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Project
Portfolio
Management
A Model for Improved
Decision Making
Clive N. Enoch
Portfolio and
Project Management Collection
Timothy Kloppenborg, Editor
PROJECT
PORTFOLIO
MANAGEMENT
ENOCH
Project Portfolio Management
A Model for Improved Decision
Making
Clive N. Enoch
Project portfolio management (PfM) is a
critically
important discipline,which organizations must embrace
in order to extract the maximum value from their

project investments. Essentially, PfM can be
defined as
the translation of strategy and organizational
objectives
into
projects, programs, and
operations (portfolio

components); the allocation of resources to
portfolio
components according to organizational
priorities;
alignment of components to one or more
organizational
objectives; and the management and control of
these components in order to achieve
organizational

objectives and benefits.
The focus of this book is aimed at providing a

mechanism to determine the individual and
cumulative
contribution of portfolio components to strategic

objectives so that the right decisions can be made

regarding those components.
Dr. Clive N. Enoch has been a practitioner of
project,

program, and portfolio management, as well as a

manager of project and portfolio management offices
over the past 20 years and has worked across
multiple
industries during this time. Clive holds a master of

commerce degree in information systems manage-
ment from the University of the Witwatersrand (WITS)
in
Johannesburg and a PhD in computer science from
the University of South Africa (UNISA). His PhD
thesis

resulted in a model for decision making in project

portfolio management. Clive is passionate about project
portfolio management and has contributed to the PMI’s
The Standard for Portfolio Management, third edition, as a
core committee member.
Portfolio and
Project Management Collection
Timothy Kloppenborg, Editor
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ISBN: 978-1-63157-270-8

Project Portfolio
Management
A Model for Improved
Decision Making
Clive N. Enoch

Project Portfolio Management: A Model for Improved Decision Making
Copyright © Business Expert Press, LLC, 2015.
All rights reserved. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted in any form or by any
means—electronic, mechanical, photocopy, recording, or any other
except for brief quotations, not to exceed 400 words, without the prior
permission of the publisher.
First published in 2015 by
Business Expert Press, LLC
222 East 46th Street, New York, NY 10017
www.businessexpertpress.com
ISBN-13: 978-1-63157-270-8 (paperback)
ISBN-13: 978-1-63157-271-5 (e-book)
Business Expert Press Portfolio and Project Management Collection
Collection ISSN: 2156-8189 (print)
Collection ISSN: 2156-8200 (electronic)
Cover and interior design by Exeter Premedia Services Private Ltd.,
Chennai, India
First edition: 2015
10 9 8 7 6 5 4 3 2 1
Printed in the United States of America.

Abstract
Project portfolio management (PfM) is a critically important discipline,
which organizations must embrace in order to extract the maximum
value from their project investments. Essentially, PfM can be defined
as the translation of strategy and organizational objectives into projects,
programs, and operations (portfolio components); the allocation of
resources to portfolio components according to organizational priorities;
alignment of components to one or more organizational objectives; and
the management and control of these components in order to achieve
organizational objectives and benefits.
The interest and contribution to the body of knowledge in PfM
has been growing significantly in recent years, however, a particular
area of concern is the decision making, during the management of the
portfolio, regarding which portfolio components to accelerate, suspend,
or terminate. A lack of determining the individual and cumulative
contribution of portfolio components to strategic objectives leads to
poorly informed decisions that negate the positive effect that PfM could
have in an organization. The focus of this book is aimed at providing a
mechanism to determine the individual and cumulative contribution of
portfolio components to strategic objectives so that the right decisions
can be made regarding those components.
Having the ability to determine the contributions of portfolio
components to strategic objectives affords decision makers the opportu-
nity to conduct what-if scenarios, enabled through the use of dashboards
as a visualization technique, in order to test the impact of their decisions
before committing them. This ensures that the right decisions regarding
the project portfolio are made and that the maximum benefit regarding
the strategic objectives is achieved.
This book is intended for executives, project and program directors,
project portfolio managers, project office managers, and training providers
in project, program, and PfM.
Keywords
complexity, decision making, multicriteria utility, organizational, project
portfolio management, systems

Contents
Acknowledgments��ix
Chapter 1 Introduction��1
Chapter 2 A Model for Decision Making�� 7
Chapter 3 Extending the Model��35
Chapter 4 Using the Model��47
Chapter 5 Conclusion��75
Appendix 1: Related Theories��81
Notes��101
References��105
Index��109

Acknowledgments
I would like to take this opportunity to thank:
God, for blessing me in this endeavour and giving me the strength to
persevere through this journey.
My wife, Synthie, for her prayers, support, encouragement and for
always believing in me.
My sons, Shaun and Carlin, for their support and understanding.
My father, Stephen, and other family members for their support.
My friend, Greg Wilby, for his contribution in challenging my think-
ing on various aspects.
Professors Les Labuschagne and Tim Kloppenborg, for their guidance,
encouragement and support.

CHAPTER 1
Introduction
Introduction
Project portfolio management is concerned with managing groups of
projects, programs, and operational activities (hereafter referred to as
portfolio components) that compete for scarce resources and that are
conducted to achieve strategic business objectives. Earlier literature related
to project portfolio management focused attention on the selection and
prioritization of projects and programs; however, merely choosing the
right portfolio components is not enough as decisions made during
the management of the portfolio could negate the very effort in setting
up the portfolio. Instead, the focus needs to shift toward finding ways
to ensure that the right decisions are made with regard to terminating,
accelerating, or delaying portfolio components. This leads to portfolio
and, ultimately, business success.
Project portfolio management is by no means a solution to all an
organization’s problems; however, it is intended to enable organizations
to do more with less. As the world deals with the current financial crisis,
it is more important now than in the past few decades for organizations
to ensure they are spending their money on the right project investments.
This is reliant on influential stakeholders playing a crucial role in the
choices made when managing the portfolio.
This chapter outlines the remainder of this book and includes the
positioning of project portfolio management in terms of its (i) role in
the management of project-related investments, as well as (ii) its role in
contributing toward organizational success.
Project Portfolio Management-Overview
Many authors are of the view that while project and program management
is traditionally focused on doing projects right, portfolio management

2 PROJECT PORTFOLIO MANAGEMENT
is focused on doing the right projects. The term portfolio is also associ-
ated with a collection of financial investment instruments, that is, stocks
and bonds; however, this book does not attempt to address such types
of portfolios. Instead, the area of concern encompasses project portfolio
management and is hereafter referred to as PfM.
PfM comprises a set of managed technology assets, process invest-
ments, human capital assets, and project investments that are allocated
to business strategies according to an optimal mix based on assumptions
about future performance. The Project Management Institute (PMI)
defines PfM in The Standard for Portfolio Management as “the coordinated
management of one or more portfolios to achieve organizational strate-
gies and objectives” and “includes interrelated organizational processes
by which an organization evaluates, selects, prioritizes, and allocates its
limited internal resources to best accomplish organizational strategies
consistent with its vision, mission, and values.” They further state that,
“Portfolio management produces valuable information to support or alter
organizational strategies and investment decisions.”1
The Office of Government Commerce (OGC) in the United Kingdom
define PfM as “a co-ordinated collection of strategic processes and
decisions that together enable the most effective balance of organizational
change and business as usual.”2
A goal of PfM is to guide investment decisions to maximize value and
minimize risk or uncertainty thus optimizing the organization’s return
on investment. PfM is an effective way to communicate value in business
language. Value is achieved from balancing risk and reward and making
the right decisions in this regard. The approach of the remainder of this
book is based on this understanding of PfM.
Project Portfolio Management
The Decision-Making Challenge
Early approaches to PfM emphasized the categorizing of the landscape
of existing projects in organizations without paying much attention to
portfolio management decision making. Ward and Peppard, for example,
illustrated that categories such as strategic, operational, high potential,
and support could be used as a means for facilitating agreement between

Introduction 3
senior management on the available and required portfolio of projects.3
Individual projects could then be categorized according to their business
contribution. This is an important step forward in the developing disci-
pline of PfM; however, selecting the right projects upfront is meaningless
if the wrong decisions are taken later on in the PfM process.
PfM improves organization success if the right decisions are made
when managing the portfolio. Further, successful organizations have a
shared reporting approach to channel information flows from compo-
nent level to portfolio level. Such organizations share responsibility for
decisions at the portfolio level. The decision making at the portfolio level
is the key focus of this book, since enabling decision making is becoming
increasingly important given the economic downturn and renewed focus
on corporate governance mentioned earlier. The selection of the right
portfolio components only goes part of the way to achieve success, but
making the right decisions during the course of managing the
portfolio
will contribute further to the success of the portfolio and, by extension,
the success of the organization. Specifically, this book focuses on the

process or approach that enables decision making with regard to deter-
mining which portfolio components to delay, accelerate, or terminate.
When making decisions, consideration must be given to the contri-
bution of portfolio components (strategic fit) to organizational objec-
tives. An assessment of the contribution that portfolio components make
to organizational objectives will depend on an evaluation of multiple
criteria. Therefore, the problem statement that this book is focused on
addresses the following issue.
When managing a project portfolio, an understanding of both the
individual and cumulative contribution of portfolio components to
organizational objectives and the likely impact of such decisions on the
achievement of these objectives is important in decision making. Without
this understanding, the decisions regarding whether to delay, accelerate,
or terminate portfolio components will be poor.
Structure of the Book
The book consists of five chapters. Figure 1.1 provides a diagrammatic
layout of the book followed by a more detailed overview of each chapter.

Chapter 1 provides the introduction, motivation for the book,
problem statement, and layout of the book.
Chapter 2 discusses the complex relationship between portfolio com-
ponents and organizational objectives and presents the model, which is
developed to address the problem of determining the cumulative contri-
bution of portfolio components to organizational objectives. This is done
by taking as input the qualitative evaluations of multiple criteria for each
portfolio component and producing a single quantitative value represent-
ing the cumulative contribution.
Chapter 3 extends the conceptual model presented in Chapter 2.
The fundamental principles presented in Chapter 2 are used in this chap-
ter, but instead of viewing the problem from the perspective of the contri-
bution of multiple components to individual objectives, Chapter 3 looks
at the contribution of a single component to multiple objectives. This
chapter illustrates how the concepts presented in Chapter 2 can be used
in a different way.
Chapter 4 looks at illustrating how the model could be used using
actual portfolio components and organizational objectives from a

participating organization. The illustration of the model in this chapter
shows the mechanics of the model and confirms how the impact of deci-
sions regarding portfolio components can be quantified.
Figure 1.1 Chapter layout
Chapter 1
Introduction
Chapter 2
Decision-making model
Chapter 3
Extending the model
Chapter 4
Illustrating how the
model would be used
Chapter 5
Conclusion
Appendix 1
Related theories

Introduction 5
Chapter 5 provides a summary and makes final recommendations for
the application of the model presented in this book.
Appendix 1 presents a review of the literature on PfM and discusses the
definition for PfM. It also describes five theories that provide a theoretical
foundation for PfM. The theories described are Modern Portfolio Theory,
Multi-Criteria Utility Theory, Organization Theory, Systems Theory, and
Complexity Theory.
Conclusion
This chapter provides an overview of PfM and describes the
decision-making challenge, which is addressed by the model presented
later in this book. This chapter further outlines the structure for the rest
of the book.
PfM is intended to guide investment decisions such that value is
maximized, risk or uncertainty is minimized, and organizational suc-
cess is achieved. The global economic crisis, prevalent at the time of
conducting the research that lead to this book, forced organizations
to carefully consider their spending in terms of project-related invest-
ments. PfM is a mechanism that can address this issue provided the
decision makers have a means to evaluate component contribution to
strategy. The requirement for organizations to comply with legislative,
regulatory, and governance requirements—as well as the factors listed
earlier—means that the decisions taken during the management of the
portfolio must be well informed so that the objectives of PfM can be
achieved.
To ensure that decisions are well informed, or to put it differently,
to improve PfM decision making, it is necessary to show how decisions
will impact the success of the portfolio and ultimately the success of the
organization. Organizational success is measured by the achievement
of objectives, and portfolio components are executed to deliver organi-
zational objectives. It can be deduced that finding a way to show the
contribution of portfolio components to the organizational objectives
will enable decision makers to test the impact of their decisions regard-
ing portfolio components on the portfolio before committing them.
This will enable decisions to have a minimum impact on the portfolio
and organization while achieving maximum effect.

CHAPTER 2
A Model for Decision
Making
Introduction
This chapter discusses a decision-making model for portfolio management
(PfM) and is based on a response to findings from an investigation
into the practice of PfM in various organizations. The key finding that
motivated this chapter and the need for a model for decision making in
PfM was the fact that many organizations lacked a clear approach when
deciding which portfolio components to terminate, fast track, or put on
hold during the course of managing the portfolio. Some organizations
take the easy route and trim budgets across all portfolio components by a
specified percentage in order to make the affordability constraints. Other
organizations cancel portfolio components on the basis that they have
not commenced yet. Most, if not all, reasons are related to short-term
affordability rather than an understanding on the longer-term strategic
consequence of these decisions.
In order to understand the implications of decision making in PfM,
we need to (a) establish the relationship between organizational objec-
tives and portfolio components, (b) describe the process for evaluating
the individual and cumulative contribution of portfolio components to
organizational objectives, and (c) describe the value and utility of the
model in improving PfM decision making.
Later, motivating the need for a model, describing the objectives of
the model, and the considerations that gave rise to the development of
the model are discussed. This is followed by an exploration into the rela-
tionship between organizational objectives and portfolio components
and a description of the complex nature of this relationship. A discussion
on the model itself is then presented. The inputs, processes, and outputs

of the model are explained, showing how the qualitative evaluation of
components can be converted into a quantitative value that represents
the contribution to organizational objectives. The chapter concludes with
a discussion on the value and utility of the model with regard to PfM
decision making in organizations.
Motivation for a Model
Earlier approaches to PfM focused on the selection and categorization of
projects and had less to do with the management and decision-making
processes involved in managing the portfolio. The focus in the literature
began to shift later, however, toward aligning IT and business strategy,1
managing IT projects like an investment portfolio,2
and using IT PfM to
unlock the business value of technology.3
Subsequently, authors have given increasing focus to the role of sin-
gle project management in achieving portfolio efficiency;4
alignment of
the project portfolio to corporate strategy, vertical integration, and value
creation through PfM;5
the translation of strategy into programs and
projects, organization performance, and the role of the project/program
management office;6
project portfolio control and performance;7
and the
influence of business strategy on PfM and its success.8
Most recently, the
third edition of The Standard for Portfolio Management9
introduced three
new knowledge areas (portfolio strategic management, portfolio perfor-
mance management, and portfolio communication management) that
expand on the previous edition significantly. This illustrates the increased
emphasis on strategic alignment and portfolio performance specifically.
An understanding of the purpose or objective of PfM is important:
“The objective of portfolio management is to determine the optimal mix
and sequencing of proposed projects to best achieve the organizational
strategy and objectives.”10
They add that managing the performance of
a portfolio is critical in closing the gap between organizational strategy
and the fulfillment of that strategy. This implies that successfully man-
aged portfolios (and hence successful projects, programs, and opera-
tional activities) are measured by the achievement of organizational
strategy and objectives (hereafter referred to collectively as organizational
objectives). A key consideration, therefore, is the contribution made by

A Model for Decision Making 9
projects, programs, and operational activities (portfolio components)
toward achieving the organizational objectives. The author had to con-
sider the quantitative and qualitative measures of assessment of portfolio
components to determine the contribution of portfolio components to
organizational objectives. This enabled a form of reasoning that would be
suitable to model such a system.
The factors that served as input toward the development of the model
were:
1. The observation from an earlier investigation into the practice of
PfM that decision making regarding the management of portfolios
was poor.
2. The objective of PfM, which is the determination and management
of the optimal mix of portfolio components toward achieving the
organizational objectives.
3. The need to understand the relationship between portfolio com-
ponents and organizational objectives in order to understand the
impact of decisions regarding portfolio components on organiza-
tional objectives.
4. The consideration of qualitative and quantitative ways of determin-
ing portfolio component contributions to organizational objectives.
5. The application of the theories related to PfM (refer to Appendix 1).
The objective of the decision-making model presented in this
chapter is to qualitatively evaluate portfolio components using multiple
criteria to determine the individual and cumulative contribution of
these components to organizational objectives so that the right PfM
decisions regarding which components to stop, progress, or terminate
can be made.
Relationship Between Portfolio Components
and Organizational Objectives
Having a well-defined strategy and organizational objectives without the
ability to execute them, or having efficient and effective operations with-
out a strategy or organizational objectives limits the success organizations

could have. This notion is supported by Drs Kaplan and Norton who
state the following:
A visionary strategy that is not linked to excellent operational
and governance processes cannot be implemented. Conversely,
operational excellence may lower costs, improve quality, and
reduce process and lead times; but without a strategy’s vision and
guidance, a company is not likely to enjoy sustainable success.11
This emphasizes the need not only to link strategy and execution, but
also to be able to assess the degree of contribution the components make
toward achieving the strategy.
According to the Project Management Institute (PMI), organizations
build strategy to define how their vision will be achieved. The vision
is enabled by the mission, which directs the execution of the strategy.
The organizational strategy is a result of the strategic planning cycle, where
the vision and mission are translated into a strategic plan. The strategic
plan is subdivided into a set of initiatives that are influenced by market
dynamics, customer and partner requests, shareholders, government
regulations, and competitor plans and actions. These initiatives establish
portfolio components that, through their execution, ultimately achieve
the organizational objectives. Linking the organization’s objectives
directly to the portfolio components reveals that there is a many-to-many
relationship between objectives and components.
This relationship can be illustrated as in Figure 2.1. Each portfolio
component (PC) contributes to one or more objectives. For example,
PC1 could contribute to partly achieving objectives 1, 3, and (n), while
the remainder of objective 1 is achieved through the execution of PC3.
PC2 could contribute to fully achieving objective 2, and objective (n)
could be achieved by components 1 and (m). The degree of contribution
of each component varies one from the other.
An alternate depiction of this relationship is given in Table 2.1.
In addition to mapping the components to their related objectives, it
is also important to understand the relationships between portfolio com-
ponents. For example, while PC1 and PC3 contribute to the achievement
of objective 1, they do not necessarily have to be related to each other in

any other way. They could be singular, independent projects managed by
different teams and not dependent on each other through deliverables or
resources. On the other hand, for objective 3, PC1, PC4, and PC6 could
be run as a program where all components are related to each other and
Table 2.1 Relationship between organizational objectives and portfolio
components
Vision
Objective
1
Objective
2
Objective
3
Objective
4
Objective
(n)
Portfolio
Portfolio Component 1 a d i
Portfolio Component 2 c
Portfolio Component 3 b
Portfolio Component 4 e
Portfolio Component 5 g
Portfolio Component 6 f h
Portfolio Component (m) j
Source: Enoch and Labuschagne.13
Figure 2.1 Many-to-many relationship between organizational
objectives and portfolio components
Source: Adapted from Enoch and Labuschagne.12
OBJECTIVE
1
PORTFOLIO
COMPONENT 1
VISION
MISSION
PORTFOLIO
COMPONENT 2
PORTFOLIO
COMPONENT 3
PORTFOLIO
COMPONENT 4
PORTFOLIO
COMPONENT 5
PORTFOLIO
COMPONENT 6
PORTFOLIO
COMPONENT (m)
OBJECTIVE
2
OBJECTIVE
3
OBJECTIVE
4
OBJECTIVE
(n)

have interdependency through, for instance, deliverables and/or resources.
Each component contributes to objectives to varying degrees. For example,
the degree of contribution of PC1 to objective 1 is represented by (a), and
the degree of contribution of PC3 to objective 1 is represented by (b).
The degree of contribution of these two components to objective 1 is not
equal. Additionally, PC1 also contributes to objectives 3 and (n) and the
degree of contribution to each of these objectives (including objective 1) is
represented by (a), (d), and (i). The degree of contribution of a single com-
ponent (PC1) to each of the three objectives is not equal. The degrees of
contribution, represented by the letters (a) to (j) in Table 2.1, vary for each
component-to-objective relationship. The challenge is in understanding
the degree of contribution of each component to each objective, as well
as the collective contribution of many components to a single objective.
Understanding the degrees of contribution of portfolio components
to the achievement of organizational objectives also aids the organization
in understanding the impact of decisions made in relation to those com-
ponents. When certain constraints are applied to the portfolio, such as
a reduction in budget or a change in strategy, the organization needs a
mechanism to aid management in decision making regarding rebalanc-
ing the portfolio. For example, if there is a reduction in the available
funds for portfolio components, the organization can choose to stop or
slow down components that make a low contribution to organizational
objectives. Alternatively, a change in strategy may reprioritize certain
objectives, resulting in the fast tracking of associated components that
make a medium or high contribution. Low, medium, and high refer to the
qualitative assessment of the degree of contribution of components.
In addition to the preceding, assessing the degree of contribution
of portfolio components to objectives will also achieve the benefit of

determining gaps in the portfolio. If the combined contribution of com-
ponents 5 and 6 to objective 4 is determined to be less than 1, it may be
necessary for the organization to consider additional portfolio compo-
nents to close the gap and achieve the objective fully.
The evaluation of portfolio component contribution is done subjec-
tively. Linguistic values such as low, medium, or high are used to describe
the degree of contribution. In order to effectively compare components,
however, quantitative values would need to be used. The challenge is in

converting the qualitative assessments into quantitative values. In addi-
tion, a mechanism for dealing with the cumulative contribution of port-
folio components is required. To address these requirements, a technique
is required for the model that can deal with converting qualitative values
into quantitative values while simultaneously computing the cumulative
contribution of multiple components to single objectives. Following a
review of various techniques, it was determined that Fuzzy Logic would
be a suitable technique to use in the model as it addresses the challenge
of converting qualitative assessments into quantitative values. The use of
Fuzzy Logic when developing the model is discussed in more detail in the
upcoming paragraphs.
Model
The following discussion gets slightly technical as it goes into how the
model uses Fuzzy Logic to achieve its outcomes. However, the author
briefly describes the Fuzzy Logic process and its applicability to the model
to avoid distracting from the real purpose of the model. Fuzzy Logic is
an extensive topic and its application is varied across many disciplines.
Various publications are listed in the Reference section that provides more
detail to the Fuzzy Logic process.
Fuzzy Logic is a technique that can deal with qualitative and quanti-
tative information. It is a technique that can take subjective information
and make it more objective and has proved to be very successful in a wide
range of applications. The various disciplines in which Fuzzy Logic has
been used successfully include, but are not limited to, decision support,
control theory, artificial intelligence, genetic algorithms, and mechanical
engineering.
The use of Fuzzy Logic in the decision-making model follows a com-
bination of the systems approach, multicriteria utility theory (MCUT),
and complexity theory. These theories and their relatedness to PfM are
discussed in Appendix 1. Qualitative evaluations of portfolio components
using MCUT are taken as INPUT, PROCESSED through the applica-
tion of rules in the fuzzy system, and an OUTPUT is produced (systems
approach). The relationships between organizational objectives and port-
folio components make up a complex system—(complexity theory).

A complex system comprises numerous interacting parts, each of which
behave according to some rule(s) or force(s).
In order to represent a complex business system, such as a
portfolio
of projects and their cumulative contribution to strategic objectives, a
combination of multiple fuzzy models is required.14
The reason is to
allow for the variability in the number of portfolio components contrib-
uting to the organizational objectives. For each portfolio component,
values for the input variables are obtained, rules are applied to the input
values, and a qualitative output value is derived. The fuzzification and
application of fuzzy rules is done for each portfolio component and the
contribution is determined by aggregating the qualitative outputs of the
related components and only then applying defuzzification to produce a
crisp (numeric) value that represents the cumulative quantitative contri-
bution of portfolio components to objectives. This process is illustrated
in Figure 2.2 and a detailed description of the model and its processes
follows.
The stages and phases of the model will now be described.
Stage A
Before we get into the description of the model in detail, it is import-
ant to outline the responsibilities of the executive management team and
the PfM team. Table 2.2 describes the responsibilities while Figure 2.3
illustrates the interaction between both teams.
Figure 2.2 Combined Fuzzy Logic model
PCVar1
FUZZIFICATION
OUTPUT
(before defuzzification)
AGGREGATION OUTPUT DEFUZZIFICATION
FINAL
OUTPUT
FUZZIFICATION
INFERENCE ENGINE
(RULES)
INFERENCE ENGINE
(RULES)
Portfolio Component 1
Portfolio Component2
Stage A
Stage B
PCVar2
PCVar1
PCVar2
OUTPUT

The process for stage A of the fuzzy model is illustrated in Figure 2.4,
followed by an explanation of the steps involved.
For each portfolio component that contributes to an
organizational
objective (in this case portfolio components 1 and 2), the model considers
input values for the input linguistic variables PCVar1 and PCVar2.
The input values are passed through a fuzzification process, after which
the rules in the inference engine are applied to determine a qualitative
value of contribution for each portfolio component. Linguistic
variables
are variables of the system whose values are words from a natural

language, instead of numerical values. Each input variable is qualified
by values, such as poor, average, and good for PCVAR1 and low, medium,
and high for PCVAR2. Different linguistic terms are used for PCVAR1
and PCVAR2 here to show that different terms can be used—provided
they describe the evaluation of the relevant criteria appropriately. In other
Table 2.2 Responsibilities of the executive management and PfM
teams
Team Responsibilities
Executive Management
(Investment management
Committee)
• Provide criteria for portfolio component evaluation.
• Evaluate portfolio components in terms of the selected
criteria.
• Makes decisions regarding the project portfolio.
PfM (Enterprise PfM
Office)
• Facilitates a meeting with the executive to agree to the
criteria to be used for evaluating portfolio components.
Criteria should remain constant but may change to a
limited extent when circumstances in the organization
change.
• Sets up the model for evaluating portfolio components.
This should only need to be done once and updated
when evaluation criteria change.
• Apply the model. This entails facilitating the evaluation
of portfolio components based on the selected criteria
and determining the individual and cumulative contribu-
tions of the portfolio components to the objectives.
• Present the portfolio component as an objective matrix
to the investment committee. The matrix indicates the
portfolio component contributions to objectives and is
used to determine which components can be terminated
or fast tracked when such a decision is required.
• Facilitate scenario planning and record the decisions
made at the investment committee meetings.

Figure
2.3
Interaction
between
the
executive
and
PfM
teams
Executive
management
/investment
committee
Project
portfolio
management/enterprise
portfolio
office
Provide
portfolio
component
evaluation
criteria
Define
portfolio
component
evaluation
criteria
Setup
model
for
evaluating
portfolio
components
Apply
model
to
determine
component
contribution
to
organizational
objectives
Present
portfolio
component/
objective
matrix
Evaluate
portfolio
components
Portfolio
decision
making
based
on
scenario
planning
Capture
portfolio
decisions

words, poor may be a better term than low for a particular criterion. Alter-
natively, the PfM team may choose to use low, medium, and high for all
criteria evaluations. The output variable (contribution) is qualified by the
values very low, low, moderate, high, and very high. Five values were chosen
for the output variable to facilitate a clearer distinction when determin-
ing the contribution values. However, it is not recommended to exceed
seven values for the output variable. Membership functions are used in
the fuzzification process to quantify a linguistic variable value. A mem-
bership function is a curve (triangular in this case) that defines how each
point in the input space (domain) is mapped to a membership value (or
degree of membership) between 0 and 1 (y-axis). Refer to Figures 2.5 and
2.6 for a depiction of membership functions.
Figure 2.4 Stage A of the combined fuzzy model
PCVar1
FUZZIFICATION
INFERENCE ENGINE
(RULES)
OUTPUT
FUZZIFICATION
Stage A
PCVar2
PCVar1
PCVar2
INFERENCE ENGINE
(RULES)
OUTPUT
Figure 2.5 PCVar1—Value
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
MEMBERSHIP
VALUES
POOR AVERAGE GOOD
µ (PCVar1 = POOR) = 0.6 µ (PCVar1 = AVERAGE) = 0.4 µ (PCVar1 = GOOD) = 0.0
a

Figure 2.6 PCVar2—Durability of competitive advantage
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
MEMBERSHIP
VALUES
LOW MEDIUM HIGH
b
µ (PCVar2 = LOW) = 0.2 µ (PCVar2 = MEDIUM) = 0.8 µ (PCVar2 = HIGH) = 0.0
An important characteristic of Fuzzy Logic is that a numerical value
does not have to be fuzzified using only one membership function.
In other words, a value can belong to multiple sets at the same time.
Phase 1—Input Variables
For the purpose of illustrating the model, only two input variables are used.
In a typical organization, a group of PfM experts could decide on a number
of input variables to be used for evaluating the contribution of portfolio
components to organizational objectives. The model is designed to cater
for more than two input variables but for illustrative purposes, only two are
used. The two input variables are described in the following text.
Portfolio Component Variable 1 (PCVar1)
To give some meaning to the following example, PCVar1 represents value.
The value that a portfolio component is expected to deliver is an import-
ant criterion when determining the portfolio component’s contribution.
Value considers the strategic alignment of the portfolio component—in
particular, the decision maker’s perception of how the component serves
the organization’s objectives in the long term—as well as the financial

attractiveness of the component—that is, the economic feasibility, which
is measured by the component’s cost, contribution to profitability, and
the component’s growth rate.
Portfolio Component Variable 2 (PCVar2)
In this example, PCVar2 represents the durability of competitive advan-
tage. If the portfolio component is delivering a product for which a

competitor already exists, then the portfolio component will be rated
low. If the product can be copied within a specified period, let us say
two years, then the portfolio component will be rated as medium. If the
likelihood of copying the product extends beyond two years, then the
portfolio
component is rated as high, as the contribution of the portfolio
component to an objective related to market share is high.
Phase 2—Fuzzification
Fuzzy Logic starts with the concept of a fuzzy set. A fuzzy set is a set
without a clearly defined boundary. It can contain elements with only a
partial degree of membership. For each input variable in this example,
three membership functions are defined. The qualitative categories for the
membership functions for PCVar1 are poor, average, and good, while the
qualitative categories for the membership functions for PCVar2 are low,
medium, and high.
The membership functions for PCVar1 and PCVar2 are illustrated in
Figures 2.5 and 2.6, respectively.
In Figures 2.5 and 2.6, the x-axis represents the domain and the y-axis
represents the membership values.
As mentioned earlier, a membership function is a curve (triangular
in this case) that defines how each point in the input space (domain)
is mapped to a membership value (or degree of membership) between
0 and 1 (y-axis). The PfM experts in the organization in accordance with
their knowledge and experience in PfM and the organization would do
the definition of the membership functions. This will be done before the
model is used for the first time. The membership functions will vary from
one organization to the next.

The domain is not numeric since the input values are qualitative.

Subjective information can now be modeled mathematically as the

qualitative inputs can be converted into quantitative values.
The next step in the fuzzification process is to take the qualitative
inputs, PCVar1 (represented by a in Figure 2.5) and PCVar2 (represented
by b in Figure 2.6), and determine the degree to which these inputs belong
to each of the respective membership functions. In an organization, the
PfM experts would evaluate the input variables of a portfolio component
and determine to what degree it is poor, average, or good or low, medium,
or high—as the case may be.
As an example, in Figure 2.5, this is represented by the dark bold verti-
cal line that intersects POOR at a membership value of 0.6 and AVERAGE
at a membership value of 0.4. In other words, PCVar1 is assessed as being
poor to a degree of 0.6 as well as average to a degree of 0.4 simultaneously.
Similarly, the PfM experts would evaluate PCVar2 of the same

portfolio component and determine to what degree it is low, medium, or
high. In Figure 2.6, the dark bold vertical line intersects LOW at a mem-
bership value of 0.2 and MEDIUM at a membership value of 0.8. In this

example, the input variable PCVar2 is assessed as being low (to a degree
of 0.2) as well as medium (to a degree of 0.8) simultaneously.
Phase 3—Inference Engine
A number of rules are determined by a knowledgeable group of individ-
uals in the organization who can determine the outputs based on specific
conditions within the inference engine. This would also be done before
using the model for the first time. An example of a rule would be:
IF PCVar1 is Poor AND PCVar2 is Low, THEN Contribution is
VeryLow.
The rules in Table 2.3 were applied to the input variables in the infer-
ence engine.
Rule Evaluation
The next step in the Fuzzy Logic process is to take the fuzzified
inputs (for the preceding example these would be: μ(PCVar1 = poor)
= 0.6,

μ(PCVar1 = average)
= 0.4, μ(PCVar2 = low)
= 0.2, and μ(PCVar2 = medium)
= 0.8) and
apply them to the antecedents of the fuzzy rules. If a given fuzzy rule
has multiple antecedents, the fuzzy operator (AND or OR) is used to
obtain a
single value that represents the result of the antecedent evalua-
tion. The rules used here have been developed for illustration purposes.
In an organization, a group of PfM experts would need to design the rules
and agree on the consequent values for the respective input value combi-
nations before using the model for the first time.
The rules transform the input variables into an output that will indi-
cate the degree of contribution of the portfolio component. This output
variable is defined with membership functions (very low, low, medium,
high, very high). Once the rules have been defined according to expert
knowledge, they become the knowledge base of the model. Table 2.4
represents the knowledge base associated with the rules described in
Table 2.3.
How the Rule Base Works
The next step is to compute the degree of membership to the membership
functions (Very Low, Low, Moderate, High, or Very High) of the output
variable (contribution). Once a variable is fuzzified (refer to the section
on fuzzification described earlier), it takes a value between 0 and 1 indi-
cating the degree of membership to a given membership function of that
specific variable. The degrees of membership of the input variables have
Table 2.3 Fuzzy rules
Rule 1 If PCVar1 is Poor AND PCVar2 is Low, THEN Contribution is Very Low.
Rule 2 If PCVar1 is Good AND PCVar2 is High, THEN Contribution is Very High.
Rule 3 If PCVar1 is Poor AND PCVar2 is Medium, THEN Contribution is Low.
Rule 4 If PCVar1 is Poor AND PCVar2 is High, THEN Contribution is Moderate.
Rule 5 If PCVar1 is Average AND PCVar2 is Low, THEN Contribution is Low.
Rule 6 If PCVar1 is Average AND PCVar2 is Medium, THEN Contribution is
Moderate.
Rule 7 If PCVar1 is Average AND PCVar2 is High, THEN Contribution is High.
Rule 8 If PCVar1 is Good AND PCVar2 is Low, THEN Contribution is Moderate.
Rule 9 If PCVar1 is Good AND PCVar2 is Medium, THEN Contribution is High.

to be combined to get the degree of membership of the output variable.
In this instance where there is more than one input variable, the degree of
membership for the output value will be the minimum value of the degree
of membership for the different inputs. Referring back to
Figures 2.5 and
2.6 as well as Tables 2.3 and 2.4, input (a) for PCVar1 has a membership
degree of 0.6 to the membership function POOR, which applies to rules
1, 3, and 4 (Table 2.3), and a membership degree of 0.4 to the membership
function AVERAGE, which applies to rules 5, 6, and 7. Similarly, input
(b) for PCVar2 has a membership degree of 0.2 to the membership func-
tion LOW, which applies to rules 1, 5, and 8, and a membership degree
of 0.8 to the membership function MEDIUM, which applies to rules 3,
6, and 9. When a rule is totally satisfied (indicated by  in Figure 2.7), it
will have an output with a membership degree to an
output membership
function equal to the lower degree among the inputs. The rules satisfied
in this example are given in Table 2.5.
Figure 2.7 shows the graphical representation (rule view) of the rules
in the system. The MATLAB
tool from MathWorks
was used to build
the simple fuzzy system and generate the rule view using the Fuzzy Logic
Toolbox
. In Figure 2.7, each row, numbered 1 to 9, represents a rule in
the system. The two input variables are shown alongside each other and
the output variable is to the right of the figure. The extended vertical lines
indicate the points of intersection on the relevant membership functions
associated with the membership values for each input variable.
The next section describes how the output values are derived.
Phase 4—Outputs
The output is the aggregation or sum of the membership functions from
the satisfied rules. Aggregation is the process of unification of the outputs
Table 2.4 Knowledge base associated with fuzzy rules
PCVar2
Low Medium High
PCVar1 Poor Very low Low Moderate
Average Low Moderate High
Good Moderate High Very high

of all rules. We take the membership functions of all rule consequents and
combine them into a single fuzzy set. The input of the aggregation process
is the list of consequent membership functions, and the output is one
fuzzy set for each output variable. Among the satisfied rules, the member-
ship degree of each output membership function will be the higher among
the rules that have as a result that membership function.
In Figure 2.8, the shading of the triangles indicates the degree of
membership.
• For the membership function Very Low the degree of mem-
bership is 0.2 (based on the result of rule 1 in Table 2.5).
• For the membership function Low the degree of membership
is 0.6 (based on the higher result of rules 3 and 5 in Table 2.5).
Table 2.5 The satisfied rules
Rule 1 IF PCVar1 is Poor (degree of 0.6) AND PCVar2 is Low (degree of 0.2), THEN
Contribution is Very Low (degree of 0.2), the lowest degree among the inputs.
Rule 3 IF PCVar1 is Poor (degree of 0.6) AND PCVar2 is Medium (degree of 0.8),
THEN Contribution is Low (degree of 0.6).
Rule 5 IF PCVar1 is Average (degree of 0.4) AND PCVar2 is Low (degree of 0.2),
THEN Contribution is Low (degree of 0.2).
Rule 6 IF PCVar1 is Average (degree of 0.4) AND PCVar2 is Medium (degree of 0.8),
THEN Contribution is Moderate (degree of 0.4).
Figure 2.7 Rule View
PCVar1
1
2
3
4
5
6
7
8
9
0 1 0 1
0 1
PCVar2 Contribution

• For the membership function Moderate the degree of

membership is 0.4 (based on the result of rule 6).
• For the membership function High the degree of membership
is 0.
• For the membership function Very High the degree of

membership is 0.
To calculate the quantitative contribution of a single portfolio com-
ponent with two input variables, the aggregated output must be defuzzi-
fied to get a single output value. While the most popular defuzzification
method is the centroid method, the method used here is the MOM (mean
of maximum) defuzzification method.
In this example, the output value 0.25 represents the contribution
of the portfolio component to an objective. An output value of 1 would
imply that the objective is fully achieved; hence, the output value in this
example (0.25) indicates that the portfolio component contributes to
the objective to a degree of 0.25. This implies that if this were the only
portfolio components selected to achieve an organizational objective,
then only a low degree of the objective would be achieved. The organi-
zation would need to select other portfolio components or amend the
scope of the component such that more of, or the entire, objective, is
achieved.
Figure 2.8 Output of rules
1
2
3
4
5
6
7
8
9
0 1
Output
Very
Low
Low
Moderate
High
Very
High

However, we want to determine the cumulative contribution of two
or more components and so, before we defuzzify the qualitative output
of a single component, we move to stage B where the contribution of
multiple components is considered.
Stage B
Phase 5—Additive Aggregation
The aggregation in stage A earlier is the unification of the outputs of
all rules per portfolio component. The aggregation in stage B is the
aggregation (sum) of the outputs of all portfolio components before
defuzzification.
To maintain the information in the complete system, the fuzzy
regions (outputs of portfolio components in stage A) are combined using
the additive aggregation method before defuzzification.15
The process
adds the truth membership values of the consequent fuzzy set and the
solution fuzzy set at each point along their mutual membership functions.
The bounded sum method is applied so that the composite member-
ship value can never exceed 1.0. Figures 2.10 through 2.13 illustrate the
aggregation of the portfolio component outputs into a single aggregated
output before defuzzification.
The additive technique adds the consequent fuzzy sets (stage A
outputs) to the solution variable’s output fuzzy region. The process adds
the truth membership value of the consequent fuzzy sets and the solution
fuzzy set at each point along their mutual membership functions.
Using the output of the example used earlier for one portfolio compo-
nent, Figure 2.10 shows the first step in the aggregation process.
For the second portfolio component, let us assume the stage A process
is followed as was done for the first portfolio component, and an output
for the second portfolio component is derived, such that
• For the membership function Very Low the degree of

membership is 0.0.
• For the membership function Low the degree of membership
is 0.2.

• For the membership function Moderate the degree of
membership is 0.4.
• For the membership function High the degree of membership
is 0.2.
• For the membership function Very High the degree of
membership is 0.
Figure 2.11 shows how the second output is added to the final output
(solution fuzzy region).
The combined output of both portfolio components is illustrated in
Figure 2.12.
To summarize, Figure 2.10 showed the addition of the consequent
fuzzy set for portfolio component 1 being added to the final output
region (cumulative contribution).
Figure 2.11 showed the addition of the consequent fuzzy set for port-
folio component 2 being added to the final output region. Figure 2.12
showed the combined view of Figures 2.10 and 2.11.
Phase 6—Aggregated Output
The aggregated output, also known as the solution fuzzy region, is
illustrated in Figure 2.13.
The solution fuzzy region (cumulative contribution) is described as
satisfying the membership functions Very Low to Very High such that:
The membership function Very Low has a membership value of 0.2.
The membership function Low has a membership value of 0.6.
The membership function Moderate has a membership value of 0.4.
The membership function High has a membership value of 0.2.
The membership function Very High has a membership value of 0.0.
Figure 2.9 Stage B of the combined fuzzy model
AGGREGATION OUTPUT DEFUZZIFICATION
FINAL
OUTPUT
Stage B

Figure
2.10
Additive
aggregation—first
portfolio
component
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
MEMBERSHIP
VALUES
LOW
MODERATE
HIGH
VERY
HIGH
VERY
LOW
CUMULATIVE
CONTRIBUTION
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
MEMBERSHIP
VALUES
LOW
MODERATE
HIGH
VERY
HIGH
VERY
LOW
INDIVIDUAL
CONTRIBUTION
0.0
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.1
0.2
0.0
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.1
0.2

Figure
2.11
Additive
aggregation—second
portfolio
component
0.0
0.3
0.7
1.0
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
MEMBERSHIP
VALUES
LOW
MODERATE
HIGH
VERY
HIGH
VERY
LOW
CUMULATIVE
CONTRIBUTION
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
MEMBERSHIP
VALUES
LOW
MODERATE
HIGH
VERY
HIGH
VERY
LOW
INDIVIDUAL
CONTRIBUTION
0
0
0
3
0
7
1
0
0.1
0.2
0.4
0.5
0.6
0.9
0.8
0.0
0.3
0.7
1.0
0.1
0.2
0.4
0.5
0.6
0.9
0.8

Figure
2.12
Additive
aggregation—combining
both
portfolio
components
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
MEMBERSHIP
VALUES
LOW
MODERATE
HIGH
VERY
HIGH
INDIVIDUAL
CONTRIBUTION
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
MEMBERSHIP
VALUES
LOW
MODERATE
HIGH
VERY
HIGH
INDIVIDUAL
CONTRIBUTION
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
MEMBERSHIP
VALUES
LOW
MODERATE
HIGH
VERY
HIGH
CUMULATIVE
CONTRIBUTION
0.0
0.3
0.7
1.0
0.1
0.2
0.4
0.5
0.6
0.9
0.8
0.0
0.3
0.7
1.0
0.1
0.2
0.4
0.5
0.6
0.9
0.8
0.0
0.3
0.7
1.0
0.1
0.2
0.4
0.5
0.6
0.9
0.8
VERY
LOW
VERY
LOW
VERY
LOW

Now that the aggregated output (solution fuzzy region) has been
determined, the quantitative value representing cumulative contribution
must be determined through the process of defuzzification.
Phase 7—Defuzzification
The last step in the Fuzzy Logic process is defuzzification. Fuzzification
helps us to evaluate the rules, but the final output of a fuzzy system has
to be a crisp number. The input for the defuzzification process is the
aggregate output fuzzy set and the final output is a single number. For this
model, the MOM defuzzification method16
proved to be more predictable
and accurate than other defuzzification methods.
Phase 8—Final Output
As indicated earlier, the application of the MOM defuzzification method
results in a quantitative value. In this instance, the defuzzification method
is applied to the aggregated fuzzy output to produce a quantitative value.
The quantitative value (result) represents the combined contribution of
the portfolio components. In this example, the combined contribution
is less than one, implying that the objective is partially achieved. This
Figure 2.13 Aggregated output
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.8 0.9 1.0
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
MEMBERSHIP
VALUES
LOW MODERATE HIGH
VERY
HIGH
VERY
LOW
CUMULATIVE CONTRIBUTION

would mean that if these were the only portfolio components considered
for achieving this objective, the organization would fail in achieving the
objective completely.
Interpretation and Utility of the Model
From the preceding discussion, while the portfolio components make a
contribution to the organizational objective, it can be seen that there is
still a gap in fulfilling the objective completely. This is indicated by the
fact that the degree of contribution is not equal to one. There is still
potential for additional portfolio components to be added to achieve the
objective fully. Alternatively, the scope of the selected portfolio compo-
nents could be amended such that their contribution can be improved
toward meeting the objective. The results obtained from the model can
assist in decision making regarding the composition of the portfolio.
Value of the Model
The ability to quantitatively determine the cumulative contribution of
portfolio components in achieving objectives after making qualitative
assessments of those components using multiple criteria improves the
decision-making capability of decision makers when considering the
portfolio mix and the potential to achieve organizational objectives.
Decisions regarding the portfolio composition still lie with people but the
model acts as a tool for enabling better-informed decisions. For example,
if the organization, due to budget constraints, wants to determine which
portfolio component can be terminated, it would use the model to test
the effect on the whole system by removing individual components and,
based on the results, make the decision as to which components can be
terminated.
Many current approaches focus on assessing only individual portfolio
components and lack the ability to determine the cumulative contribution
of portfolio components to organizational objectives. The assessment of
components is usually based on decision makers offering a subjective
score in order to rank components in the portfolio, whereas this model

uses Fuzzy Logic—a tried and tested technique—for taking linguistic
evaluations of components based on multiple criteria, and converting
them into quantitative values, based on predefined rules, to determine
the individual and cumulative contribution of portfolio components to
organizational objectives.
This model considers the complex relationship between
portfolio
components and organizational objectives and it is illustrated in a sub
sequent chapter, how the model can be used to improve decision
making
when managing the project portfolio. Instead of simply applying a

percentage reduction in budget across all portfolio components when
the organization is faced with budget constraints, for example, the model
shows the contributions of portfolio components and the impact on
the achievement of organizational objects if any of the components are
terminated.
Conclusion
During the investigation into the practice of PfM, it was observed that
decision making regarding portfolio components were being made with
little knowledge of the contribution of these components to organiza-
tional objectives. This led to a lack of understanding of the impact of the
decisions to stop or terminate the components. The focus of this chapter,
therefore, was to present a model that would address the problem.
This chapter began with a motivation for a conceptual model by firstly
describing the factors that led to the need for a model and,
secondly,
describing the objective of the conceptual model. The relationship
between portfolio components and organizational objectives was then
discussed, illustrating that components have varying degrees of contri-
bution to objectives and that one or more objectives can contribute to
one or more objectives. This results in a complex relationship between
components and objectives. The model, using Fuzzy Logic as a technique,
considers the qualitative evaluation of portfolio components, applies a set
of rules to convert the input values into qualitative outputs, aggregates
the outputs, and defuzzifies the aggregated outputs to produce a quan-
titative value that represents the cumulative contribution of portfolio

components to organizational objectives.

The ability to determine the contribution of portfolio components
using this model implies that decision makers now have a mechanism to
enable them to determine the impact of their decisions on the achieve-
ment of organizational objectives, as they now understand the degree of
contribution the components make to organizational objectives.
This model is significant for a number of reasons. First, it provides
a mechanism for taking qualitative evaluations and converting them
to quantitative values for comparison. Second, multiple criteria can be
used when evaluating portfolio components. This allows flexibility as any
organization can choose whichever criteria and any number of criteria
to apply in this process. Third, while other models evaluate individual
portfolio components, this model allows the simultaneous evaluation of
multiple components and is able to determine a cumulative contribution
value. Fourth, the approach or thinking of a number of theories discussed
in Appendix 1 was applied in the development of the model. Lastly, by
being able to also determine the individual contribution values, decision
makers can view the component—objective relationship from an alterna-
tive perspective—that is, the contribution of individual components to
multiple objectives.
Chapter 3 uses the fundamental concepts presented in this chapter
and discusses the alternate perspective mentioned earlier. This implies that
the concepts presented here could be applied in other ways and would be
useful in dealing with various aspects that influence PfM decision making.

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“Oh dear!” sighed Priscilla, “there is nothing, nothing that I feel I
want to do, and there is more than an hour before we can see the
guests coming.”
Loveday glanced at the clock, too. “So there is,” she sighed; “it isn’t
free yet.”
“Don’t be silly,” said Priscilla crossly; “you know you can’t tell the
time, so why pretend?”
“You said so, too,” protested Loveday; “and I know the people are
going to begin to come at four, ’cause mother said so, and if it is
more than an hour before they come, that shows that it isn’t free yet
by the clock.”
In her heart Priscilla thought that it was very clever of her little sister
to have found out all that, but she did not tell her so; she thought
Loveday was a vain enough little person already. She dropped down
with a weary sigh beside her doll’s house, but they had already given
that a thorough cleaning from top to bottom, and there was nothing
more to do to it. They had dressed and undressed all their dolls and
put them to bed, so that they were settled for the night, and wanted
no more attention. Every animal had gone out of the ark for a walk,
and marched back to it again, and there really seemed nothing left
to do that was worth doing.
“I wish I could help mother,” sighed Priscilla, who always loved real
work much more than play work—she would far rather help to dust a
room than dust or tidy her doll’s house; “and if they are so busy,”
she added, “I am sure there must be lots that I can do.”
After another moment or two had passed, she shut the doll’s house
door with a bang, and got up from the floor. “I am going downstairs
just a teeny-tiny way,” she said softly. “Don’t you come too, Loveday;
you needn’t do everything that I do.”
But it was really too much to expect Loveday to stay in that dull
nursery by herself, and very soon she was creeping out after
Priscilla.

Priscilla had reached the foot of the nursery stairs, and was standing
on the landing looking over the banisters, and listening for any
sounds of life below, and Loveday joined her. No one was about,
that they could see, but from the dining-room came the rattle of
china. Presently, however, they heard their mother’s voice; she was
speaking to Nurse.
“I will leave you to finish arranging the cups and saucers,” she said,
“and I will go to the kitchen and place the cakes out on the plates;
then it will be time for me to dress. I ought to rest for a few
minutes, for I am so tired already I can scarcely stand.”
Priscilla and Loveday drew back while their mother passed along the
hall below, for they did not want to be seen; they were doing no
harm, they thought, and it was very much more interesting to be
there than in the nursery. They must run away, though, before
mother came upstairs to dress, but by that time it would be nearly
time for them to watch from the nursery windows to see the first
guests arrive.
“I do wish I could help mother,” sighed Priscilla again. “She is so
tired, and has such lots to do. Can’t we do something to help? Oh!”
with sudden delight, “I know what I’ll do! I’ll dust the drawing-room!
Now, don’t you come too, Loveday. I thought of it first, and I can do
it by myself, and you are sure to break something and get us both a
scolding.”
But Loveday was not to be put off in that way, and, to save a howl,
Priscilla said, “Well, come along; you may come if you will promise to
be good.”
The drawing-room was on the very landing on which they stood.
Priscilla crept over to the door and looked in. Of course it was empty,
and to her it looked as though the furniture had all been pushed
back, just as when the room was going to be swept, only there were
no dust-sheets over the things.
“I believe it hasn’t even been swept yet!” she whispered, in a
shocked voice. “We’ll sweep it first, shall we?”

It was a grand idea, and Loveday agreed delightedly. Nurse still kept
her nursery brushes in a cupboard on the top landing; they would
get those, then no one would know what they were doing, and when
Nurse came up presently, all hot and tired, to sweep and dust the
room she would find it all done, and have a most beautiful surprise;
and she would not scold them at all; she would be so glad, and
perhaps she would let them have some of the “At Home” cakes for
their tea!
They hurried up the stairs very gently, and Loveday carried down a
long-handled brush, while Priscilla carried the dustpan in one hand
and the brush in the other, so that they should not clatter.
“Now close the door,” whispered Priscilla; and Loveday turned to do
it, bringing her broom-handle with a sharp tap against a picture
which hung by it. Priscilla was too busy to hear the blow, or to see
what had happened.
“It was such a little tap,” said Loveday to herself, as she gazed
ruefully up at the crack which ran quite across the glass of the
picture.
Priscilla was on her knees by that time, brushing the carpet as hard
as she could with the short-handled brush.
“What shall I do?” asked Loveday. “I can’t use this brush; it is so tall
it knocks my head.”
“You shall dust,” panted Priscilla, looking up with a very red face.
“But I haven’t a duster!”
“You have a handkerchief, haven’t you? Use that.”
“No, I haven’t,” said Loveday.
“Oh, how you do worry! Here, take mine!”
Loveday pounced on it gladly, and began to rub the legs of a chair.
“I think mother will be surprised to see the carpet so well swept.
Won’t she?” said Priscilla contentedly.

“Yes; and to see everything so well dusted. P’r’aps the guests will
notice it, too, and will say, ‘Here, Mrs. Carlyon, is sixpence for the
person who dusts your room so well.’”
But Priscilla scouted the idea with the utmost scorn.
“As if they would!” she cried. “Why, you silly child, people don’t say
things about other people’s rooms, not even if they aren’t dusted at
all. Of course, you can dust easy things like chairs, but I’ll have to do
the vases, and all the—take care, Loveday, the door is opening; oh,
do mind your head!” and Loveday stepped back just in time to allow
the door to be opened a little way. “Who is there? You can’t come in
yet,” cried Priscilla.
But the door opened wider, and Nurse’s agonised face appeared, and
behind her, gazing amazedly at Priscilla through a haze of dust,
stood Lady Carey.
“Miss Priscilla! Oh, what are you doing? Oh, you naughty, naughty,
mischievous children!” cried Nurse, horrified, and not knowing what
to do, or which to attend to first. “Excuse me, ma’am,” she said,
turning to the visitor, “but—but—oh, what can I do? The guests will
all be coming in a few minutes, and the room is like this!”
Lady Carey smiled.
“Are the little people too zealously industrious?” she asked. She saw
at once that something was amiss, and wanted to make as light of it
as possible. “How do you do, children? Are you Mrs. Carlyon’s two
little daughters?”
Priscilla dropped her brush, sprang to her feet, and went forward to
shake hands. Her checks were crimson with hard work and shame.
“How do you do?” she said breathlessly. “Yes, I am the eldest; I am
Priscilla, and this is Loveday. Loveday” (in an angry aside), “stop
dusting, do! I am very sorry the dust is flying,” she went on, turning
to Lady Carey again. “We wanted to help mother and Nurse because
they were so busy getting ready for the ‘At Home,’ and I was
sweeping the carpet and Loveday was dusting the easy things, like

chairs and table-legs, but we didn’t know it was time for the guests
to be coming. Nurse,” turning to her with a distressed air, “what can
we do?”
“Aren’t you very early?” asked Loveday of Lady Carey, as soon as
she had shaken hands with her, and said “How d’ye do?”
“Well, you see, dear, I am not come to the ‘At Home’; I did not know
your mother was having one. I came to return your mother’s call,
and I have unfortunately chosen an inconvenient day.” Then, turning
to the servant: “The dust has gone, I think, and I can sit here—
unless, of course, you want to be going round with a duster.” But
before Nurse could reply she went on: “No, I tell you what I would
much rather do, and what would be by far the best plan,” she added
kindly; “I have some other calls to pay, and Mrs. Carlyon is very
busy, and as I wanted to have a nice long talk with her, I will go
away now and come one day soon when she has more time. Don’t
tell her about this call, at least until after all her guests have gone,
and then be sure to tell her I quite understood, and would rather
come when I can have her all to myself.”
“I—I—but I am sure my mistress would wish to see you, ma’am,”
said Nurse, who was perplexed to know what she ought to do.
“Yes, I know,” said Lady Carey; “but it would be much more pleasant
for us both if I called another day. Now let me out, and hurry back
to set this room to rights. It is striking the quarter to four. Good-bye,
children. I hope I shall see you again soon.”
“Good-bye,” said Priscilla, but very, very shamefacedly; and as soon
as Lady Carey had gone she flew up the stairs to her own room,
and, flinging herself on her bed, burst into tears of shame and pain.
“And I meant to help! I meant to make such a nice surprise for
mother, and oh! I’ve done such a dreadful thing!” and poor Priscilla
sobbed and sobbed until her head ached.
Presently soft footsteps came lightly up the stairs and to her room,
but Priscilla, with her hot face buried in the bed-clothes, did not hear
them.

“Prissy, dear,” said her mother, as gently and kindly as though
nothing had happened, “will you do something for me? Will you run
down very quickly and help Nurse to dust the drawing-room? If you
will help her, there will be just time to set it all straight again before
our guests arrive.”
“Oh yes, mother.”
Priscilla scrambled off the bed in a moment, and pushed her hair
back from her face.
“Here is a nice soft duster,” said mother; “run quickly, dear.”
But Priscilla, using the soft duster to mop her eyes with, stayed for
just a moment to throw her arms about her mother’s neck.
“Oh!” she cried, “I do think you are the very nicest mother in all the
world. I am so glad I haven’t got any other,” and she hugged and
kissed her again.
“Now, don’t wipe your eyes on the duster any more, dear,” said Mrs.
Carlyon laughingly, and returning the kiss, “or it will make the things
quite dull instead of polishing them.”
Priscilla did not answer; she was gazing at her mother, lost in
admiration. Mrs. Carlyon had on a pretty brown silk gown, trimmed
with bands of little pink roses and green leaves, and the gown suited
her fair hair and delicate complexion to a nicety.
“I don’t wonder father married you, mother. You do look nice in that
gown.”
“Run away and dust my drawing-room,” cried Mrs. Carlyon, laughing
again, “and don’t waste time thinking of flattering things to say to
your mother. Hurry; it is close on four, and people will be coming
soon.”
“I wonder,” thought Priscilla, as she ran off, “if I shall ever have a
gown like that. But”—with a sigh—“if I had I shouldn’t look as pretty
in it as mother does.”

“I
CHAPTER VI
MRS. TICKELL, MRS. WALL, AND AN ACCIDENT
NFANTS!” said Geoffrey, popping his head round the nursery
door, “come up in the orchard; I’ve rigged up such a jolly
swing there!”
Priscilla and Loveday looked up from their play quite excited by the
news. They were keeping a shop at the moment—a book-shop—and
had all their nursery books and all the bits of paper and string they
could collect arranged before them on the window-seat, which made
a splendid counter. Books made such nice parcels, and were so easy
to wrap up. On the counter, too, they had an old Japanese jewel-
case that their mother had given them some time ago; it had two
drawers, with handles, so made a beautiful till for their money, and
they were doing such good business that already the till was heavy
with the weight of the cowries it held.
Priscilla had just wrapped up her “Playing Trades,” and handed it
across the counter to a customer, saying, “That will be half-a-crown
—thank you,” and was searching the till for a sixpenny-piece, when
Geoffrey opened the nursery door and popped his head in. Business
came to a standstill at once, and the two little shopwomen hurried
away, leaving books, and till, and everything. Half-way down the
stairs Priscilla stopped.
“Loveday,” she said, “don’t you think it would be rather nice if you
bought some sweets with your penny, and we ate them while we
were swinging?”
Loveday nodded.
“You will both wait for me while I am gone to buy them, won’t you?
You won’t be mean, and go on and begin to swing till I come?”

“All right,” said Geoffrey; “we’ll wait if you don’t take too long.”
Loveday, being the only one possessed of any wealth, had to be
treated with consideration. “Cut along, infant!”
Loveday had actually taken two steps, but Geoffrey’s words brought
her back again.
“I don’t think you ought to call us infants,” she said severely. “It
doesn’t sound at all nice, and if you do it again I don’t think I shall
give you a single sweet. We aren’t infants; father said so. Infants are
—are—well, we aren’t infants.”
“I think we will go on and begin to swing,” said Geoffrey, to tease
her—“don’t you, Prissy? If we wait for the end of this conversation I
am afraid the tree will die of old age.”
“I don’t know how you can like to be such a rude boy,” said Loveday
cuttingly. “Nobody thinks rude boys funny or nice.”
There were two sweet-shops quite near to Dr. Carlyon’s house, and
the children were allowed to go alone to both of them. Mrs. Tickell’s
was on one side of the street, and Mrs. Wall’s was almost opposite.
Mrs. Tickell was the favourite with the children; she was always
more pleasant and smiling and patient than Mrs. Wall, and gave
more generous measure. On the other hand, the children found Mr.
Tickell rather a drawback. True, he was not often in the shop, as he
was generally busy in the bakehouse, for the Tickells, in addition to
having sweets and apples, and prize-packets and little china figures,
made cakes and pasties and jam-tarts to sell. But when Mr. Tickell
was in the shop he always stood by the half-door, and asked the
most trying questions, such as: “Now, can you say to me your six
times right through without a mistake?” or, “Can you tell me when
Henry the Eighth began to reign?” Once he even asked Geoffrey to
say his dates right through, before the Conquest and all. It was
really dreadful, and as he always stood by the door, there was no
escaping him.
But Mrs. Tickell was so kind, and Emily, their daughter, was so
beloved by the children, that they bore with Mr. Tickell for their

sakes, and the shop remained their favourite.
Mr. Wall was of no account at all; the children had a notion that he
would be kind if he were left to himself, but that he was afraid of
Mrs. Wall. He very seldom spoke, and when he did it was only to say
something that they all thought very silly, such as “Fine weather this
for little ducks,” or something equally aggravating. So they put him
down in their minds as a weak creature, and took very little interest
in him. Mrs. Wall was a very solemn and unsmiling person. She
never grew friendly as Mrs. Tickell did. Priscilla heard some one once
telling a story of the Walls’ only son, who had died, she gathered, in
some tragic, mysterious way a long time ago, before she was born
or was old enough to remember anything. But what struck her even
more than the story was the remark, “And Mrs. Wall has never
smiled since.”
After that, whenever she was within sight of Mrs. Wall, Priscilla was
always watching her to see if this was true or not. She would hardly
believe that she did not forget sometimes, and smile before she
remembered; but Priscilla had never yet seen her do so.
“It must be dreadful for Mr. Wall to have her always looking so—so
cross,” she confided to her father one day. “As for him, I don’t think
he could smile if he wanted to; his mouth is so very wide it couldn’t
possibly go any wider.”
To-day Loveday ran off with her penny in her hand to buy some
bull’s-eyes at Mrs. Tickell’s, but, as usual, she examined both the
shop windows thoroughly first, that she might get some idea as to
how best to lay out her money, and she was very glad she did, for in
Mrs. Wall’s window there was quite a large assortment of new
things; there were pink and white sugar mice, black liquorice babies
with red lips and blue eyes, sugar bird-cages, and little cocoa-nut
fish-cakes. They were all two a penny but the mice, and those were
a farthing each.
Loveday felt, after gazing for some time, that she must have one of
the dolls, and that she wanted two of the mice. So she pushed open

the shop door and went in. A bell behind the door jangled loudly, so
Loveday knew that Mrs. Wall was upstairs “cleaning,” and that Mr.
Wall was absent, for the bell was always unhung and placed on the
counter if they were at hand.
Loveday liked to find the shop empty—it gave her time to look
about; but to-day, when she had looked about her for a few
minutes, she remembered that Geoffrey and Priscilla were waiting
for her, and would begin without her if she did not make haste, so
she hammered sharply on the counter with her penny, to make Mrs.
Wall hurry. Silence followed. She waited again what seemed to her a
very long time, then knocked once more, this time even more loudly.
Still silence.
During the next few minutes Loveday quite changed her mind as to
what she would spend her money on. She suddenly remembered
that Emily Tickell had told her she had some beautiful rose-drops
coming in, and some honey-drops; and Loveday loved both. Besides
which, the thought crossed her mind that it might not be easy to
divide the two mice and the one doll. The mice were very hard to
break, and she could not give the whole doll to one; it would not be
fair. She wished then that she had not come to Mrs. Wall’s, and was
just wondering if she could creep out of the shop again without
being seen, when she heard a sound, and Mrs. Wall opened the little
glass-topped door, and came up the two steps leading from the
parlour to the shop. She looked rather crosser and sterner than
usual.
“I had only just gone up to change,” she said sharply, “and as sure
as ever I go, that bell is certain to ring. What can I do for you,
miss?”
Loveday felt uncomfortable; her heart was quite set now on getting
the rose-drops and the honey-drops, and not the doll or the mice,
but what could she say or do! Then a way out of her difficulty
suddenly opened out before her.
“Please, can you change a penny for me?” she asked very politely.

Mrs. Wall did not say anything, but her lips set a little more tightly
than usual as she went to the till and took out two halfpennies.
“Thank you,” said Loveday, with a sigh of relief, and, hurrying out,
she flew across the road to the Tickells’ shop, almost opposite. As
she reached the door she glanced back for one more look at Mrs.
Wall’s fascinating store, but all she saw was Mrs. Wall’s cold stern
eye looking after her with anything but an amiable expression in it,
and she turned with relief to Emily Tickell’s welcoming smile.
When at last she reached the orchard with her two precious packets
in her hands, Geoffrey and Priscilla were busy arranging a bit of
wood for a seat for the swing. They had not been swinging, they
assured her, at least only just trying it to see if it was all right, and
Loveday was satisfied and distributed her sweets.
But as soon as the sweets were in their mouths they began, and
what a glorious time they did have for a while!
They swung so high, and it seemed so dangerous and exciting, and
sometimes they took it in turns to swing, sometimes two got on
together, and once even the three of them.
“Perhaps we hadn’t better all get on together again,” said Priscilla
after that, looking at the slim skipping-rope they had all been
depending on. “It isn’t a very strong one, is it?”
“Strong enough,” said Geoffrey.
“Let’s play something else now,” said Loveday, flinging herself down
on the grass. “I am tired of swinging, and it makes me feel rather
sick.”
Priscilla was sitting in the swing, just lazily moving it. “What shall we
do, then?” she asked reluctantly. “I don’t think we will stop quite yet;
let’s go on for a little while longer, just one or two more swings, and
you watch us, Loveday, like a darling.”
“I can’t watch you,” said Loveday; “it makes my head swing too.”

“I tell you what,” said Geoffrey, “we’ll just have one more good turn,
then I’ll get out the sticks and hoops, and we’ll have a game of ‘La
Grace.’ You sit where you are, Prissy, and when I’ve given you a
good start I’ll spring up at the back of you. Loveday, you can look
away if it makes you giddy;” and with the same he sent the swing
with Prissy in it flying up through the air, then back she came, and
up she went again and back; but this time Geoffrey held on the
ropes, and as the swing swung forward the third time, he sprang up
on his feet on to the seat. The ropes quivered and strained, and for
a moment their flight was checked; then on they went again, up and
down and up; then, with a scream and a heavy thud, they both
came down to the ground, Priscilla underneath, Geoffrey on top of
her.
Loveday was too bewildered to cry or to scream. At first, in fact, she
did not realise what had happened. She thought they were playing
some game, and that in a moment they would both jump up with a
laugh and a shout; and yet—Priscilla was so very white and still, and
lay so long, and though Geoffrey often groaned in fun and
pretended to be hurt, it was somehow not quite like this; and when
at last Geoffrey tried to get up, but only screamed and fell back
again, Priscilla still never made a sound or a movement. Geoffrey
made one more effort, and dragged himself off Priscilla; but he could
not get up, for every time he tried to raise himself on his arm, the
pain was greater than he could bear.
“I believe I’ve broken my shoulder—or something!” he gasped.
“Loveday, run quick, and tell some one to come! Get father, and—
Prissy, Prissy”—he broke off to call his sister. “Oh, why doesn’t she
open her eyes? Prissy, speak; do speak.”
He tried to move her, but he could not manage that.
“Run, Loveday, as fast as ever you can—do!”
He looked so ill and scared, and Priscilla looked so dreadful, lying so
still with her arms all crumpled up under her, that Loveday nearly
fainted with fear; but she ran and ran as she had never run before,

and all the way her clear shrill voice rang out: “Daddy, mother,
Nurse, come quick! Where are you? Oh, do come!” She called so
loudly, and there was such real distress in her voice, that by the time
she reached the house her father was hurrying out to meet her; and
before she had gasped out half her tale of woe, he had gathered her
up in his arms, and, followed by, it seemed, the whole household,
was rushing to the orchard, where Priscilla lay as Loveday had left
her, and Geoffrey, as pale now as Priscilla, was still struggling to get
up and at the same time to choke back the tears of pain that would
force their way up.
Then there followed a busy, sad, painful time, when, between them
all, they got the two injured ones to bed, and attended to their
hurts. Geoffrey’s shoulder was not fractured, but it was dislocated,
and he had strained and bruised both arms.
“If you had fallen backwards,” said Dr. Carlyon gravely, “instead of
forwards, you would probably have dislocated your neck. How could
you run yourself and your sisters into such a danger? It was most
culpable of you.”
“It seemed all right,” groaned poor Geoffrey, “and I don’t know now
why we fell. The branch was a strong one——”
“Yes, but the rope was not, and you put it up loosely, so that it
rubbed every time you swung, and, of course, rubbed through in a
very little while. You shall see the frayed ends when you are well
enough; perhaps it will help to teach you how a swing should not be
hung.”
Poor Priscilla had a fractured arm and a cut head, and was badly
bruised all over; and when, poor child, she awoke from her
unconsciousness, she found herself one big block of pain from head
to heels, or so it seemed to her. But worst of all, perhaps, was the
dreadful pain in her head from the blow, and the jerk, and the
shock. She could not endure a ray of light, nor a sound, nor to speak
or be spoken to.

Poor Loveday crept into the bedroom time after time to be near her.
She brought her best books and her favourite toys, her paint-box,
and even her pink parasol to lend, or to give to Priscilla, if by doing
so Priscilla could only be got to look better and to take some interest
in things. But Priscilla lay very still and white, moaning occasionally,
and did not look at Loveday or her treasures, or seem able to take
any interest in anything, and poor little Loveday crept away again,
feeling perfectly miserable, and at her wits’ end, for if those things
failed, she really did not know what could be done. And if she went
to Geoffrey she only felt more miserable, for he was so remorseful
and unhappy, and kept on saying such dreadful things about himself
for having caused it all, that one could not dare ask him to play, or
even to read aloud, or to do anything.
At last Loveday grew to look so ill and moped, that her father and
mother decided it would be better for her to go away for a little
while to more cheerful surroundings, or she would be ill too. But
then came the question: “Where could she go?”
“Granny would have her, and be delighted to,” said Mrs. Carlyon,
“but I don’t know how to get her up there. I couldn’t possibly travel
up and back all in one day, and I should not like to be longer away
from home just now. Nor can you be spared either.”
“And I would like her to have sea air,” said Dr. Carlyon. “I think it
would be much better for her.”
“And I would like her to be where she could have a child or so to
play with,” added Mrs. Carlyon.
So it seemed they had to find a place for Loveday with children, not
very far from home, but by the sea. It was Nurse who settled the
difficulty at last.
“I suppose you wouldn’t like to send her to Bessie, down at
Porthcallis, sir, would you? She’s got a nice little cottage, and close
to as nice a bit of safe, sandy beach as you could find anywhere,
made on purpose for children, I should think, and her own little boy

must be nearly as old as Miss Loveday. Bessie does understand
children too, and she is very fond of Miss Loveday.”
This was one of Nurse’s great anxieties. She could not bear the idea
of her “baby” being sent away; but if it was better for her that she
should—and Nurse saw that it was—she was anxious that she should
go to some one who loved her and would make her happy.
Bessie Lobb had been a housemaid for a few years with Dr. and Mrs.
Carlyon when Geoffrey and Priscilla were babies. She had left to get
married before Loveday was born, but she had been back several
times to Trelint to visit her relations, and had always come several
times to see her former master and mistress, and children, and
Nurse.
Every one hailed Nurse’s suggestion with joy, for Porthcallis was only
about fifteen miles from Trelint. The beach was, as Nurse said, very
safe, the air was beautiful; and Bessie was a good, kind, trustworthy
body, and her husband was a nice respectable man, and devoted to
children.
Mrs. Carlyon wrote to Bessie at once, and very quickly a reply came
to say that Bessie would be proud and pleased to have Miss
Loveday. She had a spare bedroom that Miss Loveday could have,
and she would do her best to make her comfortable and happy.
“That is capital,” said Mrs. Carylon, greatly relieved that matters
were settling themselves so well. “I will write to Bessie at once, and
say I will bring Loveday on Thursday.”
“Then I had better set to work at once to sort out my toys and begin
to pack, I suppose,” said Loveday, in a tone of great importance, “or
I am sure I shall never be ready in time.”

B
CHAPTER VII
LOVEDAY GOES VISITING
UT though she began her packing at once, and went on with it
most industriously for the two following days, yet, when
Thursday morning came, she was not, according to her own
accounts, nearly ready.
There really was a great deal to be done. First of all she had to find a
basket in which to pack her cat, “Mrs. Peters,” and her three kittens,
for until that was done she could not make any other plans or attend
to anything else.
Fortunately, however, she found at once a nice shiny hat-box, with a
leather handle and a lock and key, which would just hold the Peters
family, for the kittens were quite tiny. “I will pack all my white flannel
petticoats in the bottom of it,” she said to herself, “for they will be
nice for Mrs. Peters and the kittens to lie on, and it will be a good
thing to get the petticoats in out of the way.”
So in went the petticoats, and then the kittens, but Mrs. Peters was
out, and had to be waited for. She came in, though, in such good
time that she and her family and the petticoats were packed and
locked and strapped up long before Loveday’s dinner-time came; and
what would have been the end of the poor kittens and their mother if
their own dinner-time had not come very soon, and Nurse had not
come in search of them to feed them, no one can imagine, for the
box had no ventilation holes, and the lid shut down quite close.
If Mrs. Peters and the kittens suffered, though, Loveday suffered too;
for Nurse was so angry when she saw the petticoats in the box with
the cats, that she ordered Loveday to sit down and pick off from
them every single hair that the cats had left behind, and they had
left so many that to Loveday it seemed a marvel that they were not

all quite bald. She did not get rid of quite all the hairs, though, for by
tea-time her eyes were so swelled and smarting with crying, she was
excused the rest, after promising never, never to do such a thing
again.
“Don’t you think, dear, that you had better leave Mrs. Peters and her
family behind?” suggested her mother, when Loveday, after
ransacking the whole house, had found a basket to take the place of
the hat-box.
“Oh no!” cried Loveday; “Mrs. Peters would fret dreadfully for me.”
“Do you think she would, dear, now she has her little ones to interest
her?”
“Oh yes, I am sure she would. You see she would have no one to
talk to her.”
“I would talk to her,” said mother, “and make much of her,” and
looking rather grave, “you see there is a great deal of water at
Porthcallis, and the kittens are so very young. If they escaped from
you or their mother, and got down on the sands and a wave came in,
and——”
“Can kittens swim?” asked Loveday, looking very anxious.
“No, dear; such baby things, too, would be too frightened to do
anything. I really think it would be kinder to leave them at home with
Nurse and me, and Priscilla would be glad, too, to have them to
watch and play with when she gets better. She will be rather lonely
and dull without you, you know.”
“So she will,” sighed Loveday, “but of course I shall come home at
once if Prissy wants me.”
“You must breathe in all the sea air you can, and grow strong and
rosy, and you must collect all the pretty shells you can find, for
Priscilla, and then, perhaps—but remember it is only perhaps—when
Priscilla and Geoffrey are well enough we may all come down to
Porthcallis for a holiday with you.”

“Oh, how lovely!” cried Loveday, dancing and clapping her hands
with joy. “I shall like going ever so much better now than I did.” She
went over and leaned on her mother, and looked up into her face. “I
—I didn’t want to go before you said that,” she confided to her in a
half whisper, “at least not very much; but I do now, and I will get all
the shells I can for Prissy, and I will get to know my way everywhere
so as to be able to lead you all about when you come. And now,”
bustling away, “I am going to take out all my toys to see which of
them I shall pack;” and off she ran. In a moment or two, though, she
was back again.
“Mother, don’t you think I ought to take one of my toys, or one of
Prissy’s, to Aaron Lobb? I don’t expect he has very many, and little
boys and girls always like to have something brought to them when
people come on a visit.”
“Yes, certainly, dear. Take one of your own—something you think a
boy would like.”
Loveday thought for a moment. “I fink I’ll take him the big monkey.
It is very ugly, but boys like ugly things;” and off she ran again, and
this time really reached the nursery, where Mrs. Peters and her
family were frantically clawing at the basket in their longing to get
outside it.
Loveday untied the lid and let them all out. “You are not to go after
all,” she said. “I hope you won’t be dis’pointed, but mother finks
Prissy may want you, and, after all, the fish at Porthcallis isn’t better
than any other, and there’s a dreadful lot of water.”
Whether Mrs. Peters understood the change of plan or not, who can
say? But it is a fact that she lay down purring with happiness, and,
drawing all her children about her, talked to them for a long time.
Three days later, about noon, Loveday and Mrs. Carlyon started. It
was not a very long journey by train—an engine soon covers fifteen
miles; and the afternoon sun was still shining bright and hot when
they stepped out on the platform of the little bare country station,
which was not very far from Mrs. Lobb’s cottage. Though one could

not actually see the sea from the platform, one felt that it was close
by, for one could smell it in the air, and on stormy days one could
hear it; and, though I don’t know how it came there, there certainly
was sea-sand all about the platform, which made it look and feel as
though the sea certainly must reach that far sometimes.
It was all very open and breezy, and there seemed to be an endless
amount of air and space, and sea and sand, and sky and everything.
Loveday almost wished there was not quite so much; it made her
feel so small, and rather forlorn. But she had not much time to think
about it, for things kept on happening. There were no omnibuses or
cabs or anything to take them anywhere.
“How are we going to get my box to Bessie’s house?” she asked
anxiously.
A man with a wheelbarrow had come up, and was standing by them.
“I’ll take the box, little lady,” he said, touching his hat and smiling at
her. “For the rest, hereabouts, we mostly goes on Shanks’s mare.”
“Oh, thank you,” said Loveday.
Mrs. Carlyon explained to the man where she wanted him to take the
box, and paid him; and when he had gone, and she had gathered up
the little things she wished to carry herself, she and Loveday started
to follow. Outside the station, Loveday stopped and looked about her.
“Come along, darling,” said mother rather impatiently. “What are you
looking for? This is the way. I want to go to one or two shops first.”
“I was looking for Shanks and his mare,” she explained, “to take us
to Bessie’s.”

“‘I’ll take Thomas,’ she said.”
“I don’t think the station-master need have laughed like that,” she
said indignantly, as, a moment later, they walked quickly away.
“Everybody makes mistakes, and we don’t call legs by such silly
names at home, and—and one can’t know everything. Even grown-
ups don’t know everything, but they do laugh at such silly things. I
don’t see anything funny in it.”

“No, I don’t suppose you do, dear. But look! here is a fine shop,” said
Mrs. Carlyon, drawing up before a window full of toys, and china,
and a few books, and some boxes of chocolates, and a long string of
tin buckets all painted different colours. “We will go in, shall we? I
want to get you a spade and bucket.”
“Oh, thank you!” gasped Loveday. “How lovely!” and she forgot in a
moment all her troubles and the trying habit grown-ups have of
laughing at nothing.
Some of the buckets had names painted on their sides.
“Have you one with ‘Loveday’ on it?” she asked eagerly of the
woman who came out to serve them.
“Oh no, miss,” said the woman, shaking her head. “I never heard of
no such name as that before. I’ve got one with ‘Thomas’ on it, and
‘Ada,’ and ‘Susan.’”
Loveday hesitated a moment; then, “I’ll take ‘Thomas,’” she said.
“You see,” she explained to her mother when they got outside, “if I
had chosen ‘Ada’ or ‘Susan,’ people would have thought it was my
own real name, but they can’t think I am called ‘Thomas.’”
“I don’t suppose people have much time for thinking about little girls
and the names on their buckets,” said Mrs. Carlyon quietly.
“No, not people, mummy, but boys and girls have. They have lots of
time, and they notice everything.”
Armed with her spade and her scarlet bucket, Loveday walked on
quite cheerfully to Bessie’s house. From the station it had looked
quite close, only just across a green, and along a strip of level road
and a little bit of beach, and there you were. But the country just
there was flat and deceptive; the road wound and curved, and they
found it quite a longish walk by the time they had passed the green
and followed the windings of the road, and crossed the stretch of
sands. But there they were at last, and there was Bessie out to
welcome them, and Aaron, too, though he disappeared behind his
mother’s skirts as soon as the strangers came really close.

Loveday thought him a very funny little boy, and not at all pretty. He
had very round red cheeks, and a snub nose, and big dark eyes; his
hair was dark, too, and quite straight, and cut very close to his head.
Loveday looked at him with the greatest interest and curiosity. He
was very different from what she had expected; for one thing, he
was older and more manly.
“He is like a boy, not a baby,” she said to herself, and felt a little
disappointed.
She had thought she was to have had a play-fellow whom she could
have “mothered” and managed a little. But she soon found out her
mistake. Aaron Lobb was not at all a baby, nor did he think himself
one or allow others to do so. He was a sturdy little fellow, and full of
a knowledge of the sea and the tides, and boats, and shells, and
fishing, which to Loveday seemed simply amazing, and clever beyond
words.
When they had all talked a little, Bessie led the way into the house,
and Loveday thought it was the most interesting, funny, and
charming house she had ever seen in her life. It stood back from the
beach, close under the towering cliff, and was a long low house, only
one storey high, with big windows, and a porch over the door, and a
verandah on each side of the door, and it was painted white, all but
the window-frames and the doors, and they were green.
Bessie explained that it had been built by a gentleman who lived in a
big house on the top of the cliff. He had had it built years ago for his
boatman to live in, “and there is the path he had made for the man
to go up and down by to the big house.”
Loveday looked, and saw a dear little winding path going up and up,
with here and there a flight of little steps where the cliff was
particularly steep, and all the way there was a strong hand-rail to
prevent one’s falling over.
“Does your husband take charge of the boats for the gentleman
now?” asked Mrs. Carlyon.

“Oh no, ma’am,” said Bessie, shaking her head and looking very
grave. “He doesn’t keep one now, poor gentleman! His only son was
drowned one day out there, right in front of his windows, and Mr.
Winter—he—he saw it, and—and it pretty nearly drove him out of his
mind. The next day he sent down to Button—Button was his man—
and ordered every boat to be broke up, and he got rid of Button—not
’cause ’twas his fault, but ’cause he couldn’t abide the sight of
anything that had to do with that dreadful day. He was going to have
this little place pulled down too, but my husband begged and prayed
him not to, houses here being so scarce there’s no getting one. And
Mr. Winter, he gave in. You see, ma’am, he’d had the little place built
low like this, and right back under the cliff, so’s it shouldn’t be seen
from the house, so he was never worried by the sight of it, and after
the accident he wouldn’t be likely to, for he had the blinds on that
side of the house that faced the sea drawn down, and he dared
anybody ever to raise them again in his lifetime.”
Loveday was very much impressed by this sad story. She seemed to
see the poor father sitting lonely and sad in his dark house, while his
only son lay for ever at the bottom of the cruel sea, which stretched
before his very eyes. There were tears in Mrs. Carlyon’s eyes as she
listened, and quite a sadness lay for the moment over the whole
scene as they followed Bessie into the bungalow. It was quite a large
bungalow, and so well built and nicely finished inside. On one side of
the little entrance was a cosy, spotlessly clean kitchen-parlour, with
scullery behind it, and beyond that was Bessie’s bedroom; both had
windows looking out to sea, and Bessie’s room had a little door at
the end, by which she could get in and out without having to go
through the kitchen. On the other side of the entrance was a nice
little room, which had been built, said Bessie, for the young
gentleman and his friends to have a meal in, or sit in, and behind it
were two little rooms which had been built for dressing-rooms or
bedrooms, for him to change in if he came home wet, or to sleep in
if he was going to start very early on a fishing expedition, or come
home late.

The front room, which looked out to sea, Bessie had made her
parlour, while the others were two dear little bedrooms, one of which
was now Aaron’s, while the other was to be Loveday’s.
Loveday’s eyes sparkled when she saw hers. It had a wooden bed in
it—such a curious-looking one, for it had been a four-poster, but, as
it wouldn’t go into any room in the bungalow, they had had to cut
the top off, so that now it seemed to have two sets of legs, the four
it stood on and four that stood up in the air. The window was hung
with curtains of blossom-white muslin, and the looking-glass and
dressing-table and bed were all hung with the same. So snowy and
soft and billowy it looked, the little room might almost have been
filled with white clouds or foam. The woodwork was painted white,
and the walls were white too, but for a frieze around the top,
whereon white-sailed ships scudded along over a glorious blue-green
sea, while gulls hovered and swooped, or stood stiffly on the bright
green grass on the cliff-top.
Loveday was enchanted. “Oh, I wish Prissy could see it too!” she
cried, and that was the only flaw in her great delight.

P
CHAPTER VIII
PISKIES STILL LIVE AT PORTHCALLIS
RESENTLY though, just for a time another shadow fell, for it
seemed only a very, very little while before it was time for her
mother to leave.
“I wish you could stay all the time, mother,” she whispered eagerly.
“Couldn’t you, mother? It would do you good too.”
“But, darling, think of poor Priscilla. She will be wanting me, and I
know you wouldn’t like to keep me away from her.”
Loveday was not quite sure of that at the moment, but she would
not have said so; and when she thought of pale, suffering Prissy, she
tried hard to choke down any selfish feeling, and to be very brave.
“But—you will come again soon, won’t you, mother?”
“Yes, darling, very soon; and I expect father will run down to see
you in a very little while, and we will always let you know if any of us
are coming, so that you can come to meet us. Now, are you going to
see me off at the station, or will you stay here and wave your
handkerchief to me?”
“Oh, please, I’ll go to the station.”
They all had tea on the beach outside the cottage, and when that
was done it was almost time for Mrs. Carlyon to start on her
homeward journey. Bessie was to go to the station too, and take
Aaron with her; and Mrs. Carlyon felt pretty sure that by the time
Loveday had had the double walk, she would be too tired to fret
much, or feel lonely, or to do anything but go to bed and sleep.
She was a very brave little woman, on the whole, considering that
she was alone in a strange place, and with people who were almost

strangers to her. A few tears did force themselves through her lids,
but she did not say anything.
“When you get back, darling, you must help Bessie to unpack your
box, and you will be able to give Aaron his monkey, then you will be
ready for bed, and when you wake up again it will be morning, and
you will feel so happy, and there will be so much to see and do, that
you will scarcely know what to see and do first. But don’t forget to
collect a nice lot of shells for Priscilla.”
Then the engine gave two or three snorts and puffs, and a loud
whistle—away moved the train, and Loveday found herself left alone.
She might have shed a few tears more when the train puffed away—
in fact, it is pretty certain that she would have if she had not, at that
moment, caught sight of the station-master, and remembered his
rude laughter about Shanks’s mare. He had not caught sight of her
yet, and Loveday was anxious to hurry away before he did, and in
her eagerness and hurry she quite forgot about her tears and her
loneliness; and then it was such fun to watch the ducks and geese
on the green, and to make them run at one, and stretch their necks
and scream, that she was soon laughing instead of crying; and when
they got back there was a boat drawn up on the beach, and that
was very exciting, for Mr. Lobb had come back with a big catch of
crabs and lobsters, and Loveday, after being introduced to him, was
for quite a long while perfectly fascinated, watching the creatures
trying to get out of the great lumbering crab-pots which he had
brought them home in.
“I wish now, missie, as yer ma hadn’t a-been gone, for she could
have took home two or three of these, and welcome to ’em.”
“Oh, I wish she hadn’t,” said Loveday earnestly. “Father loves
lobsters and crabs; he would have been so glad—so would Geoffrey.”
“Well, look here now,” said John Lobb good-naturedly. “Bessie’ll bile
these presently, and then if she’ll pop one or two into a basket, I’ll
take them up and post ’em, and your pa’ll have ’em in time for his
breakfast in the morning.”

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