CFA 2018 level 3 schweser practice exam CFA 2018 level 3 question bank CFA 2018 CFA 2018 r21 introduction to fixed income portfolio management IFT notes

R21 Introduction to Fixed-Income Portfolio Management

IFT Notes

Introduction to Fixed-Income Portfolio Management
1. Introduction .............................................................................................................................................. 2
2. Roles of Fixed-Income Securities in Portfolios .......................................................................................... 2
2.1 Diversification Benefits ....................................................................................................................... 2
2.2 Benefits of Regular Cash Flows ........................................................................................................... 3
2.3 Inflation Hedging Potential ................................................................................................................. 3
3. Fixed-Income Mandates ........................................................................................................................... 4
3.1 Liability-Based Mandates .................................................................................................................... 4
3.1.1 Cash Flow Matching ................................................................................................................ 4
3.1.2 Duration Matching .................................................................................................................. 5
3.1.3 Contingent Immunization ....................................................................................................... 6
3.1.4 Horizon Matching.................................................................................................................... 6
3.2 Total Return Mandates ....................................................................................................................... 7
3.2.1 Pure Indexing .......................................................................................................................... 7
3.2.2 Enhanced Indexing .................................................................................................................. 8
3.2.3 Active Management ................................................................................................................ 8
4. Bond Market Liquidity............................................................................................................................... 9
4.1 Liquidity among Bond Market Sub-Sectors ...................................................................................... 10
4.2 The Effects of Liquidity on Fixed-Income Portfolio Management .................................................... 10
4.2.1 Pricing ................................................................................................................................... 10
4.2.2 Portfolio Construction........................................................................................................... 11
4.2.3 Alternatives to Direct Investment in Bonds .......................................................................... 11
5. A Model for Fixed-Income Returns ......................................................................................................... 11
5.1 Decomposing Expected Returns ....................................................................................................... 12
5.2 Estimation of the Inputs.................................................................................................................... 13
5.3 Limitations of the Expected Return Decomposition ......................................................................... 13
6. Leverage .................................................................................................................................................. 13

6.1 Using Leverage .................................................................................................................................. 13
6.2 Methods for Leveraging Fixed-Income Portfolios............................................................................. 14
6.2.1 Futures Contracts .................................................................................................................. 14
6.2.2 Swap Agreements ................................................................................................................. 14
6.2.3 Structured Financial Instruments.......................................................................................... 15
6.2.4 Repurchase Agreements ....................................................................................................... 15
6.2.5 Securities Lending ................................................................................................................. 16
6.3 Risks of Leverage ............................................................................................................................... 17
7. Fixed-Income Portfolio Taxation ............................................................................................................. 17
7.1 Principles of Fixed-Income Taxation ................................................................................................. 17
7.2 Investment Vehicles and Taxes ......................................................................................................... 18
Summary from the Curriculum ................................................................................................................... 19
Examples from the Curriculum ................................................................................................................... 22
Example 1. Adding Fixed-Income Securities to a Portfolio ..................................................................... 22
Example 2. Liability-Based Mandates (1) ................................................................................................ 23

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Example 3. Liability-Based Mandates (2) ................................................................................................ 23
Example 4. The Characteristics of Different Total Return Approaches .................................................. 23
Example 5. Decomposing Expected Returns........................................................................................... 25

Example 6. Components of Expected Return ......................................................................................... 27
Example 7. Managing Taxable and Tax-Exempt Portfolios ..................................................................... 27
This document should be read in conjunction with the corresponding reading in the 2018 Level III CFA®
Program curriculum. Some of the graphs, charts, tables, examples, and figures are copyright
2017, CFA Institute. Reproduced and republished with permission from CFA Institute. All rights reserved.
Required disclaimer: CFA Institute does not endorse, promote, or warrant the accuracy or quality of the
products or services offered by IFT. CFA Institute, CFA®, and Chartered Financial Analyst® are
trademarks owned by CFA Institute.

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R21 Introduction to Fixed-Income Portfolio Management

IFT Notes

1. Introduction
Fixed-income markets include publicly traded securities (such as commercial paper, notes, and bonds)
and non-publicly traded instruments (such as loans and privately placed securities).
This reading discusses the role of fixed-income securities in portfolios, types of fixed-income portfolio
mandates, bond market liquidity and its effects on pricing and portfolio construction, determining a
model for fixed-income returns, use of leverage in fixed-income portfolios, and considerations in
managing fixed-income portfolios for both taxable and tax-exempt investors.
This section addresses LO.a:
LO.a: discuss roles of fixed-income securities in portfolios;

2. ROLES OF FIXED-INCOME SECURITIES IN PORTFOLIOS
Fixed-income securities play different important roles in investment portfolios, including diversification,
regular cash flows, and possible inflation hedging.

2.1 Diversification Benefits
In general, fixed-income securities have low correlation with other asset classes (including equity
securities, real estate, and commodities); hence, adding fixed-income securities to portfolios provide
diversification benefits. Refer to the table below. There are various fixed income indexes and other asset
classes, i.e., US S&P500 (which represents US equity). If we take Bloomberg Barclays US Aggregate
(representing an overall index for US bonds), its correlation with S&P500 is -0.27.

Source: Authors’ calculations for the period January 2003 to September 2015, based on data from
Barclays Risk Analytics and Index Solutions; J.P. Morgan Index Research; S&P Dow Jones Indices.
However, it is important to note that these correlations are not constant over time. The correlation
between the asset classes may increase or decrease, depending on the circumstances and capital
market dynamics. For example, during periods of market stress, the correlation between riskier assets

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such as equity securities and high-yield bonds may increase while at the same time, the correlation
between government bonds and equity securities, as well as between government bonds and high-yield

bonds may decrease.
Besides having a lower correlation with other asset classes, bonds are generally less volatile than other
major asset classes and thus help in reducing the overall risk of a portfolio. Like correlation, volatility
(standard deviation) of asset class returns may also vary over time. For example, if interest rate volatility
increases, the near-term volatility of returns tends to increase relative to the average volatility over a
long historical period. Similarly, lower credit quality (high-yield) bonds may exhibit higher volatility of
returns during times of financial stress, because a decline in credit quality leads to increase in the
probability of default.

2.2 Benefits of Regular Cash Flows
Fixed-income investments play another important role in investment in the form of regular cash flows.
Regular and predictable cash flows help investors in meeting their known future obligations such as
tuition payments, pension obligations, or payouts on life insurance policies. Investors can select fixedincome securities whose timing and magnitude of cash flows match the timing and magnitude of the
projected future liabilities. For example, a 10-year coupon paying bond can be used to cover an
investor’s living expenses over a 10-year horizon. Sometimes, investors may create “ladder” bond
portfolios which comprise bonds of different maturities. Ladder portfolios help investors in balancing
price and reinvestment risk.
Regular cash flows benefit relies on the assumption that no credit event (such as an issuer defaulting on
scheduled interest or principal payment) or other market events (such as a decrease in interest rates
increasing prepayments of mortgages underlying mortgage-backed securities) will occur.

2.3 Inflation Hedging Potential
Bonds with floating-rate coupons provide a hedge against inflation because the reference rate is
adjusted for inflation. However, the principal payment at maturity is unadjusted for inflation. Inflationlinked bonds provide inflation hedging benefits as their coupon is directly linked to an index of
consumer prices and the principal is also adjusted for inflation. In inflation-linked bonds, the volatility of
the returns depends on the volatility of real, rather than nominal, interest rates. As a result, inflationlinked bonds exhibit lower return volatility than conventional bonds and equities. Owing to lower
volatility and inflation hedging benefits, adding inflation-indexed bonds to diversified portfolios of bonds
and equities results in superior risk-adjusted real portfolio returns.
Exhibit 2 below illustrates inflation protection provided by type of bond.
Exhibit 2

Coupon
Fixed-coupon bonds

Principal

Inflation unprotected

Inflation unprotected

Floating-coupon bonds

Inflation protected

Inflation unprotected

Inflation-linked bonds

Inflation protected

Inflation protected

Zero-coupon inflation-linked
bonds

Not applicable

Inflation protected

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R21 Introduction to Fixed-Income Portfolio Management
Capital-indexed inflation-linked
bonds

IFT Notes

A fixed coupon rate is applied to a principal amount that is adjusted
for inflation throughout the bond’s life.

Refer to Example 1 from the curriculum.
This section addresses LO.b:
b. describe how fixed-income mandates may be classified and compare features of the mandates;

3 FIXED-INCOME MANDATES
There are two types of fixed-income mandates, i) liability-based mandates and ii) total return mandates.

3.1 Liability-Based Mandates
Liability-based mandates aim at matching or covering expected liability payments with future projected
cash inflows. They are also called structured mandates, asset/liability management (ALM), or liabilitydriven investments (LDI). Users of liability-based mandates include individuals funding specific cash flow
and lifestyle needs as well as institutions such as banks, insurance companies, and pension funds.
Approaches to liability-based mandates: Liability-based mandates rely on immunization. Immunization
is an asset/liability management approach that focuses on minimizing the risks associated with a change
in market interest rates in a fixed-income portfolio over a known time horizon. Immunization
approaches include:
i.

ii.
iii.
iv.

Cash flow matching
Duration matching
Contingent immunization
Horizon matching

3.1.1 Cash Flow Matching
Cash flow matching aims at precisely matching all future liability payouts by cash flows from bonds or
fixed-income derivatives, such as interest rate futures, options, or swaps.
Exhibit 3 shows the results of a cash flow matching approach for a liability stream and a bond portfolio.
Future liability payouts are exactly matched by coupon and principal payments from bond portfolio. As a
result, cash inflows are not required to be reinvested.

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Limitations of cash flow matching approach:







It is quite difficult to perfectly match cash flows.
It is a costly approach as it involves high transaction costs.
This approach suffers from timing mismatches because some cash inflows tend to precede
corresponding cash outflows. This mismatch results in reinvestment risk.
As market conditions change, the lowest cost cash flow matching portfolio may change.
This approach may fail to meet its objective in case of a default event or a prepayment event.

3.1.2 Duration Matching
As the name implies, duration matching approach aims at matching the duration of assets and liabilities,
such that the liability portfolio and the bond portfolio are affected similarly by a change in interest rates.
In duration matching following two conditions need to be met:
i.
ii.

A bond portfolio’s duration must equal the duration of the liability portfolio;
The present value of the bond portfolio’s assets must equal the present value of the liabilities at
current interest rate levels.

This implies the following,
 If interest rates decrease, an increase in bond prices offsets the decrease in reinvestment
income.
 If interest rates increase, higher reinvestment income offsets the decrease in bond prices.
It is important to note that immunized portfolio is not fully immunized and some immunization risk
almost always exists. Following are some important considerations for an immunized portfolio:
 Immunization protects only against a parallel shift in the yield curve.
 A portfolio is an immunized portfolio only at a given point in time and thus portfolio needs to be

rebalanced periodically in response to changes in market conditions in order to maintain
immunization.
 Owing to periodic rebalancing requirement, it is important to consider the liquidity of the bond
portfolio; rebalancing and the need to liquidate positions can result in high portfolio turnover
 Immunized portfolio is not fully immunized because immunization assumes that there is no default
risk.
 Immunization can be used for bonds with embedded options if we use effective duration of bonds in
place of duration as an input to the methodology.
Exhibit 4 gives an overview of key features of duration matching and cash flow matching.
Duration Matching

Cash Flow Matching

Yield curve
assumptions

Parallel yield curve shifts

None

Mechanism

Risk of shortfall in cash flows is
minimized by matching duration
and present value of liability stream

Bond portfolio cash flows match
liabilities

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R21 Introduction to Fixed-Income Portfolio Management

Rebalancing

Frequent rebalancing required

Not required but often desirable

Complexity

High

Low

IFT Notes

3.1.3 Contingent Immunization
Contingent immunization is a hybrid approach, which combines immunization with an active
management approach when the value of asset portfolio is greater than the present value of the liability
portfolio. The portfolio manager is allowed to actively manage the asset portfolio, or some portion of
the asset portfolio by investing it into any asset category, including equity, fixed-income, and alternative
investments, as long as the value of the actively managed portfolio exceeds a specified value
(threshold). However, if the actively managed portfolio value falls to the specified threshold, active
management ceases and a conventional duration matching or a cash flow matching approach is put in

place. This strategy requires careful monitoring and adjusting down risk when approaching safety net
level.

3.1.4 Horizon Matching
This approach is a hybrid of cash flow and duration matching approaches. Under this approach, shortterm liability portion (i.e. four or five years) is covered by a cash flow matching approach, whereas the
long-term liability portion of total liability portfolio is covered by a duration matching approach. In other
words, the cash flows due up to a certain intermediate horizon are matched on a cash flow basis, and
the cash flows due after this intermediate horizon are matched on a duration basis.
Refer to Example 2 from the curriculum.
Refer to Example 3 from the curriculum.

3.2 Total Return Mandates
Total return mandates aim at meeting objectives based on a specified absolute return or a relative
return. For example, they focus on either tracking or outperforming a market-weighted fixed-income
benchmark. Unlike liability-based mandate, total return mandate does not attempt to match the
liabilities. Nevertheless, both mandates aim at achieving the highest risk-adjusted returns, given a set of
constraints.
Total return mandates can be classified into the following three approaches based on their target active
return and active risk levels.
1. Pure indexing
2. Enhanced indexing
3. Active management

3.2.1 Pure Indexing
Under pure indexing approach, portfolio fully replicates the bond index by including all of the underlying
securities in the same proportions as the index. This implies that the targeted active return and active

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risk are both zero.
Advantages:




This approach results in very little, or zero, tracking error.
Risk exposure (such as duration, credit (or quality) risk, sector risk, call risk, and prepayment risk) of
the bond portfolio is the same as that of the index.
This approach involves relatively low administrative fees.

Disadvantages:





It is difficult and expensive to precisely replicate most bond indexes because many bonds included in
standard indexes are illiquid.
Although all or most of the known systematic risk factors can be matched with the benchmark index
to the extent possible, but the issuer-specific (or idiosyncratic) risk remains. This risk can be
mitigated if both the benchmark index and the portfolio are sufficiently diversified.

Even if the tracking error is zero, the portfolio return will almost always be lower than the
corresponding index return because of trading costs and management fees.

3.2.2 Enhanced Indexing
Enhanced indexing approach attempts to precisely track the benchmark’s primary risk factor exposures
(particularly duration) while allowing for mismatches for minor risk factors (e.g. sector or quality bets) in
order to generate higher returns than the benchmark. This approach involves higher turnover compared
with pure indexing.
Advantages:




It is relatively easy and less expensive to implement as compared with pure indexing approach.
This approach may generate returns higher than pure indexing approach while at the same time
exposure to primary risk factor is matched with that of benchmark index.
Administration/management fees are relatively lower than that of fully active management
approach.

Disadvantages:




This approach has higher administration/management fees relative to pure indexing approach.
Owing to relatively higher turnover, close monitoring of turnover and the associated transaction
costs is required in order to generate positive active returns net of fees and cost.
This approach has higher tracking error than pure indexing.

3.2.3 Active Management

Active management involves large risk factor deviations from the benchmark (in particular, duration) in
an attempt to outperform the underlying benchmark.
Advantages:


This approach may result in higher expected return.

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R21 Introduction to Fixed-Income Portfolio Management


IFT Notes

This approach provides more flexibility to managers.

Disadvantages:




This approach involves higher tracking error and higher risk.
This approach has higher management fees than pure or enhanced index managers. As a result, it is
quite difficult to generate positive active returns net of fees and cost.
This approach results in significant portfolio turnover.

Refer to the table below that summarizes all the three approaches.
Pure Indexing

Enhanced Indexing

Active Management

Objective

Match benchmark
return and risk as
closely as possible

Modest outperformance
(generally 20 bps to 30 bps) of
benchmark while active risk is
kept low (typically around 50 bps
or lower)

Higher outperformance
(generally around 50 bps or
more) of benchmark and
higher active risk levels

Portfolio
weights

Ideally the same as
benchmark or only

slight mismatches

Small deviations from underlying
benchmark

Significant deviations from
underlying benchmark

Risk factor
matching

Risk factors are
matched exactly

Most primary risk factors are
closely matched (in particular,
duration)

Turnover

Similar to underlying
benchmark

Slightly higher than underlying
benchmark

Large risk factor deviations
from benchmark (in
particular, duration)
Considerably higher turnover

than the underlying
benchmark

Historically, active portfolio performance < index fund performance < benchmark index performance
Refer to Example 4 from the curriculum.
This section addresses LO.c:
c. describe bond market liquidity, including the differences among market sub-sectors, and discuss the
effect of liquidity on fixed-income portfolio management;

4 BOND MARKET LIQUIDITY
A liquid security is one that can be bought or sold quickly and with little effect on its price. Fixed-income
securities are generally less liquid compared with equities owing to various reasons as discussed below.





Unlike company’s common stock which has identical features, bonds are very heterogeneous. Each
individual bond may have its own unique maturity dates, coupon rates, early redemption features,
and other specific features.
Fixed-income markets are typically over-the- counter dealer markets and are less transparent
relative to equity markets.
Fixed income markets have higher search costs as investors have to locate desired bonds and get

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quotes from multiple dealers to obtain the most advantageous pricing.
Example: Bonds of a highly creditworthy government issuer are more liquid, have greater price
transparency, and have lower search costs than bonds of, for example, a corporate issuer with a lower
credit quality.
Bond liquidity is typically highest right after issuance; e.g., on-the-run issues are more liquid than offthe-run issues. This is because soon after bonds are issued, dealers have a supply of the bonds in their
inventory, but as time passes, many of these bonds are purchased by buy-and- hold investors.
Liquidity also has an impact on bond yields as investors demand an incremental yield (referred to as
liquidity premium) for investing in illiquid bonds, wherein the magnitude of the premium depends on
issuer, issue size and date of maturity. For example, the off-the-run 10-year US Treasury bond typically
trades at several basis points higher yield than the on-the-run bond.

4.1 Liquidity among Bond Market Sub-Sectors
Bond market liquidity varies across sub-sectors such as issuer type, credit quality, issue size, and
maturity.






Larger issue size implies higher liquidity: Due to large issuance size, use as benchmark bonds,
acceptance as collateral in the repo market, and well-recognized issuers, sovereign government
bonds are typically more liquid than corporate and non-sovereign government bonds. Similarly, in
the corporate bond market, smaller issues are generally less liquid than larger issues. Further, Bonds
of infrequent issuers are less liquid than the bonds of issuers with many outstanding issues.

High credit quality implies higher liquidity: sovereign government bonds of countries with high
credit quality are typically more liquid than bonds of lower-credit- quality countries and corporate
bonds.
Shorter maturity implies higher liquidity: Bonds with shorter term maturities tend to be more liquid
than longer-term bonds because bonds are typically purchased by buy-and- hold investors, so
longer-term bonds may be unavailable for trading for a long period.

4.2 The Effects of Liquidity on Fixed-Income Portfolio Management
Liquidity affects fixed-income portfolio management in multiple ways, including pricing, portfolio
construction, and consideration of alternatives to bonds (such as derivatives).

4.2.1 Pricing
Pricing in bond markets is less transparent than in equity markets. Bonds typically trade infrequently;
hence, it is not appropriate to use recent transaction prices to represent current value. Similarly, last
traded prices are also not representative of current market conditions, as they may be out dated. For
less frequently traded bonds, it is preferred to use matrix pricing. In matrix pricing, we use recent
transaction prices of comparable bonds (i.e. bonds which have similar features such as credit quality,
time to maturity, and coupon rate) to estimate the market discount rate or required rate of return on
less frequently traded bonds.
Benefit of matrix pricing: It is not based on complex financial modeling of bond market characteristics

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such as term structure and credit spreads.
Limitation of matrix pricing: Matrix pricing method ignores some value-relevant features between
different bonds (for example, call features).

4.2.2 Portfolio Construction
Investors who prefer higher yield (e.g. buy-and-hold investors) will likely prefer less liquid bonds for
their higher yields. In contrast, investors with higher liquidity needs would prefer more liquid bonds
despite their low yields relative to illiquid bonds. Hence, it is important to take into account the tradeoff between yield and liquidity of fixed income securities while constructing fixed income portfolios.
Since, dealers often have to carry an inventory of illiquid bonds because buy and sell orders do not
arrive simultaneously, illiquid bonds also tend to have higher bid-ask spread, which implies higher
trading costs. Higher transaction costs reduce the benefits to active portfolio decisions.
Bid-ask spreads are influenced by illiquidity, riskiness and complexity of securities. For example,




Riskiness: Bid–ask spreads in corporate or asset-backed securities tend to be higher than spreads in
government bonds.
Complexity: Conventional (plain vanilla) corporate bonds tend to have lower spreads than corporate
bonds with complex features, such as embedded options.
Illiquidity: Bonds of large, high-credit-quality corporations with many outstanding bond issues are
relatively more liquid and thus, they tend to have lower spreads compared with smaller, less
creditworthy companies.

4.2.3 Alternatives to Direct Investment in Bonds
Since transactions in fixed-income markets involve multiple challenges, investors can use fixed-income
derivatives as an alternative to direct investment in fixed income securities. Fixed-income derivatives
include exchange-traded (standardized) derivatives (for example, futures and options on futures) and

over the counter (OTC) derivatives (for example, interest rate swaps and credit default swaps). Based on
notional amount outstanding, interest rate swaps are the most widely used OTC derivative world-wide.
Other alternative to transacting in individual bonds include fixed-income exchange-traded funds (ETFs)
and pooled investment vehicles (such as mutual funds). ETFs are pooled investment vehicles and are
more liquid than underling individual securities as they allow certain qualified financial institutions
(authorized participants) to transact through in-kind deposits and redemptions (delivering and receiving
a portfolio of securities, such as a portfolio of bonds).
This section addresses LO.d:
d. describe and interpret a model for fixed-income returns;

5. A MODEL FOR FIXED-INCOME RETURNS
Investment strategies should be evaluated in terms of expected returns rather than just yields. In this
section, we will discuss the model used to decompose expected returns, estimation of inputs used in the

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model and limitations of this model.

5.1 Decomposing Expected Returns
Expected returns can be decomposed (approximately) in the following manner. It is important to note
that this model only provides an approximate output and does not reflect taxes.

Expected Return = E (R) ≈ Yield income+ Roll down return + E (Change in price based on investor's
views of yields and yield spreads) - E (Credit losses) + E (Currency gains or losses)
Where,


Yield income (or Current yield) = Annual coupon payment/Current bond price
 Assuming there is no reinvestment income, yield income = bond’s annual current yield.



𝐀𝐧𝐧𝐮𝐚𝐥𝐢𝐳𝐞𝐝 𝐑𝐨𝐥𝐥𝐝𝐨𝐰𝐧 𝐑𝐞𝐭𝐮𝐫𝐧 =
(𝐁𝐨𝐧𝐝 𝐩𝐫𝐢𝐜𝐞𝐄𝐧𝐝−𝐨𝐟−𝐡𝐨𝐫𝐢𝐳𝐨𝐧 𝐩𝐞𝐫𝐢𝐨𝐝 − 𝐁𝐨𝐧𝐝 𝐩𝐫𝐢𝐜𝐞𝐁𝐞𝐠𝐢𝐧𝐧𝐢𝐧𝐠−𝐨𝐟−𝐡𝐨𝐫𝐢𝐳𝐨𝐧 𝐩𝐞𝐫𝐢𝐨𝐝 )
𝐁𝐨𝐧𝐝 𝐩𝐫𝐢𝐜𝐞𝐁𝐞𝐠𝐢𝐧𝐧𝐢𝐧𝐠−𝐨𝐟−𝐡𝐨𝐫𝐢𝐳𝐨𝐧 𝐩𝐞𝐫𝐢𝐨𝐝

 The rolldown return represents the bond’s percentage price change assuming an
unchanged yield curve over the strategy horizon.
 As time passes and issuer does not default, a bond’s price typically moves closer to par.
This price movement is referred to as “pull to par” effect on the price of a bond trading
at a premium or a discount to par value.
 Bonds trading at a premium to their par value will experience capital losses during their
remaining life, and bonds trading at a discount relative to their par value will experience
capital gains during their remaining life.


Bond’s rolling yield = Yield income + Rolldown return.



𝐄 (𝐂𝐡𝐚𝐧𝐠𝐞 𝐢𝐧 𝐩𝐫𝐢𝐜𝐞 𝐛𝐚𝐬𝐞𝐝 𝐨𝐧 𝐢𝐧𝐯𝐞𝐬𝐭𝐨𝐫 ′ 𝐬 𝐯𝐢𝐞𝐰𝐬 𝐨𝐟 𝐲𝐢𝐞𝐥𝐝𝐬 𝐚𝐧𝐝 𝐲𝐢𝐞𝐥𝐝 𝐬𝐩𝐫𝐞𝐚𝐝𝐬) =
1

2

[−MD × ∆Yield] + [ × Convexity × (∆ Yield)2 ]
Where, MD is the modified duration of a bond, ΔYield is the expected change in yield based on
expected changes to both the yield curve and yield spread, and convexity1 estimates the effect
of the non-linearity of the yield curve.
 The expected change in price reflects an investor’s expectation of changes in yields and yield
spreads over the investment horizon. If yield curves and yield spreads are expected to
remain unchanged, this expected change is zero.


1

𝐄𝐱𝐩𝐞𝐜𝐭𝐞𝐝 𝐜𝐫𝐞𝐝𝐢𝐭 𝐥𝐨𝐬𝐬𝐞𝐬 =
Bond′ s probability of default × Expected loss severity (also known as loss given default)

Effective duration and effective convexity in case of bonds with embedded options.
Floating-rate notes have modified duration near zero.

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 Expected credit losses represent the expected percentage of decline in par value resulting
from default.
Note: In case of foreign currency denominated bonds, we need to factor in any expected fluctuations in
the currency exchange rate or expected currency gains or losses over the investment horizon.
Refer to Example 5 from the curriculum.

5.2 Estimation of the Inputs
In general,




yield income is easy to estimate;
rolldown return is relatively easy to estimate but depends on the curve-fitting technique.
Investor’s views of changes in yields and yield spreads, expected credit losses, and expected
currency movements are not easy to estimate. These components are normally based on purely
qualitative (subjective) criteria, on survey information, or on a quantitative model.

5.3 Limitations of the Expected Return Decomposition
Following are some of the limitations of expected return decomposition model:






Expected return decomposition model is an approximation and uses only duration and convexity to
summarize the price–yield relationship.
Expected return decomposition model implicitly assumes that all intermediate cash flows of the
bond are reinvested at the yield to maturity.

Expected return decomposition model ignores local richness/cheapness effects which represent
deviations of individual maturity segments from the fitted yield curve, which was obtained using a
curve estimation technique, which produces relatively smooth curves.
Expected return decomposition model ignores potential financing advantages (e.g. use of securities
for short-term borrowing).

Refer to Example 6 from the curriculum.
This section addresses LO.e:
e. discuss the use of leverage, alternative methods for leveraging, and risks that leverage creates in
fixed-income portfolios;

6. LEVERAGE
Leverage refers to the use of borrowed capital to increase the magnitude of portfolio positions.

6.1 Using Leverage
Leverage increases portfolio returns if the return on the portfolio is higher than the cost of borrowing.
The leveraged portfolio return, rp, can be expressed as follows:

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𝐫𝐏 =

𝐏𝐨𝐫𝐭𝐟𝐨𝐥𝐢𝐨 𝐫𝐞𝐭𝐮𝐫𝐧

𝐏𝐨𝐫𝐭𝐟𝐨𝐥𝐢𝐨 𝐞𝐪𝐮𝐢𝐭𝐲

=

[𝐫𝐈 × (𝐕𝐄 + 𝐕𝐁 )− (𝐕𝐁 × 𝐫𝐁 )]
𝐕𝐄

=

IFT Notes

Total return on portfolio− cost of borrowing
Portfolio′ sequity

Or
𝑽

𝐫𝐏 = 𝒓𝑰 + 𝑽 𝑩 (𝒓𝑰 − 𝒓𝑩 )
𝑬

Equation A

Where,
VE = value of the portfolio’s equity
VB = borrowed funds
rB = borrowing rate (cost of borrowing)
rI = return on the invested funds (investment returns)
rp = return on the levered portfolio
Equation A implies that the degree to which the leverage increases or decreases portfolio returns is
proportional to the use of leverage (amount borrowed), VB/VE, and the amount by which investment

return differs from the cost of borrowing, (rI – rB).



If the return of invested funds (rI) is higher than the cost of borrowing (rB), then leverage increases
the portfolio’s return.
If the return of invested funds (rI) is lower than the cost of borrowing (rB), then leverage decreases
the portfolio’s return.

6.2 Methods for Leveraging Fixed-Income Portfolios
In fixed-income portfolio, there are varieties of tools available to create leveraged portfolio exposures.
These include futures contracts, swap agreements, structured financial instruments, repurchase
agreements, and securities lending.

6.2.1 Futures Contracts
We can calculate the futures leverage using the following equation:
LeverageFutures =

Notional value − Margin
Margin

Where,
Notional value = Current value of the underlying asset × Multiplier, or the quantity of the underlying asset
controlled by the contract.

Futures contracts can be obtained for a modest investment in the form of a margin deposit.

6.2.2 Swap Agreements
Swap agreements are derivative contracts, which typically exchange – or swap – fixed-rate interest
payments for floating-rate interest payments. For example, in an interest rate swap, the fixed-rate payer

(receiver) has a short (long) position in a fixed-rate bond and long (short) position in a floating-rate

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bond.




When interest rates increase, the value of the swap to the fixed-rate payer increases because
the present value of the fixed-rate liability decreases and the floating-rate payments received
increase.
When interest rates decline, the value of the swap to the fixed-rate receiver increases because
the present value of the fixed-rate asset increases and the floating-rate payments made
decrease.

Interest rate swaps can be viewed as a portfolio of bonds. Like futures, swap agreements do not require
significant capital up front. The only capital required to enter into swap agreements is collateral
required by the counterparties.

6.2.3 Structured Financial Instruments

Structured products are synthetic investment instruments specially created to meet specific needs that
cannot be met from the standardized financial instruments available in the markets. An example of a
structured financial instrument with embedded leverage is an inverse floating-rate note, also known as
an inverse floater. For example,
Coupon rate = 15% − (1.5% × Libor3−month )
The above inverse-floater has an embedded leverage as it is linked to LIBOR; as the LIBOR decreases, the
coupon rate increases and vice versa. An inverse floating-rate note allows a bondholder to benefit from
declining interest rates. However, owing to embedded leverage, the losses may also magnify in case
interest rates rise.

6.2.4 Repurchase Agreements
A repurchase agreement (repo) is an agreement between two parties whereby one party (the
cash borrower) sells the other party (the cash lender) a security at a specified price with a
commitment to buy the security back at a fixed time and price. Repos are thus effectively
collateralized loans. From the lender’s perspective, these agreements are referred to as reverse repos.
The interest rate on a repurchase agreement, called the repo rate, is the difference between the
security’s selling price and its repurchase price. For example, consider a dealer wishing to finance a $15
million bond position with a repurchase agreement. The dealer enters into an overnight repo at a repo
rate of 5%. The interest amount is computed as follows:
Dollat interest = Principal amount × (Term of Repo in days /360)
In the above example, dollar interest = $15 million × 5% × (1/360) = = $2,083.33. Thus, the dealer will
repurchase the bond the next day for $15,002,083.33.
A repo agreement may be cash driven or security driven.


A cash-driven transaction is one where the collateral provider (party that owns bond) is seeking to
borrow cash. In such cases, the securities backing the transaction are typically “general collateral”,
meaning that they are part of a class of acceptable securities rather a specific one, e.g. Treasury

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

IFT Notes

bonds.
A security-driven transaction is one where the cash lender is seeking to borrow securities (for
hedging, arbitrage, or speculation). In such cases, the security is usually specific.

Repos can be categorized as bilateral repos or tri-party repos based on the way they are settled.




Bilateral repos involve two institutions, and settlement is typically conducted as “delivery versus
payment,” meaning that the exchanges of cash and collateral occur simultaneously through a
central custodian (for example, the Depository Trust Company in the United States). In general,
security-driven transactions are conducted as bilateral repos.
Tri-party repo transactions involve a third party that provides settlement and collateral
management services. Most cash-motivated repo transactions against general collateral are
conducted as tri-party repo transactions.

In repo agreement, the counterparty that lends capital faces credit risk. Protection against a default by

the borrower is provided by the underlying collateral bonds. Additional credit protection can be
provided in the form of “haircut,” which refers to the amount by which the collateral’s value exceeds
the repo principal amount. For example, haircuts for high-quality government bonds typically range
from 1% to 3%. Besides providing protection against default risk, the size of the haircut also limits the
borrower’s net leverage capacity. Generally, the higher the volatility of underlying collateral, the greater
the size of the haircut will be.

6.2.5 Securities Lending
In a securities lending transaction, one party gives legal title to a security or basket of securities to
another party for a limited period of time, in exchange for legal ownership of collateral. The first party is
called the ‘lender’ and the other party is called the ‘borrower’. The primary motive of securities lending
transactions is to facilitate short sales (sale of securities the seller does not own). Another motive for
securities lending transactions is financing, or collateralized borrowing.
The underlying collateral in security lending transactions can either be cash or high-credit-quality bonds.
In general, the value of collateral is greater than the value of the borrowed securities when bonds are
used as collateral.




When underlying collateral is cash, the security borrower typically pays the security lender a fee
equal to a percentage of the value of the securities loaned. The security lender earns an additional
return by reinvesting the cash collateral. However, if securities loan is used for financing purposes,
the lending fee is typically negative, indicating that the security lender pays the security borrower a
fee in exchange for its use of the cash.
When underlying collateral is bond, the security lender usually repays the security borrower a
portion of the interest earned on the bond collateral. Rebate rate represents the following.
Rebate rate = Collateral earnings rate – Security lending rate
 Rebate rate is negative when securities are difficult to borrow;
 Negative rebate rate implies that the security borrower pays a fee to the security lender in

addition to forgoing the interest earned on the collateral.

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Unlike repurchase agreements, security lending transactions are typically open-ended, which means
that the securities lender may recall the securities at any time. Similarly, the borrower may deliver the
borrowed securities back to the lender at any time.

6.3 Risks of Leverage
A leveraged fixed income portfolio is exposed to various risks as discussed below.






Leverage alters the risk-return properties of an investment portfolio;
Both gains and losses are magnified in a leveraged portfolio;
If the value of the portfolio decreases, the portfolio’s equity relative to borrowing levels is reduced
and the portfolio’s leverage increases. Increased leverage might lead to forced liquidation at prices
which are below fair value;

In a financial crisis, counter parties to short-term financing arrangements may withdraw their
financing, which in turn undermine the ability of leveraged market participants to maintain their
investment exposures.

This section addresses LO.f:
f. discuss differences in managing fixed-income portfolios for taxable and tax exempt investors.

7 FIXED-INCOME PORTFOLIO TAXATION
Taxes can complicate investment decisions in fixed-income portfolio management because taxes vary
across investor types, countries, and income sources (interest income or capital gains). Portfolio
managers who manage assets for taxable individual investors, as opposed to tax-exempt investors, need
to consider a number of issues related to taxes.

7.1 Principles of Fixed-Income Taxation
Following are six principles of fixed-income taxation.
1) The two primary sources of investment income that affect taxes for fixed-income securities are
coupon payments (interest income) and capital gains or losses.
2) In general, tax is payable only on capital gains and interest income that have actually been received.
An exception would be zero-coupon bonds, wherein tax is charged on imputed interest throughout
a zero-coupon bond’s life.
3) Capital gains are frequently taxed at a lower effective tax rate than interest income.
4) Capital losses generally cannot be used to reduce sources of income other than capital gains. Capital
losses reduce capital gains in the tax year in which they occur. If capital losses are greater than the
capital gains in the year, they can be “carried forward” and applied to gains in future years. In some
countries, losses may also be “carried back” to reduce capital gains taxes paid in prior years.
5) In some countries, short-term capital gains are taxed at usually a higher rate than long-term capital
gains.
Key points for managing taxable fixed-income portfolios include the following:


Selectively offset capital gains and losses for tax purposes.

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R21 Introduction to Fixed-Income Portfolio Management





IFT Notes

If short-term capital gains tax rates are higher than long-term capital gains tax rates, then be
judicious when realizing short term gains.
Realize losses taking into account tax consequences. They may be used to offset current or future
capital gains for tax purposes.
Control turnover in the fund. In general, the lower the turnover, the longer capital gains tax
payments can be deferred.
Consider the trade-off between capital gains and income for tax purposes.

7.2 Investment Vehicles and Taxes
The choice of investment vehicle often affects how investments are taxed at the final investor level.







In pooled investment vehicles (i.e. mutual funds), interest income is generally taxed at the final
investor level when it occurs—regardless of whether the fund reinvests interest income or pays it
out to investors.
Taxation of capital gains arising from the individual investments within a fund is often treated
differently in different countries. For example, in U.S., a pass-through treatment of capital gains is
used in mutual funds, whereby, investors need to include the gains on their tax returns because
realized net capital gains in the underlying securities of a fund are treated as if distributed to
investors in the year that they arise.
In a separately managed account, an investor typically pays tax on realized gains in the underlying
securities at the time they occur.
Tax loss harvesting (which involves deferring the realization of gains and realizing capital losses
early), investors can accumulate gains on a pre-tax basis, which leads to increase in the present
value of investments.

Refer to Example 7 from the curriculum.

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Summary
LO.a: discuss roles of fixed-income securities in portfolios;
Diversification Benefits
 Correlation with other asset classes is less than 1
 Fixed income volatility is less than equity volatility
Benefits of Regular Cash Flows
 Regular and predictable cash flows help investors meet future goals and obligations
 Assumes no credit event or market event will occur
Inflation Hedging Potential
 Inflation linked bonds provide a hedge against inflation
 Return includes real return plus return tied to inflation rate
 Lower return volatility relative to conventional bonds
 Offer returns that differ from other asset classes, leading to superior risk adjusted portfolio
returns
LO.b: describe how fixed-income mandates may be classified and compare features of the mandates;
Two types of mandates:
1) Liability-Based: match or cover expected liability payments with future projected cash flows.
Immunization: process of structuring and managing a fixed-income portfolio to minimize the variance in
the realized rate of return over a known time horizon
 Cash flow matching
 Duration matching
 Contingent immunization
 Horizon matching
Duration Matching
Cash Flow Matching
Yield curve
Parallel yield curve
None
assumptions

shifts
Rebalancing
Frequent rebalancing
Not required but
required
often desirable
Complexity
High
Low
2) Total Return Based: Generally structured to either track or outperform a benchmark. They can be
classified into different approaches based on their target active return and active risk levels.
Pure Indexing
Match benchmark return
and risk as closely as
possible

IFT Notes for the Level III Exam

Enhanced Indexing
Modest outperformance (generally 20
bps to 30 bps) of benchmark while
active risk is kept low (typically around
50 bps or lower)

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Active Management
Higher outperformance (generally
around 50 bps or more) of benchmark
and higher active risk levels

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Ideally the same as
benchmark or only slight
mismatches

Small deviations from underlying
benchmark

Significant deviations from underlying
benchmark

Risk factors are matched
exactly

Most primary risk factors are closely
matched (in particular, duration)

Large risk factor deviations from
benchmark (in particular, duration)

Similar to underlying
benchmark

Slightly higher than underlying
benchmark

Considerably higher turnover than the
underlying benchmark

LO. c. describe bond market liquidity, including the differences among market sub-sectors, and discuss
the effect of liquidity on fixed-income portfolio management;


Bond market liquidity varies across sub-sectors such as issuer type, credit quality, issue size, and
maturity.
 Higher credit quality  higher liquidity
Sovereign government bonds are more liquid than
 Larger issue size  higher liquidity
corporate bonds and non-sovereign government
bonds. Recently issued bonds have relatively high
 Shorter maturity  higher liquidity
liquidity.



Pricing in bond markets is less transparent than in equity markets
 Infrequent trades  recent transaction price does not necessarily reflect value
 Use matrix pricing
When constructing portfolios consider trade-off between yield and liquidity
 Dealers often carry an inventory of bonds because buy and sell orders do not arrive
simultaneously
 Bid-ask spreads are influenced by illiquidity, riskiness and complexity
 Higher bid-ask spread  higher trading costs

To overcome liquidity issues use fixed income derivatives and ETFS





LO. d. describe and interpret a model for fixed-income returns;
E(R)

≈ Yield income
+ Rolldown return
+ E(Change in price based on investor’s views)
- E(Credit losses)
+ E(Currency gains or losses)

Estimation of inputs



Yield income and rolldown return are easy to estimate
Investor’s views of changes in yields and yield spreads, expected credit losses, and expected

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currency movements are not easy to estimate
Limitations of the model




Only duration and convexity are used to summarize the price–yield relationship
Model assumes that all intermediate cash flows of the bond are reinvested at the yield to
maturity
Model ignores local richness/cheapness effects and potential financing advantages

LO. e. discuss the use of leverage, alternative methods for leveraging, and risks that leverage creates in
fixed-income portfolios;


Leverage increases returns if returns on invested funds > cost of borrowing.

Methods for Leveraging
1. Futures Contracts
2. Swap Agreements
3. Structured Financial Instruments
4. Repurchase Agreements
5. Securities Lending
Risks of Leverage
 Leverage alters the risk-return properties of an investment portfolio
 Gains and losses are magnified
 If portfolio value decreases, leverage increases

 Increased leverage might lead to forced liquidation at prices which are below fair value
 In a financial crisis, counter parties my withdraw their financing
LO. f. discuss differences in managing fixed-income portfolios for taxable and tax exempt investors.
Key points for managing taxable fixed-income portfolios:
a) Consider the trade-off between capital gains and income for tax purposes.
b) Selectively offset capital gains and losses for tax purposes.
c) If short-term capital gains tax rates are higher than long-term capital gains tax rates, then be
judicious when realizing short term gains.
d) Realize losses taking into account tax consequences.
e) Control turnover in the fund.
Choice of investment vehicle often affects how investments are taxed at the final investor level




Pooled investment vehicles: interest income taxed at final investor level even if reinvested
Some countries use pass-through treatment of capital gains
Separately managed account: investor typically pays tax on realized gains in the underlying

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securities at the time they occur.
Tax loss harvesting: defer realization of gains and realize capital losses early  accumulate gains on a
pre-tax basis  increase present value of investments.

Examples from the Curriculum
Example 1. Adding Fixed-Income Securities to a Portfolio
Mary Baker is anxious about the level of risk in her portfolio based on a recent period of increased
equity market volatility. Most of her wealth is invested in a diversified global equities portfolio.
Baker contacts two wealth management firms, Atlantic Investments (AI) and West Coast Capital (WCC),
for advice. In conversation with each adviser, she expresses her desire to reduce her portfolio’s risk and
to have a portfolio that generates a cash flow stream with consistent purchasing power over her 15-year
investment horizon.
The correlation coefficient of Baker’s diversified global equities portfolio with a diversified fixed-coupon
bond portfolio is –0.10 and with a diversified inflation-linked bond portfolio is 0.10. The correlation
coefficient between a diversified fixed-coupon bond portfolio and a diversified inflation-linked bond
portfolio is 0.65.
The adviser from AI suggests diversifying half of her investment assets into nominal fixed-coupon bonds.
The adviser from WCC also suggests diversification but recommends that Baker invest 25% of her
investment assets into fixed-coupon bonds and 25% into inflation-linked bonds.
Evaluate the advice given to Baker by each adviser based on her stated desires regarding portfolio risk
reduction and cash flow stream. Recommend which advice Baker should follow, making sure to discuss
the following concepts in your answer:
a. Diversification benefits
b. Cash flow benefits
c. Inflation hedging benefits
Solution:
Advice from AI:
Diversifying into fixed-coupon bonds would offer substantial diversification benefits in lowering overall
portfolio volatility (risk) given the negative correlation of –0.10. The portfolio’s volatility, measured by
standard deviation, would be lower than the weighted standard deviations of the diversified global

equities portfolio and the diversified fixed-coupon bond portfolio. The portfolio will generate regular
cash flows because it includes fixed-coupon bonds. This advice, however, does not address Baker’s
desire to have the cash flows maintain purchasing power over time and thus serve as an inflation hedge.
Advice from WCC:
Diversifying into both fixed-coupon bonds and inflation-linked bonds offers additional diversification
benefits beyond that offered by fixed-coupon bonds only. The correlation between diversified global
equities and inflation-linked bonds is only 0.10. The correlation between nominal fixed-coupon bonds
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and inflation-linked bonds is 0.65, which is also less than 1.0. The portfolio will generate regular cash
flows because of the inclusion of fixed-coupon and inflation-linked bonds. Adding the inflation-linked
bonds helps to at least partially address Baker’s desire for consistent purchasing power over her
investment horizon.
Based on her stated desires and the analysis above, Baker should follow the advice provided by WCC.
Back to Notes.

Example 2. Liability-Based Mandates (1)
Dave Wilson, a fixed-income analyst, has been asked by his manager to analyze different liability-based
mandates for a pension fund client. The pension plan currently has a very large surplus of assets over
liabilities. Evaluate whether an immunization or contingent immunization approach would be most
suitable for the pension fund.

Solution:
Because the pension fund currently has a large surplus of assets over liabilities, a contingent
immunization approach would be most suitable. A pure immunization approach would not be
appropriate, because a key assumption under this approach is that the present value of the fund’s assets
equals the present value of its liabilities. The contingent immunization approach allows the pension
fund’s portfolio manager to follow an active management approach as long as the portfolio remains
above a specified value. If the pension fund’s portfolio decreases to the specified value, a duration
matching or even a cash flow matching approach would be put in place to ensure adequate funding of
the pension plan’s liabilities.
Back to Notes.

Example 3. Liability-Based Mandates (2)
If the yield curve experiences a one-time parallel shift of 1%, what is the likely effect on the match
between a portfolio’s assets and liabilities for a duration matching approach and a cash flow matching
approach?
Solution:
There should be no effect on the match between assets and liabilities for either a duration matching or
cash flow matching portfolio. Duration matching insures against any adverse effects of a one-time
parallel shift in the yield curve. By contrast, non-parallel shifts would cause mismatches between assets
and liabilities in a duration matching approach. In a cash flow matching approach, asset and liability
matching remains in place even if market conditions change.
Back to Notes.

Example 4. The Characteristics of Different Total Return Approaches
Diane Walker is a consultant for a large corporate pension plan. She is looking at three funds (Funds X, Y,
and Z) as part of the pension plan’s global fixed-income allocation. All three funds use the Bloomberg
Barclays Global Aggregate Index as a benchmark. Exhibit 6 provides characteristics of each fund and the

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index as of February 2016. Identify the approach (pure indexing, enhanced indexing, or active
management) that is most likely used by each fund, and support your choices by referencing the
information in Exhibit 6.

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Solution to 1:
Fund X most likely uses an enhanced indexing approach. Fund X’s modified duration and convexity are
very close to those of the benchmark but still differ slightly. The average maturity of Fund X is slightly
longer than that of the benchmark, whereas Fund X’s average yield is slightly higher than that of the
benchmark. Fund X also has deviations in quality, maturity exposure, and country exposures from the
benchmark, providing further evidence of an enhanced indexing approach. Some of these deviations are

meaningful; for example, Fund X has a relatively strong underweight in Japan. Fund Y most likely uses a
pure indexing approach because it provides the closest match to the Bloomberg Barclays Global
Aggregate Index. The risk and return characteristics are almost identical between Fund Y and the
benchmark. Furthermore, quality, maturity exposure, and country exposure deviations from the
benchmark are very minor. Fund Z most likely uses an active management approach because risk and
return characteristics, quality, maturity exposure, and country exposure differ markedly from the index.
The difference can be seen most notably with the mismatch in modified duration (7.37 for Fund Z versus
6.34 for the benchmark). Other differences exist between Fund Z and the index, but a sizable duration
mismatch provides the strongest evidence of an active management approach.
Back to Notes.

Example 5. Decomposing Expected Returns
Ann Smith works for a US investment firm in its London office. She manages the firm’s British pound–
denominated corporate bond portfolio. Her department head in New York has asked Smith to make a
presentation on the next year’s total expected return of her portfolio in US dollars and the components
of this return. Exhibit 7 shows information on the portfolio and Smith’s expectations for the next year.
Calculate the total expected return of Smith’s bond portfolio, assuming no reinvestment income.

Solution:

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