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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


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.


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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.


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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


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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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.


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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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

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