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