Chapter SixteenManaging Bond PortfoliosCopyright © 2014 McGr.docx

Chapter Sixteen
Managing Bond Portfolios
Copyright © 2014 McGraw-Hill Education. All rights reserved.
No reproduction or distribution without the prior written
consent of McGraw-Hill Education.
INVESTMENTS | BODIE, KANE, MARCUS
Interest rate risk
Interest rate sensitivity of bond prices
Duration and its determinants
Convexity
Passive and active management strategies
Chapter Overview
16-‹#›
Interest Rate Sensitivity
Bond prices and yields are inversely related
An increase in a bond’s yield to maturity results in a smaller
price change than a decrease of equal magnitude
Long-term bonds tend to be more price sensitive than short-term
bonds
Interest Rate Risk
16-‹#›

Interest Rate Sensitivity
As maturity increases, price sensitivity increases at a decreasing
rate
Interest rate risk is inversely related to the bond’s coupon rate
Price sensitivity is inversely related to the yield to maturity at
which the bond is selling
Interest Rate Risk
16-‹#›
Figure 16.1 Change in Bond Price as a Function of Change in
Yield to Maturity
16-‹#›
Table 16.1 Prices of 8% Coupon Bond (Coupons Paid
Semiannually)
16-‹#›
Table 16.2 Prices of Zero-Coupon Bond (Semiannually
Compounding)

16-‹#›
Duration
A measure of the effective maturity of a bond
The weighted average of the times until each payment is
received, with the weights proportional to the present value of
the payment
It is shorter than maturity for all bonds, and is equal to maturity
for zero coupon bonds
Interest Rate Risk
16-‹#›
Duration calculation:
CFt = Cash flow at time t
Interest Rate Risk

16-‹#›
Duration-Price Relationship
Price change is proportional to duration and not to maturity
D* = Modified duration
Interest Rate Risk
16-‹#›
Two bonds have duration of 1.8852 years
One is a 2-year, 8% coupon bond with YTM=10%
The other bond is a zero coupon bond with maturity of 1.8852
years
Duration of both bonds is 1.8852 x 2 = 3.7704 semiannual
periods
Modified D = 3.7704/1 + 0.05 = 3.591 periods
Example 16.1 Duration and
Interest Rate Risk
16-‹#›

Suppose the semiannual interest rate increases by 0.01%. Bond
prices fall by
= -3.591 x 0.01%
= -0.03591%
Bonds with equal D have the same interest rate sensitivity
Interest Rate Risk
16-‹#›
Interest Rate Risk
Coupon Bond
The coupon bond, which initially sells at $964.540, falls to
$964.1942, when its yield increases to 5.01%
Percentage decline of 0.0359%
Zero
The zero-coupon bond initially sells for $1,000/1.053.7704 =
$831.9704
At the higher yield, it sells for $1,000/1.053.7704 = $831.6717,
therefore its price also falls by 0.0359%

16-‹#›
What Determines Duration?
Rule 1
The duration of a zero-coupon bond equals its time to maturity
Rule 2
Holding maturity constant, a bond’s duration is higher when the
coupon rate is lower
Rule 3
Holding the coupon rate constant, a bond’s duration generally
increases with its time to maturity
Interest Rate Risk
16-‹#›
What Determines Duration?
Rule 4
Holding other factors constant, the duration of a coupon bond is
higher when the bond’s yield to maturity is lower
Rules 5
The duration of a level perpetuity is equal to:
(1 + y) / y
Interest Rate Risk
16-‹#›

Figure 16.2 Bond Duration versus
Bond Maturity
16-‹#›
Table 16.3 Bond Durations (Yield to Maturity = 8% APR;
Semiannual Coupons)
16-‹#›
The relationship between bond prices and yields is not linear
Duration rule is a good approximation for only small changes in
bond yields
Bonds with greater convexity have more curvature in the price-
yield relationship
Convexity
16-‹#›
Figure 16.3 Bond Price Convexity: 30-Year Maturity, 8%
Coupon; Initial YTM = 8%

16-‹#›
Convexity
Correction for Convexity:
16-‹#›
Figure 16.4 Convexity of Two Bonds
16-‹#›
Bonds with greater curvature gain more in price when yields
fall than they lose when yields rise
The more volatile interest rates, the more attractive this
asymmetry
Bonds with greater convexity tend to have higher prices and/or
lower yields, all else equal
Why Do Investors Like Convexity?
16-‹#›

Callable Bonds
As rates fall, there is a ceiling on the bond’s market price,
which cannot rise above the call price
Negative convexity
Use effective duration:
Duration and Convexity
16-‹#›
Figure 16.5 Price –Yield Curve for
a Callable Bond
16-‹#›
Mortgage-Backed Securities (MBS)
The number of outstanding callable corporate bonds has
declined, but the MBS market has grown rapidly
MBS are based on a portfolio of callable amortizing loans
Homeowners have the right to repay their loans at any time
MBS have negative convexity

16-‹#›
Mortgage-Backed Securities (MBS)
Often sell for more than their principal balance
Homeowners do not refinance as soon as rates drop, so implicit
call price is not a firm ceiling on MBS value
Tranches – the underlying mortgage pool is divided into a set of
derivative securities
16-‹#›
Figure 16.6 Price-Yield Curve for
a Mortgage-Backed Security
16-‹#›
Figure 16.7 Cash Flows to Whole Mortgage
Pool; Cash Flows to Three Tranches
16-‹#›
Two passive bond portfolio strategies:

Indexing
Immunization
Both strategies see market prices as being correct, but the
strategies are very different in terms of risk
Passive Management
16-‹#›
Bond Index Funds
Bond indexes contain thousands of issues, many of which are
infrequently traded
Bond indexes turn over more than stock indexes as the bonds
mature
Therefore, bond index funds hold only a representative sample
of the bonds in the actual index
Passive Management
16-‹#›
Figure 16.8 Stratification of
Bonds into Cells
16-‹#›
Immunization
A way to control interest rate risk that is widely used by

pension funds, insurance companies, and banks
In a portfolio, the interest rate exposure of assets and liabilities
are matched
Match the duration of the assets and liabilities
Price risk and reinvestment rate risk exactly cancel out
As a result, value of assets will track the value of liabilities
whether rates rise or fall
Passive Management
16-‹#›
Table 16.4 Terminal value of a
Bond Portfolio After 5 Years
16-‹#›
Figure 16.9 Growth of Invested Funds
16-‹#›
Table 16.5 Market Value Balance Sheet

16-‹#›
Figure 16.10 Immunization
16-‹#›
Cash Flow Matching and Dedication
Cash flow matching = Automatic immunization
Cash flow matching is a dedication strategy
Not widely used because of constraints associated with bond
choices
Passive Management
16-‹#›
Swapping Strategies
Substitution swap
Intermarket spread swap
Rate anticipation swap
Pure yield pickup swap
Tax swap
Active Management
16-‹#›

Horizon Analysis
Select a particular holding period and predict the yield curve at
end of period
Given a bond’s time to maturity at the end of the holding period
its yield can be read from the predicted yield curve and the end-
of-period price can be calculated
Active Management
16-‹#›
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Running head: UNITED STATES PATRIOTIC ACT
1
UNITED STATES PATRIOTIC ACT 3
Topic
Students Name
Professors Name
Institution
Course Title
Date

UNITED STATES PATRIOTIC ACT
1. Introduction
a. The USA PATRIOTIC act was formed as a response to
growing fears of another terrorist attack after the September
11th, 2001 terrorist attack.
b. The acronym USA stands for ‘Uniting and Strengthening
America’
c. The bill contained policies and plans aimed at preventing
terrorist attacks.
d. The act was aimed at protecting both local citizens and
Americans on foreign soil around the world.
2. Literature review
1. According to McCarthy, the Act is divided into nine
categories which are surveillance, terrorism, prevention of
terrorism by money laundering practices, improved intelligence,
domestic security and border security just to mention a few.
1. This act motivates American citizens to take the right
protective measures against terrorism.
1. Criticism against the act because of overhauled procedures
used in investigations.
1. The role of the FBI in all these issues.
1. The role of the INS and the United States Attorney General in
the investigative process.
3. Reasons for choosing the topic
a. The USA PATRIOTIC Act is very useful for the protection
and security of the citizens of America which justifies the
reason for choosing this topic.
b. There has not been a major terrorist attack on American soil
since 2001
c. National cohesion was improved through this act.
4. My interest in the topic
a. My interest in this topic is from the fact that the USA

PATRIOTIC Act came with its fair share of concerns over civil
liberties and privacy issues.
b. Curiosity over the ignored civil rights and infringement over
personal privacy in the context of protection.
c. The authority given to government institutions under the USA
PATRIOTIC Act
d. The impacts of the “secrecy clause” and how it has changed
operations in the National Intelligence Service, FBI and other
government departments in relation to accountability.
e. The government is allowed to conduct “sneak and peak”
seizures and search without probable cause on American
citizens with no terrorist links.
5. Research questions
1. What is the significance of the act?
1. To what extent did the act improve the lives of American
citizens?
1. Are American citizens satisfied with the provisions of the
act?
1. Does this act give hope to the Americans that such an attack
can never occur again?
6. Results
1. The good and bad elements of the USA PATRIOTIC act.
1. How the act aided in securing the USA borders.
1. The evidence of misuse of government authorities
1. The outcomes of the USA PATRIOTIC Act.
Chapter 16 - Managing Bond Portfolios
Chapter sixteen
Managing Bond PortfoliosChapter Overview
This chapter discusses active and passive bond portfolio
management strategies. The concept and use of duration are
explained, as are the various types of portfolio immunization
strategies utilizing duration. In addition, it describes various
active strategies, or bond swaps.Learning Objectives
After studying this chapter, the student should have a thorough

understanding of duration and how to calculate it for various
bond portfolios. Students will be able to construct immunized
portfolios appropriate for different investor categories. The
student should also understand the difference between passive
and active bond portfolio management and the implications of
each management style.
PRESENTATION OF MATERIAL
16.1 Interest Rate Risk
The traditional bond pricing relationships and interest rate
relationships are discussed in this section. The relationships
with respect to maturity are not exact. In discussing the pricing
relationships, it is helpful to discuss how maturity and cash
flows as measured by coupon rates must be considered together
to get exact relationships.
This section continues with a detailed look at duration. The
description of duration used here stresses the concept of average
life. Since the measurement of duration considers the timing
and value of intermediate payments, it is an accurate measure of
average life and is more meaningful than maturity for any bond
that has coupon payments. Calculation of duration is presented
and though an Excel worksheet can be created easily to do the
calculations (see the example), it is recommended that the
student work through a duration calculation manually to
increase understanding. The weight of each cash flow for a
fixed income instrument is the present value of the cash flow as
a percentage of total value. Duration is the sum of the product
of the weights of each cash flow and the period that it is
received. The measure is in units of the cash flow payment
during the year. For example, with monthly mortgage
payments, duration would be in months. For a bond with
semiannual compounding, the measure would be in 6-month
periods. Spreadsheet 16.1 illustrates the calculation.

Price changes on fixed-income securities are proportional to
duration. The financial industry uses modified duration
extensively. This section presents some key properties of
duration for different fixed income instruments and some useful
simplifications of the duration formula. Figure 16.2 displays
duration measures for coupon bonds of different maturities and
Table 16.3 presents duration calculations for with varying
maturities and coupon rates.
16.2 Convexity
Calculating the second order price change, known as the bond’s
convexity reduces pricing results in pricing error when used
with duration. Convexity creates problems for passive
management since duration changes with changes in rates. For
target date immunization, this leads to rebalancing problems.
The correction for convexity is used to adjust the price-duration
relationship.
When bonds have imbedded options, convexity behaves
differently. A callable bond has a limit on price appreciation so
when rates decline, the likelihood of call increases and the
value is capped. Understanding convexity is particularly
important for asset backed securities. Mortgage-backed
securities are also subject to negative convexity and often sell
for more than their principal balance.
16.3 Passive Bond Management
Major strategies for passive management are discussed here.
Bond indexing is similar to stock indexing except that it
requires more rebalancing and is in many ways more difficult to
implement. Many bonds trade in relatively thin markets and
indexing for fixed income instruments can be more costly.
Figure 16.8 illustrates how stratification is used in bond
indexing.
The second passive management strategy is immunization,
which attempts to protect a bond portfolio from interest rate
risk. Duration can be used for immunization. It is

recommended that students immunize a portfolio and then
observe changes in interest rate and the subsequent stability of
portfolio value. Networth immunization is used by financial
institutions to hedge against interest rate risk. Target date
immunization is used by institutional investors to lock-in a
yield to maturity for a bond or a bond portfolio. Cash flow
matching involves selection of fixed income securities that
exactly match cash outflow requirements.
16.4 Active Bond Management
Bond swapping strategies are presented here. Swapping
strategies are used when the fixed income portfolio is actively
managed. Substitution, intermarket and rate anticipation swaps
require some level of market disequilibrium. With a
substitution swap, two bonds that are substitutes offer different
rates of return. The strategy involves purchase of the bond that
is offering the higher rate of return and selling the bond that has
the lower rate of return. The intermarket swap requires some
disequilibrium in the markets as well. In an intermarket swap,
the bonds could be of different credit risk but the interest rate
differential is not correct. The rate anticipation swap involves
changing the duration of the fixed-income portfolio to profit
from a change in interest rates. The change in interest rates
must not be anticipated by the rest of the market for the swap to
result in superior profits. A pure yield pick-up involves a
risk/return trade-off decision by an investor. A tax swap
involves a purchase and sale of fixed income securities to take
advantage of an individual investor’s tax position.
Horizon analysis selects a particular holding period and then
predicts the yield curve at the end of the period. Contingent
immunization involves both an active and passive component.
The strategy allows active management with a constraint of
portfolio immunization if return falls to a target level.Excel
Models
The Online Learning Center (www.mhhe.com/bkm) contains
spreadsheets for calculating duration and for immunization.
One is constructed to help students understand the concepts

related to holding period immunization. The spreadsheet is
built with closed-end equations that make it easy to work with
bonds of any maturity. Students can compare return with
different holding periods and understand how returns are
affected by interest rate change. The other spreadsheets
calculate duration using 1) the individual cash flows and 2) the
closed-end equation. The models are also very useful in-class
teaching tools.
16-2
Copyright © 2014 McGraw-Hill Education. All rights reserved.
No reproduction or distribution without the prior written
consent of McGraw-Hill Education.
Week 4 - Assignment: Assess Bond Pricing and Analysis to
Build a Portfolio
Instructions
Examine some important theories and concepts associated with
interest rates. Safe investments usually have fixed interest rates.
You have been asked to assemble this presentation for a weekly
staff meeting, so your audience will be senior managers and a
couple of vice presidents. Note their interest in this topic is
very high so you need to be very succinct and clearly explain
the risks and rewards of building a successful portfolio. In
reference to term structure, interest rate risks, and duration
supported by numerical illustration where applicable, in a
PowerPoint presentation, evaluate the following:
1. The pricing of bonds, the calculation of the bond yield, and
how bond prices adjust across time for premium, par, and
discount bonds.
2. An evaluation of the yield curve and the theories to explain
the shape. Discuss how these theories can be helpful in bond

investing.
3. The interest rate risk for bond investments. Form a graphical
presentation of the concepts.
4. The concept of duration and how it is useful in the context of
bond portfolio analysis. You want to clearly discuss both the
price risk measurement value for duration as well as how
duration can measure the dynamics of price and re-investment
rate risk across time for a bond portfolio.
It is critical that with each discussion above that examples are
formed to illustrate the concept. Whenever possible, you want
to demonstrate concepts using graphical approaches.
The required length of the PowerPoint Presentation option for
this assignment is 12-15 slides (with a separate reference slide).
Your presentation MUST include notes that contain 100-150
words per slide (this is your script). Be sure to include citations
for quotations and paraphrases with references in APA format
and style. Save the file as a PPT file with the correct course
code information in the name.
Bond Investments
According to Bodie, Kane, and Marcus (2014), to effectively
understand bond analysis, we want to first review some of the
meaningful interest rate theories. The first is the term structure
of interest rates, or in a less formal development - the yield
curve (although the actual metrics used between the two are
different). The yield curve maps the maturities on bonds or
fixed income securities to the associated interest rate of yield.
The most common shape of the yield curve will be upward
sloping. The shape of the yield curve is explained by several
optional theories with the best known being the Expectations
Theory. The Expectations Theory explains the shape as a
function of future expected interest rate movements. This is
useful for bond investors as the yield curve reveals then the
markets expectations for the direction of interest rate changes in

the future.
Even default-free bonds such as Treasury issues are subject to
interest rate risk. Longer-term bonds generally are more
sensitive to interest rate shifts than are short-term bonds. A
measure of the average life of a bond is Macaulay's duration,
defined as the weighted average of the times until each payment
made by the security, with weights proportional to the present
value of the payment. Duration is a direct measure of the
sensitivity of a bond's price to a change in its yield. The
proportional change in a bond's price equals the negative of
duration multiplied by the proportional change in 1 + y.
Convexity refers to the curvature of a bond's price-yield
relationship. Accounting for convexity can substantially
improve on the accuracy of the duration approximation for the
response of bond prices to changes in yields. Immunization
strategies are characteristic of passive fixed-income portfolio
management. Such strategies attempt to render the individual or
firm immune from movements in interest rates. This may take
the form of immunizing net worth or, instead, immunizing the
future accumulated value of a fixed-income portfolio.
Immunization of a fully funded plan is accomplished by
matching the durations of assets and liabilities. To maintain an
immunized position as time passes and interest rates change, the
portfolio must be periodically rebalanced. Classic immunization
also depends on parallel shifts in a flat yield curve. Given that
this assumption is unrealistic, immunization generally will be
less than complete. To mitigate the problem, multifactor
duration models can be used to allow for variation in the shape
of the yield curve.
A more direct form of immunization is dedication, or cash flow
matching. If a portfolio is perfectly matched in cash flow with
projected liabilities, rebalancing will be unnecessary.
Review the resources listed in the Books and Resources area
below to prepare for this week's assignments.
Book:

Investments
Bodie, Z., Kane, A., & Marcus, A. J. (2013). Investments New
York, NY McGraw-Hill-Irwin.
Read Chapter 16
Investing in Bonds YouTube Video:
https://youtu.be/_7e4B7LLMeI

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