related to Prices are Inversely Related to Yield to MaturityYield to Maturity

• Price-Yield Relationship is Price-Yield Relationship is ConvexConvex

5® 1999 South-Western College Publishing

Bond Price Sensitivity And Maturity

• Different for Various Bond MaturitiesDifferent for Various Bond Maturities

• The Longer the MaturityThe Longer the Maturity

– The more sensitive the bond’s price to The more sensitive the bond’s price to change in the yield to maturitychange in the yield to maturity

® 1999 South-Western College Publishing

Does a 1-year or 10-year 10% bond have more interest rate (or price) risk?

kd 1-year Change 10-year Change

5% $1,048 $1,386

10% 1,000+4.8%

-4.4%1,000

+38.6%

-25.1%15% 956 749

Interest rate risk: Rising kd causes bond’s price to fall.

® 1999 South-Western College Publishing

0

500

1,000

1,500

0% 5% 10% 15%

1-year

10-year

kd

Value

.

..

. ..

8® 1999 South-Western College Publishing

Changes In Bond Price Sensitivity And Changes In

Time To Maturity For Various Maturities

• Increases at a Decreasing RateIncreases at a Decreasing Rate

– With the length to maturityWith the length to maturity

• 5 and 10-Year Bond5 and 10-Year Bond

• 25 and 30-Year Bond25 and 30-Year Bond

® 1999 South-Western College Publishing

M

Bond Value ($)

Years remaining to Maturity

1,372

1,211

1,000

837

775

30 25 20 15 10 5 0

kd = 7%.

kd = 13%.

kd = 10%.

10® 1999 South-Western College Publishing

Bond Price And Coupon

• Linear RelationshipLinear Relationship

• Drift Towards Par ValueDrift Towards Par Value

– With just the passage of timeWith just the passage of time

• The Higher the Coupon RateThe Higher the Coupon Rate

– The less sensitive the bond to changes in The less sensitive the bond to changes in yield to maturityyield to maturity

11® 1999 South-Western College Publishing

Is There A Way To Reduce Or Eliminate The Interest-Rate

Risk?• DurationDuration

– Holding periodHolding period

– Price effectPrice effect

– Reinvestment effectReinvestment effect– Calculating duration Calculating duration next slidenext slide

– Measures the sensitivityMeasures the sensitivity

– Used by investment analystsUsed by investment analysts

12® 1999 South-Western College Publishing

Calculating Duration

D = tWt

T

t = 1

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Duration Principles• DurationDuration

– Declines over timeDeclines over time– Inversely related to yield to maturityInversely related to yield to maturity– Directly related to maturityDirectly related to maturity– Inversely related to level of coupon paymentInversely related to level of coupon payment– Bond portfolioBond portfolio

• More Than One FactorMore Than One Factor– Relationship becomes more complexRelationship becomes more complex

14® 1999 South-Western College Publishing

How Do You Measure The Curvature Of A Bond’s Price-

Yield Relationship?

• ConvexityConvexity

– Basic principlesBasic principles

• Inversely related to yield to maturityInversely related to yield to maturity

• Inversely related to the couponInversely related to the coupon

• Positively related to durationPositively related to duration

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Immunization

Income

Price

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Income Immunization

• StrategiesStrategies

– Cash matchingCash matching

– Duration matchingDuration matching

– Horizon matchingHorizon matching

• Protects Future Income NeedsProtects Future Income Needs

• Ignores Current Market ValueIgnores Current Market Value

17® 1999 South-Western College Publishing

Price Immunization

• Protects Current Market ValueProtects Current Market Value

• Uses ConvexityUses Convexity

• The Greater the ConvexityThe Greater the Convexity

– The greater the gain from changes in The greater the gain from changes in interest ratesinterest rates

18® 1999 South-Western College Publishing

Passive Bond Management

• Mimic a Bond IndexMimic a Bond Index

• Is the Bond Market Efficient?Is the Bond Market Efficient?

– Yes Yes Passive managementPassive management

– No No Active managementActive management

• Refining Immunization TechniquesRefining Immunization Techniques

19® 1999 South-Western College Publishing

Active Bond Management• Contingent ImmunizationContingent Immunization

– Timing strategiesTiming strategies– Duration mismatchesDuration mismatches– Floor on active manager’s performanceFloor on active manager’s performance

• Popular Active Bond Management StrategiesPopular Active Bond Management Strategies– Substitution swapSubstitution swap– Pure Yield pickup swapPure Yield pickup swap– Intermarket spread swapIntermarket spread swap– Rate anticipation swapRate anticipation swap