Bond Mgmt Strategy

7/29/2019 Bond Mgmt Strategy

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Bond Portfolio Management

Strategies

Active, Passive, and

Immunization Strategies


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Alternative Bond Portfolio

Strategies

1. Passive portfolio strategies

2. Active management strategies

3. Matched-funding techniques

4. Contingent procedure (structured active

management)


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Passive Portfolio Strategies

Buy and hold

Can be modified by trading into more

desirable positions Indexing

Match performance of a selected bond

index Performance analysis involves

examining tracking error


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Passive Portfolio Strategies

Advantages to using indexing strategy

Historical performance of active managers

Reduced fees Indexing methodologies

Full participation

Stratified sampling (cellular approach) Optimization approach

Variance minimization


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Determinants of Price Volatility

1. Bond prices move inversely to bond yields (interestrates)

2. For a given change in yields, longer maturity bonds post

larger price changes, thus bond price volatility is directlyrelated to maturity

3. Price volatility increases at a diminishing rate as term tomaturity increases

4. Price movements resulting from equal absoluteincreases or decreases in yield are not symmetrical

5. Higher coupon issues show smaller percentage pricefluctuation for a given change in yield, thus bond pricevolatility is inversely related to coupon


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Duration

Since price volatility of a bond varies

inversely with its coupon and directly with

its term to maturity, it is necessary todetermine the best combination of these

two variables to achieve your objective

A composite measure considering bothcoupon and maturity would be beneficial


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Duration

price

)(

)1(

)1(

)(

1

1

1

n

t

t

n

t

t

t

n

t

t

tCPVt

i

C

i

tC

D

Developed by Frederick R. Macaulay, 1938

Where:

t= time period in which the coupon or principal payment occurs

Ct= interest or principal payment that occurs in period t

i = yield to maturity on the bond


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Characteristics of Duration

Duration of a bond with coupons is always less than itsterm to maturity because duration gives weight to theseinterim payments

A zero-coupon bonds duration equals its maturity An inverse relation between duration and coupon

A positive relation between term to maturity andduration, but duration increases at a decreasing rate with

maturity An inverse relation between YTM and duration

Sinking funds and call provisions can have a dramaticeffect on a bonds duration


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Duration and Price Volatility

An adjusted measure of duration can be

used to approximate the price volatility of

a bond

m

YTM1

durationMacaulaydurationmodified

Where:

m = number of payments a year

YTM = nominal YTM


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Bond price movements will vary proportionally with

modified duration for small changes in yields

An estimate of the percentage change in bond prices

equals the change in yield time modified duration

iD

P

P

mod100

Where:

P= change in price for the bond

P= beginning price for the bond

Dmod = the modified duration of the bond

i = yield change in basis points divided by 100


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Duration in Years for Bonds

Yielding 6% with Different Terms

COUPON RATES

Years to

Maturity 0.02 0.04 0.06 0.08

1 0.995 0.990 0.985 0.981

5 4.756 4.558 4.393 4.254

10 8.891 8.169 7.662 7.286

20 14.981 12.980 11.904 11.232

50 19.452 17.129 16.273 15.829

Source: L. Fisher and R. L. Weil, "Coping with the Risk of Interest Rate Fluctuations:

Returns to Bondholders from Nave and Optimal Strategies," Journal of Business 44,

(October 1971): 418. Copyright 1971, University of Chicago Press.


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Longest duration security gives maximum pricevariation

Active manager wants to adjust portfolioduration to take advantage of anticipated yieldchanges Expect rate declines (parallel shift in YC), increase

average modified duration to experience maximum

price volatility Expect rate increases (parallel shift in YC), decrease

average modified duration to minimize price decline


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Convexity

Modified duration approximates price change forsmall changes in yield

Accuracy of approximation gets worse as size ofyield change increases WHY?

Modified duration assumes price-yield relationship ofbond is linear when in actuality it is convex.

Result MD overestimates price declines andunderestimates price increases

So convexity adjustment should be made to estimateof % price change using MD


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Convexity

Convexity of bonds also affects rate at whichprices change when yields change

Not symmetrical change As yields increase, the rate at which prices fall

becomes slower

As yields decrease, the rate at which prices increaseis faster

Result convexity is an attractive feature of a bond insome cases Positive convexity

Negative convexity


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Convexity

The measure of the curvature of the price-

yield relationship

Second derivative of the price functionwith respect to yield

Tells us how much the price-yield curve

deviates from the linear approximation weget using MD


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Active Management Strategies

Potential sources of return from fixed incomeport:

1. Coupon income

2. Capital gain

3. Reinvestment income

Factors affecting these sources:1. Changes in level of interest rates

2. Changes in shape of yield curve

3. Changes in spreads among sectors

4. Changes in risk premium for one type of bond


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Interest rate expectations strategy

Need to be able to accurately forecast future level

of interest rates

Use duration to change sensitivity of portfolio to

future rate changes

Alter portfolio duration by:

1. Swapping or exchanging bonds in portfolio for new bonds

to achieve target duration (rate anticipation swaps)

2. Interest rate futures buying futures increases duration

and selling futures decreases duration


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Yield Curve strategies

Positioning portfolio to capitalize on

expected changes in shape of Treasury YC Parallel shift

Nonparallel shift

1. Bullet strategies

2. Barbell strategies


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3. Ladder strategies

4. Riding the YC

Strategies result in different performancedepending on size and type of shift hard to

generalize which gives optimal strategy

Valuation analysis Identification of misvalued securities

Credit analysis


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High-Yield Bonds

Spread in yield between safe and junk

changes over time

Ave. Cumul. Default Rates Corp BondsYears Since Issue

Ratings 5 10

AAA 0.08% 0.08%

AA 1.20% 1.30%

A 0.53% 0.98%

BBB 2.39% 3.66%

BB 10.79% 15.21%

B 23.71% 35.91%

CCC 45.63% 57.39%


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Bond swaps

Pure yield pickup swap

Substitution swap

Intermarket spread swap

Tax swap


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Matched Funding Strategies

Classical immunization

Interest rate risk

Investment horizon

Maturity strategy

Duration strategy

Price risk

Reinvestment risk


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Maturity Strategy vs. Duration

Strategy

Year CF Reinv. end val CF end val

1 80 .08 80.00 80 80.00

2 80 .08 166.40 80 166.403 80 .08 259.71 80 259.71

4 80 .08 360.49 80 360.49

5 80 .06 462.12 80 462.12

6 80 .06 596.85 80 596.85

7 80 .06 684.04 80 684.04

8 1080 .06 1805.08 1120.64 1845.72


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Immunization

Parallel shift in YC

Net worth immunization

Banks, thrifts

Gap management

ARMs


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Immunization

Target date immunization

Pension funds, insurance companies

Immunize future value of fund at some targetdate to protect against rate changes


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Immunization Strategies

Difficulties in maintaining good protection

Rebalancing is necessary as duration

declines more slowly than term to maturity MD changes when market interest rates

change

YC shifts


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Matched-Funding Techniques

Dedicated portfolio

Exact cash match

Optimal match with reinvestment

Horizon matching

Combination of immunization strategy and

dedicated portfolio


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Contingent Immunization

Structured Active Management

Manager follows active strategy to point

where trigger point is reached Switch made to passive strategy to meet

minimum acceptable return

Cushion spread

Safety margin

Documents

Bond Mgmt Strategy