Risk Assessment Models and Methodologies Study Guide PDF

BACHELOR OF COMMERCE IN BUSINESS MANAGEMENT RISK ASSESSMENT MODELS AND METHODOLOGIES STUDY GUIDE COPYRIGHT © EDUCOR, 2019 All rights reserved. No part of this publication may be reproduced, distributed, or transmitted in any form or by any means, including photocopying, recording, or other electronic or mechanical methods, without the prior written permission of Educor Holdings. Individual’s found guilty of copywriting will be prosecuted and will be held liable for damages. i TABLE OF CONTENTS 1. About Brand......................................................................................................................................... 1 2. Our Teaching and Learning Methodology............................................................................................. 2 2.1. Icons............................................................................................................................................. 3 3. Introduction to the Module.................................................................................................................. 5 3.1. Module Information...................................................................................................................... 5 3.2. Module Purpose........................................................................................................................... 5 3.3. Outcomes..................................................................................................................................... 5 3.4. Assessment................................................................................................................................... 6 3.5. Pacer............................................................................................................................................ 7 3.6. Planning Your Studies................................................................................................................... 7 4. Prescribed Reading............................................................................................................................... 8 4.1. Prescribed Book............................................................................................................................ 8 5. Module Content................................................................................................................................... 9 5.1. Study Unit 1 - Principles of Management Applied to Managing Risk............................................ 10 5.1.1. Introduction........................................................................................................................ 10 5.1.2. Definitions........................................................................................................................... 11 5.1.3. Case of Risk Management................................................................................................... 12 5.1.4. Reasons to Risk Management.............................................................................................. 12 5.1.5. Functional Approach to Management................................................................................. 13 5.1.6. Risk Management Model..................................................................................................... 14 5.1.7. History of Risk Management in South Africa........................................................................ 16 5.1.8. Conclusion.......................................................................................................................... 17 5.1.9. Revision Questions.............................................................................................................. 18 5.2. Study Unit 2 - Concept of Risk..................................................................................................... 19 5.2.1. Introduction........................................................................................................................ 19 5.2.2. Basic Risk Classification....................................................................................................... 19 5.2.3. Strategic Risks: Sustainability............................................................................................... 22 5.2.4. Managerial Risk Classifications............................................................................................ 23 5.2.5. Psychological Influences on Risk.......................................................................................... 24 5.2.6. Market Failure..................................................................................................................... 24 ii 5.2.7. Economic Viability of Insurance Companies......................................................................... 25 5.2.8. Conclusion.......................................................................................................................... 28 5.2.9. Revision Questions.............................................................................................................. 29 5.3. Study Unit 3 - Decision Making Under Conditions of Risk and Uncertainty................................... 30 5.3.1. Introduction........................................................................................................................ 30 5.3.2. Expected Monetary Value (EMV) Criterion.......................................................................... 30 5.3.3. Probability Theory............................................................................................................... 33 5.3.4. Probability Distribution....................................................................................................... 34 5.3.5. Expected Utility Criterion.................................................................................................... 39 5.3.6. Maximin Decision Criterion................................................................................................. 40 5.3.7. Minimax Regret Decision Criterion...................................................................................... 41 5.3.8. Maximax Decision Criterion................................................................................................. 41 5.3.9. Conclusion.......................................................................................................................... 45 5.3.10. Revision Questions.............................................................................................................. 46 5.4. Study Unit 4 – Risk Identification................................................................................................. 47 5.4.1. Introduction........................................................................................................................ 47 5.4.2. Risk Identification................................................................................................................ 48 5.4.3. Risk Evaluation.................................................................................................................... 54 5.4.4. Conclusion.......................................................................................................................... 60 5.4.5. Revision Questions.............................................................................................................. 60 5.5. Study Unit 5 – Risk Response: Risk Control.................................................................................. 61 5.5.1. Introduction........................................................................................................................ 61 5.5.2. Risk Control......................................................................................................................... 61 5.5.3. General Principles and Objectives of Risk Control................................................................ 62 5.5.4. Approaches to Loss Presentation......................................................................................... 63 5.5.5. Risk Control Legislation....................................................................................................... 64 5.5.6. Specific Risk Control Programmes and Codes of Practice..................................................... 65 5.5.7. Conclusion.......................................................................................................................... 79 5.5.8. Revision Questions.............................................................................................................. 79 5.6. Study Unit 6 – Risk Financing....................................................................................................... 80 5.6.1. Introduction........................................................................................................................ 80 5.6.2. Interrelationship Between Risk Control and Financial Elements in the Risk Management Process 81 iii 5.6.3. Risk Financing Elements...................................................................................................... 85 5.6.4. Risk Management within a Financial Decision-Making Structure.......................................... 85 5.6.5. Conclusion.......................................................................................................................... 88 5.6.6. Revision Questions.............................................................................................................. 89 5.7. Study Unit 7 – Risk Retention...................................................................................................... 90 5.7.1. Introduction........................................................................................................................ 90 5.7.2. Unfunded Retained Risk...................................................................................................... 90 5.7.3. Funded Retained Risk.......................................................................................................... 91 5.7.4. Implementing A Retention Programme............................................................................... 91 5.7.5. Evaluation of Retention Funding.......................................................................................... 92 5.7.6. Case of Retention Programmes........................................................................................... 93 5.7.7. Conclusion.......................................................................................................................... 94 5.7.8. Revision Questions.............................................................................................................. 95 6. References......................................................................................................................................... 96 iv 1. ABOUT BRAND Damelin knows that you have dreams and ambitions. You’re thinking about the future, and how the next chapter of your life is going to play out. Living the career you’ve always dreamed of takes some planning and a little bit of elbow grease, but the good news is that Damelin will be there with you every step of the way. We’ve been helping young people to turn their dreams into reality for over 70 years, so rest assured, you have our support. As South Africa’s premier education institution, we’re dedicated to giving you the education experience you need and have proven our commitment in this regard with a legacy of academic excellence that’s produced over 500 000 world – class graduates! Damelin alumni are redefining industry in fields ranging from Media to Accounting and Business, from Community Service to Sound Engineering. We invite you to join this storied legacy and write your own chapter in Damelin’s history of excellence in achievement. A Higher Education and Training (HET) qualification provides you with the necessary step in the right direction towards excellence in education and professional development. 1 2. OUR TEACHING AND LEARNING METHODOLOGY Damelin strives to promote a learning-centred and knowledge-based teaching and learning environment. Teaching and learning activities primarily take place within academic programmes and guide students to attain specific outcomes. A learning-centred approach is one in which not only lecturers and students, but all sections and activities of the institution work together in establishing a learning community that promotes a deepening of insight and a broadening of perspective with regard to learning and the application thereof. An outcomes-oriented approach implies that the following categories of outcomes are embodied in the academic programmes: Culminating outcomes that are generic with specific reference to the critical cross-field outcomes including problem identification and problem-solving, co-operation, self-organisation and self-management, research skills, communication skills, entrepreneurship and the application of science and technology. Empowering outcomes that are specific, i.e. the context specific competencies students must master within specific learning areas and at specific levels before they exit or move to a next level. Discrete outcomes of community service learning to cultivate discipline-appropriate competencies. Damelin actively strives to promote a research culture within which a critical-analytical approach and competencies can be developed in students at undergraduate level. Damelin accepts that students’ learning is influenced by a number of factors, including their previous educational experience, their cultural background, their perceptions of particular learning tasks and assessments, as well as discipline contexts. Students learn better when they are actively engaged in their learning rather than when they are passive recipients of transmitted information and/or knowledge. A learning-oriented culture that acknowledges individual student learning styles and diversity and focuses on active learning and student engagement, with the objective of achieving deep learning outcomes and preparing students for lifelong learning, is seen as the ideal. These principles are supported through the use of an engaged learning approach that involves interactive, reflective, cooperative, experiential, creative or constructive learning, as well as conceptual learning via online-based tools. Effective teaching-learning approaches are supported by: Well-designed and active learning tasks or opportunities to encourage a deep rather than a surface approach to learning. Content integration that entails the construction, contextualization and application of knowledge, principles and theories rather than the memorisation and reproduction of information. 2 Learning that involves students building knowledge by constructing meaning for themselves. The ability to apply what has been learnt in one context to another context or problem. Knowledge acquisition at a higher level that requires self-insight, self-regulation and self- evaluation during the learning process. Collaborative learning in which students work together to reach a shared goal and contribute to one another’s learning at a distance. Community service learning that leads to collaborative and mutual acquisition of competencies in order to ensure cross cultural interaction and societal development. Provision of resources such as information technology and digital library facilities of a high quality to support an engaged teaching-learning approach. A commitment to give effect teaching-learning in innovative ways and the fostering of digital literacy. Establishing a culture of learning as an overarching and cohesive factor within institutional diversity. Teaching and learning that reflect the reality of diversity. Taking multi culturality into account in a responsible manner that seeks to foster an appreciation of diversity, build mutual respect and promote cross-cultural learning experiences that encourage students to display insight into and appreciation of differences. 2.1. Icons The icons below act as markers, that will help you make your way through the study guide. 3 Additional information Find the recommended information listed. Case study/Caselet Apply what you have learnt to the case study presented. Example Examples of how to perform a calculation or activity with the solution / appropriate response. Practice Practice the skills you have learned. Reading Read the section(s) of the prescribed text listed. Revision questions Complete the compulsory revision questions at the end of each unit. Self-check activity Check your progress by completing the self-check activity. Study group / Online forum discussion Discuss the topic in your study group or online forum. Think point Reflect, analyse and discuss, journal or blog about the idea(s). Video / audio Access and watch/listen to the video/audio clip listed. 4 Vocabulary Learn and apply these terms. 3. INTRODUCTION TO THE MODULE Welcome to the Risk Assessment Models and Methodology Module. The information contained in this study guide is intended to guide you in your studies and assist you in your preparation for the examinations. The tutorial guide discusses the learning outcomes covered in this module and the assessment strategies applicable to this module. Various study tips and study information will be provided in this tutorial guide to assist you with your learning process. 3.1. Module Information Qualification title Bachelor of Commerce in Business Management Module Title Risk Assessment Models and Methodologies NQF Level 7 Credits 15 Notional hours 150 3.2. Module Purpose The purpose of the study module is to ensure that students have the knowledge and skills in order to understand and practice risk assessment in support of effective risk management within the business environment. 3.3. Outcomes At the end of this module learners should be able to:  Investigate and the key principles of risk assessment in order to support a risk management strategy and approach in the business organisation;  Evaluate business requirements in order to identify and describe the scope for a risk assessment and determine risk impact and probability in order to select a risk assessment approach; 5  Investigate risk management models and their potential future evolvement in relation to business risk management requirements;  Use and apply a top-down Risk assessment approach in order to determine the scope of risk; and  Investigate special risk situations in order to determine specific risk response strategies in relation to risk analysis outcomes within business so as to maximise impact and minimise risk exposure. 3.4. Assessment You will be required to complete both formative and summative assessment activities. Formative assessment: These are activities you will do as you make your way through the course. They are designed to help you learn about the concepts, theories and models in this module. This could be through case studies, practice activities, self-check activities, study group / online forum discussions and think points. You may also be asked to blog / post your responses online. Summative assessment: You are required to do one test and one assignment. For online students, the tests are made up of the revision questions at the end of each unit. A minimum of five revision questions will be selected to contribute towards your test mark. Mark allocation The marks are derived as follows for this module: Test 20% Assignment 20% Exam 60% TOTAL 100% 6 3.5. Pacer The table below will give you an indication of which topics you need to include from the module pacer. Week Topics 1 Principles of Management Applied to Managing Risk 2 Principles of Management Applied to Managing Risk 3 Concept of Risk 4 Concept of Risk 5 Decision Making Under Conditions of Risk and Uncertainty 6 Decision Making Under Conditions of Risk and Uncertainty 7 Risk Identification and Risk Evaluation 8 Risk Identification and Risk Evaluation 9 Risk Response: Risk Control 10 Risk Response: Risk Control 11 Risk Financing 12 Risk Financing 13 Risk Retention 3.6. Planning Your Studies You will have registered for one or more modules in the qualification and it is important that you plan your time. To do this look at the modules and credits and units in each module. Create a time table / diagram that will allow you to get through the course content, complete the activities, and prepare for your tests, assignments and exams. Use the information provided above (How long will it take me?) to do this. What equipment will I need?  Access to a personal computer and internet. This module will take you approximately 150 hours to complete. The following table will give you an indication of how long each module will take you. Unit Number Hours 1 22 2 22 3 28 4 22 5 28 6 16 7 12 7 4. PRESCRIBED READING 4.1. Prescribed Book  Valsamakis, A.C., Vivian, R.W., Du Toit, G.S. 2016. Risk Management. Cape Town: Pearson 8 5. MODULE CONTENT You are now ready to start your module! The following diagram indicates the topics that will be covered. These topics will guide you in achieving the outcomes and the purpose of this module. Please make sure you complete the assessments as they are specifically designed to build you in your learning. Unit 1: Principles of Management Applied to Managing Risk Unit 2: Concept of Risk Unit 3: Decision Making Under Conditions of Risk and Uncertainty Unit 4: Risk Identification and Risk Evaluation Unit 5: Risk Response: Risk Control Unit 6: Risk Financing Unit 7: Risk Retention 9 5.1. Study Unit 1 - Principles of Management Applied to Managing Risk The aim of this unit is to introduce the concepts and scope of risk assessment Purpose models and methodologies in risk management. By the end of this unit, you will be able to:  Describe case for risk management Learning  Define risk management Outcomes  Discuss the reasons to manage risk  Describe the functional approach to management It will take you 22 hours to make your way through this unit. Time Important terms Ameliorate Refers to improving the condition and definitions Economic- fluctuations Refer to economic instabilities (upswing and downswing) Inflation Refers to the general price increases Cascade Refers to a condition where there is a flow 5.1.1. Introduction Risk management is a natural practice of humans who seek to avoid risk or ameliorate risk in order to maximise reward. In the modern sense risk management has become a discipline on its own. Entrepreneurs and shareholders understand risk in the context of business; they accept that when there is high risk there is a strong potential for reward and benefit. An example, when one invests in the construction industry, which is subjected to cyclical economic fluctuations and carries substantial risk, there is always higher profits and dividend payments; compared to investing in a stable industry like electricity, with low risks. There are two types of risk:  Systematic risks are linked to market and economic conditions, such as interest rates, inflation.  Unsystematic risks are associated with the industry it participates in. For example, the fashion industry is dependent on the demand in that market. While the major part of the risk can be bought, rented or borrowed, it is the management of this that cannot be outsourced. The main part of this book is the management of the unsystematic aspects of the company. This chapter focuses on the case for risk management, functions of management and how it applies to the management of risk in an organization. 10 Once you have studied this section, you will be able to explain the reasons for risk management and the functional approach to management. 5.1.2. Definitions In this module risk assessment and risk management are used interchangeably. Risk management has become important due to global competition and volatile markets; the cost of failure and the benefits of properly managing risk, further highlight the critical nature of how to manage risk. The approach to define risk management can be studied through the following:  Comprehensive method in understanding risk management involves three key aspects: strategy, processes and people.  Inclusive method involves all levels of the organisation. At the strategic level, the risk-to-reward will provide an indication of the present level of risk. In practice, the board of directors will set a risk framework that will provide management with a guide to determine what level of risk is acceptable, what risks can be transferred and what can be insured. The guidelines will then be integrated into processes, procedures and systems in the organisation to regulate the day-to-day affairs of the enterprise. Management’s role is to develop a risk management culture to underpin risk management principles so that it is embedded in all functions and departments in the organisation. Risk awareness must be cascaded from the strategic level to operational level. This requires employees to embrace risk management behaviours (Valsamakis, Vivian and Du Toit, 2016:12).  Proactive nature concerns assessing and addressing in advance, clear risk control and financial discipline. These interventions must be integrated into general management to become part of the management system of risk management and risk financing. To understand risk management the following definition is adopted: Risk management is managerial function aimed at protecting the organisation and its people, assets and profits against the physical and financial consequences of risk. It involves planning, coordinating and directing the risk control and the risk-financing activities in the organisation. (Valsamakis, Vivian and Du Toit, 2016:18) 11 5.1.3. Case of Risk Management Peter Drucker commented that risk management is important for entrepreneurship to drive economic development in the Western world. He posits that the ability to manage uncertainty is the difference between the developed and developing nations. A society that can assess risk, control risk and deploy its resources wisely to cushion its effects, improves its success rate of attaining their goals. To appreciate the importance of risk management we only need to look at the major disasters in the world, for example coal and gold mining disasters in South Africa, where hundreds have perished. In 1984, the Bhopal gas leak of highly toxic chemicals killed 1 500 people and 34 000 sustained eye injuries. These global disasters highlight the risks and consequences that need to be managed and for industry leaders to be aware of these risks and how to reduce them (Valsamakis, Vivian and Du Toit, 2016:14). Managing risks requires an integrated organisational wide approach, especially when one considers the:  Increasing sophistication of risk – New types of risks arise from the increase of new technologies, use of toxic chemicals and innovation. Often management of risk is sacrificed for innovation and progress. People proceed with the use of technology and inventions, to only become aware of the dangers after a tragic incident; only then people are jolted into action to manage risk.  Increasing concentration of risk – This form of concentration of risk may not appear obvious in the first instance when compared to high rise buildings and manufacturing plants, but the complexity of risk rises from the advanced technologies of Silicon Valley.  Increasing awareness of risk – The public is more aware of risk and safety, to the extent that they often avoid taking personal responsibility for any mishap. Rather, they tend to look at the state or to others to reimburse them for any misfortune suffered.  Decline of insurance as a risk (financing technique) – There has been a decline on what is spent on insurance than on what is spent on risk control and risk retention. This trend shows that the risk control and risk financing aspects must be integrated and companies must be aware of the level of risk they are able to control, or retain and what level of risk can be covered by insurance. 5.1.4. Reasons to Risk Management Reasons for managing risks are linked to growth, survival and optimising profits. Decisions are influenced by corporate policy and good citizenship. There is a relation between risk and return; when an organisation manages its risk so that it is reduced then it will have a good risk-to-return trade-off. This causes company’s risk profile to be given prominence in its annual results and various codes of good corporate governance (Valsamakis, Vivian and Du Toit, 2016:12). Justification of Specific Decisions Decisions have to be made with regard to minimising risk, to do this the firm needs to develop and apply criteria in a manner to have the desired effect of risk reduction. Four such criteria are indicated:  Steps taken are cost beneficial – The advantage of employing risk reduction measures must deliver cost reduction and provide a favourable trade-off of risk and return. The firm’s managers want to know whether the expenditure incurred in introducing risk reduction interventions can produce 12 sufficient return to justify the cost. Most of the time, risk reduction interventions produce returns in the long term. This can cause the firm to disregard risk interventions as they look for short-term results, without realising that risk reduction is a long-term exercise that delivers positive results (Valsamakis, Vivian and Du Toit, 2016:7).  Risk aversion – Psychologically, people value what they have rather than what they may gain in the future. People are more likely to sacrifice what they have now to safeguard what they have left of their existing wealth. Therefore, we can conclude that people are risk averse and consequently they take steps to reduce risk. Even under cost-benefit assessment of risk, there is an awareness of risk that drives people towards risk aversion. Notwithstanding the inefficiencies of insurance, many people buy insurance to transfer their risk. Such behaviour also determines what types of risk they are prepared to retain and control. Risk management is an expenditure with no income forthcoming. Further, even if there is excellent performance by the risk manager, which is not often acknowledged, no short-term results are shown. However, when an event occurs with far reaching negative consequences that hurts the firm, the management and shareholders start to question or look out for risk reduction measures and seek answers from the risk manager.  Policy based decisions – Many decisions to implement risk minimisation interventions are already in the organisation’s policies, which originally developed for some other purposes. For example, the quality assurance policy was designed to ensure that products meet the specifications of the customer and the standards of the industry without the issue of exposure of legal liability. Similarly, the health and safety policies protect employees from injury but fits into the risk reduction profile by implementing the policy to reduce accidents in the work place. The risk manager should encourage the correct implementation of these policies to reduce risk.  Authoritative reasons – Governments have laws to protect employees and citizens with regards to fire, health and safety. This authority must be followed otherwise it will be subject to legal sanction. 5.1.5. Functional Approach to Management Risk management refers to the management of risk in an organisation. Management principles have been well defined and it will make sense to apply these principles to risk management. Management is the planning, organising, leading and controlling of organisation’s resources to realise their goals. A description of these management functions will provide a full understanding of management.  Planning is the development of the vision, mission and goals of the organisation to reach a future position; it acts as a road map of the organisation.  Organising follows planning, in that the plan needs to be given life by allocating resources in the form of human, financial and physical resources. For example, systems and procedures need to be designed, and job descriptions need to be designed in terms of the skills and competencies required to carry out the mandate of the vision of the organisation.  Leading is the directing and deploying of human resources in such a manner that they are motivated, with minimum pressure, to perform at the best of their ability to achieve the organisation’s goals (Valsamakis, Vivian and Du Toit, 2016:10).  Controlling is ensuring that the organisation is on the right path in terms of the set goals and 13 objectives. Any deviations are analysed and corrected by bringing all stakeholders back on track to comply with the firm’s processes and procedures. 5.1.6. Risk Management Model While risk practices may differ, there is a common set of elements associated to all risk management programmes, which is referred to as risk management model or risk management process. The elements of the programme are listed in Figure 5.1.1. Figure 5.1.1: Risk Management Model Adapted from Valsamakis, A.C., Vivian, R.W., Du Toit, G.S. 2016. Risk Management. Cape Town: Pearson: p236 14 Determining the Objectives of the Risk Management Function The alignment and relationship of the risk management goals, objectives and mission of the organisation, is a key task of the risk manager. The first step is to establish the risk management goals. The second step is to use the goals as a yardstick to measure the success or failure of the organisation’s programmes. The objectives are included in the risk management policy of the organisation. Risk Identification Risk management requires identification of the source of the risk; some risks are self-evident, while others may require investigation with specialists and managers to obtain information of the underlying causes for the risk. Risk identification has two related functions:  Identification of the hazard refers to identifying the risks that increase the likelihood of loss.  Exposure to hazards is when a person is open to injury to e.g. a person working on poorly maintained equipment. Identification is followed by analysis. It is not sufficient to show that the hazard or exposure risks exist; the risk manager must know how the risk interacts with production to produce loss. Perceptions of risks held by the employees frame their reference on how they handle, for example, poisonous chemicals. If management believes that a particular risk is not serious, while the employee believes the risk is hazardous; this perception may influence the reassessment of how management may classify this risk (Valsamakis, Vivian and Du Toit, 2016:15). Risk Evaluation and Assessment The first step in assessment is to identify the risk and work towards reducing the impact of the risk. Risk evaluation also involves identifying how frequent and how severe the probability of the risk causing loss to the organisation can be. In summary, risk evaluation and assessment deals with:  Loss frequency and loss severity; the two measures will be average loss and maximum possible loss.  The analysis of the financial strength focuses on the retention capacity of the firm, impact of risk on the firm’s financial situation and the ability to withstand the risk. The evaluation process requires the input of various relevant departments and units of the organisation. For example, information of contractual agreements might require information from the legal department. Risk Control The next step is to reduce the risk through the design and development of interventions and programmes. The aim will be to:  Reduce the size of the risk exposure; 15  Minimise the frequency of the loss-producing events;  Address the loss-producing event through practical ways; and  Recover from the loss-producing event in tangible and practical ways. Risk control is targeted at the source of the risk. Risk management is a staff function and it entails implementation and monitoring loss of control and is a responsibility of line management. There are three responses to risk: Avoidance – when a risk is completely circumvented by avoiding certain tasks; this is impractical and rarely possible. For example, to avoid injury at work one does not work.  Acceptance – when a risk is accepted in that the risk is an inherent part of the job or project. Avoiding them will mean not participating in the project and business at all. However, most business are likely to accept the risks if the risk-return properties are acceptable.  Mitigation – when the business accepts the risk and works towards lessening the impact of the risk. Risk control activities are avoiding, preventing, minimising or otherwise controlling risks and uncertainties. The scale of risk control can vary from a basic intervention of installing a fire extinguisher in a kitchen, to making emergency plans in a nuclear plant. Risk Financing The last step in risk management is the provisioning of financial support to cope with losses that may occur. Risk financing includes the reimbursements of funds for losses incurred and for funding programmes to minimise risk or enhance positive results. In normal business activities, risks are possible and the organisation can cover their losses through insurance coverage. In determining the most efficient method of managing risks, the following options arise:  The decision to retain risk with a self-funding plan;  The combination of different risks and using the probability method in predicting events;  Spreading the risks across different businesses; this is often used by insurers; and  Transferring risks to third parties by using insurance. Programme Monitoring and Administration Organisations do not need to sequentially follow the above steps; every risk could present itself in different ways, require alternative combinations and possibly in a different sequence of responses. Therefore, the application will be determined by the risk situation the organisation is faced with. 5.1.7. History of Risk Management in South Africa 16 Risk management was founded in 1970 in South Africa, when Barlow Rand Group signed a risk management statement. In 1975 the South African Risk Management Association was formed to promote risk management. By 1979 this organisation was dissolved due to the lack of interest by the large insurance houses, as their focus was rather on loss control and a lack of understanding of risk. In 1986, the risk fraternity formed South African Risk and Insurance Management Association (SARIMA) and the Society of Risk Managers was formed in 1990. In 2003, both these organisations merged to form the Institute of Risk Managers. The subject Risk Management is taught at major universities and colleges throughout South Africa as a specialised discipline (Valsamakis, Vivian and Du Toit, 2016:24). Reading Refer to page 3 of your prescribed textbook Self-check activity  Discuss the five major disasters in South Africa.  Use the spreadsheet on p.3; discuss your opinion on how this disaster can be averted.  How could the effects have been reduced? Reading Read pp.7–10 of the prescribed textbook. Self-check activity  What are the main reasons for the development of risk management?  Discuss the role of management in risk management.  Discuss the four fundamental functions of management, make use of examples. 5.1.8. Conclusion Risk management is important due to the wide competition and the unpredictable markets; the cost of failure and the benefits of properly managing risk. Risk management benefits the organization with regard to growth, survival and maximising profits. Risk practices are not necessarily the same, however, there is a common process of risk management to be used by organisations in order to achieve results. 17 5.1.9. Revision Questions Answer the compulsory revision questions below: a) Provide a comprehensive definition of risk. b) Discuss risk reduction and the interventions needed to have the desired effect on risk. c) Discuss the different steps in the risk management process. 18 5.2. Study Unit 2 - Concept of Risk The aim of this unit is to study the concept of risk and its influence in the Purpose operation of the ogarnisation. By the end of this unit, you will be able to:  Define risk  Discuss the basic risk classification  Describe in detail the strategic risks – sustainability Learning Outcomes  Discuss managerial risk classification  Describe psychological influences on risk  Describe market failure  Discuss economic viability of insurance; and insurance markets Time It will take you 22 hours to make your way through this unit. Important terms Peril Refers to a serious harm. and definitions Hazard Refers to things that can cause damage Viability Refers to a success condition 5.2.1. Introduction The Unit studies the different elements of risk and risk classification so that they can be identified and evaluated for risk amelioration or prevention. Some business risks may provide certainty as well as uncertainty in terms of the event outcomes. There have been many definitions of risk, emphasising uncertainty of loss, probability of an event occurring and deviation of actual outcomes from expected outcomes. Risk can be defined as a deviation from the expected value. It implies the presence of uncertainty as to the occurrence and outcome of an event producing a loss. The degree of risk is interpreted with reference to the degree of variability and not with reference to the probability that will display a particular outcome. The standard deviation becomes a good measure of risk (Valsamakis, Vivian and Du Toit, 2016:24). 5.2.2. Basic Risk Classification Two classifications of risk that are used:  Basic classification refers to the popular ways in which risks have been classified; and 19  Managerial classification is those used in practice so that risks can be managed. Managing risks requires a quantification of risk in the first instance so as to make decisions under conditions of uncertainty and taking into consideration the qualitative forms of risk, for example the psychological aspects of risk. To understand the risk management process, the probability theory will be studied by using a simple integrated model to support decision making under conditions of risk. The model identifies two underlying facets:  Physical management or control of risk; and  Financing of risk where it can be transferred through the insurance market. This unit approaches risk from a financing perspective through the insurance market discipline (Valsamakis, Vivian and Du Toit, 2016:32). To understand the management of risk, it is necessary to represent risk in a framework. The below sections discuss quantitative and psychological aspects of risk. Certainty and Uncertainty Certainty is when there is complete trust that a particular outcome will come to fruition. Examples of certainty include the laws of gravity or laws of energy and motion etc. The outcomes of these can be predicted with a high degree of accuracy. Under conditions of uncertainty, there is a lack of knowledge or information to predict the outcome and its consequences with utmost certainty. The level of uncertainty is determined by the amount of knowledge or information available to evaluate the likelihood of a particular outcome occurring and the individual’s ability in evaluating the information. Uncertainty is the inability to foresee the future or predict the future with certainty. As a result, we are unable to control the various outcomes that may arise (Valsamakis, Vivian and Du Toit, 2016:34). Uncertainty is concerned with the following two elements: Uncertainty of the event or outcome occurring; and if the event occurs, what are the consequences. Table 5.2.1: Uncertainty in Levels or Degrees Level of Uncertainty Characteristic Examples None (absolute certainty) Outcomes can be predicted with Physics, natural sciences precision. Level 1: Objective uncertainty Outcomes are identified and Games of dice, chance, probabilities are known. Roulette Level 2: Subjective uncertainty Outcomes are identified and Fire, car accidents, probabilities are unknown. investments Level 3: Total uncertainty Outcomes are not fully identifiable Space exploration, genetics and probabilities. Adapted from Williams, Smith and Young, 1998 20 With reference to Table 5.2.1, Level 3 represents a high degree of uncertainty due to lack of knowledge of the situation and circumstances, resulting in a low level of confidence, and predictions in the outcomes is impossible. Risk Where there is uncertainty in any form, there will be risk. Willett and Knight have studied various approaches and relationships between risk and uncertainty; they have based their definition on the similarities between risk and uncertainty. The modern trend is to interpret risk as the absence of certainty, where certainty represents one outcome. A risky outcome assumes a number of possible outcomes, and it is important to bear in mind is that the values are not known in advance. Perils and Hazards The definition of peril is the source of the loss. Therefore, it is different from risk, which is related to uncertainty. Risk should include both quantitative and qualitative perspectives. Typical examples of perils are fires, explosions, storms etc. These perils give rise to risk but they are not risks in themselves. For example, a fire in a storage facility is a peril that insurance can be purchased, while the oil drums in the storage facility is a loss-causing situation. Mehr attempts to consolidate and integrate this as the cause of the loss is the peril and the surrounding circumstances like the oil drums represent the hazard. The definition of a hazard relates to the circumstances surrounding the cause of the loss. The material or physical aspects in the situation surrounding the cause or the loss are referred to as physical hazards and the personal aspects or characteristics are termed moral hazards. Pure (or Event) and Speculative Risks A pure risk is related to an event that may produce a possibility of loss only, e.g. destruction of a factory due to fire. A speculative risk can result in either a profit or a loss, e.g. a profit-making venture is a speculative risk. Insurable and Non-Insurable Risks There does not appear to be a satisfactory test to distinguish between these two risks, however, in theory, most pure risks are insurable. There are pure risks that cannot be insured, like destruction of a building due to war. Fundamental and Particular Risks Fundamental risks are impersonal risks when many losses can be traced to a single source in origin and in consequence. They emerge from the economic, political, social interactions in society and physical events like damage due to the Chernobyl nuclear disaster or due to wear and tear or corrosion. Fundamental risk affects large parts of society or even countries and the world. They are often risks that 21 are uninsurable due to the catastrophic nature of the loss. Particular risks are losses that arise from discrete events that are personal with respect to its cause, e.g. an explosion in a boiler room, fire damage in the factory. The categorisation of whether a risk is either fundamental or particular is not definitive. The circumstances must be investigated and evaluated to determine its classification. For example, unemployment was believed to be caused by lack of ability or work ethic, nowadays, unemployment is linked to the economic system. It is the responsibility of society and not of the person and therefore, is a fundamental risk as opposed to a particular risk (Valsamakis, Vivian and Du Toit, 2016:38). One way of determining whether the risk is fundamental or particular is to establish whether commercial insurance can be used to insure the risk through financing the loss arising from an event (Valsamakis, Vivian and Du Toit, 2016:40). Systematic and Systemic Risk Systematic risk is considered as a market related risk. For example, if the rand-dollar exchange changes, then there could be an increase of shares changing hands on the stock exchange. An event could occur within a company, for example a pharmaceutical company could withdraw the registration of a drug and this would result in its share price dropping. Systemic risk is when a single event can cause a whole system to collapse. In South Africa, the Regal Bank got into financial difficulties, the Reserve Bank as a lender of last resort refused to intervene to save the bank. Similarly, Nedcor, and ABSA experienced difficulties but the Reserve Bank was able to save these banks by intervening and guaranteeing their deposits. 5.2.3. Strategic Risks: Sustainability Strategic risks include sustainability, which includes the four pillars of strategic planning, financial, environmental, social and human resources. King III requires that companies report on their sustainability practices and performances, making it a governance criterion. One of the important consequences of integrating sustainability with financial reporting, according to King III, causes sustainability to be a key risk factor that needs to be considered and managed. King III argues the case of sustainability that drives opportunity. By integrating sustainability in all aspects of the business, it is able to preserve the environment by cutting down its carbon footprint, and in the long term can bring down the cost of fuel as they move to reusable sources of energy. The issue of sustainability is a key requirement of business, given the consequences of climate change that is exacerbated by harmful emissions and global warming; the cumulative effect on agriculture and food production. Integrating sustainability with financial sustainability, is in line with the Millennium Development Goals that mandates a report on priorities in order to protect the world against climate change and in the process, make sustainability a key risk management issue. This presents businesses with a challenge to reduce carbon emissions and seek alternatives to fossil fuel or risk the consequences of climate change. Organisations need to come up with innovative solutions and 22 current development has focussed on reusable energy e.g. wind and solar energy. Battery driven cars have been tested and they show promise as they significantly reduce the carbon footprint. Various global conventions and agreements have been concluded to cut greenhouse gases. 5.2.4. Managerial Risk Classifications In managing risks, the directors may divide risks into two categories, future risk (strategic risks) and day-to-day risks (operational risks). The day-to-day risks are further divided into departments e.g. Marketing, Human Resources and Finance. The organisation is also vulnerable from the possibility of fire, theft and fraud. For the purposes of accommodating all different types of risk the following categories are used:  Inherent business risks and incidental risks;  Pure and speculative risks; and  Operational risks. Inherent Risks Inherent business risk refers to events, activities and decisions that impact and cause fluctuations on the operating profits of the company and the value of shares held by shareholders (Valsamakis, Vivian and Du Toit, 2016:39). Inherent risk consists of two different types of risk:  Specific risk, affects the company only and has no impact on the wider economy.  Systematic risk or market risk, affects the whole economy. Specific business risk or the fluctuations of operating profit is further divided into the following:  Sales variability refers to the demand of a product over time and depends on promotion, marketing and design of the product.  Operating leverage is dependent on the production function and includes fixed and variable costs. It is measured by the percentage change in operation costs over percentage change of sales. Fixed costs remain the same irrespective of the change in sales. Variable costs vary directly in relation to sales volume. Operating cost variability is the proportion of fixed cost over total cost.  Resource risks cause variability in the operating profits. Resources include capital, labour, materials and technology.  Operating profit is affected by profit margin and turnover; an increase in competition results in lower profit. The management of risk means repositioning the company by determining the amount of risk the company can absorb to produce more profit. Incidental Risks Incidental risks are not central to the main business but are necessary for the continuation of the business. The principal subcategory is financial risk and includes transactions in financial assets and those that result 23 in financial claims. Businesses exposed to this risk must manage the operational risk and financial assets. Financial risks are divided into the following headings:  Interest rate risk refers to changes in the net interest income received.  Liquidity risk occurs when the business cannot fund its business activities; it is the difference between the size of the asset and the liability (funding needed).  Investment risk is when capital is adversely affected by losses due to the exposure of the investments to certain risks.  Credit risk is the inability to fulfil a contract in terms of the original agreement.  Currency risk is when the exchange rate changes and influences the foreign currency held by the organisation. Operational Risks Operational risk has no potential for showing a profit and in most cases, can be insured. For example, if a fire breaks out at a business, loss may be incurred, however, if no fire occurs then no loss is suffered. Pure risks are referred to as insurable losses, whose risks can be transferred by insuring against these events or occurrences. 5.2.5. Psychological Influences on Risk The discipline of psychology emerges from the study of human behaviour. There is growing interest of how risk influences decision making and how risks can be substituted in decision making. These substitutes are usually quantitative forms that reflect the level of uncertainty. The individual’s ability to perceive risk and decide what level of risk to absorb is key in understanding risk management and insurance. Each person views risk differently, depending on the situation they find themselves in, or their attitude to risk, which shapes their decision making either towards risk aversion or to aggressively confront risk. An individual’s perception and reaction to risk is largely shaped by one’s previous experience with risk, position, wealth and background. Studies have shown that attitudes to risk can change if exposed to the attitude of the group and individuals feel capable to take on more risks. This is referred to as group dynamics, which forms part of organisational behaviour. 5.2.6. Market Failure Common meaning of market failure is the failure to provide goods and services to a specific market, causing insurance to rise. Where the private sector fails to provide a good, then it is a reason for the state to intervene and provide the goods for its citizens (Valsamakis, Vivian and Du Toit, 2016:40). It can be argued that the state should provide goods and services categorised as public goods and the 24 private sector to provide private goods and services; the grey area in between is classed as merit goods. For example, if the state provides protection to its citizens through its national defence force, this represents a public good. The definition of a public good is characterised by two factors i.e. there must be zero cost to the citizens and the impossibility of excluding some citizens. If the government is providing protection then there will be no market for private defence force because no one is excluded, which is a key requirement for market and competition. There are some consumer goods that not all citizens can participate in; this can be categorised as a merit good. For example, it is generally believed that all children should receive education, however, education can be a private good for those who can afford the higher fees. For those cannot pay, they can access state provided education either for free or at an affordable rate. 5.2.7. Economic Viability of Insurance Companies An insurer faces different types of risk; the main risk that could cause the collapse of an insurance company is when the liabilities exceed the assets. This could be due to the claims exceeding the premium income because of the high competition in the insurance industry; the deficit can be covered by the investment income. Due to the severe risk it represents, the insurance regulator prescribes a minimum amount of funds available to guard against the unbridled increase of liabilities over assets. However, should this happen the regulator will take steps to underwrite losses that will lead to insolvency. The insurer will set a pure premium after assessing the risk and likelihood and extent of the loss. To cover expense related to the premium, the amount is increased to accommodate these additional expenses, referred to as the commercial premium. The difference between the two premiums is defined in terms of a ratio i.e. 60:40. Sixty per cent of the commercial premium is used to pay for the loss and 40 per cent is needed for expenses and profits. The insurer’s risk is not that a single event will occur, but rather an aggregate of cost of claim will exceed income premiums. Therefore, it is necessary to use a normal distribution around a mean pure premium value and determine a standard deviation around the mean. This will assist in quantifying acceptable risk that the insurer can absorb without exposing the business to liquidity and insolvency risks. Insurers use a system of pooling, where a large number of risk exposures are considered, the insurer acts as underwriter to this large number and reduces the risk by increasing the predictability of the average losses. This pooling effect is the law of large numbers. Insureds Rational for Purchasing Insurance For an insurer to be viable they must charge a commercial premium in excess of the insured’s own loss. On a cost-to-benefit analysis, insurance produces a negative benefit. So why do insureds pay in excess of their own losses? To understand this, we need to put risk and uncertainty into a framework. Both quantitative and qualitative assessment of risk was discussed; now we need to consider the economic and management rationale to develop a model of choice that informs how the market for insurance is developed. It is centred around the concept of utility and characterised by insured’s preferences of goods and services. The model 25 explains the workings of the market from the insured’s perspective. It is critical to understand that in an uncertain world an insurance market is bound to arise to minimise the effects of risk. Important principles underlying the theory of utility is:  The more goods and income are preferred, the more an individual receives a level of utility or satisfaction depending on the package received.  The more the person has, the less satisfaction he will receive from every other unit. Figure 5.2.1 shows the economist’s basic model of decision making, under conditions of uncertainty, the assumption is made that the utility curve applies to a consumer, whose preference for income is represented by OU. Figure 5.2.1: Utility Adapted from Valsamakis, A.C., Vivian, R.W., Du Toit, G.S. 2016. Risk Management. Cape Town: Pearson: p.51. Let us make a further assumption that the following prevails: Table 5.2.2: Premiums Value of The House R30000 Probability of The House Being Totally Destroyed by Fire 0.20 Pure Premium R6000 Commercial Premium R10000 Adapted from Valsamakis, A.C., Vivian, R.W., Du Toit, G.S. 2016. Risk Management. Cape Town: Pearson: p.52 26 Table 5.2.2 indicates that the commercial premium is higher than the pure premium, therefore, it is beneficial to the insurer and should not be purchased. Once utility is introduced the picture changes the decision, using Figure 5.2.3. the monetary values are replaced by utility. Table 5.2.3: Utiles No Insurance Wealth (Income) Utiles per OU Event: No Fire R40 000 31 Event Fire R10 000 10 Expected Utiles (0.20) (10) + (0.8) (31) 26.8 Insurance Purchased Event: No Fire R30 000 28 Event Fire R30 000 28 Expected Utiles 28 Adapted from Valsamakis, A.C., Vivian, R.W., Du Toit, G.S. 2016. Risk Management. Cape Town: Pearson: p.52 The question arising from the consideration of utility is whether the person will purchase insurance; this is dependent on the cover and premium offered. If the owner does not purchase insurance then two states exists i.e. no fire and fire, each dependent on probabilities. If the person does not purchase insurance cover, then his wealth will increase by the commercial premium or 26.8 utiles. If the consumer buys in insurance then his wealth remains constant at the value of the house, refer to Table 5.2.3. Therefore, the consumer buys insurance notwithstanding that it costs higher than the potential losses. The utility theory explains why consumers buy insurance (Valsamakis, Vivian and Du Toit, 2016:42). Reading Read p.28 Section 2.3 Definition of Risk of the prescribed textbook. Self-Check Activity  Discuss the various definitions of risk resulting in the most accepted definition.  Discuss the relationship between risk and uncertainty.  What principal do the insurance markets use to absorb risks? 27 Reading Read pp.37–39 of the prescribed textbook. Self-Check Activity  Discuss the difference between systematic and systemic risks, make use of examples.  Research the case study on the collapse of Saambou Bank. What caused its collapse?  What could the bank’s owners have done to avoid this collapse? Discuss your answer in the context of risk. Reading Read pp.40–43 of the prescribed textbook. Self-Check Activity  Discuss the difference between systematic and systemic risks, make use of examples.  Research the case study on the collapse of Saambou Bank. What caused its collapse?  What could the bank’s owners have done to avoid this collapse? Discuss your answer in the context of risk. 5.2.8. Conclusion Risk can be described as a deviation from the expected or desired results in business. For organisations to manage the risks better, they need to be classified according to their similarities. It is also a fact that at times, market fails to provide goods; this is where the state intervenes and provide the goods for its citizens. It is important to understand that in an uncertain world an insurance market is bound to arise to minimise the effects of risk. 28 5.2.9. Revision Questions Answer the compulsory revision questions below: a) Discuss the law of large numbers. How do insurance companies use this to manage their risks? b) Commercial premiums are higher than pure premiums. Discuss this statement with the use of examples. c) Define market failure with reference to state and private roles. d) Discuss the insured’s rationale for purchasing insurance, include examples. 29 5.3. Study Unit 3 - Decision Making Under Conditions of Risk and Uncertainty The purpose of this unit is to introduce students in decision making under Purpose conditions of risk and uncertainty By the end of this unit, you will be able to explain, describe or determine the following:  Expected monetary value (EMV) criterion; Learning  Probability theory; Outcomes  Probability distribution;  Maximin decision criterion;  Minimax regret decision criterion; and  Maximax decision. Time It will take you 28 hours to make your way through this unit. Important terms Probability Refers to the chance of something occurring and definitions Minimax Refers to minimising the maximum value 5.3.1. Introduction Attempts have been made over a long period to develop a theory of decision making in general, and in particular those situations that involve risk and uncertainty. This unit studies the instruments and theories that apply to risk management. Reading The prescribed textbook for this unit is: Valsamakis, A.C., Vivian, R.W., Du Toit, G.S. 2016. Risk Management. Cape Town: Pearson: pp.55-78. 5.3.2. Expected Monetary Value (EMV) Criterion This theory suggests that decisions are made in terms of EMV criterion. When making decisions faced with outcomes that can be expressed in monetary terms and where the probabilities are known, the decision maker can choose the path that has the greatest EMV, represented by the symbol E(X) (Valsamakis, Vivian and Du Toit, 2016:56). This is shown in an example, Figure 5.3.1 and Table 5.3.1. 30 Figure 5.3.1 Decision Tree P1 A1 P2 A1 S (Stake) Adapted from Valsamakis, A.C., Vivian, R.W., Du Toit, G.S. 2016. Risk Management. Cape Town: Pearson: p.56. Table 5.3.1: State of Nature Matrix 7 8 State of Nature 9 Totals 10 Fire 11 No Fire 12 Outcomes 13 A1 14 A2 15 n/a 16 Probability 17 p1 18 p2 19 20 Contribution to 21 p1 A1 22 p2 A2 23 EMV Adapted from Valsamakis, A.C., Vivian, R.W., Du Toit, G.S. 2016. Risk Management. Cape Town: Pearson: p.57. If the EMV of the profit generating business/projects is greater than the stake (S) then the decision maker will embark on the project. This theory relies heavily on probability theory and its relationship with risk and risk management. Think point A warehouse has a capital value of R100 million and the probability of fire is causing a complete loss of 0.0001. What will be the premium charged by the insurer? Make use of the EMV decision tree and Table 5.3.1. 31 Table 5.3.2: Example of State of Nature Matrix State of Nature Totals Fire No Fire Outcomes (R100million) 0 n/a Probability 0.0001 0.9999 1 Contribution to EMV (R10 000) 0 (R10 000) Adapted from Valsamakis, A.C., Vivian, R.W., Du Toit, G.S. 2016. Risk Management. Cape Town: Pearson: p.57. Think point A If a fire takes place, the insurer will incur a loss of R100 million. The EMV of the loss is R10 000 to cover the cost of the loss. However, the insurer needs to add to the pure premium an amount for administrative and profit for it to be economically viable. Self-Check Activity  Define pure premium.  Calculate what the commercial premium will be if the insurer adds administration and profit. There are many other non-quantitative risks to be considered, to obtain a true extent of the risk. The normal EMV= p A is inadequate since this calculation does not consider the level of confidence whether the EMV will be achieved. For example, a person with a car valued at R200 000 will take out insurance, they are advised that the probability of loss occurring on a vehicle of this type is 0.1. They decide not take out an insurance but rather save the premium to cope with the potential loss. The pure premium is 0.1 x R200 000 = R20 000. This is not accurate. A person will either have one of two outcomes 0 (no loss) or R200 000 (complete loss), the premium of R20 000 will never be able to compensate for the entire loss. However, if you have a fleet of 50 vehicles at R20 000 then the total value in the fund will be R1 000 000. This can pay for the loss of five vehicles. The question is how can you be sure that this fund of R1 000 000 will be adequate. An amount R1 000 000 + Rλ is used where Rλ is chosen to give the desired degree of confidence. To understand Rλ a more in-depth understanding of probability and probability distribution is required (Valsamakis, Vivian and Du Toit, 2016:58). 32 5.3.3. Probability Theory Risk includes the extent of the outcome and the likelihood of it occurring. Probability theory is when the range of outcomes are identified together with the probability of it occurring. The three types of probabilities are discussed below. Priori Probabilities A priori probabilities or objective probabilities have a basis of being known. For example, when a coin is tossed, it has a 50 per cent chance of being either head or tail. A priori probability is not conducted by observing the frequency of occurrences; rather by deductive reasoning and assuming the event is subject to randomness or chance. However, it is not possible to determine most probability outcomes by intuitive reasoning, they can be estimated or computed through experimentation or observation. Subjective Probabilities Subjective probabilities, the decision maker must estimate in contrast to a known probability. Subjective probability is used when there is insufficient information to predict the probability in an objective manner. For example, if one is to determine the probability of dying of anthrax then it is best to estimate the probability of dying in an accident, which is 0.0001, then estimate dying by anthrax. Experiments have shown that people tend to underestimate well known events and overstate rare events, therefore, the probability of dying through anthrax will be overestimated. Relative Frequencies Leading to Empirical Probabilities This method of probability is obtained through observation, experimentation, measurement, the collection of data and extrapolation; it is not possible to determine the probability of death through intuition. Some events can be measured over a period and then extrapolated into the future. For example, deaths can be measured over a period of the sample number alive and those who died over the period. The ratio of number of deaths to the number alive can be obtained. This is called relative frequency. When there is confidence in the relative frequency, this is referred to as empirical, it comes with increasing numbers. Probabilities like this are referred to as statistical or inductive probabilities. The reliability of these evaluations is based on large number of events and the causal influence of the past remains in the future. The future is not a neat repeat of the past. Margins of error must be considered for these statistics to be meaningful. Statistical techniques have been developed to accommodate the margins of error by determining the probable range of deviation of the actual from the expected results. These techniques are used to determine happenings or occurrences like death, car accidents. Problems with empirical probabilities:  They can be misleading if it is based on infrequent events, which are sometimes called Black Swan occurrences. A database of empirical estimations will not include infrequent events.  They have survivor bias, where data collected includes only survivors. Therefore, statistical probabilities can change because of the changes in the state of our knowledge of causes (affecting deductive reasoning) or changes in the underlying forces (affecting inductive probabilities). For the purpose of this guide, empirical probability is the relative frequency of events that 33 takes place over a long period. In the short-term insurance industry, traditional probability theory is not used, rather the loss ratios are used. In short-term insurance, the total income (P) from a class of business is known and as the losses are recorded they become known. To understand this, we assume that the total premium is known P=N.p where (P) is the total premium. It is the fund that will pay for the losses (L) and (N) is the number of insured units upon which identical premiums (p) are levied. The losses (L) are distributed in different class intervals C or L=ΣnC, the losses (L) equal the sum of the losses in each class interval. Since the pure premium (P) is equal to the Loss L= ΣnC; by definition it is the amount required to pay for the losses, i.e. the ratio L/P equals 1. In this event: P.N = ΣnC Or P = Σ(n/N).C This loss ratio formula is used to determine the premium if probability theory is applied and the premium for a range of losses that occurs. To make provision for expenses and returns, the ratio must be less than 1, e.g. 0.6. This is not only for a single loss but applies to situations where more than one loss occurs per insured. This is applicable where previous events have taken place. 5.3.4. Probability Distribution If the probability distribution of the risk is known, it is easier to calculate the probable outcome of the riskiness of the occurrence. To evaluate risk, three probability distributions are used: binomial distribution, normal distribution and Poisson distribution. The type of problem will determine the appropriate distribution that can be used. The Binomial Distribution A risk manager will find the binomial distribution useful as it can denote two stats i.e. no loss and loss. The example illustrated in the previous unit can be used to illustrate this point; we considered a 50-car fleet with a risk probability of 0.1 chance that the vehicle will be written off. Each vehicle can suffer a loss or no loss. It is possible that a vehicle can suffer more than one loss, however, this will not be considered in this example. The fleet can suffer the following, 0 loss, 1 loss, 2 losses, … 50 losses, there are 51 possible outcomes. If the fleet has (N) vehicles, N+1 losses are possible. The binomial distribution can be described as a two-parameter distribution:  Total number of events; and  The probability (p) that the event will come to fruition. The formula for binomial distribution is: 𝑁! 𝑥𝑝𝑟 (1 − 𝑝)N−r P= 𝑟!(𝑁−𝑟)! 34 Risk Assessment Models and Methodologies Educor © Where: P(r) = Probability that exactly r accidents will take place N! = N (N-1) (N-2)........................ (2) (1) (N! is called factorial) 0 is equal to 1 For example, a firm that transports cars to customers face the prospect of damages to the cars in transit. If a car is damaged and is considered to be a total loss, the probability of a single car is 0.1, the binominal distribution can be used to determine a distribution of a number of damaged cars. When two cars are considered, N=2 and p=0.1. The probabilities of 0, 1 or 2 losses can be calculated using the formula. Probability of exactly 0 losses = 2! (0!)(2!) 𝑋0.10 (0.9)2 = 0.81 Probability of exactly 1 loss = 2! (1!)(1!) 𝑋0.11 (0.9)1 = 0.18 Probability of exactly 2 losses = 2! (2!)(2!) 𝑋0.12 (0.9)2= 0.01 To understand this form of probability let us look at another example. Assume that there are 40 items, each exposed to a loss of equal probability, therefore, there are 41 possible occurrences ranging from 0 to 40 items suffering a loss. The probability distribution is shown in Figure 5.3.2 below. Figure 5.3.2: Binomial Distribution Adapted from Valsamakis, A.C., Vivian, R.W., Du Toit, G.S. 2016. Risk Management. Cape Town: Pearson: p.62. 35 Risk Assessment Models and Methodologies Educor © The expected value is µ = Np = 40 X ½ = 20, with the probability of this exact number of accidents being 0.1123 (derived from the formula). We are now ready to determine the degree of confidence. We can be 66.41 per cent confident that there will be 21 or fewer accidents, 76.01 per cent that there will be 22 or fewer and 83.89 per cent that there will be 23 or fewer accidents. Think point In the example above, show your calculations for the probability of 3 losses. Normal Distribution Two parameters are used in this distribution: the expected mean value (µ) and the standard deviation (ό). Once these two values are known then the probability can be worked out. The normal distribution is bell shaped and can be used to calculate the other distributions, for example, binomial distribution. Figure 5.3.3: Normal Distribution Adapted from Valsamakis, A.C., Vivian, R.W., Du Toit, G.S. 2016. Risk Management. Cape Town: Pearson: p.63. The normal distribution has multiple uses. Take an example of 500 units with mean losses of R5 000 and a standard deviation of R500. The expected value of the pure premium is R5 000 (or the total budget to fund losses is R2.5 million). What is the likelihood that the cost of claims will exceed the size of the fund? There is 50 per cent probability that the fund will be depleted because of the symmetrical nature of the distribution. Another way to preserve the fund will be to set the premium at a higher level, this could be set as a multiple of the standard deviation, refer to Table 5.3.3. 36 Risk Assessment Models and Methodologies Educor © Table 5.3.3: Threshold Points for a Binomial Distribution Selected Premium Fund Size = Expected Value Plus Probability That the Fund Will Multiple of Standard Deviation Be Exhausted Expected value (µ) + 0ό R2 500 000 0.500 Expected value (µ) + 0.5ό R2 515 500 0.309 Expected value (µ) + 1ό R2 525 000 0.159 Expected value (µ) + 1.5ό R2 537 500 0.067 Expected value (µ) + 2ό R2 550 000 0.021 Expected value (µ) + 2.5ό R2 562 500 0.006 Expected value (µ) + 3ό R2 575 000 0.001 Expected value (µ) + 3.5ό R2 587 500 0.000 Adapted from Valsamakis, A.C., Vivian, R.W., Du Toit, G.S. 2016. Risk Management. Cape Town: Pearson: p.64. By using normal distribution to plot the binomial scores, it is now possible to determine the confidence level λ, for example, if λ = ό the confidence level will be 84.13 per cent. Poisson Distribution The Poisson distribution is similar to the binomial distribution in that it considers discrete distribution, making it appropriate in describing the possible number of accidents. Unlike the binomial, this is a single value-parameter distribution. The formula is: _𝑢 p(r) = µ𝑒 𝑟! µ – Average or expected value of accidents e – the base of natural logarithms (approximately 2.718) 𝑟! – r(r-1)(r-2)....(2)(1), with 0! p(r) = probability of each factor Poisson distribution approximates the binomial distribution where (N) is very large and (p) is very small, and expected value is Np = µ. For example, a ratio vehicle-kilometre may be used to assess the exposure to accidents which is a very small probability of happening from a single kilometre. This distribution can evaluate the possibility of multiple accidents from the same vehicle, which the binomial does not allow. An example can be used to understand the application of Poisson distribution in a worker’s day (one worker for one day) as a unit of exposure to worker injury for one day. Table 5.3.4 shows the Poisson distribution with an expected value (µ) of 2. In the example µ = 2 and e 2 = 0.1353. The standard deviation of a Poisson is the square root of its expected value: ό = √µ 37 Risk Assessment Models and Methodologies Educor © Table 5.3.4: Poisson Distribution Probability of 0 accidents (20)(0.1353)/0! 0.1353 Probability of 1 accidents (21)(0.1353)/1! 0.2706 Probability of 2 accidents (22)(0.1353)/2! 0.2706 Probability of 3 accidents (23)(0.1353)/3! 0.1804 Probability of 4 accidents (24)(0.1353)/4! 0.0902 Probability of 5 accidents (25)(0.1353)/5! 0.0361 Probability of 6 accidents (26)(0.1353)/6! 0.012 Probability of 7 accidents (27)(0.1353)/7! 0.0034 Probability of 8 accidents (28)(0.1353)/8! 0.009 Probability of 9 accidents (29)(0.1353)/9! 0.0002 Total 1.0078 Adapted from Valsamakis, A.C., Vivian, R.W., Du Toit, G.S. 2016. Risk Management. Cape Town: Pearson: p.66. The Poisson distribution becomes very difficult to compute when the number of accidents become larger. However, the normal distribution comes into play when there are large numbers to work out probability. Accuracy of Estimates To predict the outcome with some degree of certainty, then it is required that the distribution costs should be known or approximated to estimate the maximum probable cost (MPC), or to predict the outcomes under certain conditions. The accuracy of estimates is based on two requirements:  A known probability distribution of costs or an approximation and parameters that can be estimated; and  An estimation of risk tolerance or the chance of incorrect prediction. Assuming these are met then the following equation will apply: Probability threshold = required accuracy This can be illustrated in Figure 5.3.4. 38 Risk Assessment Models and Methodologies Educor © Figure 5.3.4: Example of Estimates Adapted from Valsamakis, A.C., Vivian, R.W., Du Toit, G.S. 2016. Risk Management. Cape Town: Pearson: p.67. 5.3.5. Expected Utility Criterion Utility theory attempts to explain why people make decisions differently from their EMV criterion. Bernoulli (1738) explains his theory in an example: a poor man finds a lottery ticket valued at R10 000, however, he could win up to R20 000 if he plays a game. In terms of the EMV theory the poor man should not expect less than R10 000. A wealthy man offers to buy the ticket from the poor man for R8 000. It is likely that the poor man might accept R8 000 for the ticket rather than play the game and lose, and get nothing. The man takes less than the EMV, which illustrates the way people make decisions. It does not follow a linear process. Marginal utility of wealth decreases as wealth increases. If the poor man values R8 000 as 1 utile, then in terms of the linear perception of money, R20 000 will be 2.5 utiles. If he plays the game then EMV is 1.25 utiles (R10 000) which is greater than 1 represented by R8 000. Therefore, he should play the game under these circumstances. Alternatively, if he views R20 000 as 2 utiles, then the EMV is 1 utile, which is R8 000. In this situation, it is better to sell the ticket for any amount higher than R8 000 and rather not gamble. This indicates that expected utility value (EUV) approach is similar to EMV criterion: EUV = Σp.U(W) Utility refers to an individual’s preference for goods and services. It is accepted that most people prefer more goods and services than less; generally, the more a person has, the less satisfaction (measured in utiles) will be experienced for every other unit of the goods. Hence, it is referred to as diminishing marginal utility as seen in Figure 5.3.5. 39 Risk Assessment Models and Methodologies Educor © Figure 5.3.5: Utility Curve Adapted from Valsamakis, A.C., Vivian, R.W., Du Toit, G.S. 2016. Risk Management. Cape Town: Pearson: p.69. The concept of utility is a personalised situation based on the many factors that affects a person’s decision such as wealth, age and income. 5.3.6. Maximin Decision Criterion In the maximin decision criterion, the parties all aim to win in the insurance scenario, however, it may be difficult and costly for the losing party. It would be disastrous if a fire were to occur and the company does not have insurance; one needs to avoid looking only at the favourable outcomes but to unfavourable circumstances (a fire) and select the best option faced with a worst-case scenario. This is known as maximin strategy; this follows the principle that a person will prefer wealth, which will influence his decision. When the maximin strategy is adopted the probabilities are ignored. If probabilities of events are assigned to various outcomes (expected losses and disutility) it will be different to the position where the objective is to minimise monetary loss. This can be applied to the purchase of insurance. Under this situation the cost of premiums will be higher than the expected losses. The resulting choice would be to favour purchase of insurance rather than retention of risk. Table 5.3.5: Maximin Decision Criterion States of Nature Pessimistic State of Nature (fire) Alternatives Fire No Fire No Insurance (R10 million) 0 (R10 million) Purchase Insurance (Pay (R8 000) (R8 000) (R8 000) Premium) Yes Purchase Insurance with (R105 000) (R5 000) (R105 000) R100 000 Deductible Adapted from Valsamakis, A.C., Vivian, R.W., Du Toit, G.S. 2016. Risk Management. Cape Town: Pearson: p.70. As indicated in Table 5.3.5, the decision would be to purchase insurance without deductible in the unintended event of a fire occurring. 40 Risk Assessment Models and Methodologies Educor © 5.3.7. Minimax Regret Decision Criterion Regret can be defined and quantified as the difference between the monetary loss of a course of action taken and the value of the outcome. This is the regret experienced after a resulting decision, giving rise to an outcome (normally a loss). Regret is often evaluated when performance is evaluated on decisions that resulted in losses. This applies to the purchase of insurance where a course of action is chosen to minimise the regret factor. This is played out by the level of regret when premiums are paid but no loss occurs; it is exceeded by the regret of loss incurred when no insurance is purchased. The level of regret influences the way decisions are made, often

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