R21 Fixed Income Portfolio Management - Part I

Market value risk of portfolio and benchmark index shouldbe comparable Given a normal yield curve and a risk-averse investor should we go with a long duration or short duration index?. L

Reading 21

Fixed Income Portfolio Management – Part I

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1 Introduction

2 Framework for Fixed Income Portfolio Management

3 Managing Funds Against a Bond Market Index

4 Managing Funds Against Liabilities

2 Framework for

Fixed-Income Portfolio

Management

3 Managing Funds Against a Bond Market Index

3.1 Classification of Strategies

3.2 Indexing (Pure and Enhanced)

3.3 Active Strategies

3.4 Monitoring/Adjusting Portfolio and Performance Evaluation

What type of investorsmight follow this strategy?

3.1 Classification of Strategies

1 Pure Bond Indexing (or full replication approach)

2 Enhanced Indexing by Matching Primary Risk Factors

3 Enhanced Indexing by Small Risk Factor Mismatches

4 Active Management by Larger Risk Factor Mismatches

5 Full-blown Active Management

Passive Style:

Manager has no reason

to disagree with market

expectations

Active Style:

Manager believes he has

superior forecasting and/or

valuation skills

3.2 Indexing (Pure and Enhanced)

• Indexed funds have lower fees than actively managed accounts

• Outperforming market index consistently is difficult

• Broad based index portfolios provide diversification

Why

Index?

How do you select the benchmark index?

Market value risk of portfolio and benchmark index should

be comparable

Given a normal yield curve and a risk-averse investor should we

go with a long duration or short duration index?

Income risk should be comparable

Credit risk should be comparable

Liability framework risk should be minimized

General Considerations in Selecting an Index

Manager’s Indexed Portfolio Mimics Benchmark Bond Market Index Mimics Market of All Bonds

(e.g Lehman Brothers Aggregate Index)

Risk in Detail: Risk Profiles

Risk profile: detailed tabulation of index’s risk exposures

Changes in the yield curve represent a major source of risk for the bond market

Exhibit 3: Typical Fixed Income Exposures

Strategies for Constructing a Portfolio

Cell Matching Technique (also called Stratified Sampling)

Divide benchmark into (weighted) cells that represent qualities that should reflect

the risk factors of the index

Select bonds from each cell to create portfolio

Multifactor Model Technique

Use set of primary risk factors that drive bond returns

1 Duration

2 Key Rate Duration and PV Distribution of Cash Flows (match portfolio’s cash flow

PV with that of benchmark)

Agency MBS(40%)

3 Sector and Quality Percent

4 Sector Duration Contribution

5 Quality Spread Duration Contribution

6 Sector/Coupon/Maturity Cell Weights

7 Issuer Exposure

Other risk factors that drive bond returns (cont…)

Tracking Risk

Active Return = Portfolio Return – Index Return

Tracking Risk = Stddev (Active Return)

Example 2/Exhibit 4

Tracking risk arises from mismatches between a portfolio’s risk profile and benchmark’s risk profileExamples of mismatches:

1 Portfolio duration What if benchmark duration is 5 and portfolio duration is 5.5?

2 Key rate duration and present value distribution of cash flows

3 Sector and quality percent

4 Sector duration contribution Say sector % matched but duration different…

5 Quality spread duration contribution

Spread duration describes how a non-Treasury security’s price will change due to

widening or narrowing of the spread

Spread duration for a 60-bond portfolio and benchmark index based on sectors

Enhanced Indexing Strategies

• Lower cost enhancements

• Issue selection enhancements

• Yield curve positioning

• Sector and quality positioning

– Corporate bonds with maturity < 5 years

– Periodic over or underweighting of sectors (treasuries vs corporate bonds)

Index  no transaction costs Portfolio  transaction costs Index return > portfolio return

Minimize difference through enhancements

3.3 Active Strategies

1 Identify which index mismatches are to be exploited

2 Extrapolate the market’s expectations (or inputs) from the market data

3 Independently forecast the necessary inputs and compare these with the market’s

expectations

4 Estimate the relative values of securities in order to identify areas of under or

Active managers look for large positive active return and are willing to accept high

active risk

Active managers need to…

Total Return Analysis and Scenario Analysis

Total return is the rate of return that equates the future value of the bond’s cash flows with

the full price of the bond It takes into account:

a) Coupon income

b) Reinvestment income

c) Change in price

Formula:

Total is based on a single interest rate term structure forecast

What if the forecast is wrong?

Also use scenario analysis because…

1 You can assess distribution of possible outcomes

2 Analysis can be reversed… start with range of acceptable outcomes and then

determine interest rate movements (inputs) that would result in desirable outcome

3 Contribution if individual components (parallel shift, twist) can be evaluated

4 Can evaluate a range of strategies

Section 3 Summary

4 Managing Funds Against Liabilities

4.1 Dedication Strategies

Immunization aims to construct a portfolio which, over

a specified horizon, will earn a predetermined return

regardless of interest rate changes

Cash flow matching provides future

funding of a liability stream from couponand mature principal payments of theportfolio

Classical Single Period Immunization

1 Specified time horizon

2 Assured rate of return during holding period to a fixed horizon date

3 Insulation from the effects of interest rate changes on the portfolio

value at the horizon date

Immunization Strategies

Implementation of an immunization strategy depends on the type of liabilities that the

manager is trying to meet:

1 Single Liability

2 Multiple Liabilities (DB Plan Promised Payouts)

3 General Cash Flows

You sell a 5 year GIC7.5% guaranteed

$9,642,899  $13,934,413

In you invest $9,642,899 in parvalue bonds with a YTM of 7.5%are you covered?

Are you concerned about rates

up or rates down?

Rebalancing an Immunized Portfolio

Duration changes as market yield changes and due to passage of time

Portfolio needs to be rebalanced to adjust duration, but how often?

Determining the Target Return

Say you have a normal yield curve and YTM = 7.5%

Should immunization target rate be less than or greater than YTM (7.5%)?

Portfolio should consist of liquid, high quality instruments because rebalancing is

needed to keep the portfolio duration synchronized with horizon date

The heart of a bond immunization strategy for a single liability is to match the average

duration of assets with the time horizon of the liabilities; furthermore, the initial PV of

cash flows should equal the PV of future liability

Dollar Duration is a measure of the change in portfolio value for a 100 bps change in market yieldsDollar Duration = Duration x Portfolio Value x 0.01

Example 7: Rebalancing Based on the Dollar Duration

In many ALM applications, goal is

to re-establish dollar duration to a

desired level This involves:

1) Move forward in time and

calculate new dollar duration

using new yield curve

2) Calculate rebalancing ratio

which is: original / new rr - 1

tells us % amount each

position needs to change in

order to rebalance portfolio

3) Multiply new mkt value with %

from 2 This is the cash needed

for rebalancing

Spread Duration

Spread duration is a measure of the market value of a risky bond (portfolio) will

change with respect to a 100 bps change in spread above comparable benchmark

security (portfolio)

Nominal spread

Static (zero volatility) spread

Option-adjusted spread

(Why We Need) Extensions of Classical Immunization Theory

Classical immunization theory is based on several assumptions:

1 Any changes in the yield curve are parallel changes  interest rates move either

up or down by the same amount for all maturities

2 The portfolio is valued at a fixed horizon date, and there are no interim cash

inflows or outflows before the horizon date

3 The target value of the investment is defined as the portfolio value at the horizon

date if the interest rate structure does not change (i.e., there is no change in

forward rates)

Classically immunized portfolio: target value of investment is the lower limit of the

value of the portfolio at the horizon date if there are parallel interest rate changes

But what if the if the interest rate change is not parallel???

Exhibit 13 (right) shows different

scenarios for yield curve twists

Exhibit 14 (below) shows impact on a

6-year, 6.75% bond selling to yield 7.5%

investment

Extensions of Classical Immunization Theory

Extension 1: Consider possibility of non-parallel shifts

a) Multi-functional duration = functional duration = key rate duration

b) Establish measure of immunization risk… try to minimize this risk

Extension 2: Overcome fixed-horizon limit

Extension 3: Analyze risk and return tradeoff for immunized portfolio;

try to maximize return

Extension 4: Contingent immunization Include elements of active

management

Contingent Immunization

Contingent immunization is possible when prevailing immunization rate > required rate

Example: 3 year investment horizon (6 periods) Required return = 3%

Portfolio can be immunized at 4.75%

Duration and Convexity of Assets and Liabilities

Need to consider duration and convexity of assets and liabilities

We’ve talked about duration matching

Convexity should also be matched

Types of Risk (risk of not being able to pay liabilities when due…)

Interest rate risk

Contingent Claims Risk

Ex: Callable security is called when interest rates fall

Cap Risk

Risk Minimization for Immunized

Portfolios

Assume interest rates might change

in an arbitrary non-parallel way What

is more risky: barbell portfolio or

bullet portfolio?

Portfolio with least reinvestment risk

will have the least immunization risk

Return Maximization for Immunized

Portfolios

If a substantial increase in expected

return can be accomplished with little

effect on immunization risk, the high

Multiple Liability Immunization

To assure multiple liability immunization in the case of parallel rate shifts, the

following must hold:

1 PV of assets = PV of liabilities

2 The (composite) duration of the portfolio must equal the (composite)

duration of the liabilities

3 The distribution of durations of individual portfolio assets must have a wider

range than the distribution of the liabilities

Immunization for General Cash Flows

What if a given schedule of liabilities must be met by investment funds that are not

available when portfolio is constructed?

Expected cash contributions can be considered the payments on hypothetical

securities that are part of the initial holdings

4.2 Cash Flow Matching Strategies

Select securities to match timing and amount of liabilities

Exhibit 18

Cash Flow Matching vs Multiple Liability Immunization

Cash flow matching is easy to understand

Eliminates reinvestment risk (hence no immunization risk)

But there are some challenges:

1) Cash flow matching restricts the set of securities we can work with

2) Funds from cash flow matched portfolios must be available before each

liability is due

3) Cash flow matching is more expensive

4) Cash flow matching requires a conservative rate of return for short-term

cash which is an issue because cash balances might be substantial By

contrast, an immunized portfolio is essentially fully invested at the remaining

horizon duration

Extensions of Basic Cash Flow Matching

Multiple liability immunization + cash flow matching  combination matching

Duration matched and cash flow matched in the first few years

Advantages over multiple liability immunization:

1 Liquidity needs are provided in the initial cash-flow matched period

2 Most of the curvature of yield curves is in the first few years; initial cash flow

matching reduces risk of non-parallel yield curve shifts

Major disadvantage is the higher cost