683_Chapt_6 [Part 1]
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Transcript of 683_Chapt_6 [Part 1]
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Chapter 6
FIXED-INCOME
PORTFOLIO
MANAGEMENT
The Yield Curve http://stockcharts.com/freecharts/yieldcurve.php
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Butterfly Shifts
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Moodys S&P Fitch Description
Investment grade high credit worthiness
Aaa AAA AAA Gilt edge, prime, maximum safety
Aa1
Aa2
As3
AA+
AA
AA-
AA+
AA
AA-
High-grade, high credit quality
A1
A2
A3
A+
A
A-
A+
A
A-
Upper-medium grade
Baa1
Baa2
Baa3
BBB+
BBB
BBB-
BBB+
BBB
BBB-
Lower-medium grade
Bond Ratings
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Moodys S&P Fitch Description
Speculative lower credit worthiness
Ba1
Ba2
Ba3
BB+
BB
BB-
BB+
BB
BB-
Low grade, speculative
B1
B2
B3
B
B+
B
B-
Highly speculative
Predominantly speculative Substantial risk, or in default
Caa CCC+
CCC
CCC+
CCC
Substantial risk, in poor standing
Ca CC CC May be in default, highly speculative
C C C Extremely speculative
CI Income bonds no interest being paid
D DDD
DD, D
Default
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2. A FRAMEWORK
1. Select the benchmark (bond index or client's liability structure) and specify a
desired outcome relative to that
benchmark
2. Identify the risks (tracking error or relevant
risks for a liability structure)
3. Specify the constraints imposed by the
client, government regulators, or client'stax needs
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3. MANAGING FUNDS AGAINST A BONDMARKET INDEX
Passive management:
markets expectations are essentially correct
the manager has no reason to disagree with
these expectations
the manager has no particular expertise in
forecasting
Active management: active managers believe that they possess
superior skills in interest rate forecasting, credit
valuation, or in some other area that can be
used to exploit opportunities in the market
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3. Enhanced indexing by small risk factor
mismatches:
Match duration, but tilt the portfolio in favor of
any of the other risk factors
The mismatches are small
4. Active management by larger risk factor
mismatches:
may overweight A bonds relative to AA/Aaa
bonds
corporates versus Treasuries
position to take advantage of an anticipated
twist in the yield curve
adjust the portfolios duration
3.2. Reasons for Indexing
Indexed portfolios have lower fees than
actively managed accounts
Outperforming a broadly based market
index on a consistent basis is difficult
Broadly based bond index portfolios
provide excellent diversification. Popular U.S. bond market indices each have
a minimum of 5,000 issues
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Which benchmark index should I
choose? Choice depends on 3 factors:
Market value risk: the market value risk of the
portfolio and benchmark index should be
comparable.
Income risk: the portfolio and benchmark
should provide comparable assured income
streams
Liability framework risk: investors with long-term liabilities should select a long index
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3.2.2. Risk Profile Matching
Cell-matching (or stratified sampling):
Divide the benchmark into cells representing
risk factors
Select sample bonds from each cell to
represent the entire cell
The total dollar amount selected from a cell
may be based on that cells percentage of thetotal
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Multifactor model technique:
Match risk factors, such as:
1. Duration
2. Key rate durations: sensitivity of bond price
to changes in eleven key rates: 3 months, and 1, 2, 3, 5, 7, 10, 15, 20, 25, and 30 years
Useful for nonparallel changes in yield curve
Match the portfolios present value distributionof cash flows to that of the benchmark:
present value distribution of cash flows
3.2.2. Risk Profile Matching
PV distribution of cash flows A list that associates with each time period
the fraction of the portfolios duration that
is attributable to cash flows falling in that
period.
Calculation steps:
1. Project the cash flow for each issue in the
index for specific periods (usually six-monthintervals). Compute a total present value.
1( )PV C ( )tall
PV C2( )PV C 3( )PV C
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PV distribution of cash flows
Calculation steps:2. Divide each periods present value by the
total present value
3. Calculate the contribution of each periods
cash flows to portfolio duration:
1( )
( )t
all
PV C
PV C2( )
( )t
all
PV C
PV C3( )
( )t
all
PV C
PV C
1( )1( )
t
all
PV C
PV C
2( )2( )
t
all
PV C
PV C
3( )3( )
t
all
PV C
PV C
PV distribution of cash flows Calculation steps:
4. Add each periods contribution to obtain the
total duration:
5. Divide each contribution by the total duration:
1( )1( )
t
all
PV C
PV C
D
2( )2( )
t
all
PV C
PV C
D
3( )3( )
t
all
PV C
PV C
D
3( )
( )t
all
PV CD t
PV C
=
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PV distribution of cash flows
We get a list:
It is this distribution that the indexer will try
to duplicate.
3. Sector and quality percent
match the percentage weight in the various
sectors and qualities of the benchmark index
4. Sector duration contribution
match the index duration proportionally to
sector duration contributions
5. Quality spread duration contribution spread duration: measure that describes how a
non-Treasury securitys price will change as a
result of the widening or narrowing of the
spread. Match it to the quality categories.
3.2.2. Risk Profile Matching
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6. Sector/coupon/maturity cell weights
7. Issuer exposure
do not replicate the index with too few
securities, as to minimize event risk exposure.
3.2.2. Risk Profile Matching
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3.2.3. Tracking Risk/Tracking Error
Tracking risk arises primarily from
mismatches between a portfolios risk
profile and the benchmarks risk profile.
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3.2.3. Tracking Risk/Tracking Error
If the tracking risk for a portfolio is 30 bps,
one standard deviation either side of the
mean captures approximately 68% of all the
observations:
3.2.4. Enhanced Indexing
Strategies
1. Lower cost enhancements:
Maintain tight controls on trading costs and
management fees (e.g. have outside
managers re-bid their fees every 2/3 years)
2. Issue selection enhancements:
Find undervalued securities
3. Yield curve positioning:
overweight the undervalued areas of the yield
curve
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3.3. Active Strategies
3.3.1. Extra Activities Required for theActive Manager:
1. Identify which index mismatches are to be
exploited
2. Extrapolate the markets expectations from the
market data
3. Independently forecast the necessary inputs
and compare these with the markets
expectations4. Estimate the relative values of securities in
order to identify areas of under- or
overvaluation
3.3.2. Total Return Analysis and
Scenario Analysis
Before executing a trade, a manager must
analyze its impact on the portfolios return.
2 primary tools:
total return analysis:
assess the expected effect of a trade on the
portfolios total return given an interest rate
forecast - usually one rate change only.
scenario analysis:
evaluate the impact of the trade on expected total
return under all reasonable sets of assumptions
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4. MANAGING FUNDS
AGAINST LIABILITIES Dedication strategies are designed toaccommodate specific funding needs of the
investor:
Liability Classes
The more uncertain the liabilities, the more
difficult it becomes to use a passivededication strategy to achieve the
portfolios goals.
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4.1.1. Immunization Strategies
Immunization:
locks in a rate of return over a particular
time horizon, determined as the duration of
the asset portfolio.
4.1.1.1. Classical Single-Period
Immunization:
1. Specified time horizon.
2. Assured rate of return to horizon.3. Initial PV of cash flows = PV of future liability
4.1.1.1. Classical Single-Period
Immunization
Periodical rebalancing is required
trade-off between costs and benefits of
rebalancing
Target yield depends on shape of yield
curve
Immunized time horizon Typical is five years, a common planningperiod for GICs.
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4.1.1.1. Classical Single-Period
Immunization Dollar Duration
measure of change in portfolio value for a 100
bps change in market yields:
mB D B i
Rebalancing Steps1. Move forward in time, shift the yield
curve. Compute new dollar duration
2. Calculate the rebalancing ratio by dividing
the original dollar duration by the new
dollar duration.
3. Multiply the new market value of the
portfolio by the desired percentagechange in Step 2. This number is the
amount of cash needed for rebalancing.
See example 6-7.
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Controlling Position
We can also rebalance by changing the
weight of one particular security (the
controlling position).
Benefits/disadvantages?
4.1.2. Extensions of Classical
Immunization Classical immunization assumes:
Yield curve changes are parallel shifts only
There are no interim cash inflows or outflows
before the horizon date.
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4.1.2. Extensions of Classical
Immunization Extension 1: nonparallel shifts
use multifunctional duration (= functional
duration, or key rate duration)
Fong and Vasicek (discussed later)
Extension 2: non-fixed time horizon
Marshall and Yawitz (1982)
Extension 3: multiple liabilities
Extension 4: adding an active element
Leibowitz and Weinberger (1981) "contingent
immunization"
Matching Duration + Convexity
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4.1.2.2. Types of Risk
Interest rate risk
duration
Contingent claim risk
presence of calls/puts
Cap risk
presence of a cap in coupon payments for
floating-coupon bonds
Fong and Vasicek (1984)
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4.2. Cash-Flow Matching
Strategies
Buy a bond with a maturity matching last
liability, with principal equal to liability size
Do the same for the next-to-last liability,
etc.
Previous liabilities are decreased by the
coupons of bonds already bought:
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4.2.2. Extensions of Basic
Cash-Flow Matching Symmetric cash-flow matching allow cash flows occurring both before and after the
liability date to be used to meet a liability
Combination matching / horizon matching
create a portfolio that is duration-matched with the
added constraint that it be cash-flow matched in the
first few years, usually the first five years
liquidity needs are provided for in the initial cash-flow matched
period
cost to fund liabilities is greater than immunization only
5. OTHER FIXED-INCOME
STRATEGIES
5.1. Combination Strategies
active/passive combination
active/immunization combination
5.2. Leverage
leverage magnifies a portfolios rate of return
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5.2.2. Repurchase Agreements
Contract involving the sale of securities
such as Treasury instruments coupled with
an agreement to repurchase the same
securities on a later date
Very much like a collateralized loan: the
difference in selling price and purchase
price is referred to as the interest on the
transaction.
5.2.2. Repurchase Agreements
Term to maturity:
typically short (overnight or a few days)
can roll over
Transfer of securities may be:
Physical (high cost)
Processed through bank accounts Through a custodial account at the sellers
bank
Not done, if relationship is established
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5.2.2. Repurchase Agreements
Repo rate depends on:
Quality of the collateral
Term of the repo
Delivery requirement
Availability of collateral (high/low supply)
Prevailing interest rates in the economy
Seasonal factors