2Types of Bond Strategies Active StrategiesPassive StrategiesHybrid Strategies
3Types of Bond Strategies Active Strategies: Strategies that involve taking active bond positions with the primary objective of obtaining an abnormal return.Active strategies are typically speculative.Types:Interest Rate Anticipation StrategiesCredit StrategiesFundamental Valuation Strategies
4Types of Bond Strategies Passive Strategies: Strategies in which no change in the position is necessary once the bonds are selected.Types:IndexingCash-Flow MatchingClassical Immunization
5Types of Bond Strategies Hybrid Strategies: Strategies that have both active and passive features.Immunization with RebalancingContingent Immunization
6Active: Interest Rate Anticipation Strategies Types of Interest-Rate Anticipation Strategies:Rate-Anticipation StrategiesStrategies Based on Yield Curve Shifts
7Rate-Anticipation Strategies Rate-Anticipation Strategies are active strategies of selecting bonds or bond portfolios with specific durations based on interest rate expectations.Rate-Anticipation Swap is a rate-anticipation strategy that involves simultaneously selling and buying bonds with different durations.
8Rate-Anticipation Swap Rate-Anticipation Swap for bond portfolio manager when interest rates are expected to decrease across all maturitiesStrategy: Lengthening the portfolio’s duration: Manager could sell her lower duration bonds and buy higher duration ones.By doing this, the portfolio’s value would be more sensitive to interest rate changes and as a result would subject the manager to a higher return-risk position, providing greater upside gains in value if rates decrease but also greater losses in value if rates decrease.
9Rate-Anticipation Swap Rate-Anticipation Swap for bond portfolio manager when interest rates are expected to increase across all maturitiesStrategy: Shorten the portfolio’s duration: Manager could sell her higher duration bonds and buy lower duration ones.Defensive Strategy: Objective is to preserve the value of a bond fund.
10Rate-Anticipation Swap: Cushion Bond One way to shorten the fund’s duration is for the manager to sell high-duration bonds (possibly option-free) and then buy cushion bonds.A cushion bond is a callable bond with a coupon that is above the current market rate.
11Rate-Anticipation Swap: Cushion Bond Cushion bond has the following features:High coupon yieldWith its embedded call option, a market price that is lower than a comparable noncallable bond.Note: The interest rate swap of option-free bonds for cushion bonds provides some value preservation.
12Rate-Anticipation Swap: Cushion Bond Example:Suppose a bond manager had a fund consisting of 10-year, 10% option-free bonds valued at per $100 par to yield 8% and there were comparable 10-year, 12% coupon bonds callable at 110 that were trading in the market at a price close to their call price.If the manager expected rates to increase, he could cushion the negative price impact on the fund’s value by:Selling option-free bondsBuying higher coupon, callable bonds – cushion bonds
13Rate-Anticipation Swap: Cushion Bond Example:The swap of existing bonds for the cushion bonds provides:An immediate gain in income = 3.42A higher coupon income in the future: 12% instead of 10%
14Rate-Anticipation Swap: Cushion Bond NoteA callable bond has a lower duration than a noncallable one with the same maturity and coupon rate.The 10-year cushion bond with it call feature and higher coupon rate has a relatively lower duration than the 10-year option-free bond.Thus, the swap of cushion bonds for option-free bonds in this example represents a switch of longer duration bonds for shorter ones – a rate-anticipation swap.
15Yield Curve Shifts and Strategies Yield Curve Strategies: Some rate-anticipation strategies are based on forecasting the type of yield curve shift and then implementing an appropriate strategy to profit from the forecast.
16Yield Curve Shifts and Strategies Three types of yield curve shifts occur with some regularity:Parallel ShiftsShifts with TwistsShifts with Humpedness
17Yield Curve Shifts: Parallel Parallel Shifts: Rates on all maturities change by the same number of basis points.
18Yield Curve Shifts: Twist Shifts with a Twist: A twist is a non-parallel shift, with either a flattening or steepening of the yield curve.Flattening: The spread between long-term and short-term rates decreases.Steepening: The spread between long-term and short-term rates increases.
19Yield Curve Shifts: Twist Shifts with a Twist:Flattening:Steepening:
20Yield Curve Shifts: Humpedness Shifts with Humpedness: A shift with humpedness is a non-parallel shift in which short-term and long-term rates change by greater magnitudes than intermediate rates.Positive Butterfly: There is an increase in both short and long-term rates relative to intermediate rates.Negative Butterfly: There is a decrease in both short and long-term rates relative to intermediate rates.
21Yield Curve Shifts: Humpedness Positive Butterfly: ST and LT rates change more than intermediate:Negative Butterfly: Intermediate rates change more than ST and LT:
22Yield Curve Shift Strategies Yield Curve StrategiesThe bullet strategy is formed by constructing a portfolio concentrated in one maturity area.The barbell strategy is formed with investments concentrated in both short-term and long-term bonds.The ladder strategy is formed with equally allocated investments in each maturity group.
24Yield Curve Shift Strategies Strategies Based on ExpectationsBullet strategy could be formed based on an expectation of adownward shift in the yield curve with a twist such that long-termrates were expected to decrease more than short-term.If investors expected a simple downward parallel shift in the yieldcurve, a bullet strategy with longer duration bonds would yieldgreater returns than an investment strategy in intermediate orshort-term bonds if the expectation turns out to be correct.The barbell strategy could be profitable for an investor who isforecasting an upward negative butterfly yield curve shift.
25Yield Curve Strategies: Total Return Analysis The correct yield curve strategy depends on the forecast.One approach to use in identifying the appropriate strategy is Total Return Analysis.Total Return Analysis involves determining the possible returns from different yield curve strategies given different yield curve shifts.
26Total Return AnalysisTotal Return Analysis Example (Ch. 8, Problem 3):Consider three bonds:Assume yield curve is currently flat at 6%.Consider two strategies:Bond A: 5-year, 6% bond selling at par, with duration of 4.46.Bond B: 11-year, 6% bond selling at par, with duration of 8.36.Bond C: 20-year, 6% bond selling at par, with a duration of 12.161. Barbell: Invest 50% in A and 50% in C.2. Bullet: 100% in Bond B
27Total Return AnalysisConsider two types of yield curve shifts one year later:Parallel shifts ranging between -200 BP and BP.Yield curve shifts characterized by a flattening where for each change in Bond B (intermediate bond), Bond A increases 25 BP more and Bond C decreases by 25 BP less:∆yA = ∆yB + 25BP and ∆yC = ∆yB - 25BP
28Total Return Analysis: Parallel Shifts Bond Return = (Value-100) + 6Bullet Return = .5(Bond Return for A) + .5(Bond Return for C)Note: The bullet portfolio has a duration of 8.31 (= (.5)(4.46) + (.5)(12.16)).This is approximately the same as the duration of Bond B.
29Total Return Analysis: Parallel Shifts Observations:For different parallel shifts in the yield curve, there is not much difference in the returns on the bullet portfolio and the barbell. This is due to both having the same duration.If one were expecting a significant downward shift in the yield curve, Bond C with the largest duration would give you the greatest gains.If one were expecting a significant upward shift in the yield curve, Bond A with the lowest duration would give you the minimum loss.Comment: The returns are consistent with duration as a measure of a bond’s price sensitivity to interest rate changes.
30Total Return Analysis: Yield Curve Shifts Characterized by a Flattening ∆yA = ∆yB + 25BP and ∆yC = ∆yB - 25BP
31Total Return Analysis: Yield Curve Shifts Characterized by a Flattening Observation: In contrast to parallel shifts, there are differences between the barbell and bullet portfolios when the yield curve shift has a twist, even though they have the same durations.
32Active Credit Strategies Two active credit investment strategies of note are quality swaps and credit analysis strategies:A quality swap is a strategy of moving from one quality groupto another in anticipation of a change in economic conditions.A credit analysis strategy involves a credit analysis of corporate,municipal, or foreign bonds in order to identify potential changesin default risk. This information is then used to identify bonds toinclude or exclude in a bond portfolio or bond investment strategy.
33Quality SwapsQuality Swap: Strategy of going long and short in bonds with high or low quality rating based on the expectation of a change in economic states.Strategy:
34Quality SwapsQuality swaps often involve a sector rotation in which more funds are allocated to a specific quality sector in anticipation of a price change.ExampleSuppose a bond fund manager expected a recession accompanied by a flight to safety in which the demand for higher quality bonds would increase and the demand for lower quality ones would decrease.To profit from this expectation, the manager could change the allocation of her bond fund by selling some of her low quality ones and buying more high quality bonds.
35Quality SwapsQuality swaps can also be constructed to profit from anticipated changes in yield spreads between quality sectors.If the economy were at the trough of a recession and wasexpected to grow in the future, speculators or a hedge fundmight anticipate a narrowing in the spread between lowerand higher quality bonds.To exploit this, they could form a quality swap by taking along position in lower quality bonds and a short position inhigher quality bonds with similar durations.Whether rates increase or decrease, speculators would still profit from these positions, provided the quality spread narrows.
36Quality SwapsIf rates decrease but the quality spread narrows, then the percentage increase in price for the lower quality bonds would be greater than the percentage increase for the higher quality bonds.In this case, the capital gain from the long position in lower quality bonds would dominate the capital loss from the short position in the higher quality bonds.If rates increase but the quality spread narrows, then the percentage decrease in the price of lower quality bonds would be less than the percentage decrease in the price of higher quality bonds.In this case, the capital gain from the short position in the higher quality bonds would dominate the capital loss from the long position in the lower quality bonds.
37Credit Analysis Strategy If changes in quality ratings of a bond can be projected prior to an upgrade or downgrade announcement, bond investors can realized gains by buying bonds they project will be upgraded, and they can avoid losses by selling or not buying bonds they project will be downgraded.The objective of a credit analysis strategy is to determine expected changes in default risk.
38Credit AnalysisOver the last two decades, the spread between low investment-grade bonds and Treasuries has ranged from 150 basis points (BP) to over 1,000 BP.At the same time, though, the default risk on such bonds has been relatively high.
39Credit Analysis: Douglass and Lucas Study In their empirical study of bonds, Douglass and Lucas found:For B-rated bonds, the 5-year cumulative default rate was approximately 24% and the 10-year cumulative default rate was approximately 36%.For CCC-rated bonds, the 5-year cumulative default rates was approximately 46% and the 10-year cumulative default rate was 57%.In contrast, Douglass and Lucas found:The 5-year and 10-year cumulative default rates for A-rated bonds were only .53% and .98% and for BBB-rated, the rates were 2.4% and 3.67%.
40Credit Analysis: Douglass and Lucas Study The Douglass and Lucas study, as well as several other studies on cumulative default rates, shows there is high degree of default risk associated with low-quality bonds.The study also suggests, though, that with astute credit analysis there are significant gains possible by being able to forecast upgrades and significant losses that can avoided by projecting downgrades.
41Credit Analysis Strategy The strategy of many managers of high-yield bond funds isto develop effective credit analysis models so that they canidentify bonds with high yields and high probabilities ofupgrades to include in their portfolios, as well as identifybonds with high probabilities of downgrades to exclude fromtheir fund.Credit analysis can be done through basic fundamentalanalysis of the bond issuer and the indenture and withstatistical-based models, such as a multiple discriminant model.
42Fundamental Credit Analysis Many large institutional investors and banks have their own credit analysis departments to evaluate bond issues in order to determine the abilities of companies, municipalities, and foreign issuers to meet their contractual obligations, as well as to determine the possibility of changes in a bond’s quality ratings and therefore a change in its price.
43Fundamental Credit Analysis: Corporate Issues Industrial Analysis: Assessment of the growth rate of the industry, stage of industrial development, cyclically of the industry, degree of competition, industry and company trends, government regulations and labor costs and issues.
44Fundamental Credit Analysis: Corporate Issues 2. Fundamental Analysis: Comparison of the company’s financial ratios with other firms in the industry and with the averages for bonds based on their quality ratings.Ratios often used for analysis include: (1) interest coverage (EBIT/Interest), (2) leverage (long-term debt/total assets), and (3) cash flow (net income + depreciation + amortization + depletion + deferred taxes) as a proportion of total debt (cash flow/debt), and (4) return on equity.
45Fundamental Credit Analysis: Corporate Issues 3. Asset and Liability Analysis: Determination of the market values of assets and liabilities, age and condition of plants, working capital, intangible assets and liabilities, and foreign currency exposure.4. Indenture Analysis: Analysis of protective covenants, including a comparison of covenants with the industry norms.
46Fundamental Credit Analysis: Corporate Issues FINANCIAL RATIOS (%) BY RATING CLASSIFICATIONSRatingsInterest CoverageEBIT/InterestLeverage RatioL-T Debt/Total AssetsCash FlowOperating CF/L-T DebtAAAAAABBBBBB21.410.25.618.104.22.1689.718.928.840.750.262.253.827.922.214.171.124(1.7)Source: Standard and Poor’s, Global Sector Review, 1995.
47Fundamental Credit Analysis: Municipal Issues Debt burden: This analysis involves assessing the total debt burden of the municipal issuer.For GOs, debt burden should include determining the total debt outstanding, including moral obligation bonds, leases, and unfunded pension liabilities.For revenue bonds, debt burden should also focuses on relevant coverage ratios relating the debt on the revenue bond to user charges, earmarked revenue, lease rental, and the like.
48Fundamental Credit Analysis: Municipal Issues 2. Fiscal Soundness: The objective of this analysis is to determine the issuer’s ability to meet obligations.For example, for GOs, the areas of inquiry can include: What are the primary sources of revenue? Is the issuer dependent on any one particular source of revenue?For revenue bonds, relevant questions relate to the soundness of the project or operation being financed.
49Fundamental Credit Analysis: Municipal Issues 3. Overall Economic Climate: General economic analysis includes:Examining fundamentals such as growth rates for income, population, and property values.Determining the status of the largest property values and employers.
50Fundamental Credit Analysis: Municipal Issues 4. Red Flags: Some of the negative indicators suggesting greater credit risk are:Decreases in populationUnemployment increasesDecreased in the number of building permitsDeclines in property valuesLoss of large employersUse of debt reserves and declines in debt coverage ratiosFor revenue bonds, additional red flags could includeCost overruns on projectsSchedule delaysFrequent rate or rental increases
51Fundamental Credit Analysis: Foreign Issues The credit analysis of international bonds issued by corporations needs to take into account the same issues of any corporate bond.In addition, the analysis also needs to consider:Cross-border risk: risk due to changes in political, social, and economic conditions in countries where the bonds are issued or where the company is incorporated.
52Fundamental Credit Analysis: Foreign Issues In the case of sovereign foreign debt, especially the debt of emerging markets, analysis needs to also include:An examination of sovereign risk: The risk that the government is unable or unwilling (due to political changes) to service its debt.
53Fundamental Credit Analysis: Foreign Issues Some of the key areas of inquiry in a credit analysis of a sovereign or private debt issuers of debt from an emerging market country relate to the following fundamental issues:Size and diversification of the country’s exports.Countries that specialize in exporting only a few products may be more susceptible to recessions.Political stability: Strength of the legal system, amount of unemployment, and distribution of wealth.History of meeting debt obligations
54Fundamental Credit Analysis: Foreign Issues 4. Balance of payments ratios: Country’s total debt to export ratio.5. Economic factors: Inflation, growth in gross domestic product, interest rates, and unemployment.6. Susceptibility of the country’s economy and exports to changes in economic conditions in industrialized countries.
55Multiple Discriminant Analysis Multiple disciminant analysis is a statistical technique that can be used to forecast default or changes in credit ratings.When applied to credit analysis, the model estimates a bond’s credit score or index, S, to determine its overall credit quality.The score is based on a set of explanatory variable, Xi, and estimated weights or coefficients, ci, measuring the variables relative impact on the bond’s overall credit quality:
56Multiple Discriminant Analysis For corporate bonds, possible explanatory variables include:Interest coverage ratioLeverage ratioCapitalization levelProfitability (earnings before interest and taxes to total assets)Variability (variance of profitability ratio)
57Multiple Discriminant Analysis One way to apply multiple discriminant analysis is to compute and then rank the credit quality scores of a number of bonds.To do this, requires estimating the c coefficient (possibly using a cross-sectional regression techniques) and then determining the explanatory variables (X) for the companies.Given c and X values for a number of companies, each company’s current credit quality score S can be computed using the above equation.Once the scores are estimated, then the bonds can be ranked in the order of their scores to assess each bond’s relative default risk.
58Multiple Discriminant Analysis Discriminant analysis can also be used to forecast a change in default risk.In this case, the expected future financial ratios of each company are estimated and then used in the above equation to determine the company’s future score or expected change in score.
59Credit analysis is an important tool for managing high-yield funds. High-Yield Bond FundsCredit analysis is an important tool for managing high-yield funds.Successful funds have fund managers that are able to identify:Those low quality bonds that have the potential for being upgraded and therefore should be included in the fund, andthose bonds that are in jeopardy of being downgraded and therefore should be excluded.
60Chapter 11 FundsA special type of high-yield fund is the Chapter 11 Fund: A fund consisting of the bonds of bankrupt or distressed companies.Such bonds consist of issues of corporations who are going through a bankruptcy process or those that are in distressed, but have not yet filed.The general strategy is to buy bonds whose prices have plummeted as a result of a filing but where there is a good expectation that there will be a successful reorganization or possible asset sale that will lead in the future to an increase in the debt’s value or to the replacement of the debt with a more valuable claim.
61Chapter 11 FundsChapter 11 funds are sometimes set up as a hedge fund in which large investors buy, through the fund, a significant block of debt of a specific bankrupt company, giving them some control in the reorganization plan.The funds are also set up as so-called vulture funds that invest in the securities of a number of bankrupt firms.
62Fundamental Valuation Strategies The objective of fundamental bond analysis is the same as that of fundamental stock analysis.It involves determining a bond’s intrinsic value and then comparing that value with the bond’s market price.The active management of a bond portfolio using a fundamental strategy, in turn, involves buying bonds that are determined to be underpriced and selling or avoiding those determined to be overpriced.
63Fundamental Valuation Strategies A bond fundamentalist often tries to determine a bond’s intrinsic value by estimating the required rate for discounting the bond’s cash flows.This rate, R, depends on the current level of interest rates as measured by the risk-free rate, Rf, and the bond’s risk premiums: default risk premium (DRP), liquidity premium (LP), and option-adjusted spread (OAS):
64Fundamental Valuation Strategies Fundamentalists use various models to estimate the various spreads. These include:RegressionsMultiple discriminant analysisOption pricing models
65Yield Pickup Swaps Strategy: A variation of fundamental bond strategies is a yield pickup swap. In a yield pickup swap, investors or arbitrageurs try to find bonds that are identical, but for some reason are temporarily mispriced, trading at different yields.Strategy:When two identical bonds trade at different yields,abnormal return can be realized by going long inthe underpriced (higher yield) bond and short in theoverpriced (lower yield) bond, then closing the positionsonce the prices of the two bonds converge.
66Yield Pickup SwapsThe strategy underlying a yield pickup swap can be extended from comparing different bonds to comparing a bond with a portfolio of bonds constructed to have the same features.For example, suppose a portfolio consisting of an AAA quality,10-year, 10% coupon bond and an A quality, 5-year, 5% couponbond is constructed such that it has the same cash flows and featuresas say an AA quality, 7.5-year, 7.5% coupon bond.If an AA quality, 7.5-year, 7.5% coupon bond and the portfolio donot provide the same yield, then an arbitrageur or speculator couldform a yield pickup swap by taking opposite positions in the portfolioand the bond.A fundamentalist could also use this methodology for identifyingunderpriced bonds: buying all AA quality, 7.5-year, 7.5% couponbonds with yields exceeding the portfolio formed with those features.
67Other Swaps: Tax SwapIn a tax swap, an investor sells one bond and purchases another in order to take advantage of the tax laws.
68Other Swaps: Tax Swap Example: Suppose a bond investor purchased $10,000 worth of a particular bond and then sold it after rates decreased for $15,000, realizing a capital gain of $5,000 and also a capital gains tax liability.One way for the investor to negate the tax liability would be to offset the capital gain with a capital loss. If the investor were holding bonds with current capital losses of say $5,000, he could sell those to incur a capital loss to offset his gain.Except for the offset feature, though, the investor may not otherwise want to sell the bond. If this were the case, then the investor could execute a bond swap in which he sells the bond needed for creating a capital loss and then uses the proceeds to purchase a similar, though not identical, bond.Thus, the tax swap allows the investor to effectively hold the bond he wants, while still reducing his tax liability.
69Other Swaps: Tax Swap Note: For the capital loss to be tax deductible, the bond purchased in the tax swap cannot be identical to the bond sold; if it were, then the swap would represent a wash sale that would result in the IRS disallowing the deduction.In contrast to the IRS’s wash sales criterion on stocks, though, the wash sale criterion used for bonds does permit the purchase of comparable bonds that have only minor differences.
70Other Swaps: Tax SwapAnother type of tax swap involves switching between high and low coupon bonds to take advantage of different tax treatments applied to capital gains and income.This swap can be used if the tax rate on capital gains differs from the tax rate on income. If it does, then an investor might find it advantageous to swap a low coupon bond for a high coupon bond with the same duration.
71Other Swaps: Callable/Noncallable Swap During periods of high interest rates, the spread between the yields on callable and noncallable bonds is greater than during periods of relatively low interest rates.Accordingly, if investors expect rates to decrease in the future, causing the spread between callable and noncallable bonds to narrow, they could capitalize by forming a callable/noncallable bond swap: short in the callable bond and long in the noncallable one.To effectively apply this bond swap requires investors to not only forecast interest rate changes, but to also forecast changes in the spread.
72Passive StrategiesPassive Strategies: Strategies that once they are formed do not require active management or changes.
73Passive StrategiesThe objectives of passive management strategies can include:A simple buy-and-hold approach of investing in bonds with specific maturities, coupons, and quality ratings with the intent of holding the bonds to maturityForming portfolios with returns that mirror the returns on a bond indexConstructing portfolios that ensure there are sufficient funds to meet future liabilities.
74Passive Strategies Here we look at the following passive strategies: Bond IndexingCash-flow MatchingClassical Immunization
75Bond IndexingBond Indexing is constructing a bond portfolio whose returns over time replicate the returns of a bond index.Indexing is a passive strategy, often used by investment fund managers who believe that actively managed bond strategies do not outperform bond market indices.
76Bond IndexingThe first step in constructing a bond index fund is to select the appropriate index. Bond indices can beGeneral:Shearson-Lehman Aggregate IndexMerrill-Lynch Composite IndexSpecialized:Salomon Smith Barney’s Global Government Bond Index.Customized:Some investment companies offer their own customized index specifically designed to meet certain investment objectives.
77Composite and by ratings Bond Market IndexesIndexNo. of IssuesMaturitySizeSubindexesU.S. Investment Grades BondLehman Brothers AggregateMerrill Lynch CompositeSalomon Smith Barney Composite5000Over 1 yearOver $100MOver $50MGovernment, corporate, Government/corporate mortgage-backed, asset-backedGovernment, corporate, government/corporate mortgage-backed,Bond Investment Grades, Treasury/Agency, corporate, mortgagesU.S. High Yield bondFirst BostonLehman BrotherMerrill LynchSalomon Smith Barney423624735300All maturitiesOver 7 yearsOver $75MOver $25MComposite and by ratings
78Bond Market Indexes Index Number of Issues Maturity Size Subindexes Global Government BondLehman BrothersMerrill LynchJ.P. MorganSalomon Smith Barney8009735445525Over 1 yearOver $200MOver $100MOver $250MComposite and 13 countries in local currency and U.S.$Composite and 9 countries in local currency and U.S.$Composite and 11 countries in local currency and U.S.$Composite and 14 countries in local currency and U.S.$The Handbook of Fixed-Income Securities, editor F. Fabozzi, 6th edition, p. 158.
79Bond IndexingThe next step is to determine how to replicate the index's performance.One approach is to simply purchase all of the bonds comprising the index in the same proportion that they appear in the index. This is known as pure bond indexing or the full-replication approach.This approach would result in a perfect correlation between the bond fund and the index.However, with some indices consisting of as many as 5,000 bonds, the transaction costs involved in acquiring all of the bonds is very high.
80Bond IndexingAn alternative to selecting all bonds is to use only a sample.By using a smaller size portfolio, the transaction costs incurred in constructing the index fund would be smaller.However with fewer bonds, there may be less than perfect positive correlation between the index and the index fund.The difference between the returns on the index and the index fund are referred to as tracking errors.
81Bond IndexingWhen a sample approach is used, the index fund can be set up using an optimization approach to determine the allocation of each bond in the fund such that it minimizes the tracking error.
82Bond Indexing: Cell Matching Another approach is to use a cell matching strategy.A cell matching strategy involves decomposing the index into cells, with each cell defining a different mix of features of the index (duration, credit rating, sector, etc.).
83Bond Indexing: Cell Matching Example:Suppose we decompose a bond index into2 durations (D > 5, D < 5)2 sectors (Corporate, Municipal)2 quality ratings (AA, A)
84Bond Indexing: Cell Matching With these feature, eight cells can be formed:The index fund is constructed by selecting bonds to match each cell and then allocating funds to each type of bond based on each cell’s allocation.C1 = D < 5, AAA, CorpC2 = D < 5, AAA, MuniC3 = D < 5, AA, CorpC4 = D < 5, AA, MuniC5 = D > 5, AAA, CorpC6 = D > 5, AAA, MuniC7 = D > 5, AA, CorpC8 = D > 5, AA, Muni
85Bond Indexing: Cell Matching One cell matching approach is to base the cell identification on just two features such as the durations and sectors or the durations and quality ratings.
86Bond Indexing: Cell Matching Duration/sector index is formed by matching the amounts of the index’s durations that make up each of the various sectors.This requires estimating the duration for each sector comprising the index and determining each sector’s percentage of value to the index.
87Bond Indexing: Cell Matching Duration/quality index is formed by determining the percentages of value and average durations of each quality-rating group making up the index.
88Duration/Sector and Duration/Quality Cell Matching Percentage of ValueDurationTreasuryFederal AgencyMunicipalsCorporate IndustryCorporate UtilityCorporate ForeignSovereignAsset-Backed20%10%15%4.503.255.256.006.255.555.75100%Weighted Average = 5.29Quality SectorAAAAAABBBBBB60%5%5.355.655.30
89Bond Indexing: Enhanced Bond Indexing A variation of straight indexing is enhanced bond indexing. This approach allows for minor deviations of certain features and some active management in order to try attain a return better than the index.Usually the deviations are in quality ratings or sectors, and not in durations, and they are based on some active management strategy.Example: A fund indexed primarily to the Merrill-Lynch composite butwith more weight given to lower quality bonds based on an expectation ofan improving economy would be an enhanced index fund combiningindexing and sector rotation.
90Cash Flow MatchingA cash flow matching strategy involves constructing a bond portfolio with cash flows that match the outlays of the liabilities.Cash flow matching is also referred to as a dedicated portfolio strategy.
91Cash Flow Matching: Method One method that can be used for cash flow matching is to start with the final liability for time T and work backwards.
92Cash Flow Matching: Method For the last period, one would select a bond with a principal (FT) and coupon (CT) that matches the amount of that final liability (LT):To meet this liability, one could buyLT /(1+ CR0) of par value of bonds maturing in T periods.
93Cash Flow Matching: Method 2. To match the liability in period T-1, one would need to select bonds with a principal of FT-1 and coupon CT-1 (or coupon rate of CR1 = CT-1/ FT-1) that is equal to the projected liability in period T-1 (LT-1) less the coupon amount of CT from the T-period bonds selected:To meet this liability, one could buy (LT-1-CT)/(1+ CR1) of par value of bonds maturing in T-1 periods.
94Cash Flow Matching: Method 3. To match the liability in period T-2, one would need to select bonds with a principal of FT-2 and coupon CT-2 (or coupon rate of CR2 = CT-2/ FT-2) that is equal to the projected liability in period T-2 (LT-2) less the coupon amounts of CT and CT-1 from the T-period and T-1-period bonds selected:To meet this liability, one could buy(LT-2 – CT - CT-1)/(1+ CR2) of par value of bonds maturing in T-2 periods.
95Cash Flow Matching: Example Example: A simple cash-flow matching case is presented in the following exhibits.The example in the exhibits shows the matching of liabilities of $4M, $3M, and $1M in years 3, 2, and 1 with 3-year, 2-year, and 1-year bonds each paying 5% annual coupons and selling at par.Year123Liability$1M$3M$4M
96Cash Flow Matching: Example BondsCoupon RateParYieldMarketValueLiabilityYear3-Year2-year1-year5%100$4M$3M$1M321
97Cash Flow Matching: Example Cash-Flow Matching Strategy:The $4M liability at the end of year 3 is matched by buying $3,809,524 worth of three-year bonds: $3,809,524 = $4,000,000/1.05.The $3M liability at the end of year 2 is matched by buying $2,675,737 of 2-year bonds: $2,675,737 = ($3,000,000 – (.05)($3,809,524))/1.05.The $1M liability at the end of year 1 is matched by buying $643,559 of 1-year bonds: $643,559 = ($1,000,000 – (.05)($3,809,524) – (.05)($2,675,737))/1.05
98Cash Flow Matching: Example 123456YearTotal Bond ValuesCoupon IncomeMaturing PrincipalLiabilityEnding Balance(3) + (4) – (5)$7,128,820$6,485,261$3,809,524$356,441$324,263$190,476$643,559$2,675,737$1,000,000$3,000,000$4,000,000
99Cash Flow Matching: Features With cash-flow matching the basic goal is to construct a portfolio that will provide a stream of payments from coupons, sinking funds, and maturing principals that will match the liability payments.A dedicated portfolio strategy is subject to some minor market risk given that some cash flows may need to be reinvested forward.It also can be subject to default risk if lower quality bonds are purchased.The biggest risk with cash-flow matching strategies is that the bonds selected to match forecasted liabilities may be called, forcing the investment manager to purchase new bonds yielding lower rates.
100Classical Immunization Immunization is a strategy of minimizing market risk by selecting a bond or bond portfolio with a duration equal to the horizon date.For liability management cases, the liability payment date is the liability’s duration, DL.Immunization can be described as a duration-matching strategy of equating the duration of the bond or asset to the duration of the liability.
101Classical Immunization When a bond’s duration is equal to the liability’s duration, the direct interest-on-interest effect and the inverse price effect exactly offset each other.As a result, the rate from the investment (ARR) or the value of the investment at the horizon or liability date does not change because of an interest rate change.
102Classical Immunization: History The foundation for bond immunization strategies comes from a 1952 article by F.M. Redington:“Review of the Principles of Life – Office Foundation,” Journal of the Institute of Actuaries 78 (1952):Redington argued that a bond investment position could be immunized against interest rate changes by matching durations of the bond and the liability.Redington’s immunization strategy is referred to as classical immunization.
103Classical Immunization: Example A fund has a single liability of $1,352 due in 3.5 years, DL = 3.5 years, and current investment funds of $The current yield curve is flat at 10%.Immunization Strategy: Buy bond with Macaulay’s duration of 3.5 years.Buy 4-year, 9% annual coupon at YTM of 10% for P0 = $ This Bond has D = 3.5.This bond has both a duration of 3.5 years and is worth $968.50, given a yield curve at 10%.
104Classical Immunization: Example If the fund buys this bond, then any parallel shift in the yield curve in the very near future would have price and interest rate effects that exactly offset each other.As a result, the cash flow or ending wealth at year 3.5, referred to as the accumulation value or target value, would be exactly $1,352.
105Classical Immunization: Example DURATION-MATCHINGEnding Values at 3.5 Years Given Different Interest Ratesfor 4- Year, 9% Annual Coupon Bond with Duration of 3.5Time (yr)9%10%11%1233.5Target Value$ 90(1.09)2.5 = $111.6490(1.09)1.5 = $102.4290(1.09).5 = $ 93.961090/(1.09).5 = $$1352$ 90(1.10)2.5 = $114.2190(1.10)1.5 = $103.8390(1.10).5 = $ 94.391090/(1.10).5 = $$ 90(1.11)2.5 = $116.8390(1.11)1.5 = $105.2590(1.11).5 = $ 94.821090/(1.11).5 = $
106Classical Immunization Note that in addition to matching duration, immunization also requires that the initial investment or current market value of the assets purchased to be equal to or greater than the present value of the liability using the current YTM as a discount factor.In this example, the present value of the $1,352 liability is $ (= $1,352/(1.10)3.5), which equals the current value of the bond and implies a 10% rate of return.
107Classical Immunization Redington’s duration-matching strategy works by having offsetting price and reinvestment effects.In contrast, a maturity-matching strategy where a bond is selected with a maturity equal to the horizon date has no price effect and therefore no way to offset the reinvestment effect.This can be seen in the next exhibit where unlike the duration-matched bond, a 10% annual coupon bond with a maturity of 3.5 years has different ending values given different interest rates.
108Classical Immunization: Example MATURITY-MATCHINGEnding Values at 3.5 Years Given Different Interest Rates for10% Annual Coupon Bond with Maturity of 3.5 YearsTime (yr)9%10%11%1233.5$ 100(1.09)2.5 = $124.04100(1.09)1.5 = $113.80100(1.09).5 = $104.40= $1050__$1392$ 100(1.10)2.5 = $126.91100(1.10)1.5 = $115.37100(1.10).5 = $1050 = $1050__$1397$ 100(1.11)2.5 = $129.81100(1.11)1.5 = $116.95100(1.11) = $= $1050_$1402
109Immunization and Rebalancing In a 1971 study, Fisher and Weil compared duration-matched immunization positions with maturity-matched ones under a number of interest rate scenarios. They found:The duration-matched positions were closer totheir initial YTM than the maturity-matchedstrategies, but that they were not absent of market risk.
110Immunization and Rebalancing Fisher and Weil offered two reasons for the presence of market risk with classical immunization.To achieve immunization, Fisher and Weil argued that the duration of the bond must be equal to the remaining time in the horizon period.1. The shifts in yield curves were not parallel2. Immunization only works when the durationof assets and liabilities are match at all times.
111Immunization and Rebalancing The durations of assets and liabilities change with both time and yield changes:(1) The duration of a coupon bond declines more slowly than the terms to maturity.In our earlier example, our 4-year, 9% bond with a Maculay duration of 3.5 years when rates were 10%, one year later would have duration of 2.77 years with no change in rates.(2) Duration changes with interest rate changes.Specifically, there is an inverse relation between interest rates and duration.
112Immunization and Rebalancing Thus, a bond and liability that currently have the same durations will not necessarily be equal as time passes and rates change.Immunized positions require active management, called rebalancing, to ensure that the duration of the bond position is always equal to the remaining time to horizon.
113Immunization and Rebalancing Rebalancing Strategies when DB ≠ DLSell bond and buy new oneAdd a bond to change DpReinvest cash flows differentlyUse futures or options.
114Bond Immunization: Focus Strategy For a single liability, immunization can be attained with a focus strategy or a barbell strategy.In a focus strategy, a bond is selected with a duration that matches the duration of the liability or a bullet approach is applied where a portfolio of bonds are selected with all the bonds close to the desired duration.Example: If the duration of the liability is 4 years, one could select a bond with a 4-year duration or form a portfolio of bonds with durations of 4 and 5 years.
115Bond Immunization: Barbell Strategy In a barbell strategy, the duration of the liability is matched with a bond portfolio with durations more at the extremes.Example: For a duration liability of 4 years, an investor might invest half of his funds in a bond with a two-year duration and half in a bond with a six-year duration.Note: The problem with the barbell strategy is that it may not immunize the position if the shift in the yield curve is not parallel.
116Bond Immunization: Immunizing Multiple-Period Liabilities For multiple-period liabilities, bond immunization strategies can be done by either:Matching the duration of each liability with the appropriate bond or bullet bond portfolioConstructing a portfolio with a duration equal to the weighted average of the durations of the liabilities (DPL)
117Bond Immunization: Immunizing Multiple-Period Liabilities Example: If a fund had multiple liabilities of $1M each in years 4, 5, and 6, it could either:invest in three bonds, each with respective durations of 4 years, 5 years, and 6 years, orit could invest in a bond portfolio with duration equal to 5 years:
118Bond Immunization: Immunizing Multiple-Period Liabilities The portfolio approach is relatively simple to construct, as well as to manage.The Bierwag, Kaufman, and Tuevs study found that matching the portfolio's duration of assets with the duration of the liabilities does not always immunize the positions.Bierwag, G. O., George G. Kaufman, and Alden Toevs, eds. Innovations in Bond Portfolio Management: Duration Analysis and Immunization. Greenwich, Conn.: JAI Press, 1983.
119Bond Immunization: Immunizing Multiple-Period Liabilities Thus, for multiple-period liabilities, the best approach is generally considered to be one of immunizing each liability.As with single liabilities, this also requires rebalancing each immunized position.
120Combination MatchingAn alternative to frequent rebalancing is a combination matching strategy:Combination Matching:Use cash flow matching strategy for early liabilitiesandImmunization for longer-term liabilities.
121Immunization: Surplus Management The major users of immunization strategies are pensions, insurance companies, and commercial banks and thrifts.Pensions and life insurance companies use multiple-period immunization to determine the investments that will match a schedule of forecasted payouts.Insurance companies, banks and thrifts, and other financial corporations also use immunization concepts for surplus management.
122Immunization: Surplus Management Surplus management refers to managing the surplus value of assets over liabilities.This surplus can be measured as economic surplus, defined as the difference between the market value of the assets and the present value of the liabilities:Example: A pension with a bond portfolio currently valued at $200M and liabilities with a present value of $180M would have an economic surplus of $20M.
123Immunization: Surplus Management An economic surplus can change if interest rates change.The direction and extent of the change depends on the surplus’s duration gap.Duration gap is the difference in the duration of assets and the duration of the liabilities.
124Immunization: Surplus Management Duration Gap:If the duration of the bond portfolio exceeds the duration of the liabilities, then the economic surplus will vary inversely to interest rates.If the duration of the bond portfolio is less than the duration of the liabilities, then the surplus value will vary directly with interest rates.If the durations of the bond portfolio and liabilities are equal, then the surplus will be invariant to rate changes – an immunized position.
125Immunization and Surplus Management Duration Gap and Economic Surplus and Rate Relation:
127Immunization: Duration Gap Analysis by Banks Duration gap analysis is used by banks and other deposit institutions to determine changes in the market value of the institution’s net worth to changes in interest rates.With gap analysis, a bank’s asset sensitivity and liability sensitivity to interest rate changes is found by estimating Macaulay’s duration for the assets and liabilities and then using the formula for modified duration to determine the percentage change in value to a percentage change in interest rates.%P = -(Macaulay’s Duration) (R/(1+R)
128Immunization: Duration Gap Analysis by Banks Example: Consider a bank with the following balance sheet:Assets and liabilities each equal to $150MWeighted Macaulay duration of 2.88 years on its assetsWeighted duration of on its liabilitiesInterest rate level of 10%.
130Immunization: Duration Gap Analysis by Banks The bank’s positive duration gap of suggests an inverse relation between changes in rates and net worth.If interest rate were to increase from 10% to 11%, the bank’s asset value would decrease by 2.62% and its liabilities by 1.33%, resulting in a decrease in the bank’s net worth of $1.93M:If rates were to decrease from 10% to 9%, then the bank’s net worth would increase by $1.93M.%P = -(Macaulay’s Duration) (R/(1+R)Assets: %P = -(2.88) (.01/1.10) =Liabilities: %P = -(1.467) (.01/1.10) =Change in Net Worth = (-.0262)($150M) – (-.0133)($150M)= -$1.93M
131Immunization: Duration Gap Analysis by Banks With a positive duration gap an increase in rates would result in a loss in the bank’s capital and a decrease in rates would cause the bank’s capital to increase.If the bank’s duration gap had been negative, then a direct relation would exist between the bank’s net worth and interest rates,If the gap were zero, then its net worth would be invariant to interest rate changes.
132Immunization: Duration Gap Analysis by Banks As a tool, duration gap analysis helps the bank’s management ascertain the degree of exposure that its net worth has to interest rate changes.
133Hybrid Strategies Immunization and Rebalancing Rebalancing Immunized PositionsContingent Immunization
134Immunization, Rebalancing, and Active Management Since the durations of assets and liabilities change with both time and yield changes, immunized positions require some active management – rebalancing.Immunization strategies should therefore not be considered as a passive bond management strategy.Immunization with rebalancing represents a hybrid strategy.
135Contingent Immunization Contingent immunization is an enhanced immunization strategy that combines active management to achieve higher returns and immunization strategies to ensure a floor.Contingent immunization was developed by Leibowitz and Weinberger:Martin Leibowitz and Alfred Weinberger, “Contingent Immunization – Part I: Risk Control Procedures,” Financial Analyst Journal 38, November-December 1982: 17-32;Martin Leibowitz and Alfred Weinberger, “Contingent Immunization – Part II: Problem Areas,” Financial Analyst Journal 39, January-February 1983:
136Contingent Immunization In a contingent immunization strategy, a client of an investment management fund agrees to accept a potential return below an immunized market return.The lower potential return is referred to as the target rate, andthe difference between the immunized market rate and the target rate is called the cushion spread.
137Contingent Immunization The acceptance of a lower target rate means that the client is willing to take an end-of-the period investment value, known as the minimum target value, which is lower than the fully immunized value.This acceptance, in turn, gives the management fund some flexibility to pursue an active strategy.
138Contingent Immunization Example:Suppose an investment company offers a contingent immunization strategy for a client with HD = 3.5 years based on a current 4-year, 9% annual coupon bond trading at a YTM of 10% (assume flat yield curve at 10%).The bond has a duration of 3.5 years and an immunization rate of 10%.Suppose the client agrees to a lower immunization rate of 8% in return for allowing the fund to try to attain a higher rate using some active strategy.
139Contingent Immunization By accepting a target rate of 8%, the client is willing to accept a minimum target value of $1,309,131 at the 3.5-year horizon date:Minimum Target Value = $1M(1.08)3.5 = $1,309,131
140Contingent Immunization The difference between the client’s investment value (currently $1M) and the present value of the minimum target value is the management fund’s safety margin or cushion.The initial safety margin in this example is $62,203:Safety Margin = Investment Value – PV(Minimum Target Value)Safety Margin = $1,000,000 - $1,309,131/(1.10)3.5 = $62,203
141Contingent Immunization As long as the safety margin is positive, the management fund will have a cushion and can therefore pursue an active strategy.
142Contingent Immunization For example, suppose the fund expected long-term rates to decrease in the future and invested the client’s funds in bonds with the following features:Maturity of 10-year10% annual couponTrading at par (YTM = 10%)
143Contingent Immunization If rates in the future decreased as expected, then the value of the investment and the safety margin would increase.For example, suppose one year later the yield curve shifted down (as the management fund was hoping) to 8% (continue to assume a flat yield curve).The value of the investment (value of the original 10-year bonds plus coupons) would now be $1,224,938.The present value of the minimum target value would be $1.08M.The safety margin would be $144,938.
145Contingent Immunization Thus, the downward shift in the yield curve has led to an increase in the safety margin from $62,203 to $144,938.At this point, the investment management fund could maintain its position in the original 10-year bond, take some other active position, or it could immunized the position.
146Contingent Immunization If the company immunizes, it would liquidate the original 10-year bond and purchase a bond with HD = 2.5 years yielding 8% (assume flat yield curve at 8%). If it did this, it would be able to provide the client with a 11.96% rate for the 3.5 year period:
147Contingent Immunization If rates increased, though, the value of the investment and safety margin would decrease.Moreover, if rates increased to the point that the investment value were equal to the present value of the minimum target value (that is, where the safety margin is zero), then the management fund would be required to immunize the investment position.
148Contingent Immunization Suppose after one year, the yield curve shifted up to 12.25% instead of down to 8%.At 12.25%, the value of investment would be only $981,245 and the present value of the minimum target value would be $980,657, leaving the fund with a safety margin that is close to zero ($588).
150Contingent Immunization The investment management fund now would be required to immunize the portfolio.This could be done by selling the bond and reinvesting the proceeds plus the coupon (total investment of $981,245) in bonds with durations of 2.5 years and yielding the current rate of 12.25% (assume flat yield curve).
151Contingent Immunization Doing this would yield a value of $1,309,916, which is approximately equal to the minimum target value of $1,309,131 and the target rate of 8%:The exhibit on the next slide summarizes the investment values, present values of the minimum target value, safety margins, and ARRs after one year for various interest rates.
154Contingent Immunization: Points The contingent immunization strategy provides investors with a return-risk opportunity that is somewhere between those provided by active and fully-immunized strategies.
155Contingent Immunization: Points 2. In practice, setting up and managing contingent immunization strategies are more complex than this example suggests.Safety margin positions must be constantly monitored to ensure that if the investment value decreases to the trigger point it will be detected and the immunization position implemented.Active positions are more detailed, non-parallel shifts in the yield curve need to be accounted for, and if the immunization position is implemented, it will need to be rebalanced.
156WebsitesFor information on bond funds go toFor information on bond funds for emerging economies go toInformation on state and local economic conditions and industries:For information on industry trends go to and click on “Industries.”
157WebsitesFor bonds on the watch list or subject to ratings changes go to the websites of Moody’s, Standard and Poor’s and Fitch:For information on specific bonds go to and click on “Market System” and “Bond Information.”For information on bond strategies and trends go to