Bond Investment Strategies

1
Chapter 8

• Bond Investment Strategies

2
Types of Bond Strategies

• Active Strategies
• Passive Strategies
• Hybrid Strategies

3
Types 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 Strategies
• Credit Strategies
• Fundamental Valuation Strategies

4
Types of Bond Strategies

• Passive Strategies Strategies in which no change
  in the position is necessary once the bonds are
  selected.
• Types
• Indexing
• Cash-Flow Matching
• Classical Immunization

5
Types of Bond Strategies

• Hybrid Strategies Strategies that have both
  active and passive features.
• Immunization with Rebalancing
• Contingent Immunization

6
Active Interest Rate Anticipation Strategies

• Types of Interest-Rate Anticipation Strategies
• Rate-Anticipation Strategies
• Strategies Based on Yield Curve Shifts

7
Rate-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.

8
Rate-Anticipation Swap

• Rate-Anticipation Swap for bond portfolio manager
  when interest rates are expected to decrease
  across all maturities
• Strategy Lengthening the portfolios duration
  Manager could sell her lower duration bonds and
  buy higher duration ones.
• By doing this, the portfolios 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.

9
Rate-Anticipation Swap

• Rate-Anticipation Swap for bond portfolio manager
  when interest rates are expected to increase
  across all maturities
• Strategy Shorten the portfolios 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.

10
Rate-Anticipation Swap Cushion Bond

• One way to shorten the funds 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.

11
Rate-Anticipation Swap Cushion Bond

• Cushion bond has the following features
• High coupon yield
• With 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.

12
Rate-Anticipation Swap Cushion Bond

• Example
• Suppose a bond manager had a fund consisting of
  10-year, 10 option-free bonds valued at 113.42
  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
  funds value by
• Selling option-free bonds
• Buying higher coupon, callable bonds cushion
  bonds

13
Rate-Anticipation Swap Cushion Bond

• Example
• The swap of existing bonds for the cushion bonds
  provides
• An immediate gain in income 113.42-110 3.42
• A higher coupon income in the future 12 instead
  of 10

14
Rate-Anticipation Swap Cushion Bond

• Note
• A 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.

15
Yield 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.

16
Yield Curve Shifts and Strategies

• Yield Curve Shifts
• Three types of yield curve shifts occur with some
  regularity
• Parallel Shifts
• Shifts with Twists
• Shifts with Humpedness

17
Yield Curve Shifts Parallel

• Parallel Shifts Rates on all maturities change
  by the same number of basis points.

18
Yield 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.

19
Yield Curve Shifts Twist

• Shifts with a Twist
• Flattening
• Steepening

20
Yield 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.

21
Yield Curve Shifts Humpedness

• Positive Butterfly ST and LT rates change more
  than intermediate
• Negative Butterfly Intermediate rates change
  more than ST and LT

22
Yield Curve Shift Strategies

• Yield Curve Strategies
• The 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.

23
Yield Curve Strategies

• Yield Curve Strategies
• Bullet Strategy
• Barbell Strategy
• Ladder Strategy

24
Yield Curve Shift Strategies

• Strategies Based on Expectations

Bullet strategy could be formed based on an
expectation of a downward shift in the yield
curve with a twist such that long-term rates
were expected to decrease more than short-term.
If investors expected a simple downward parallel
shift in the yield curve, a bullet strategy with
longer duration bonds would yield greater
returns than an investment strategy in
intermediate or short-term bonds if the
expectation turns out to be correct.
The barbell strategy could be profitable for an
investor who is forecasting an upward negative
butterfly yield curve shift.
25
Yield Curve StrategiesTotal 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.

26
Total Return Analysis

• Total Return Analysis Example (Ch. 8, Problem 3)
• Consider three bonds
• Assume yield curve is currently flat at 6.
• Consider two strategies

1. Barbell Invest 50 in A and 50 in C. 2.
Bullet 100 in Bond B
27
Total Return Analysis

• Consider two types of yield curve shifts one year
  later
• Parallel shifts ranging between -200 BP and 200
  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

28
Total Return Analysis Parallel Shifts
Bond Return (Value-100) 6 Bullet 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.
29
Total 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 bonds price sensitivity to
  interest rate changes.

30
Total Return Analysis Yield Curve Shifts
Characterized by a Flattening
?yA ?yB 25BP and ?yC ?yB - 25BP
31
Total 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.

32
Active 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 group to 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 changes in
default risk. This information is then used to
identify bonds to include or exclude in a bond
portfolio or bond investment strategy.
33
Quality Swaps

• Quality 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

34
Quality Swaps

• Quality swaps often involve a sector rotation in
  which more funds are allocated to a specific
  quality sector in anticipation of a price change.
  
• Example
• Suppose 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.

35
Quality Swaps

• Quality 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 was expected to grow in the future,
speculators or a hedge fund might anticipate a
narrowing in the spread between lower and higher
quality bonds.
To exploit this, they could form a quality swap
by taking a long position in lower quality bonds
and a short position in higher quality bonds
with similar durations.
Whether rates increase or decrease, speculators
would still profit from these positions, provided
the quality spread narrows.
36
Quality Swaps
37
Credit Analysis Strategy

• The objective of a credit analysis strategy is to
  determine expected changes in default risk.

38
Credit Analysis

• Over 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.

39
Credit 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.

40
Credit AnalysisDouglass 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.

41
Credit Analysis Strategy
The strategy of many managers of high-yield bond
funds is to develop effective credit analysis
models so that they can identify bonds with high
yields and high probabilities of upgrades to
include in their portfolios, as well as identify
bonds with high probabilities of downgrades to
exclude from their fund.
Credit analysis can be done through basic
fundamental analysis of the bond issuer and the
indenture and with statistical-based models, such
as a multiple discriminant model.
42
Fundamental 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
  bonds quality ratings and therefore a change in
  its price.

43
Fundamental Credit AnalysisCorporate 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.

44
Fundamental Credit AnalysisCorporate Issues

• 2. Fundamental Analysis Comparison of the
  companys 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.

45
Fundamental Credit AnalysisCorporate 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.

46
Fundamental Credit AnalysisCorporate Issues
FINANCIAL RATIOS () BY RATING CLASSIFICATIONS
Source Standard and Poors, Global Sector
Review, 1995.
47
Fundamental Credit AnalysisMunicipal 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.

48
Fundamental Credit AnalysisMunicipal Issues

• 2. Fiscal Soundness The objective of this
  analysis is to determine the issuers 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.

49
Fundamental Credit AnalysisMunicipal 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.

50
Fundamental Credit AnalysisMunicipal Issues

• 4. Red Flags Some of the negative indicators
  suggesting greater credit risk are
• Decreases in population
• Unemployment increases
• Decreased in the number of building permits
• Declines in property values
• Loss of large employers
• Use of debt reserves and declines in debt
  coverage ratios
• For revenue bonds, additional red flags could
  include
• Cost overruns on projects
• Schedule delays
• Frequent rate or rental increases

51
Fundamental Credit AnalysisForeign 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.

52
Fundamental Credit AnalysisForeign 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.

53
Fundamental Credit AnalysisForeign 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 countrys
  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

54
Fundamental Credit AnalysisForeign Issues

• 4. Balance of payments ratios Countrys total
  debt to export ratio.
• 5. Economic factors Inflation, growth in gross
  domestic product, interest rates, and
  unemployment.
• 6. Susceptibility of the countrys economy and
  exports to changes in economic conditions in
  industrialized countries.

55
Multiple 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 bonds 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 bonds overall credit
  quality

56
Multiple Discriminant Analysis

• For corporate bonds, possible explanatory
  variables include
• Interest coverage ratio
• Leverage ratio
• Capitalization level
• Profitability (earnings before interest and taxes
  to total assets)
• Variability (variance of profitability ratio)

57
Multiple 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 companys 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 bonds relative default risk.

58
Multiple 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
  companys future score or expected change in
  score.

59
High-Yield Bond Funds

• Credit 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, and
• those bonds that are in jeopardy of being
  downgraded and therefore should be excluded.

60
Chapter 11 Funds

• A 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 debts value or to the replacement of the
  debt with a more valuable claim.

61
Chapter 11 Funds

• Chapter 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.

62
Fundamental Valuation Strategies

• The objective of fundamental bond analysis is the
  same as that of fundamental stock analysis.
• It involves determining a bonds intrinsic value
  and then comparing that value with the bonds
  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.

63
Fundamental Valuation Strategies

• A bond fundamentalist often tries to determine a
  bonds intrinsic value by estimating the required
  rate for discounting the bonds cash flows.
• This rate, R, depends on the current level of
  interest rates as measured by the risk-free rate,
  Rf, and the bonds risk premiums default risk
  premium (DRP), liquidity premium (LP), and
  option-adjusted spread (OAS)

64
Fundamental Valuation Strategies

• Fundamentalists use various models to estimate
  the various spreads. These include
• Regressions
• Multiple discriminant analysis
• Option pricing models

65
Yield Pickup Swaps

• 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 in the underpriced (higher yield)
bond and short in the overpriced (lower yield)
bond, then closing the positions once the prices
of the two bonds converge.
66
Yield Pickup Swaps

• The 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 coupon
• bond is constructed such that it has the same
  cash flows and features
• as 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 do
• not provide the same yield, then an arbitrageur
  or speculator could
• form a yield pickup swap by taking opposite
  positions in the portfolio
• and the bond.

A fundamentalist could also use this methodology
for identifying underpriced bonds buying all AA
quality, 7.5-year, 7.5 coupon bonds with yields
exceeding the portfolio formed with those
features.
67
Other Swaps Tax Swap

• In a tax swap, an investor sells one bond and
  purchases another in order to take advantage of
  the tax laws.

68
Other 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.

69
Other 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 IRSs 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.

70
Other Swaps Tax Swap

• Another 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.

71
Other 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.

72
Passive Strategies

• Passive Strategies Strategies that once they are
  formed do not require active management or
  changes.

73
Passive Strategies

• The 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 maturity
• Forming portfolios with returns that mirror the
  returns on a bond index
• Constructing portfolios that ensure there are
  sufficient funds to meet future liabilities.

74
Passive Strategies

• Here we look at the following passive strategies
• Bond Indexing
• Cash-flow Matching
• Classical Immunization

75
Bond Indexing

• Bond 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.

76
Bond Indexing

• The first step in constructing a bond index fund
  is to select the appropriate index. Bond indices
  can be
• General
• Shearson-Lehman Aggregate Index
• Merrill-Lynch Composite Index
• Specialized
• Salomon Smith Barneys Global Government Bond
  Index.
• Customized
• Some investment companies offer their own
  customized index specifically designed to meet
  certain investment objectives.

77
Bond Market Indexes
78
Bond Market Indexes
The Handbook of Fixed-Income Securities, editor
F. Fabozzi, 6th edition, p. 158.
79
Bond Indexing

• The 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.

80
Bond Indexing

• An 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.

81
Bond Indexing

• When 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.

82
Bond 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.).

83
Bond Indexing Cell Matching

• Example
• Suppose we decompose a bond index into
• 2 durations (D gt 5, D lt 5)
• 2 sectors (Corporate, Municipal)
• 2 quality ratings (AA, A)

84
Bond 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 cells allocation.

C1 D lt 5, AAA, Corp C2 D lt 5, AAA, Muni C3
D lt 5, AA, Corp C4 D lt 5, AA, Muni C5 D gt 5,
AAA, Corp C6 D gt 5, AAA, Muni C7 D gt 5, AA,
Corp C8 D gt 5, AA, Muni
85
Bond 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.

86
Bond Indexing Cell Matching

• Duration/sector index is formed by matching the
  amounts of the indexs durations that make up
  each of the various sectors.
• This requires estimating the duration for each
  sector comprising the index and determining each
  sectors percentage of value to the index.

87
Bond 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.

88
Duration/Sector and Duration/Quality Cell Matching
89
Bond 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 but with more weight
given to lower quality bonds based on an
expectation of an improving economy would be an
enhanced index fund combining indexing and
sector rotation.
90
Cash Flow Matching

• A 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.

91
Cash 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.

92
Cash 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 buy
• LT /(1 CR0) of par value of bonds maturing
  in T periods.

93
Cash 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.

94
Cash 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.

95
Cash 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.

96
Cash Flow Matching Example
97
Cash Flow Matching Example
98
Cash Flow Matching Example
99
Cash 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.

100
Classical 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 liabilitys 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.

101
Classical Immunization

• When a bonds duration is equal to the
  liabilitys 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.

102
Classical 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) 286-340.
• Redington argued that a bond investment position
  could be immunized against interest rate changes
  by matching durations of the bond and the
  liability.
• Redingtons immunization strategy is referred to
  as classical immunization.

103
Classical 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 968.30.
• The current yield curve is flat at 10.
• Immunization Strategy Buy bond with Macaulays
  duration of 3.5 years.
• Buy 4-year, 9 annual coupon at YTM of 10 for P0
  968.30. 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.

104
Classical 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.

105
Classical Immunization Example
DURATION-MATCHING Ending Values at 3.5 Years
Given Different Interest Rates for 4- Year, 9
Annual Coupon Bond with Duration of 3.5
106
Classical 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 968.50 ( 1,352/(1.10)3.5), which
  equals the current value of the bond and implies
  a 10 rate of return.

107
Classical Immunization

• Redingtons 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.

108
Classical Immunization Example
MATURITY-MATCHING Ending Values at 3.5 Years
Given Different Interest Rates for 10 Annual
Coupon Bond with Maturity of 3.5 Years


109
Immunization 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 to
their initial YTM than the maturity-matched
strategies, but that they were not absent of
market risk.
110
Immunization 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 parallel
2. Immunization only works when the duration of
assets and liabilities are match at all times.
111
Immunization 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.

112
Immunization 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.

113
Immunization and Rebalancing

• Rebalancing Strategies when DB ? DL
• Sell bond and buy new one
• Add a bond to change Dp
• Reinvest cash flows differently
• Use futures or options.

114
Bond 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.

115
Bond 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.

116
Bond ImmunizationImmunizing 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 portfolio
• Constructing a portfolio with a duration equal to
  the weighted average of the durations of the
  liabilities (DPL)

117
Bond ImmunizationImmunizing 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, or
• it could invest in a bond portfolio with duration
  equal to 5 years

118
Bond ImmunizationImmunizing 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.

119
Bond ImmunizationImmunizing 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.

120
Combination Matching

• An alternative to frequent rebalancing is a
  combination matching strategy
• Combination Matching
• Use cash flow matching strategy for early
  liabilities
• and
• Immunization for longer-term liabilities.

121
Immunization 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.

122
Immunization 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.

123
Immunization Surplus Management

• An economic surplus can change if interest rates
  change.
• The direction and extent of the change depends on
  the surpluss duration gap.
• Duration gap is the difference in the duration of
  assets and the duration of the liabilities.

124
Immunization 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.

125
Immunization and Surplus Management

• Duration Gap and Economic Surplus and Rate
  Relation

126
Bond Immunization Surplus Management

• Example

127
Immunization 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 institutions net worth to
  changes in interest rates.
• With gap analysis, a banks asset sensitivity and
  liability sensitivity to interest rate changes is
  found by estimating Macaulays 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 -(Macaulays Duration) (?R/(1R)
128
Immunization Duration Gap Analysis by Banks

• Example Consider a bank with the following
  balance sheet
• Assets and liabilities each equal to 150M
• Weighted Macaulay duration of 2.88 years on its
  assets
• Weighted duration of 1.467 on its liabilities
• Interest rate level of 10.

129
Immunization Duration Gap Analysis by Banks
130
Immunization Duration Gap Analysis by Banks

• The banks positive duration gap of 1.413
  suggests an inverse relation between changes in
  rates and net worth.
• If interest rate were to increase from 10 to
  11, the banks asset value would decrease by
  2.62 and its liabilities by 1.33, resulting in
  a decrease in the banks net worth of 1.93M
• If rates were to decrease from 10 to 9, then
  the banks net worth would increase by 1.93M.

?P -(Macaulays Duration) (?R/(1R) Assets
?P -(2.88) (.01/1.10) -.0262 Liabilities
?P -(1.467) (.01/1.10) -.0133 Change in
Net Worth (-.0262)(150M) (-.0133)(150M)
-1.93M
131
Immunization Duration Gap Analysis by Banks

• With a positive duration gap an increase in rates
  would result in a loss in the banks capital and
  a decrease in rates would cause the banks
  capital to increase.
• If the banks duration gap had been negative,
  then a direct relation would exist between the
  banks net worth and interest rates,
• If the gap were zero, then its net worth would be
  invariant to interest rate changes.

132
Immunization Duration Gap Analysis by Banks

• As a tool, duration gap analysis helps the banks
  management ascertain the degree of exposure that
  its net worth has to interest rate changes.

133
Hybrid StrategiesImmunization and Rebalancing

• Hybrid Strategies
• Rebalancing Immunized Positions
• Contingent Immunization

134
Immunization, 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.

135
Contingent 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 35-50.

136
Contingent 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, and
• the difference between the immunized market rate
  and the target rate is called the cushion spread.
  

137
Contingent 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.

138
Contingent 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.

139
Contingent 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
140
Contingent Immunization

• The difference between the clients investment
  value (currently 1M) and the present value of
  the minimum target value is the management funds
  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
141
Contingent Immunization

• As long as the safety margin is positive, the
  management fund will have a cushion and can
  therefore pursue an active strategy.

142
Contingent Immunization

• For example, suppose the fund expected long-term
  rates to decrease in the future and invested the
  clients funds in bonds with the following
  features
• Maturity of 10-year
• 10 annual coupon
• Trading at par (YTM 10)

143
Contingent 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.

144
Contingent Immunization
Safety Margin 1,224,938 - 1,080,000
144,938
145
Contingent 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.

146
Contingent 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

147
Contingent 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.

148
Contingent 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).

149
Contingent Immunization
150
Contingent 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).

151
Contingent 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.

152
Contingent Immunization