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PAN African e-Network Project
MFM
PORTFOLIO MANAGEMENT
Semester - VI
Session - 5
By – Suraj Prakash
Bond Investment Strategies
Types of Bond Strategies
1. Active Strategies
2. Passive Strategies
3. Hybrid Strategies
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
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
Types of Bond Strategies
• Hybrid Strategies: Strategies that
have both active and passive
features.
• Immunization with Rebalancing
• Contingent Immunization
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.
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.
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.
Year 1 2 3
Liability $1M $3M $4M
Cash Flow Matching: Example
Bonds Coupon
Rate
Par Yield Market
Value
Liability Year
3-Year
2-year
1-year
5%
5%
5%
100
100
100
5%
5%
5%
100
100
100
$4M
$3M
$1M
3
2
1
Cash 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
Cash Flow Matching: Example
1 2 3 4 5 6
Year Total Bond
Values
Coupon
Income
Maturing
Principal
Liability Ending
Balance
(3) + (4) – (5)
1
2
3
$7,128,820
$6,485,261
$3,809,524
$356,441
$324,263
$190,476
$643,559
$2,675,737
$3,809,524
$1,000,000
$3,000,000
$4,000,000
0
0
0
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.
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 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.
Classical 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.
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.
• Redington’s immunization strategy is referred to as classical
immunization.
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 Macaulay’s 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%.
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.
Classical Immunization: Example
Time (yr) 9% 10% 11%
1
2
3
3.5
Target Value
$ 90(1.09)2.5 = $111.64
90(1.09)1.5 = $102.42
90(1.09).5 = $ 93.96
1090/(1.09).5 = $1044.03
$1352
$ 90(1.10)2.5 = $114.21
90(1.10)1.5 = $103.83
90(1.10).5 = $ 94.39
1090/(1.10).5 = $1039.27
$1352
$ 90(1.11)2.5 = $116.83
90(1.11)1.5 = $105.25
90(1.11).5 = $ 94.82
1090/(1.11).5 = $1034.58
$1352
DURATION-MATCHING
Ending Values at 3.5 Years Given Different Interest Rates
for 4- Year, 9% Annual Coupon Bond with Duration of 3.5
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.
Classical 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.
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
Time (yr) 9% 10% 11%
1
2
3
3.5
$ 100(1.09)2.5 = $124.04
100(1.09)1.5 = $113.80
100(1.09).5 = $104.40
1050 = $1050__
$1392
$ 100(1.10)2.5 = $126.91
100(1.10)1.5 = $115.37
100(1.10).5 = $ 104.88
1050 = $1050__
$1397
$ 100(1.11)2.5 = $129.81
100(1.11)1.5 = $116.95
100(1.11).5 = $ 105.36
1050 = $1050_
$1402
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.
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.
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.
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.
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.
Active: Interest Rate
Anticipation Strategies
• Types of Interest-Rate Anticipation
Strategies:
• Rate-Anticipation Strategies
• Strategies Based on Yield Curve
Shifts
Rate-Anticipation Strategies
• Substitution Swap
• Pure Yield pickup Swap
• Tax Swap
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.
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.
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.
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.
Passive Strategies
• Passive Strategies: Strategies that once
they are formed do not require active
management or changes.
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.
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.
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.
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 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.
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%.
Immunization: Duration
Gap Analysis by Banks
Assets Amount Macaulay Weighted Liabilities Amount Macaulay Weighted
in millions of $ Duration Duration in millions of $ Duration Duration
Reserves 10 0.0 0.000 Demand Deposits 15 1.0 0.100
Short-Term Securities 15 0.5 0.050 Nonnegotiable Deposits 15 0.5 0.050
Intermediate Securities 20 1.5 0.200 Certificates of Deposit 35 0.5 0.117
Long-Term Securities 20 5.0 0.667 Fed Funds 5 0.0 0.000
Variable-Rate Mortgages 10 0.5 0.033 Short-Term Borrowing 40 0.5 0.133
Fixed-Rate Mortgages 25 6.0 1.000 Intermediate-Term Borrowing 40 4.0 1.067
Short-Term Loans 20 1.0 0.133 150 1.467
Intermediate Loans 30 4.0 0.800
150 2.88
Immunization: Duration
Gap Analysis by Banks
• The bank’s 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
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) = -.0262
Liabilities: %P = -(1.467) (.01/1.10) = -.0133
Change in Net Worth = (-.0262)($150M) – (-.0133)($150M)
= -$1.93M
Immunization: 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.
Immunization: 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.
Hybrid Strategies
Immunization and Rebalancing
• Hybrid Strategies
–Rebalancing Immunized Positions
–Contingent Immunization
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.
Revision of Equity
Portfolio
The Manager’s Choices
• Leave the portfolio alone
• Rebalance the portfolio
• Asset allocation and rebalancing within the
aggregate portfolio
• Change the portfolio components
• Indexing
Leave the Portfolio Alone
• A buy and hold strategy means that the
portfolio manager hangs on to its original
investments
• Academic research shows that portfolio
managers often fail to outperform a simple buy
and hold strategy on a risk-adjusted basis
Rebalance the Portfolio
• Rebalancing a portfolio is the process of
periodically adjusting it to maintain the
original conditions
Rebalancing
Within the Portfolio
• Constant mix strategy
• Constant proportion portfolio insurance
Constant Mix Strategy
• The constant mix strategy:
– Is one to which the manager makes
adjustments to maintain the relative weighting
of the asset classes within the portfolio as
their prices change
– Requires the purchase of securities that have
performed poorly and the sale of securities
that have performed the best
Constant Mix Strategy
(cont’d)
Example
A portfolio has a market value of $2 million. The
investment policy statement requires a target asset
allocation of 60 percent stock and 30 percent bonds.
The initial portfolio value and the portfolio value after
one quarter are shown on the next slide.
Equity Portfolio Management:
Active or Passive?
• Passive:
– LT buy and hold
– Indexation
• Replication of an index (broad or specialized
• Sampling and Tracking Error
•  = 0
– Rebalancing
Equity Portfolio Management:
Active or Passive?
Rebalancing an Equity Portfolio
• Why?
– to manage tracking error (if indexing or not)
– to maintain a desired set of weights or risk
level
– client needs change
– Market risk level changes
– bankruptcies, mergers, IPOs
• Why not?
– it’s costly!
Rebalancing: Example 1
Jan. 1 Price per
Share
Number
of Shares
$ Value % of
Total
Value
Beta
X 20 167 $3340 0.333 1.2
Y 15 222 $3330 0.333 1.6
Z 35 95 $3325 0.333 0.8
Total $9995 1.20
Rebalancing: Example 1
June 1 Price per
Share
Number
of Shares
$ Value % of
Total
Value
Beta
down
20%
X 16 167 $2672 0.256 1.3
up
33%
Y 20 222 $4440 0.425 1.7
unch. Z 35 95 $3325 0.319 0.8
Total 10445 1.31
Rebalancing: Example 1
• Portfolio is no longer equally weighted
• To rebalance:
– Sell Y, buy X and Z
– Positions must be reset to $10445/3 = $3482
– Sell 4440 - 3482 = $958 of Y (48 shares)
– Buy 3482 - 2672 = $810 of X (51 shares)
– Buy 3482 - 3325 = $157 of Z (4 shares)
Rebalancing: Example 1
June 1
Rebal-
anced
Price per
Share
Number
of Shares
$ Value % of
Total
Value
Beta
X 16 167 $3488 0.334 1.3
Y 20 222 $3480 0.334 1.7
Z 35 95 $3465 0.332 0.8
Total 10433 1.27
Rebalancing: Example 1
• LT effects of this strategy?
• Alternatives?
• Example 2: Rebalancing to reestablish a
specific level of systematic risk (Target
Beta = 1.2)
Rebalancing: Example 2
• Reestablishing a beta of 1.2:
– No unique solution for more than 2 securities
– Need to sell high  stocks and buy low 
stocks
– For example, sell Y, buy Z, hold X constant
– p = (.256)(1.3)+(WY)(1.7)+(1-.256-WY)(.8)
– Find Y such that p = 1.2
• WY = .302 => WZ = 1-.256-.302 = .442
• $3488 in X, $3151 in Y, $4611 in Z
Active Equity Strategies
• Beat the market on a risk adjusted basis!
• Need a benchmark
• More expensive: turnover, research
• Must outperform on a fee-adjusted basis
Active Equity Strategies
• Styles:
– Sector Rotation: move in/out of sectors as
economy improves/declines
– Earnings Momentum: overweight stocks
displaying above average earnings growth
– Enhanced Index Fund - majority of funds track
index, some funds are actively managed
– Quantitative Investment Management
Quantitative Investment
Management
• How do we forecast performance ?
– Screening (Fundamental or Technical factors)
– Rank based on some set of factors that
correlates with future performance (such as
regression analysis)
• How do we improve forecasting model?
– Add more data (more observations)
– Uncover new causal relationships (variables)
Quantitative Investment
Management
• Regardless of forecast, there are three basic
results common to QIM:
– 1. Information comes from unexpected events
• events with low probability have high info content!
QIM
– 2. Profitable QIM techniques won’t be
commercialized
• Starting with a multifactor model:
• Ri = b1F1 + b2F2 + . . . + bkFk + ei
• It isn’t easy to get information from these residuals:
– 1. patterns are complex
– 2. quality of data is limited
– 3. outliers may draw undue attention (although irrelevant)
– 4. human judgement is superior
– 5. analysis must be flexible (more data, constraints)
– 6. danger of data mining
– 7. even if significant, outliers are too few in number!
QIM
– 3. Non-linear models are important
• Neural Networks
• Genetic Algorithms
• Fuzzy Logic
• Non-Linear Dynamics
• Classification Trees (Recursive Partitioning)
Constant Mix Strategy
(cont’d)
Example (cont’d)
What dollar amount of stock should the portfolio
manager buy to rebalance this portfolio? What dollar
amount of bonds should he sell?
Date Portfolio
Value
Actual Allocation Stock Bonds
1 Jan $2,000,000 60%/40% $1,200,00 $800,000
1 Apr $2,500,000 56%/44% $1,400,00
0
$1,100,000
Constant Mix Strategy
(cont’d)
Example (cont’d)
Solution: a 60%/40% asset allocation for a $2.5 million
portfolio means the portfolio should contain $1.5
million in stock and $1 million in bonds. Thus, the
manager should buy $100,000 worth of stock and sell
$100,000 worth of bonds.
Constant Proportion
Portfolio Insurance
• A constant proportion portfolio
insurance (CPPI) strategy requires the
manager to invest a percentage of the
portfolio in stocks:
$ in stocks = Multiplier x (Portfolio value – Floor value)
Constant Proportion
Portfolio Insurance (cont’d)
Example
A portfolio has a market value of $2 million. The
investment policy statement specifies a floor value of
$1.7 million and a multiplier of 2.
What is the dollar amount that should be invested in
stocks according to the CPPI strategy?
Constant Proportion
Portfolio Insurance (cont’d)
Example (cont’d)
Solution: $600,000 should be invested in stock:
$ in stocks = 2.0 x ($2,000,000 – $1,700,000)
= $600,000
If the portfolio value is $2.2 million one quarter later,
with $650,000 in stock, what is the desired equity
position under the CPPI strategy? What is the ending
asset mix after rebalancing?
Constant Proportion
Portfolio Insurance (cont’d)
Example (cont’d)
Solution: The desired equity position after one quarter
should be:
$ in stocks = 2.0 x ($2,200,000 – $1,700,000)
= $1,000,000
The portfolio manager should move $350,000 into
stock. The resulting asset mix would be:
$1,000,000/$2,200,000 = 45.5%
Rebalancing Within the
Equity Portfolio
• Constant proportion
• Constant beta
• Change the portfolio components
• Indexing
Constant Proportion
• A constant proportion strategy within an
equity portfolio requires maintaining the
same percentage investment in each stock
• Constant proportion rebalancing requires
selling winners and buying losers
Constant Proportion (cont’d)
Example
A portfolio of three stocks attempts to invest approximately one
third of funds in each of the stocks. Consider the following
information:
Stoc
k
Price Shares Value % of Total Portfolio
FC 22.00 400 8,800 31.15
HG 13.50 700 9,450 33.45
YH 50.00 200 10,000 35.40
Total $28,25
0
100.00
Constant Beta Portfolio
• A constant beta portfolio requires maintaining
the same portfolio beta
• To increase or reduce the portfolio beta, the
portfolio manager can:
– Reduce or increase the amount of cash in the
portfolio
– Purchase stocks with higher or lower betas than the
target figure
– Sell high- or low-beta stocks
– Buy high- or low-beta stocks
Change the
Portfolio Components
• Changing the portfolio components is
another portfolio revision alternative
• Events sometimes deviate from what the
manager expects:
– The manager might sell an investment turned
sour
– The manager might purchase a potentially
undervalued replacement security
Indexing
• Indexing is a form of portfolio management that
attempts to mirror the performance of a market
index
– E.g., the S&P 500 or the DJIA
• Index funds eliminate concerns about
outperforming the market
• The tracking error refers to the extent to which
a portfolio deviates from its intended behavior
Window Dressing
• Window dressing refers to cosmetic
changes made to a portfolio near the end
of a reporting period
• Portfolio managers may sell losing stocks
at the end of the period to avoid showing
them on their fund balance sheets
Contributions to the Portfolio
• Periodic additional contributions to the
portfolio from internal or external sources
must be invested
• Dividends:
– May be automatically reinvested by the fund
manager’s broker
– May have to be invested in a money market
account by the fund manager
When Do You Sell Stock?
• Introduction
• Rebalancing
• Upgrading
• Sale of stock via stop orders
• Extraordinary events
• Final thoughts
Rebalancing
• Rebalancing can cause the portfolio
manager to sell shares even if they are not
doing poorly
• Profit taking with winners is a logical
consequence of portfolio rebalancing
Upgrading
• Investors should sell shares when their
investment potential has deteriorated to
the extent that they no longer merit a place
in the portfolio
• It is difficult to take a loss, but it is worse to
let the losses grow
Change in Client Objectives
• The client’s investment objectives may
change occasionally:
– E.g., a church needs to generate funds for a
renovation and changes the objective for the
endowment fund from growth of income to
income
• Reduce the equity component of the portfolio
Change in Market Conditions
• Many fund managers seek to actively time
the market
• When a portfolio manager’s outlook
becomes bearish, he may reduce his
equity holdings
Thank You
Please forward your query
To: surajamity@yahoo.com

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Cycle 6 PM Session 5.ppt

  • 1. PAN African e-Network Project MFM PORTFOLIO MANAGEMENT Semester - VI Session - 5 By – Suraj Prakash
  • 3. Types of Bond Strategies 1. Active Strategies 2. Passive Strategies 3. Hybrid Strategies
  • 4. 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
  • 5. 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
  • 6. Types of Bond Strategies • Hybrid Strategies: Strategies that have both active and passive features. • Immunization with Rebalancing • Contingent Immunization
  • 7. 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.
  • 8. 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.
  • 9. 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. Year 1 2 3 Liability $1M $3M $4M
  • 10. Cash Flow Matching: Example Bonds Coupon Rate Par Yield Market Value Liability Year 3-Year 2-year 1-year 5% 5% 5% 100 100 100 5% 5% 5% 100 100 100 $4M $3M $1M 3 2 1
  • 11. Cash 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
  • 12. Cash Flow Matching: Example 1 2 3 4 5 6 Year Total Bond Values Coupon Income Maturing Principal Liability Ending Balance (3) + (4) – (5) 1 2 3 $7,128,820 $6,485,261 $3,809,524 $356,441 $324,263 $190,476 $643,559 $2,675,737 $3,809,524 $1,000,000 $3,000,000 $4,000,000 0 0 0
  • 13. 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.
  • 14. 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 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.
  • 15. Classical 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.
  • 16. 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. • Redington’s immunization strategy is referred to as classical immunization.
  • 17. 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 Macaulay’s 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%.
  • 18. 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.
  • 19. Classical Immunization: Example Time (yr) 9% 10% 11% 1 2 3 3.5 Target Value $ 90(1.09)2.5 = $111.64 90(1.09)1.5 = $102.42 90(1.09).5 = $ 93.96 1090/(1.09).5 = $1044.03 $1352 $ 90(1.10)2.5 = $114.21 90(1.10)1.5 = $103.83 90(1.10).5 = $ 94.39 1090/(1.10).5 = $1039.27 $1352 $ 90(1.11)2.5 = $116.83 90(1.11)1.5 = $105.25 90(1.11).5 = $ 94.82 1090/(1.11).5 = $1034.58 $1352 DURATION-MATCHING Ending Values at 3.5 Years Given Different Interest Rates for 4- Year, 9% Annual Coupon Bond with Duration of 3.5
  • 20. 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.
  • 21. Classical 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.
  • 22. 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 Time (yr) 9% 10% 11% 1 2 3 3.5 $ 100(1.09)2.5 = $124.04 100(1.09)1.5 = $113.80 100(1.09).5 = $104.40 1050 = $1050__ $1392 $ 100(1.10)2.5 = $126.91 100(1.10)1.5 = $115.37 100(1.10).5 = $ 104.88 1050 = $1050__ $1397 $ 100(1.11)2.5 = $129.81 100(1.11)1.5 = $116.95 100(1.11).5 = $ 105.36 1050 = $1050_ $1402
  • 23. 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.
  • 24. 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.
  • 25. 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.
  • 26. 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.
  • 27. 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.
  • 28. Active: Interest Rate Anticipation Strategies • Types of Interest-Rate Anticipation Strategies: • Rate-Anticipation Strategies • Strategies Based on Yield Curve Shifts
  • 29. Rate-Anticipation Strategies • Substitution Swap • Pure Yield pickup Swap • Tax Swap
  • 30. 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.
  • 31. 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.
  • 32. 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.
  • 33. 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.
  • 34. Passive Strategies • Passive Strategies: Strategies that once they are formed do not require active management or changes.
  • 35. 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.
  • 36. 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.
  • 37. 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.
  • 38. 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 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.
  • 39. 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%.
  • 40. Immunization: Duration Gap Analysis by Banks Assets Amount Macaulay Weighted Liabilities Amount Macaulay Weighted in millions of $ Duration Duration in millions of $ Duration Duration Reserves 10 0.0 0.000 Demand Deposits 15 1.0 0.100 Short-Term Securities 15 0.5 0.050 Nonnegotiable Deposits 15 0.5 0.050 Intermediate Securities 20 1.5 0.200 Certificates of Deposit 35 0.5 0.117 Long-Term Securities 20 5.0 0.667 Fed Funds 5 0.0 0.000 Variable-Rate Mortgages 10 0.5 0.033 Short-Term Borrowing 40 0.5 0.133 Fixed-Rate Mortgages 25 6.0 1.000 Intermediate-Term Borrowing 40 4.0 1.067 Short-Term Loans 20 1.0 0.133 150 1.467 Intermediate Loans 30 4.0 0.800 150 2.88
  • 41. Immunization: Duration Gap Analysis by Banks • The bank’s 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 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) = -.0262 Liabilities: %P = -(1.467) (.01/1.10) = -.0133 Change in Net Worth = (-.0262)($150M) – (-.0133)($150M) = -$1.93M
  • 42. Immunization: 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.
  • 43. Immunization: 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.
  • 44. Hybrid Strategies Immunization and Rebalancing • Hybrid Strategies –Rebalancing Immunized Positions –Contingent Immunization
  • 45. 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.
  • 47. The Manager’s Choices • Leave the portfolio alone • Rebalance the portfolio • Asset allocation and rebalancing within the aggregate portfolio • Change the portfolio components • Indexing
  • 48. Leave the Portfolio Alone • A buy and hold strategy means that the portfolio manager hangs on to its original investments • Academic research shows that portfolio managers often fail to outperform a simple buy and hold strategy on a risk-adjusted basis
  • 49. Rebalance the Portfolio • Rebalancing a portfolio is the process of periodically adjusting it to maintain the original conditions
  • 50. Rebalancing Within the Portfolio • Constant mix strategy • Constant proportion portfolio insurance
  • 51. Constant Mix Strategy • The constant mix strategy: – Is one to which the manager makes adjustments to maintain the relative weighting of the asset classes within the portfolio as their prices change – Requires the purchase of securities that have performed poorly and the sale of securities that have performed the best
  • 52. Constant Mix Strategy (cont’d) Example A portfolio has a market value of $2 million. The investment policy statement requires a target asset allocation of 60 percent stock and 30 percent bonds. The initial portfolio value and the portfolio value after one quarter are shown on the next slide.
  • 53. Equity Portfolio Management: Active or Passive? • Passive: – LT buy and hold – Indexation • Replication of an index (broad or specialized • Sampling and Tracking Error •  = 0 – Rebalancing
  • 55. Rebalancing an Equity Portfolio • Why? – to manage tracking error (if indexing or not) – to maintain a desired set of weights or risk level – client needs change – Market risk level changes – bankruptcies, mergers, IPOs • Why not? – it’s costly!
  • 56. Rebalancing: Example 1 Jan. 1 Price per Share Number of Shares $ Value % of Total Value Beta X 20 167 $3340 0.333 1.2 Y 15 222 $3330 0.333 1.6 Z 35 95 $3325 0.333 0.8 Total $9995 1.20
  • 57. Rebalancing: Example 1 June 1 Price per Share Number of Shares $ Value % of Total Value Beta down 20% X 16 167 $2672 0.256 1.3 up 33% Y 20 222 $4440 0.425 1.7 unch. Z 35 95 $3325 0.319 0.8 Total 10445 1.31
  • 58. Rebalancing: Example 1 • Portfolio is no longer equally weighted • To rebalance: – Sell Y, buy X and Z – Positions must be reset to $10445/3 = $3482 – Sell 4440 - 3482 = $958 of Y (48 shares) – Buy 3482 - 2672 = $810 of X (51 shares) – Buy 3482 - 3325 = $157 of Z (4 shares)
  • 59. Rebalancing: Example 1 June 1 Rebal- anced Price per Share Number of Shares $ Value % of Total Value Beta X 16 167 $3488 0.334 1.3 Y 20 222 $3480 0.334 1.7 Z 35 95 $3465 0.332 0.8 Total 10433 1.27
  • 60. Rebalancing: Example 1 • LT effects of this strategy? • Alternatives? • Example 2: Rebalancing to reestablish a specific level of systematic risk (Target Beta = 1.2)
  • 61. Rebalancing: Example 2 • Reestablishing a beta of 1.2: – No unique solution for more than 2 securities – Need to sell high  stocks and buy low  stocks – For example, sell Y, buy Z, hold X constant – p = (.256)(1.3)+(WY)(1.7)+(1-.256-WY)(.8) – Find Y such that p = 1.2 • WY = .302 => WZ = 1-.256-.302 = .442 • $3488 in X, $3151 in Y, $4611 in Z
  • 62. Active Equity Strategies • Beat the market on a risk adjusted basis! • Need a benchmark • More expensive: turnover, research • Must outperform on a fee-adjusted basis
  • 63. Active Equity Strategies • Styles: – Sector Rotation: move in/out of sectors as economy improves/declines – Earnings Momentum: overweight stocks displaying above average earnings growth – Enhanced Index Fund - majority of funds track index, some funds are actively managed – Quantitative Investment Management
  • 64. Quantitative Investment Management • How do we forecast performance ? – Screening (Fundamental or Technical factors) – Rank based on some set of factors that correlates with future performance (such as regression analysis) • How do we improve forecasting model? – Add more data (more observations) – Uncover new causal relationships (variables)
  • 65. Quantitative Investment Management • Regardless of forecast, there are three basic results common to QIM: – 1. Information comes from unexpected events • events with low probability have high info content!
  • 66. QIM – 2. Profitable QIM techniques won’t be commercialized • Starting with a multifactor model: • Ri = b1F1 + b2F2 + . . . + bkFk + ei • It isn’t easy to get information from these residuals: – 1. patterns are complex – 2. quality of data is limited – 3. outliers may draw undue attention (although irrelevant) – 4. human judgement is superior – 5. analysis must be flexible (more data, constraints) – 6. danger of data mining – 7. even if significant, outliers are too few in number!
  • 67. QIM – 3. Non-linear models are important • Neural Networks • Genetic Algorithms • Fuzzy Logic • Non-Linear Dynamics • Classification Trees (Recursive Partitioning)
  • 68. Constant Mix Strategy (cont’d) Example (cont’d) What dollar amount of stock should the portfolio manager buy to rebalance this portfolio? What dollar amount of bonds should he sell? Date Portfolio Value Actual Allocation Stock Bonds 1 Jan $2,000,000 60%/40% $1,200,00 $800,000 1 Apr $2,500,000 56%/44% $1,400,00 0 $1,100,000
  • 69. Constant Mix Strategy (cont’d) Example (cont’d) Solution: a 60%/40% asset allocation for a $2.5 million portfolio means the portfolio should contain $1.5 million in stock and $1 million in bonds. Thus, the manager should buy $100,000 worth of stock and sell $100,000 worth of bonds.
  • 70. Constant Proportion Portfolio Insurance • A constant proportion portfolio insurance (CPPI) strategy requires the manager to invest a percentage of the portfolio in stocks: $ in stocks = Multiplier x (Portfolio value – Floor value)
  • 71. Constant Proportion Portfolio Insurance (cont’d) Example A portfolio has a market value of $2 million. The investment policy statement specifies a floor value of $1.7 million and a multiplier of 2. What is the dollar amount that should be invested in stocks according to the CPPI strategy?
  • 72. Constant Proportion Portfolio Insurance (cont’d) Example (cont’d) Solution: $600,000 should be invested in stock: $ in stocks = 2.0 x ($2,000,000 – $1,700,000) = $600,000 If the portfolio value is $2.2 million one quarter later, with $650,000 in stock, what is the desired equity position under the CPPI strategy? What is the ending asset mix after rebalancing?
  • 73. Constant Proportion Portfolio Insurance (cont’d) Example (cont’d) Solution: The desired equity position after one quarter should be: $ in stocks = 2.0 x ($2,200,000 – $1,700,000) = $1,000,000 The portfolio manager should move $350,000 into stock. The resulting asset mix would be: $1,000,000/$2,200,000 = 45.5%
  • 74. Rebalancing Within the Equity Portfolio • Constant proportion • Constant beta • Change the portfolio components • Indexing
  • 75. Constant Proportion • A constant proportion strategy within an equity portfolio requires maintaining the same percentage investment in each stock • Constant proportion rebalancing requires selling winners and buying losers
  • 76. Constant Proportion (cont’d) Example A portfolio of three stocks attempts to invest approximately one third of funds in each of the stocks. Consider the following information: Stoc k Price Shares Value % of Total Portfolio FC 22.00 400 8,800 31.15 HG 13.50 700 9,450 33.45 YH 50.00 200 10,000 35.40 Total $28,25 0 100.00
  • 77. Constant Beta Portfolio • A constant beta portfolio requires maintaining the same portfolio beta • To increase or reduce the portfolio beta, the portfolio manager can: – Reduce or increase the amount of cash in the portfolio – Purchase stocks with higher or lower betas than the target figure – Sell high- or low-beta stocks – Buy high- or low-beta stocks
  • 78. Change the Portfolio Components • Changing the portfolio components is another portfolio revision alternative • Events sometimes deviate from what the manager expects: – The manager might sell an investment turned sour – The manager might purchase a potentially undervalued replacement security
  • 79. Indexing • Indexing is a form of portfolio management that attempts to mirror the performance of a market index – E.g., the S&P 500 or the DJIA • Index funds eliminate concerns about outperforming the market • The tracking error refers to the extent to which a portfolio deviates from its intended behavior
  • 80. Window Dressing • Window dressing refers to cosmetic changes made to a portfolio near the end of a reporting period • Portfolio managers may sell losing stocks at the end of the period to avoid showing them on their fund balance sheets
  • 81. Contributions to the Portfolio • Periodic additional contributions to the portfolio from internal or external sources must be invested • Dividends: – May be automatically reinvested by the fund manager’s broker – May have to be invested in a money market account by the fund manager
  • 82. When Do You Sell Stock? • Introduction • Rebalancing • Upgrading • Sale of stock via stop orders • Extraordinary events • Final thoughts
  • 83. Rebalancing • Rebalancing can cause the portfolio manager to sell shares even if they are not doing poorly • Profit taking with winners is a logical consequence of portfolio rebalancing
  • 84. Upgrading • Investors should sell shares when their investment potential has deteriorated to the extent that they no longer merit a place in the portfolio • It is difficult to take a loss, but it is worse to let the losses grow
  • 85. Change in Client Objectives • The client’s investment objectives may change occasionally: – E.g., a church needs to generate funds for a renovation and changes the objective for the endowment fund from growth of income to income • Reduce the equity component of the portfolio
  • 86. Change in Market Conditions • Many fund managers seek to actively time the market • When a portfolio manager’s outlook becomes bearish, he may reduce his equity holdings
  • 87. Thank You Please forward your query To: surajamity@yahoo.com

Editor's Notes

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