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The basics of bond immunization

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Objective Explain the concept of immunization and understand how it relates to bond portfolio management

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Outline Definition Exemplification Discussion of immunization

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Immunization Technique that allows a bond investor to meet a future promised payment with a minimal risk

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Exemplification A manager has to pay $ 1,000,000 in two years. There are currently two bonds available for investment.

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Exemplification A manager has to pay $ 1,000,000 in two years. There are currently two bonds available for investment.

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Exemplification A manager has to pay $ 1,000,000 in two years. There are currently two bonds available for investment.

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Exemplification A manager has to pay $ 1,000,000 in two years. There are currently two bonds available for investment.

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Exemplification A manager has to pay $ 1,000,000 in two years. There are currently two bonds available for investment.

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Exemplification A manager has to pay $ 1,000,000 in two years. There are currently two bonds available for investment.

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Exemplification (cont’d) Since the discount rate is 10%, the present value of $ 1,000,000 is $826,446.3. The manager has to invest $ 826,446.3 at 10% in order to produce $ 1,000,000 two years from now.

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Alternatives: Strategy I Buy $ 826,446.3 worth of bonds A. Next year, roll-over the proceeds into a new one-year bond issue. Disadvantage Interest rates could decline one year from now A one percentage point decrease in interest rates in one year results in only [850 x $ 1,070 x (1.09)] = $991,335

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Alternatives: Strategy II Buy $ 826,446.3 worth of bonds B Reinvest the coupon and sell the bonds in two yearsDisadvantage Interest rates could increase at the time the manager has to liquidate the position. A one percentage point increase in interest rates just days before our manager liquidates the position will result in [ 870 x ($ 88 + $ 80 +$ 972.97)] = $ 992, 646.5

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Alternatives: Strategy III Construct a portfolio consisting of both bonds that has a duration of exactly 2 years (Immunization). Put 43.82% in A (372 bonds), and 56.18% (489 bonds) in B

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Immunized portfolio

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Comments When interest rates fall to 9%: the price of bond B rises the FV of reinvested proceeds falls. When interests rates rise to 11%: the price of bond B falls the FV of reinvested proceeds rises

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The terminal value of the portfolio is not exactly $1,000,0000. Why? A. Yield changes trigger changes in portfolio duration. REBALANCING When duration changes the portfolio ceases to be perfectly immunized, and needs REBALANCING. B. Rounding up errors.

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Problems with immunization It assumes that all shifts in the yield curve all parallel The portfolio is in need of permanent rebalancing There are many combinations of bonds that work out to the desired average duration, hence, it is difficult to choose the best combination

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1 Convexity Correction Straight line is what we get with %ΔPB formula (under- estimates when yield drops, over-estimates when rises) Greater a bond’s convexity,

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