Bond Portfolio Management Strategies

Active, Passive, and Immunization Strategies

Alternative Bond Portfolio Strategies

1. Passive portfolio strategies

2. Active management strategies

3. Matched-funding techniques

4. Contingent procedure (structured active management)

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

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

Determinants of Price Volatility

1. Bond prices move inversely to bond yields (interest rates)2. For a given change in yields, longer maturity bonds post

larger price changes, thus bond price volatility is directly related to maturity

3. Price volatility increases at a diminishing rate as term to maturity increases

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

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

Duration

Since price volatility of a bond varies inversely with its coupon and directly with its term to maturity, it is necessary to determine the best combination of these two variables to achieve your objective

A composite measure considering both coupon and maturity would be beneficial

Duration

price

)(

)1(

)1(

)(

1

1

1

n

tt

n

tt

t

n

tt

t CPVt

i

Ci

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

Characteristics of Duration

Duration of a bond with coupons is always less than its term to maturity because duration gives weight to these interim payments A zero-coupon bond’s duration equals its maturity

An inverse relation between duration and coupon A positive relation between term to maturity and

duration, but duration increases at a decreasing rate with maturity

An inverse relation between YTM and duration Sinking funds and call provisions can have a dramatic

effect on a bond’s duration

Duration and Price Volatility

An adjusted measure of duration can be used to approximate the price volatility of a bond

m

YTM1

durationMacaulay duration modified

Where:

m = number of payments a year

YTM = nominal YTM

Duration and Price Volatility

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

iDP

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

Duration in Years for Bonds Yielding 6% with Different Terms

COUPON RATES

Years toMaturity 0.02 0.04 0.06 0.08

1 0.995 0.990 0.985 0.9815 4.756 4.558 4.393 4.254

10 8.891 8.169 7.662 7.28620 14.981 12.980 11.904 11.23250 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 Naïve and Optimal Strategies," Journal of Business 44, no. 4

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

Duration and Price Volatility

Longest duration security gives maximum price variation

Active manager wants to adjust portfolio duration to take advantage of anticipated yield changes 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

Convexity

Modified duration approximates price change for small changes in yield

Accuracy of approximation gets worse as size of yield change increases WHY? Modified duration assumes price-yield relationship of

bond is linear when in actuality it is convex. Result – MD overestimates price declines and

underestimates price increases So convexity adjustment should be made to estimate of

% price change using MD

Convexity

Convexity of bonds also affects rate at which prices 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 increase

is faster Result – convexity is an attractive feature of a bond in

some cases Positive convexity Negative convexity

Convexity

The measure of the curvature of the price-yield relationship

Second derivative of the price function with respect to yield

Tells us how much the price-yield curve deviates from the linear approximation we get using MD

Active Management Strategies

Potential sources of return from fixed income port:

1. Coupon income2. Capital gain3. Reinvestment income

Factors affecting these sources:1. Changes in level of interest rates2. Changes in shape of yield curve3. Changes in spreads among sectors4. Changes in risk premium for one type of bond

Active Management Strategies

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

Active Management Strategies

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

Active Management Strategies

3. Ladder strategies

4. Riding the YC Strategies result in different performance

depending on size and type of shift – hard to generalize which gives optimal strategy

Valuation analysis Identification of misvalued securities

Credit analysis

High-Yield Bonds

Spread in yield between safe and junk changes over timeAve. Cumul. Default Rates Corp Bonds

Years Since IssueRatings 5 10AAA 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%

Active Management Strategies

Bond swaps Pure yield pickup swap Substitution swap Intermarket spread swap Tax swap

Matched Funding Strategies

Classical immunization Interest rate risk

Investment horizon Maturity strategy Duration strategy

Price risk

Reinvestment risk

Maturity Strategy vs. Duration Strategy

Year CF Reinv. end val CF end val1 80 .08 80.00 80 80.002 80 .08 166.40 80 166.403 80 .08 259.71 80 259.714 80 .08 360.49 80 360.495 80 .06 462.12 80 462.126 80 .06 596.85 80 596.857 80 .06 684.04 80 684.048 1080 .06 1805.08 1120.64 1845.72

Immunization

Parallel shift in YC Net worth immunization

Banks, thrifts Gap management ARMs

Immunization

Target date immunization Pension funds, insurance companies Immunize future value of fund at some target

date to protect against rate changes

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

Matched-Funding Techniques

Dedicated portfolio Exact cash match Optimal match with reinvestment

Horizon matching Combination of immunization strategy and

dedicated portfolio

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