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 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 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 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

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: 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

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

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

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

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

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 val 1 80 .08 80.00 80 80.00 2 80 .08 166.40 80 166.40 3 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

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