Preface xvii About the Author xxiii About the Website xxv PART I An Introduction to Risk Assessment Its Uses, Processes, Approaches, Benefits and Challenges CHAPTER 1 The Context and Uses of Risk Assessment 3 1.1 Risk Assessment Examples 3 1.1.1 Everyday Examples of Risk Management 4 1.1.2 Prominent Risk Management Failures 5 1.2 General Challenges in Decision-Making Processes 7 1.2.1 Balancing Intuition with Rationality 7 1.2.2 The Presence of Biases 9 1.3 Key Drivers of the Need for Formalised Risk Assessment in Business Contexts 14 1.3.1 Complexity 14 1.3.2 Scale 15 1.3.3 Authority and Responsibility to Identify and Execute Risk-Response Measures 16 1.3.4 Corporate Governance Guidelines 16 1.3.5 General Organisational Effectiveness and the Creation of Competitive Advantage 18 1.3.6 Quantification Requirements 18 1.3.7 Reflecting Risk Tolerances in Decisions and in Business Design 19 1.4 The Objectives and Uses of General Risk Assessment 19 1.4.1 Adapt and Improve the Design and Structure of Plans and Projects 20 1.4.2 Achieve Optimal Risk Mitigation within Revised Plans 20 1.4.3 Evaluate Projects, Set Targets and Reflect Risk Tolerances in Decision-Making 21 1.4.4 Manage Projects Effectively 21 1.4.5 Construct, Select and Optimise Business and Project Portfolios 22 1.4.6 Support the Creation of Strategic Options and Corporate Planning 25 CHAPTER 2 Key Stages of the General Risk Assessment Process 29 2.1 Overview of the Process Stages 29 2.2 Process Iterations 30 2.3 Risk Identification 32 2.3.1 The Importance of a Robust Risk Identification Step 32 2.3.2 Bringing Structure into the Process 32 2.3.3 Distinguishing Variability from Decision Risks 34 2.3.4 Distinguishing Business Issues from Risks 34 2.3.5 Risk Identification in Quantitative Approaches: Additional Considerations 35 2.4 Risk Mapping 35 2.4.1 Key Objectives 35 2.4.2 Challenges 35 2.5 Risk Prioritisation and Its Potential Criteria 36 2.5.1 Inclusion/Exclusion 36 2.5.2 Communications Focus 37 2.5.3 Commonality and Comparison 38 2.5.4 Modelling Reasons 39 2.5.5 General Size of Risks, Their Impact and Likelihood 39 2.5.6 Influence: Mitigation and Response Measures, and Management Actions 40 2.5.7 Optimising Resource Deployment and Implementation Constraints 41 2.6 Risk Response: Mitigation and Exploitation 42 2.6.1 Reduction 42 2.6.2 Exploitation 42 2.6.3 Transfer 42 2.6.4 Research and Information Gathering 43 2.6.5 Diversification 43 2.7 Project Management and Monitoring 44 CHAPTER 3 Approaches to Risk Assessment and Quantification 45 3.1 Informal or Intuitive Approaches 46 3.2 Risk Registers without Aggregation 46 3.2.1 Qualitative Approaches 46 3.2.2 Quantitative Approaches 48 3.3 Risk Register with Aggregation (Quantitative) 50 3.3.1 The Benefits of Aggregation 50 3.3.2 Aggregation of Static Values 51 3.3.3 Aggregation of Risk-Driven Occurrences and Their Impacts 52 3.3.4 Requirements and Differences to Non-Aggregation Approaches 54 3.4 Full Risk Modelling 56 3.4.1 Quantitative Aggregate Risk Registers as a First Step to Full Models 56 CHAPTER 4 Full Integrated Risk Modelling: Decision-Support Benefits 59 4.1 Key Characteristics of Full Models 59 4.2 Overview of the Benefits of Full Risk Modelling 61 4.3 Creating More Accurate and Realistic Models 62 4.3.1 Reality is Uncertain: Models Should Reflect This 62 4.3.2 Structured Process to Include All Relevant Factors 63 4.3.3 Unambiguous Approach to Capturing Event Risks 63 4.3.4 Inclusion of Risk Mitigation and Response Factors 66 4.3.5 Simultaneous Occurrence of Uncertainties and Risks 66 4.3.6 Assessing Outcomes in Non-Linear Situations 67 4.3.7 Reflecting Operational Flexibility and Real Options 67 4.3.8 Assessing Outcomes with Other Complex Dependencies 71 4.3.9 Capturing Correlations, Partial Dependencies and Common Causalities 73 4.4 Using the Range of Possible Outcomes to Enhance Decision-Making 74 4.4.1 Avoiding The Trap of the Most Likely or Structural Biases 76 4.4.2 Finding the Likelihood of Achieving a Base Case 78 4.4.3 Economic Evaluation and Reflecting Risk Tolerances 82 4.4.4 Setting Contingencies, Targets and Objectives 83 4.5 Supporting Transparent Assumptions and Reducing Biases 84 4.5.1 Using Base Cases that are Separate to Risk Distributions 85 4.5.2 General Reduction in Biases 85 4.5.3 Reinforcing Shared Accountability 85 4.6 Facilitating Group Work and Communication 86 4.6.1 A Framework for Rigorous and Precise Work 86 4.6.2 Reconcile Some Conflicting Views 86 CHAPTER 5 Organisational Challenges Relating to Risk Modelling 87 5.1 We Are Doing It Already 87 5.1.1 Our ERM Department Deals with Those Issues 88 5.1.2 Everybody Should Just Do Their Job Anyway! 88 5.1.3 We Have Risk Registers for All Major Projects 89 5.1.4 We Run Sensitivities and Scenarios: Why Do More? 89 5.2 We Already Tried It, and It Showed Unrealistic Results 89 5.2.1 All Cases Were Profitable 90 5.2.2 The Range of Outcomes Was Too Narrow 90 5.3 The Models Will Not Be Useful! 91 5.3.1 We Should Avoid Complicated Black Boxes! 91 5.3.2 All Models Are Wrong, Especially Risk Models! 91 5.3.3 Can You Prove that It Even Works? 92 5.3.4 Why Bother to Plan Things that Might Not Even Happen? 93 5.4 Working Effectively with Enhanced Processes and Procedures 93 5.4.1 Selecting the Right Projects, Approach and Decision Stage 93 5.4.2 Managing Participant Expectations 95 5.4.3 Standardisation of Processes and Models 95 5.5 Management Processes, Culture and Change Management 96 5.5.1 Integration with Decision Processes 96 5.5.2 Ensuring Alignment of Risk Assessment and Modelling Processes 97 5.5.3 Implement from the Bottom Up or the Top Down? 98 5.5.4 Encouraging Issues to Be Escalated: Don t Shoot the Messenger! 99 5.5.5 Sharing Accountability for Poor Decisions 99 5.5.6 Ensuring Alignment with Incentives and Incentive Systems 100 5.5.7 Allocation and Ownership of Contingency Budgets 101 5.5.8 Developing Risk Cultures and Other Change Management Challenges 102 PART II The Design of Risk Models Principles, Processes and Methodology CHAPTER 6 Principles of Simulation Methods 107 6.1 Core Aspects of Simulation: A Descriptive Example 107 6.1.1 The Combinatorial Effects of Multiple Inputs and Distribution of Outputs 107 6.1.2 Using Simulation to Sample Many Diverse Scenarios 110 6.2 Simulation as a Risk Modelling Tool 112 6.2.1 Distributions of Input Values and Their Role 113 6.2.2 The Effect of Dependencies between Inputs 114 6.2.3 Key Questions Addressable using Risk-Based Simulation 114 6.2.4 Random Numbers and the Required Number of Recalculations or Iterations 115 6.3 Sensitivity and Scenario Analysis: Relationship to Simulation 116 6.3.1 Sensitivity Analysis 116 6.3.2 Scenario Analysis 119 6.3.3 Simulation using DataTables 121 6.3.4 GoalSeek 121 6.4 Optimisation Analysis and Modelling: Relationship to Simulation 122 6.4.1 Uncertainty versus Choice 122 6.4.2 Optimisation in the Presence of Risk and Uncertainty 129 6.4.3 Modelling Aspects of Optimisation Situations 131 6.5 Analytic and Other Numerical Methods 133 6.5.1 Analytic Methods and Closed-Form Solutions 133 6.5.2 Combining Simulation Methods with Exact Solutions 135 6.6 The Applicability of Simulation Methods 135 CHAPTER 7 Core Principles of Risk Model Design 137 7.1 Model Planning and Communication 138 7.1.1 Decision-Support Role 138 7.1.2 Planning the Approach and Communicating the Output 138 7.1.3 Using Switches to Control the Cases and Scenarios 139 7.1.4 Showing the Effect of Decisions versus Those of Uncertainties 140 7.1.5 Keeping It Simple, but not Simplistic: New Insights versus Modelling Errors 144 7.2 Sensitivity-Driven Thinking as a Model Design Tool 146 7.2.1 Enhancing Sensitivity Processes for Risk Modelling 150 7.2.2 Creating Dynamic Formulae 151 7.2.3 Example: Time Shifting for Partial Periods 153 7.3 Risk Mapping and Process Alignment 154 7.3.1 The Nature of Risks and Their Impacts 155 7.3.2 Creating Alignment between Modelling and the General Risk Assessment Process 156 7.3.3 Results Interpretation within the Context of Process Stages 157 7.4 General Dependency Relationships 158 7.4.1 Example: Commonality of Drivers of Variability 159 7.4.2 Example: Scenario-Driven Variability 160 7.4.3 Example: Category-Driven Variability 162 7.4.4 Example: Fading Impacts 168 7.4.5 Example: Partial Impact Aggregation by Category in a Risk Register 170 7.4.6 Example: More Complex Impacts within a Category 171 7.5 Working with Existing Models 173 7.5.1 Ensuring an Appropriate Risk Identification and Mapping 173 7.5.2 Existing Models using Manual Processes or Embedded Procedures 174 7.5.3 Controlling a Model Switch with a Macro at the Start and End of a Simulation 175 7.5.4 Automatically Removing Data Filters at the Start of a Simulation 176 7.5.5 Models with DataTables 178 CHAPTER 8 Measuring Risk using Statistics of Distributions 181 8.1 Defining Risk More Precisely 181 8.1.1 General Definition 181 8.1.2 Context-Specific Risk Measurement 181 8.1.3 Distinguishing Risk, Variability and Uncertainty 182 8.1.4 The Use of Statistical Measures 183 8.2 Random Processes and Their Visual Representation 184 8.2.1 Density and Cumulative Forms 184 8.2.2 Discrete, Continuous and Compound Processes 186 8.3 Percentiles 187 8.3.1 Ascending and Descending Percentiles 188 8.3.2 Inversion and Random Sampling 189 8.4 Measures of the Central Point 190 8.4.1 Mode 190 8.4.2 Mean or Average 191 8.4.3 Median 193 8.4.4 Comparisons of Mode, Mean and Median 193 8.5 Measures of Range 194 8.5.1 Worst and Best Cases, and Difference between Percentiles 194 8.5.2 Standard Deviation 195 8.6 Skewness and Non-Symmetry 199 8.6.1 The Effect and Importance of Non-Symmetry 201 8.6.2 Sources of Non-Symmetry 202 8.7 Other Measures of Risk 203 8.7.1 Kurtosis 204 8.7.2 Semi-Deviation 205 8.7.3 Tail Losses, Expected Tail Losses and Value-at-Risk 206 8.8 Measuring Dependencies 207 8.8.1 Joint Occurrence 207 8.8.2 Correlation Coefficients 209 8.8.3 Correlation Matrices 210 8.8.4 Scatter Plots (X Y Charts) 212 8.8.5 Classical and Bespoke Tornado Diagrams 212 CHAPTER 9 The Selection of Distributions for Use in Risk Models 215 9.1 Descriptions of Individual Distributions 215 9.1.1 The Uniform Continuous Distribution 216 9.1.2 The Bernoulli Distribution 218 9.1.3 The Binomial Distribution 219 9.1.4 The Triangular Distribution 220 9.1.5 The Normal Distribution 222 9.1.6 The Lognormal Distribution 226 9.1.7 The Beta and Beta General Distributions 232 9.1.8 The PERT Distribution 234 9.1.9 The Poisson Distribution 236 9.1.10 The Geometric Distribution 238 9.1.11 The Negative Binomial Distribution 240 9.1.12 The Exponential Distribution 241 9.1.13 The Weibull Distribution 242 9.1.14 The Gamma Distribution 242 9.1.15 The General Discrete Distribution 244 9.1.16 The Integer Uniform Distribution 245 9.1.17 The Hypergeometric Distribution 245 9.1.18 The Pareto Distribution 246 9.1.19 The Extreme Value Distributions 246 9.1.20 The Logistic Distribution 250 9.1.21 The Log-Logistic Distribution 251 9.1.22 The Student (t), Chi-Squared and F-Distributions 252 9.2 A Framework for Distribution Selection and Use 256 9.2.1 Scientific and Conceptual Approaches 257 9.2.2 Data-Driven Approaches 258 9.2.3 Industry Standards 259 9.2.4 Pragmatic Approaches: Distributions, Parameters and Expert Input 259 9.3 Approximation of Distributions with Each Other 263 9.3.1 Modelling Choices 263 9.3.2 Distribution Comparison and Parameter Matching 265 9.3.3 Some Potential Pitfalls Associated with Distribution Approximations 267 CHAPTER 10 Creating Samples from Distributions 273 10.1 Readily Available Inverse Functions 274 10.1.1 Functions Provided Directly in Excel 274 10.1.2 Functions Whose Formulae Can Easily Be Created 276 10.2 Functions Requiring Lookup and Search Methods 277 10.2.1 Lookup Tables 277 10.2.2 Search Methods 278 10.3 Comparing Calculated Samples with Those in @RISK 279 10.4 Creating User-Defined Inverse Functions 280 10.4.1 Normal Distribution 281 10.4.2 Beta and Beta General Distributions 282 10.4.3 Binomial Distribution 283 10.4.4 Lognormal Distribution 283 10.4.5 Bernoulli Distribution 284 10.4.6 Triangular Distribution 284 10.4.7 PERT Distribution 284 10.4.8 Geometric Distribution 285 10.4.9 Weibull Distribution 285 10.4.10 Weibull Distribution with Percentile Inputs 285 10.4.11 Poisson Distribution 285 10.4.12 General Discrete Distribution 287 10.5 Other Generalisations 287 10.5.1 Iterative Methods using Specific Numerical Techniques 287 10.5.2 Creating an Add-In 289 CHAPTER 11 Modelling Dependencies between Sources of Risk 291 11.1 Parameter Dependency and Partial Causality 291 11.1.1 Example: Conditional Probabilities 293 11.1.2 Example: Common Risk Drivers 293 11.1.3 Example: Category Risk Drivers 294 11.1.4 Example: Phased Projects 294 11.1.5 Example: Economic Scenarios for the Price of a Base Commodity 295 11.1.6 Example: Prices of a Derivative Product 296 11.1.7 Example: Prices of Several Derivative Products 297 11.1.8 Example: Oil Price and Rig Cost 297 11.1.9 Example: Competitors and Market Share 298 11.1.10 Example: Resampling or Data-Structure-Driven Dependence 299 11.1.11 Implied Correlations within Parameter Dependency Relationships 302 11.2 Dependencies between Sampling Processes 302 11.2.1 Correlated Sampling 303 11.2.2 Copulas 304 11.2.3 Comparison and Selection of Parameter-Dependency and Sampling Relationships 306 11.2.4 Creating Correlated Samples in Excel using Cholesky Factorisation 309 11.2.5 Working with Valid Correlation Matrices 313 11.2.6 Correlation of Time Series 315 11.3 Dependencies within Time Series 316 11.3.1 Geometric Brownian Motion 317 11.3.2 Mean-Reversion Models 319 11.3.3 Moving Average Models 321 11.3.4 Autoregressive Models 321 11.3.5 Co-Directional (Integrated) Processes 323 11.3.6 Random State Switching and Markov Chains 323 PART III Getting Started with Simulation in Practice CHAPTER 12 Using Excel/VBA for Simulation Modelling 327 12.1 Description of Example Model and Uncertainty Ranges 327 12.2 Creating and Running a Simulation: Core Steps 328 12.2.1 Using Random Values 328 12.2.2 Using a Macro to Perform Repeated Recalculations and Store the Results 330 12.2.3 Working with the VBE and Inserting a VBA Code Module 330 12.2.4 Automating Model Recalculation 331 12.2.5 Creating a Loop to Recalculate Many Times 331 12.2.6 Adding Comments, Indentation and Line Breaks 332 12.2.7 Defining Outputs, Storing Results, Named Ranges and Assignment Statements 333 12.2.8 Running the Simulation 334 12.3 Basic Results Analysis 335 12.3.1 Building Key Statistical Measures and Graphs of the Results 335 12.3.2 Clearing Previous Results 336 12.3.3 Modularising the Code 338 12.3.4 Timing and Progress Monitoring 339 12.4 Other Simple Features 339 12.4.1 Taking Inputs from the User at Run Time 339 12.4.2 Storing Multiple Outputs 340 12.5 Generalising the Core Capabilities 340 12.5.1 Using Selected VBA Best Practices 340 12.5.2 Improving Speed 341 12.5.3 Creating User-Defined Functions 342 12.6 Optimising Model Structure and Layout 343 12.6.1 Simulation Control Sheet 343 12.6.2 Output Links Sheet 344 12.6.3 Results Sheets 344 12.6.4 Use of Analysis Sheets 346 12.6.5 Multiple Simulations 348 12.7 Bringing it All Together: Examples Using the Simulation Template 350 12.7.1 Model 1: Aggregation of a Risk Register using Bernoulli and PERT Distributions 351 12.7.2 Model 2: Cost Estimation using Lognormal Distributions 352 12.7.3 Model 3: Cost Estimation using Weibull Percentile Parameters 352 12.7.4 Model 4: Cost Estimation using Correlated Distributions 353 12.7.5 Model 5: Valuing Operational Flexibility 353 12.8 Further Possible uses of VBA 354 12.8.1 Creating Percentile Parameters 354 12.8.2 Distribution Samples as User-Defined Functions 354 12.8.3 Probability Samples as User-Defined Array Functions 355 12.8.4 Correlated Probability Samples as User-Defined Array Functions 356 12.8.5 Assigning Values from VBA into Excel 358 12.8.6 Controlling the Random Number Sequence 359 12.8.7 Sequencing and Freezing Distribution Samples 363 12.8.8 Practical Challenges in using Arrays and Assignment Operations 364 12.8.9 Bespoke Random Number Algorithms 364 12.8.10 Other Aspects 364 CHAPTER 13 Using @RISK for Simulation Modelling 365 13.1 Description of Example Model and Uncertainty Ranges 365 13.2 Creating and Running a Simulation: Core Steps and Basic Icons 366 13.2.1 Using Distributions to Create Random Samples 368 13.2.2 Reviewing the Effect of Random Samples 369 13.2.3 Adding an Output 370 13.2.4 Running the Simulation 370 13.2.5 Viewing the Results 370 13.2.6 Results Storage 373 13.2.7 Multiple Simulations 373 13.2.8 Results Statistics Functions 374 13.3 Simulation Control: An Introduction 377 13.3.1 Simulation Settings: An Overview 377 13.3.2 Static View 377 13.3.3 Random Number Generator and Sampling Methods 379 13.3.4 Comparison of Excel and @RISK Samples 381 13.3.5 Number of Iterations 382 13.3.6 Repeating a Simulation and Fixing the Seed 382 13.3.7 Simulation Speed 383 13.4 Further Core Features 384 13.4.1 Alternate Parameters 384 13.4.2 Input Statistics Functions 384 13.4.3 Creating Dependencies and Correlations 385 13.4.4 Scatter Plots and Tornado Graphs 385 13.4.5 Special Applications of Distributions 395 13.4.6 Additional Graphical Outputs and Analysis Tools 400 13.4.7 Model Auditing and Sense Checking 405 13.5 Working with Macros and the @RISK Macro Language 405 13.5.1 Using Macros with @RISK 405 13.5.2 The @RISK Macro Language or Developer Kit: An Introduction 407 13.5.3 Using the XDK to Analyse Random Number Generator and Sampling Methods 409 13.5.4 Using the XDK to Generate Reports of Simulation Data 417 13.6 Additional In-Built Applications and Features: An Introduction 417 13.6.1 Optimisation 419 13.6.2 Fitting Distributions and Time Series to Data 420 13.6.3 MS Project Integration 421 13.6.4 Other Features 421 13.7 Benefits of @RISK over Excel/VBA Approaches: A Brief Summary 421 Index 425