Mastering risk modelling a practical guide to modelling uncertainty with microsoft excel (the mastering series)

A practical guide to modelling uncertainty
with Microsoft® Excel

Alastair Day has worked in the finance
industry for more than 25 years. He has held
both treasury and marketing positions and
was formerly a director of a vendor leasing
company specializing in IT and technology
assets. Following rapid company growth, the
enterprise was sold to a public company and
Alastair established Systematic Finance plc
as a consultancy specializing in:
• Financial modelling – design, build, audit
and review
• Training in financial modelling, corporate
finance, and leasing on an in-house and
public basis
• Finance and operating lease structuring
as a consultant and lessor
Alastair is the author of a number of other
books published by Financial Times
Prentice Hall, including: Mastering Financial
Mathematics in Microsoft Excel and Mastering
Financial Modelling in Microsoft Excel, now in
its second edition.

MASTERING
RISK MODELLING
second edition
A practical guide to modelling uncertainty with Microsoft® Excel
Mastering Risk Modelling is a practical guide designed to provide useful

templates for applying risk and uncertainty.
The book:
l Improves financial managers’ abilities with Excel
l Demonstrates a systematic method of developing Excel models for fast
development and reduced errors
l Provides a library of basic templates for further development all on an
enclosed CD for immediate use
This fully revised and updated guide is an essential companion for all those who
work with risk model design and those who want to build more complex models.

FINANCE

A practical guide to modelling
uncertainty with Microsoft® Excel

mastering
RISK modelling
• H
 elps you understand and manage risk through the
confident use of models
• A
 systematic method of developing Excel models for
fast development and error checking

second edition

Mastering Risk Modelling covers:
l Review of model design
l Risk and uncertainty
l Credit risk

l Project finance
l Financial analysis
l Valuation
l Options
l Bonds
l Equities
l Value at risk
l Simulation

Visit our website at

www.pearson-books.com

www.pearson-books.com

CVR_DAY9298_02_SE_CVR.indd 1

A practical guide to modelling uncertainty
with Microsoft® Excel

second
edition

Visit our website at

An imprint of Pearson Education

MASTERING
RISK MODELLING

DAY

New material in this edition includes:
l Thoroughly revised models
l More material on credit risk modelling such as portfolios, VaR and bankruptcy
models
l Dual 2003/2007 Excel key strokes
l The use of statistics in Excel - tools and methods
l Advice on capacity to borrow and repay
l Finding optimum mix of risk and return
l Fixed income risk models
l Visual Basic approach

MASTERING RISK MODELLING

MASTERING
RISK MODELLING

Alastair L. Day

An imprint of Pearson Education

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Mastering Risk Modelling


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In an increasingly competitive world, we believe it’s quality of
thinking that gives you the edge – an idea that opens new
doors, a technique that solves a problem, or an insight that
simply makes sense of it all. The more you know, the smarter
and faster you can go.
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Under a range of leading imprints, including Financial Times
Prentice Hall, we create world-create print publications and
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To find out about Pearson Education publications, or tell us
about the books you’d like to find, you can visit us at
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Mastering Risk Modelling
A practical guide to modelling uncertainty with
Microsoft® Excel
Second Edition

ALASTAIR L. DAY


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PEARSON EDUCATION LIMITED
Edinburgh Gate
Harlow CM20 2JE
Tel: +44 (0)1279 623623
Fax: +44 (0)1279 431059

Website: www.pearsoned.co.uk
First published 2003
Second edition published in Great Britain in 2009
© Systematic Finance Plc 2009
ISBN: 978-0-273-71929-8
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
Library of Congress Cataloging-in-Publication Data
A catalogue record for this book is available from the Library of Congress
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About the author
Alastair Day has worked in the finance industry for more than 25 years in
treasury and marketing functions and was formerly a director of a vendor
leasing company specializing in the IT and technology industries. After sale
of the company to a public group, Alastair established Systematic Finance
plc as a consultancy specializing in:
■
■

■
■

■

financial modelling – design, build, audit and review;
training in financial modelling, corporate finance, leasing and credit
analysis for a range of in-house and public clients;
finance and operating lease structuring as a consultant and lessor;
financial books including those published by the FT such as Mastering
Financial Modelling (second edition), Mastering Risk Modelling, Mastering
Financial Mathematics in Excel and The Financial Director’s Guide to
Purchasing Leasing;
eLearning material.

More information at www.financial-models.com

V

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Acknowledgements
I would like to thank my family, Angela, Matthew and Frances, for their
support and assistance with this book. In addition, Liz Gooster of Pearson
Education has provided valuable support and backing for this project.
Finally I would like to acknowledge the input of all the clients and attendees of my courses who have provided inspiration and discussion of Excel
techniques and methods.

VI


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Contents
Conventions

xii

Overview

xiii

Executive Summary

xvi

1

Introduction
Scope of the book
Example model
Objectives of risk modelling
Summary

2

Review of model design
Introduction
Design objectives
Common errors
Excel features
Formats
Number formats
Lines and borders
Colour and patterns
Specific colour for inputs and results

Data validation
Controls – combo boxes and buttons
Conditional formatting
Use of functions and types of functions
Add-ins for more functions
Text and updated labels
Recording a version number, author, etc.
Using names
Pasting a names table
Comment cells
Graphics
Dynamic graphs to plot individual series
Data tables

1
3
5
6
9
11
13
13
15
18
20
20
22
24
24
25

28
33
33
36
37
38
39
40
41
42
44
46
VII


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Mastering Risk Modelling

VIII

Scenarios
Spreadsheet auditing
Summary

49
50
56

3

Risk and uncertainty
Introduction
Risk
Uncertainty
Response to risk
Methods
Summary

57
59
59
66
66
68
73

4

Project finance
Introduction
Requirements
Advantages
Risks

Risk analysis
Risk mitigation
Financial model
Inputs
Sensitivity and cost of capital
Construction, borrowing and output
Accounting schedules
Management analysis and summaries
Summary

75
77
77
79
79
84
85
86
89
94
95
97
102
110

5

Simulation
Introduction
Building blocks

Procedure
Real estate example
Summary

111
113
114
119
124
130

6

Financial analysis
Introduction
Process
Environment
Industry
Financial statements
Profit and loss
Balance sheet
Operating efficiency

133
135
137
137
139
140
141

143
145


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Contents

Profitability
Financial structure
Core ratios
Market ratios
Trend analysis
Cash flow
Forecasts
Financial analysis
Summary

148
149
150
152
152
154

158
167
172

7

Credit risk
Introduction
Cash flow
Cover ratios
Sustainability
Beaver’s model
Bathory model
Z scores
Springate analysis
Logit analysis
H-Factor model
Ratings agency
Summary
References

173
175
176
176
180
183
185
186
189

189
192
193
197
197

8

Valuation
Introduction
Inputs
Cash flow
Capital structure
Valuation and returns
Sensitivity analysis
Management summary
Summary

199
201
202
205
207
210
212
214
215

9

Bonds
Introduction
Bond prices
Interest rates
Yield
Duration and maturity
Convexity
Comparison
Summary

217
219
219
222
224
226
230
233
236
IX


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X

10 Options
Introduction
Options
Options example
Options hedging strategy
Black–Scholes
Simulation options pricing
Binomial model
Summary

237
239
240
242
245
252
257
261
264

11 Real options
Introduction
Project
Option to delay
Option to abandon
Option to expand

Summary

265
267
268
271
274
277
280

12 Equities
Introduction
Historic data
Returns summary
Simulation
Portfolio
Summary
References

281
283
285
286
292
294
300
301

13 Risk adjusted returns
Introduction

Economic capital
Risk-adjusted return on capital (RAROC)
Summary

303
305
305
309
315

14 Value at risk
Introduction
Single asset model
Two assets
Three asset portfolio
Summary

317
319
320
324
330
334

15 Credit value at risk
Introduction
Portfolio approach

335
337

338


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Contents

Overview of components
Single asset
Two-bond portfolio
Simulation
Summary

339
341
348
355
361

Appendix 1: Software installation and licence
Appendix 2: Microsoft Office 2007 (Office 12)
Index

363

369
382

XI


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Conventions
The main part of the text is set in Times Roman, whereas entries are set in
Courier. For example:
Enter the Scenario Name as Base Case
Items on the menu bars are also shown in Courier.
Select Tools, Goalseek
The names of functions are in capitals. This is the payment function, which
requires inputs for the interest rate, number of periods, present value and
future value:
=PMT(INT,NPER,PV,FV,TYPE)

Equations are formed with the equation editor and shown in normal notation. For example, net present value:
NPV = (CashFlow)N
––––––––––––––––––
(1+r)N
Genders: the use of ‘he’ or ‘him’ refers to masculine or feminine and this is

used for simplicity to avoid repetition.

XII


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Overview
WHO NEEDS THIS BOOK?
Business has always meant taking risks in order to secure a return. In the
last century, this was often a game of chance where outcomes could not be
accurately predicted. Developments in computing and theory have led to a
big change in how risk and reward is perceived, priced and managed.
Financial modelling has come into its own since the original development of Visicalc and Lotus 1-2-3 as the preferred tool for financial
calculations. Many people acquired their first computers in order to complete their budgets in Lotus 1-2-3. The omnipresence of Microsoft Office
means that techniques can be demonstrated more simply in Excel than with
hand-held financial calculators such as the HP12C or TI BA II Plus.
Banks and financial institutions increasingly use advanced risk management tools to manage portfolios and assess client credit risk. This is
reinforced by the provisions of Basel II or Solvency II. Additionally, risk
modelling plays a significant part in structured and project finance as a
method of identifying and managing potential difficulties. In the corporate
sector, directors of UK public companies are tasked with disclosing the
main risks facing the company as part of the risk management process. In
the US, the provisions of the Sarbanes–Oxley Act mean that critical spreadsheets have to be audited for accuracy. Given the emphasis on risk

management, this book mixes financial theory with practice and introduces
a number of Excel templates as the basis for more complex risk models.
The requirement for financial modelling is certain to develop further in
future owing to:
■

■

■
■

advances in computer technology and speed on the desktop and in
mobile computing;
the continued development of more specific risk software (e.g. @RISK
and Crystal Ball);
more historic data being available for analysis within organizations;
the use of models being a required skill for financial executives and business students alike.
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Mastering Risk Modelling

The key objectives of this book are to:
■

■
■

■

provide financial managers with practical templates for applying risk and
uncertainty to Excel;
improve financial managers’ abilities with Excel;
demonstrate a systematic method of developing Excel models for fast
development and reduced errors;
provide a library of basic templates for further development as an illustration of the methods.

This book aims to assist two key groups:
1 Excel users with a basic understanding of model design and a wish to
extend their Excel modelling skills;
2 practitioners who want to be able to build more complex models using
advanced Excel features.
The areas of responsibility are:
■
■
■
■
■
■
■
■
■

■

■

CFOs and finance directors;
financial controllers;
analysts;
accountants;
corporate finance personnel;
treasury managers;
risk managers;
middle office staff;
general managers;
personnel in banks, corporates and government who make complex n
decisions and who could benefit from a modelling approach;
academics, business and MBA students.

Therefore, people interested in this book range from a company accountant
who wants to be able to understand investment risk to managers who
require more complex models.
The book is international in its outlook and will provide examples relevant to both the UK and overseas.

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Overview

HOW TO USE THIS BOOK
■

■
■

■

Install the Excel application templates using the simple SETUP command. There is a key to the file names at the back of the book.
Work through each of the chapters and the examples.
Use the book, spreadsheets and templates as a reference guide for
further work.
Practise and improve your efficiency and competence with Excel.

THE SECOND EDITION
Since the publication of the first edition, the power and use of spreadsheets
has grown together with the need to measure and manage risk. Whilst
there are bespoke tools available for decision trees and simulation, the presence of Office on most executives’ desktops means that the Excel interface is
widely understood. At the same time companies are finding that models do
not always provide the correct answers when applied to securitization, ‘subprime’ portfolios or options trading. The interpretation of results and the
application of extreme scenarios also need consideration. The requirement is
for modelling to promote a decision-making framework rather than provide
all the answers.
Systematic Finance models follow a precise design specification and all
the spreadsheet models have been rewritten to take account of this uniform

approach to layout, colours and method, and to take advantage of more features in Excel. The introduction of Microsoft Office 2007 marks a radical
redesign of the Office interface since the Excel versions of the early 1990s.
Where possible the methods for Office 2003 and 2007 are shown to allow a
transition from earlier Office editions.
Alastair L. Day
www.financial-models.com

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Executive summary

This is a summary of the book by chapter presented in a tabular form.

XVI

Chapter

Topic

Items

1

Overview

Scope of the book
Example model
Basic statistics in Excel – tools and methods
Objectives of risk modelling

2

Review of model design

Model design and structure – key steps
Advantages
Disadvantages
Modelling objectives
Design objectives and mistakes
Useful features
Auditing methods

3

Risk and uncertainty

Definition of risk
Uncertainty
Response to risk
Methods used

4

Project finance model

Sources of risk
Forecasting financial data
Risk process
Methods

5

Simulation

Simulation methods
Building blocks of simulation
Procedure and programming
Real estate example

6

Financial analysis

Process
Environment
Industry
Financial statements
Profit and loss
Balance sheet

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Executive summary

7

Credit risk

Cash flow
Cover ratios
Sustainability formulas
Capacity to borrow and repay
Beaver model
Bathory model
Z scores
Springate model
Logit analysis
H Factor
Ratings agencies

8

Equity valuation

Introduction and methods
Cash flows
Capital structure
Risk factors
Sensitivity analysis
Management summary

9

Bonds

Bond prices
Interest rates
Yield, duration and convexity
Duration and maturity
Convexity
Comparison of methods

10

Options

Reasons to manage risk
Options
Options example
Options hedging strategy
Options simulation
VBA approach
Black–Scholes
Binomial trees

11

Real options

Introduction and method
Project – determining value
Option to delay a project
Option to abandon a project
Option to expand a project

▼

Operating efficiency
Profitability
Financial structure
Du Pont or core ratios
Market ratios
Trend analysis
Cash flow
Forecasts
Financial analysis summary

XVII


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Mastering Risk Modelling

XVIII

12

Equities

Portfolio optimization
Historic data
Returns summary
Simulation to find optimum risk and return
Portfolio

13

Risk adjusted return
on capital

Capital allocation
Risk adjusted return on capital calculation
Inputs and calculations
Sensitivity
Returns

14

Value at risk

Value at Risk methodology
VAR for a single asset
VAR for a two asset
Three asset VAR

15

Credit risk and
credit metrics

Introduction and theory
Portfolio approach
Overview of components
Single asset
Two bond portfolio
Simulation method

Appendix

Appendix
Excel 2007
Software specification
Installation
SFL
File list

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Introduction

Scope of the book
Example model
Objectives of risk modelling
Summary

File: MRM2_01

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1 · Introduction

SCOPE OF THE BOOK
Mastering Financial Modelling, an earlier book, provides an introduction to
Excel financial modelling and shows how to use Excel in a disciplined
manner to develop applications. Since spreadsheet models are often poorly
planned and developed with significant errors, it provides a specific method
for developing applications. This book develops these ideas to include risk
analysis and to show how techniques can be added to simpler models in
order to:
■
■

■
■
■

make the models more comprehensive;
accept that the real world is uncertain and models should be able to cope
with a range of possible outcomes;
derive more useful management information;
understand how the model ‘flexes’ with change;

act as a further method of checking the model’s outputs.

Financial modelling is the term often used for applications from simple
spreadsheets to complex models. In this book, the term financial model is
used to denote a dedicated spreadsheet written to solve a business problem.
Here are two definitions:
1 Spreadsheet: Program for organizing numerical data in tabular formats allowing rapid calculations with changing variables.
2 Model: Theoretical construct in a spreadsheet that represents numerical processes
by a set of variables and a set of logical and quantitative relationships
between them.
The basic need is to answer a business problem such as the minimum budgeted cash flow over the next 12 months, the net present value of an
investment or the price of an option. The spreadsheet does not simply hold
data but is organized as an analytical tool for decision making. The objective
is often to represent a closed system such as the investment in new equipment, together with forecast revenue and expenditure. The model therefore
represents a computer program written to solve the problem, which is different to using the spreadsheet merely for holding data or adding up a few
numbers. The model could be written in Visual Basic or C++ but it is usually quicker, easier and more intuitive to develop a model in Excel.
You could also consider a spreadsheet for personal use where you can keep
in your head the workings of the sheet. Where a spreadsheet requires distribution to others then it should be considered as a model where there should
be some rules in how it is developed and presented.

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Models underpin decisions and the basic risk process could be described as:
■

■

■

■
■
■

■

defining objectives, since you need to be clear about objectives and
output answers or reports;
identifying all possible courses of action to weigh up advantages and disadvantages;
assembling data or variables that are relevant and understanding the
extent of the accuracy and relevance of the data available;
building the computer models to assist and organize any decisions;
assessing the decision and comparing options by using the data outputs;
implementing a decision and monitoring the subsequent variances to the
original plan;
monitoring the effect of decisions and if the project fails ensuring that
lessons can be learnt.

However much effort is expended on the ‘correct’ variables for the model,
there must always be some potential for error or variance since a model is

only a best guess of the likely outcomes. Risk here is often considered to be
the potential downside resulting from a business decision.
The advantage of Excel is that most people have had some exposure to
the language and are comfortable with the interface and commands. Since
there is a similarity of presentation within the Microsoft Office suite, users
can write simple spreadsheets quickly. The disadvantages of such a free
approach are when decisions need to be taken or when an application needs
to be distributed or maintained. Whilst you can write fragments of code for
your own use, any files for use by others should be clear and auditable. In
particular, the disadvantages of many Excel models are as follows:
■
■

■

■
■

■

■

4

wide range of abilities on the part of the authors;
most people use less than 10 per cent of capability (e.g. they may never
have used the statistical or array functions or inserted a pivot table);
a lack of standard structure or design method making auditing all but
impossible;
a poor structure leads to a lack of clarity and confusing output reports;

it is easy to make mistakes since errors can lie undetected (for years!) –
users are often overconfident about their abilities and often assume their
code is error free;
Excel is not a recognized programming language and therefore there are
no standards for naming cells or documenting the work;
duplication of effort arises since most users do not develop templates for
specific types of applications;


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1 · Introduction
■

spreadsheets do not cope well with text (but then there is the option of
Microsoft Word).

Companies usually assume that executives are proficient in Excel since they
have qualified in finance, but this is not always the case. Financial modelling
demands a disciplined approach just like any other programming language.
Since Excel does not have to be compiled before use, people often produce
disorganized designs with little regard for future development or maintenance. For instance, dates can be hard coded and of course will work this
year, but next year you have to search through the model and change all
entries. Similarly, authors often mix numbers and formulas in the same cell

so that others cannot work out where to input data and of course the author
finds it impossible to check for mistakes. Owing to a lack of clear objectives,
the model may also not even produce a clear answer to the original question.
Most financial models consist of input variables, calculations and some kind
of output. The objectives of modelling should include some of the following:
■
■
■

■

■

■

■

■

analysing and processing data into information;
modelling a considered view or forecast of the future (e.g. project cash flows);
processing data quickly and accurately into clear and relevant management information;
testing assumptions in a ‘safe’ environment before mistakes are made
(e.g. project scenarios);
supporting management decision making through a structured approach.
(Modelling often produces too much information and one objective may
be to reduce the detail in summaries.);
understanding more precisely the variables or rules in a problem to
ensure that the whole system is modelled;
learning more about processes and the behaviour of variables, in particular the importance of key variables and how they behave;

discovering the sensitivity and risk inherent in the model.

EXAMPLE MODEL
Figure 1.1 shows a simple example of revenue and costs. The inputs are
shown tinted grey and the schedule below calculates the net revenue at the
end of the five-year period. This is the sum of cells C27:H27.

5


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Mastering Risk Modelling
Figure 1.1

Simple model

This is a deterministic or input–calculation–output model since the
inputs or variables are fixed. For example, sales growth is 3 per cent from a
base of 1000. These figures represent the best estimate of the value of each
input variable but they are still single points rather than ranges.

OBJECTIVES OF RISK MODELLING
The deterministic model above may not provide all the answers. The future

is uncertain and there are factors that are within the organization’s control
and those, such as the weather, over which it has little or no control. Whilst
analysts may wish to control or know the future, risk modelling seeks to
apply mathematical theory to the problem. In the simple problem above,
the organization may wish to know how likely it is to achieve the forecast
net revenue. Corporate finance theory advises that organizations and individuals are rational and risk averse. This means that they take a defined risk
for a desired return. Translated into this example, this could be rephrased as
the forecast net revenue and the possible variance or standard deviation.
There would be no point in accepting this budget if possible results ranged
from 100 to 700 since a result of 100 would be unacceptable. The managers
may then wish to know what the chance is of the forecast net revenue
falling below 200. Developing a more sophisticated model could help to
uncover the risk and uncertainty in the budget.
6