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
n
Ct (t )

t
t 1 (1  i )
D n

Ct

t
t 1 (1  i )
n
 t  PV (C )
t
t 1
price
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
Macaulay duration
modified duration 
YTM
1
m
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
P
100   Dmod  i
P
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 to
Maturity
1
5
10
20
50
0.02
0.04
0.06
0.08
0.995
4.756
8.891
14.981
19.452
0.990
4.558
8.169
12.980
17.129
0.985
4.393
7.662
11.904
16.273
0.981
4.254
7.286
11.232
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 priceyield 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.
2.
3.

Coupon income
Capital gain
Reinvestment income
Factors affecting these sources:
1.
2.
3.
4.
Changes in level of interest rates
Changes in shape of yield curve
Changes in spreads among sectors
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.
2.
Swapping or exchanging bonds in portfolio for new bonds
to achieve target duration (rate anticipation swaps)
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


1.
2.
Parallel shift
Nonparallel shift
Bullet strategies
Barbell strategies
Active Management Strategies
3.
4.


Valuation analysis


Ladder strategies
Riding the YC
Strategies result in different performance
depending on size and type of shift – hard to
generalize which gives optimal strategy
Identification of misvalued securities
Credit analysis
High-Yield Bonds

Spread in yield between safe and junk
changes over time
Ave . Cumul. De fa ult Ra te s Corp Bonds
Ye a rs Since Issue
Ra tings
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%
Active Management Strategies

Bond swaps




Pure yield pickup swap
Substitution swap
Intermarket spread swap
Tax swap
Matched Funding Strategies

Classical immunization

Price risk
Interest rate risk
Reinvestment risk



Investment horizon
Maturity strategy
Duration strategy
Maturity Strategy vs. Duration
Strategy
Year CF
1
80
2
80
3
80
4
80
5
80
6
80
7
80
8
1080
Reinv. end val CF end val
.08
80.00
80
80.00
.08 166.40
80
166.40
.08 259.71
80
259.71
.08 360.49
80
360.49
.06 462.12
80
462.12
.06 596.85
80
596.85
.06 684.04
80
684.04
.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