02-Risk Identification and Evaluation

Risk Identification and Evaluation Chapter 2 Shanghai Institute of Foreign Trade2 Chapter Objectives Explain several methods for identifying risks Identify the important elements in risk evaluation Explain three different measures of variation Explain three different measures of central tendency Discuss the concepts of a probability distribution and explain the importance to risk managers Shanghai Institute of Foreign Trade Chapter Objectives Give examples of how risk managers might use the normal, binomial, and Poisson distributions Explain how the concepts of risk mapping and value at risk are used in an enterprise-wide evaluation of risk Explain the importance of the law of large numbers for risk management Apply the risk assessment methods to financial instruments 3Fall 2011 Shanghai Institute of Foreign Trade4 Risk Identification Loss exposure  Potential loss that may be associated with a specific type of risk  Can be categorized as to whether they result from  Property  Liability  Life  Health  Loss from income risks Shanghai Institute of Foreign Trade5 Risk Identification Loss exposure Checklists  Specifies numerous potential sources of loss from the destruction of assets and from legal liability  Some are designed for specific industries  Such as manufacturers, retailers, educational institutions, religious organizations  Others focus on a specific category of exposure  Such as real and personal property Shanghai Institute of Foreign Trade6 Risk Identification Financial statement analysis  All items on a firm’s balance sheet and income statement are analyzed in regard to risks that may be present Flowcharts  Allows risk managers to pinpoint areas of potential losses  Only through careful inspection of the entire production process can the full range of loss exposures be identified Shanghai Institute of Foreign Trade7 Figure 2-1: Flowchart for a Production Process Shanghai Institute of Foreign Trade8 Risk Identification Contract analysis  It is not unusual for contracts to state that some losses, if they occur, are to be borne by specific parties  May be found in construction contracts, sales contracts and lease agreements  Ideally the specification of who is to pay for various losses should be a conscious decision that is made as part of the overall contract negotiation process  Decision should reflect the comparative advantage of each party in managing and bearing the risk Shanghai Institute of Foreign Trade Risk Identification On-site inspections  During these visits, it can be helpful to talk with department managers and other employees regarding their activities Statistical analysis of past losses  Can use a risk management information system (software) to assist in performing this task  As these systems become more sophisticated and user friendly , it is anticipated that more businesses will be able to use statistical analysis in their risk management activities 9Fall 2011 Shanghai Institute of Foreign Trade10 Risk Evaluation Risk analysis is applied to situations with multiple, uncertain outcomes.  The first task of risk analysis is to specify the relevant outcomes.  The second task is to estimate the probability distribution of outcomes.  The third task of risk analysis is to evaluate uncertain outcomes in order to facilitate choice. Shanghai Institute of Foreign Trade Risk Mapping or Profiling  Involves arraying risks in a matrix  With one dimension being the frequency of events and the other dimension the severity Each risk is marked to indicate whether it is covered by insurance or not 11Fall 2011 Shanghai Institute of Foreign Trade12 Statistical Concepts Probability  Long term frequency of occurrence  The probability is 0 for an event that is certain not to occur  The probability is 1 for an event that is certain to occur  To calculate the probability of any event, the number of times a given event occurs is divided by all possible events of that type  Probability distribution  Mutually exclusive and collectively exhaustive list of all events that can result from a chance process  Contains the probability associated with each event Shanghai Institute of Foreign Trade13 Statistical Concepts Measures of central tendency or location  Measuring the center of a probability distribution  Mean Sum of a set of n measurements divided by n Shanghai Institute of Foreign Trade14 Statistical Concepts Median  Midpoint in a range of measurements  Half of the items are larger and half are smaller  Not greatly affected by extreme values Mode  Value of the variable that occurs most often in a frequency distribution Shanghai Institute of Foreign Trade15 Probability Assessment Underlying our analysis of risk is the concept of probability. Probability principles, we argue, help us make better decisions in the face of uncertainty because it allows us to assess the likelihood of an event happening. A probability is an estimate of a proportion of outcomes in which a specified condition is expected to occur. Shanghai Institute of Foreign Trade16 Having assumed knowledge of probability in our definition of risk, I now want to briefly discuss how statisticians calculate probability.  Frequency definition of probability  Subjective definition of probability Probability Assessment Shanghai Institute of Foreign Trade17 Frequency Definition of Probability The frequency definition of probability is the proportion of times an event occurs over the long run if the experiment is repeated many times under uniform conditions.  The information used to estimate probability will come from historical data via case studies or statistical analysis.  Frequency, variance and covariance can be estimated with historical data that allows us to estimate expected value and risk. Shanghai Institute of Foreign Trade18 In general, if an experiment is repeated a very large number of times M, and if event A occurs m times, the probability of A is P(A) = m / M Based on this definition of probability, the following three fundamental propositions must be true:  The probability of an impossible event must be zero;  The probability of an event that is certain must equal 1;  The probability of any event must be no less than zero and no greater than one. Frequency Definition of Probability Shanghai Institute of Foreign Trade19 Subjective Definition of Probability Some experiments are not easy to interpret in frequency terms because they cannot be repeated over and over. There are many events of this type in business and economics. In dealing with experiments of this type, decision makers and statisticians often use a subjective definition of probability. Shanghai Institute of Foreign Trade20 In this definition, the probability of an event is the degree of confidence or belief on the part of the statistician or decision maker that the event will occur. We use whatever information we have to form a subjective probability if we don’t have a history that allows us to calculate the frequency. Subjective probability is our best estimate of the likelihood that an outcome will occur. Subjective Definition of Probability Shanghai Institute of Foreign Trade21 Probability Distribution A probability distribution relates the probability of occurrence to each possible outcome. Where outcomes are mutually exclusive and exhaustive, exactly one of these outcomes will occur with certainty, and the probabilities must add up to 100%. Mutually exclusive means that only one of these outcomes can occur at a given time; mutually exhaustive means that no other outcomes can occur than those listed are possible. Shanghai Institute of Foreign Trade 22 Measures of Variation or Dispersion  Standard deviation  Measures how all close a group of individual measurements is to its expected value or mean Coefficient of variation  Standard deviation expressed as a percentage of the mean Shanghai Institute of Foreign Trade 23 Table 2-1: Calculating the Standard Deviation of Losses Shanghai Institute of Foreign Trade24 Loss Distributions Used in Risk Management To form an empirical probability distribution  Risk manager actually observes the events that occur To create a theoretical probability distribution  Use a mathematical formula  Widely used theoretical distributions include binomial, normal, Poisson Shanghai Institute of Foreign Trade25 The Binomial Distribution Suppose the probability that an event will occur at any point in time is p  The probability q that an event will not occur can be stated as 1 – p One can calculate how often an event will happen with the binomial formula  Indicates that the probability of r events in n possible times equals Shanghai Institute of Foreign Trade26 The Normal Distribution  Central limit theorem  States that the expected results for a pool or portfolio of independent observations can be approximated by the normal distribution  Shown graphically in Figure 3.2  Perfectly bell-shaped  If risk managers know that their loss distributions are normal  They can assume that these relationships hold  They can predict the probability of a given loss level occurring or the probability of losses being within a certain range of the mean  Binomial distributions require variables to be discreet  Normal distributions can have continuous variables Shanghai Institute of Foreign Trade27 Figure 3-2: Normal Probability Distribution of 500 Losses Shanghai Institute of Foreign Trade28 The Poisson Distribution Determine the probability of an event using the following formula  Mean of the distribution is also its variance  Standard deviation is equal to the square root of m  p = probability that an event n occurs  r = number of events for which the probability estimate is needed  m = mean = expected loss frequency  e = a constant, the base of the natural logarithms, equal to 2.71828 Shanghai Institute of Foreign Trade29 The Poisson Distribution As the number of exposure units increases and the probability of loss decreases  The binomial distribution becomes more and more like the Poisson distribution Most desirable when more than 50 independent exposure units exist and  The probability that any one item will suffer a loss is 0.1 or less Shanghai Institute of Foreign Trade 30 Integrated Risk Measures Value at risk (VAR)  Constructs probability distributions of the risks alone and in various combinations  To obtain estimates of the risk of loss at various probability levels  Yields a numerical statement of the maximum expected loss in a specific time and at a given probability level  Provides the firm with an assessment of the overall impact of risk on the firm  Considers correlation between different categories of risk Shanghai Institute of Foreign Trade Integrated Risk Measures Risk-adjusted return on capital  Attempts to allocate risk costs to the many different activities of the firm  Assesses how much capital would be required by the organization’s various activities to keep the probability of bankruptcy below a specified level 31Fall 2011 Shanghai Institute of Foreign Trade 32 Accuracy of Predictions A question of interest to risk managers  How many individual exposure units are necessary before a given degree of accuracy can be achieved in obtaining an actual loss frequency that is close to the expected loss frequency? The number of losses for particular firm must be fairly large to accurately predict future losses Shanghai Institute of Foreign Trade 33 Law of Large Numbers Degree of objective risk is meaningful only when the group is fairly large States that as the number of exposure units increases  The more likely it becomes that actual loss experience will equal probable loss experience Two most important applications  As the number of exposure units increases, the degree of risk decreases  Given a constant number of exposure units, as the chance of loss increases, the degree of risk decreases Shanghai Institute of Foreign Trade 34 Number of Exposure Units Required Question arises as to how much error is introduced when a group is not sufficiently large Required assumption  Each loss occurs independently of each other loss, and the probability of losses is constant from occurrence to occurrence Formula is based on knowledge that the normal distribution is an approximation of the binomial distribution  Known percentages of losses will fall within 1, 2, 3, or more standard deviations of the mean Shanghai Institute of Foreign Trade 35 Number of Exposure Units Required Value of S indicates the level of confidence that can be stated for the results  If S is 1  It is known with 68 percent confidence that losses will be as predicted  If S is 2  It is known with 95 percent confidence Fundamental truth about risk management  If the probability of loss is small a larger number of exposure units is needed for an acceptable degree of risk than is commonly recognized Risk Identification and �Evaluation Chapter Objectives Chapter Objectives Risk Identification Risk Identification Risk Identification Figure 2-1: Flowchart for a Production Process Risk Identification Risk Identification Risk Evaluation Risk Mapping or Profiling Statistical Concepts Statistical Concepts Statistical Concepts Probability Assessment 幻灯片编号 16 Frequency Definition of Probability 幻灯片编号 18 Subjective Definition of Probability Probability Distribution Measures of Variation or Dispersion Table 2-1: Calculating the Standard Deviation of Losses Loss Distributions Used in Risk Management The Binomial Distribution The Normal Distribution Figure 3-2: Normal Probability Distribution of 500 Losses The Poisson Distribution The Poisson Distribution Integrated Risk Measures Integrated Risk Measures Accuracy of Predictions Law of Large Numbers Number of Exposure Units Required Number of Exposure Units Required 幻灯片编号 36