1. Bond Portfolio Management Strategies
Active, Passive, and Immunization Strategies

2. Alternative Bond Portfolio Strategies
1. Passive portfolio strategies
2. Active management strategies
3. Matched-funding techniques
4. Contingent procedure (structured active management)

3. 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

4. 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

5. 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

6. 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

7. Duration 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

8. 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

9. Duration and Price Volatility
An adjusted measure of duration can be used to approximate the price volatility of a bond
Where:
m = number of payments a year
YTM = nominal YTM

10. 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
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

11. Duration in Years for Bonds Yielding 6% with Different Terms

12. 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

13. 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

14. 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

15. 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

16. Active Management Strategies
Potential sources of return from fixed income port:
Coupon income
Capital gain
Reinvestment income
Factors affecting these sources:
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

17. 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:
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

18. Active Management Strategies
Yield Curve strategies
Positioning portfolio to capitalize on expected changes in shape of Treasury YC
Parallel shift
Nonparallel shift
Bullet strategies
Barbell strategies

19. Active Management Strategies
Ladder strategies
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

20. High-Yield Bonds
Spread in yield between safe and junk changes over time

21. Active Management Strategies
Bond swaps
Pure yield pickup swap
Substitution swap
Intermarket spread swap
Tax swap

22. Matched Funding Strategies
Classical immunization
Interest rate risk
Investment horizon
Maturity strategy
Duration strategy
Price risk
Reinvestment risk

23. Maturity Strategy vs. Duration Strategy
Year CF Reinv. end val CF end val

24. Immunization Parallel shift in YC Net worth immunization
Banks, thrifts
Gap management
ARMs

25. Immunization Target date immunization
Pension funds, insurance companies
Immunize future value of fund at some target date to protect against rate changes

26. 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

27. Matched-Funding Techniques
Dedicated portfolio
Exact cash match
Optimal match with reinvestment
Horizon matching
Combination of immunization strategy and dedicated portfolio

28. 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