Cycle 6 PM Session 5.ppt

PAN African e-Network Project
MFM
PORTFOLIO MANAGEMENT
Semester - VI
Session - 5
By – Suraj Prakash

Types of Bond Strategies
1. Active Strategies
2. Passive Strategies
3. Hybrid 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

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

• 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

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 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.
$2,675,737 of 2-year bonds: $2,675,737 = ($3,000,000 –
(.05)($3,809,524))/1.05.
$643,559 of 1-year bonds: $643,559 = ($1,000,000 –
(.05)($3,809,524) – (.05)($2,675,737))/1.05

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.

• 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%.

• 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.

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

• 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.

• 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.

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.

• 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.

• 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.

• 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.

• 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.

• 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%.

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

• 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

• 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.

• 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
• 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.

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

(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

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

• 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)

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

• LT effects of this strategy?
• Alternatives?
• Example 2: Rebalancing to reestablish a
specific level of systematic risk (Target
Beta = 1.2)

• 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)

(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

(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
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
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

Cycle 6 PM Session 5.ppt

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