Mark CPCU 500 Ch. 2

7-4. Assume that ABC Manufacturing's total losses per year are normally distributed. The average (mean) of the firm's losses is $500,000 and the standard deviation is $40,000. Assuming underlying conditions do not change, what is the probability that its losses next year will be between $460,000 and $540,000? What is the probability that its losses next year will be between $500,000 and $540,000?

1 Standard deviation of $40,000 = 34.13% Probability of $460,000 and $540,000 = 1 SD above (34.13%) + below (34.13%) = 68.23% Probability of $500,000 and $540,000 = 1 SD above (34.13%)

5-1. Describe the mean, median, mode and how a risk management professional uses them in assessing loss expectations.

Mean: is the numeric average (the sum of the values in a data set divided by the number o values), of often used by a risk management professional as the single best guess to forecast future events. Median: is the value at the midpoint of a sequential data set with an odd number of values, or the mean of the two middle values. A risk management professional might use the median in selecting retention levels or in selecting upper limits of insurance coverage. Mode: is the most frequently occurring value in a distribution. Knowing the mode of a distribution allows insurance and risk management professionals to focus on the outcomes that are the most common.

8-4. Describe two approaches a risk management professional may use when jointly analyzing the frequency and loss severity of a loss exposure.

One method of jointly considering both loss frequency and loss severity is the Prouty Approach, which identifies four broad categories of loss frequency and three broad categories of loss severity. Another method is more statistically based and involves combining frequency and severity distributions to create a single total claims distribution.

3-2. Identify two conditions in which probability analysis is effective for projecting losses.

Probability analysis is particularly effective for projecting losses in organizations that have (1) a substantial volume of data on past losses and (2) fairly stable operations so that (except for price level changes) patterns of past losses presumably will continue in the future.

Theoretical probability

Probability that is based on theoretical principles rather than on actual experience.

8-2. List the four categories of loss frequency and the three categories of loss severity used in the Prouty Approach.

The Prouty Approach entails four categories of loss frequency: - Almost nil -- extremely unlikely to happen; virtually no possibility - Slight -- could happen but has not happened - Moderate -- happens occasionally - Definite -- happens regularly There are three categories of loss severity: - Slight -- Organization can readily retain each loss exposure. - Significant -- Organization cannot reain the loss exposure, some part of which must be financed. - Severe -- Organization must finance virtually all of the loss exposure or endanger its survival.

8-1. List four dimensions used in the analysis of a loss exposure.

The analysis step of the risk management process involves considering the four dimension of a loss exposure: - Loss frequency -- the number of losses (such as fires, auto accidents, or liability claims) that occur during a specific period - Loss severity -- the dollar amount of loss for a specific occurrence. - Total dollar losses -- the total dollar amount of losses for all occurrences duringa specific period. - Timing -- the points at which losses occur and loss payments are made. (The period between loss occurrence and loss payment can be lengthy.)

7-3. Describe how the expected value and the standard deviation of a normal distribution can be helpful in making risk management decisions.

The characteristics of the expected value and standard deviation of a normal distribution can help management select an acceptable probability for loss and aid in scheduling maintenance or selecting retention levels on various loss exposures (pg 2.38)

6-2. Describe coefficient of variation and how insurance and risk management professionals use it in assessing loss exposures.

The coefficient of variation is a further measure of the dispersion of a distribution. Insurance and risk management professionals can use the coefficient of variation to determine whether a particular loss control measure has made losses more or less predictable (that is, whether the distribution is more or less variable). It can help an underwriter determine to which account to offer coverage if the means are the same.

Income statement

The financial statement that reports an organization's profit or loss for a specific period by comparing the revenues generated with the expenses incurred to produce those revenues.

Balance Sheet

The financial statement that reports the assets, liabilities, and owners' equity of an organization as of a specific date.

Statement of cash flows

The financial statement that summarizes the cash effects of an organization's operating, investing, and financing activities during a specific period.

3-3. List three criteria necessary to accurately forecast future events based on the law of large numbers.

The law of large numbers can be used to more accurately forecast future events only when the events being forecast meet all three of these criteria: - The events have occurred in the past under substantially identical conditions and have resulted from unchanging, basic casual forces. - The events can be expected to occur in the future under the same, unchanging conditions. - The events have been, and will continue to be, both independent of one another and sufficiently numerous.

Mode

The most frequently occurring value in a distribution.

7-1. Describe a normal distribution and why it is useful to a risk management professional in forecasting loss exposures.

The normal distribution is a probability that, when graphed, generates a bell-shaped curve. This particular probability distribution can help to accurately forecast the variability around some central, average, or expected value and has therefore proven useful in accurately forecasting the variability of many physical phenomena.

Indemnification

The process of restoring an individual or organization to a pre-loss financial condition.

Central tendency

The single outcome that is the most representative of all possible outcomes included within a probability distribution.

6-1. Describe the standard deviation and how insurance and risk management professionals use it in assessing loss exposures.

The standard deviation is the average of the differences (deviations) between the values in a distribution and the expected value (or mean) of that distribution. The standard deviation indicates how widely dispersed the values in a distribution are. It provides a measure of how sure an insurance or risk management professional can be in projecting the frequency or severity of losses.

6-3. Describe the steps used for calculating the standard deviation of a set of individual outcomes not involving probabilities.

The steps for calculating the standard deviation of a set of individual outcomes not involving probabilities (actual loss data vs theoretical) are these: 1. Calculate the mean of the outcomes (the sum of the outcomes divided by the number of outcomes) 2. Subtract the mean from each of the outcomes 3. Square each of the resulting differences 4. Sum these squares 5. Divide this sum by the number of outcomes minus one (this value is called the variance) 6. Calculate the square root of the variance

Mean

The sum of the values in a data set divided by the number of values.

8-5. Explain why timing is an important consideration when analyzing loss exposure.

The timing diension is significant because money held in reserve to pay for a loss can earn interest until the actual payment is made. In addition, when a loss is counted affects accounting and tax treatment.

5-4. The underwriter at Millwright Insurance must choose between two accounts to provide insurance coverage. Both accounts have provided a probability distribution based on past losses. Account A's distribution has a mean of $8,500. Account B's distribution has a mean of $10,000. Which account has higher expected losses?

The underwriter's decision regarding Millwright Insurance accounts A and B considers, among other things, the expected losses of each account, which are higher for Account B because the mean of past losses for it is $10,000 and only $8,500 for A.

Median

The value at the midpoint of a sequential data set with an odd number of values, or the mean of the two middle values of a sequential data set with an even number of values.

Dispersion

The variation among values in a distribution

Expected value

The weighted average of all of the possible outcomes of a probability distribution. (expected outcomes x probability) + (expected outcome x probability)

3-1. Explain the difference between theoretical and empirical probabilities.

Theoretical probability is probability that is based on theoretical principles rather than on actual experience. (coin toss) They are constant as long as the physical conditions that generate them remain unchanged. Empirical probability is probability that is based on actual experience. (historical data) They're only estimates whose accuracy depends on size and representative nature of the samples being studied.

8-3. List the three categories of loss severity used in the Prouty Approach.

There are three categories of loss severity: - Slight -- Organization can readily retain each loss exposure. - Significant -- Organization cannot reain the loss exposure, some part of which must be financed. - Severe -- Organization must finance virtually all of the loss exposure or endanger its survival.

1-2. Describe advantages and disadvantages of using questionnaires in assessing loss exposures.

These standardized documents broadly categorize the loss exposures that most organizations typically face. A questionnaire captures more descriptive information than a checklist, identifying a loss exposure and information about the amounts or values exposed to loss. Their disadvantage is that they typically require considerable expense, time, and effort to complete and may still not identify all loss exposures or may not reveal key information on the simple answers given.

4-4. Construct an empirical probability distribution from the following array of workers compensation losses.

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1-4. Describe how a compliance review may facilitate the identification of loss exposures.

A compliance review determines an organization's compliance with local, state, and federal statues and regulations. The benefit of compliance reviews is that they can help an organization minimize or avoid liability loss exposures.

Hold-harmless agreement (or indemnity agreement)

A contractual provision that obligates one of the parties to assume the legal liability of another party.

Law of large numbers

A mathematical principle stating that as the number of similar but independent exposure units increases, the relative accuracy of productions about future outcomes (losses) also increases.

Standard deviation

A measure of dispersion between the values in a distribution and the expected value (or mean) of that distribution, calculated by taking the square root of the variance.

Coefficient of variation

A measure of dispersion calculated by dividing a distribution's standard deviation by its mean. SD/meanX100%

Hazard analysis

A method of analysis that identifies conditions that increase the frequency or severity of loss.

Probability distribution

A presentation (table, chart, or graph) of probability estimates of a particular set of circumstances and of the probability of each possible outcome.

Normal distribution

A probability distribution that, when graphed, generates a bell-shaped curve.

Empirical probability (a posteriori probability)

A probability measure that is based on actual experience through historical data or from the observation of facts.

Probability analysis

A technique for forecasting events, such as accidental and business losses, on the assumption that they are governed by an unchanging probability distribution.

6-5. The underwriter at Millwright Insurance must choose between two accounts to provide insurance coverage. Both accounts have provided a probability distribution based on past losses. Accounts A's distribution has a mean of $8,500 and a standard deviation of $17,000. Account B's distribution has a mean of $10,000 and a standard deviation of $18,000. Which account has greater variability relative to its mean?

Account A: 17,000 / 8,500 = 2 Account B: 18,000 / 10,000 = 1.8 Account A has greater variability.

1-1. Identify the types of internal and external documents an organization may use to analyze loss exposures.

An organization may use the following types of internal and external documents to analyze loss exposures: - Internal documents -- financial statements, accounting records, contracts, insurance policies, policy and procedure manuals, flowcharts and organizational charts, and loss histories. - External documents -- questionnaires, checklists, and surveys, Web sites, news releases, or reports from external organizations.

4-2. List two requirements to construct an empirical probability distribution.

Empirical probability distributions (estimated from historical data) are constructed in the same way as theoretical probability distributions: The first requirement of a probability distribution is that it provide a mutually exclusive, collectively exhaustive (all outcomes are accounted for) list of outcomes with categories (bins) designed so that all losses can be included. The second requirement of a probability distribution is that it define the set of probabilities associated with each of the possible outcomes (like percentage of losses).

7-2. In a normal distribution, what percentage of outcomes is within two standard deviations above or below the mean?

For a normal distribution, 34.13 % of all outcomes are within one standard deviation above and below the mean. The portion of a normal distribution that is between one and two standard deviations above the mean contiains 13.59% of all outcomes. Consequently, 95.44 percent of all outcomes are within two standard deviations above or below the mean.

2-2. Describe how complete data can aid a risk management professional in loss exposure assessment.

Having complete information (from inside and outside the organization) helps to isolate the cause of each loss. Furthermore, having complete data enables the risk management professional to make reasonably reliable estimates of the dollar amounts of the future losses.

8-6. Describe the dilemma that insurance and risk management professionals can have when evaluating data credibility.

Insurance and risk management professionals can be left with a dilemma answering whether it is better to use older data, which are accurate but may have been generated in an environment that is substantially different from that of the period for which they are trying to predict, or to use more recent data and sacrifice some accuracy to maintain the integrety of the environment.

6-4. Explain what insurance and risk management professionals can use the coefficient of variation for when evaluating a particular loss control measure.

Insurance and risk management professionals can use the coefficient of variation to determine whether a particular loss control measure has made losses more or less predictable (that is, whether the distribution is more or less variable).

5-2. Explain how calculating the expected value is similar to calculating the mean.

Just as the expected value is calculated by weighting each possible outcome by its probability, the mean is calculated by weighting each observed outcome by the relative frequency with which it occurs.

5-3. Explain what knowing the mode of a distribution allows insurance and risk management professionals to do.

Knowing the mode of a distribution allows insurance and risk management professionals to focus on the outcomes that are the most common. For example, knowing that the most common auto physical damage losses are in the $0-$10,000 range may influence the risk financing decisions regarding deductible levels for potential insurance coverage.

4-1. Identify outcome characteristics common to both theoretical and empirical possibility distributions.

Characteristics common to outcomes of both theoretical and empirical probabilities are that the outcomes are mutually exclusive and collectively exhaustive.

2-3. Identify two factors in past loss data that must be consistent to avoid underestimating loss projections.

To reflect past patterns, loss data must also be consistent in at least two aspects to avoid underestimating loss projections: 1) The loss data must be collected on a consistent basis (same accounting methods) for all recorded losses. e.g. Estimates vs actual paid amounts 2) Data must be expressed in constant dollars, to adjust for differences in price levels that may lead to inconsistency. e.g. inflation

4-3. Describe the following two forms of probability distributions and how they are used in analyzing future losses. a. Discrete probability distributions b. Continuous probability distribution

a. Discrete probability distributions have a finite number of possible outcomes and are used to analyze how often something will occur (frequency distributions) b. Continuous probability distributions have an infinite number of possible outcomes and are used for severity distributions (depict the value of the loss rather than the number of outcomes.)

2-1. Identify relevant data an organization may use to assess the following types of loss exposures: a. Property losses b. Liability losses c. Personnel losses d. Net income losses

a. Relevant data for property losses include the property's repair or replacement cost at the time it is to be restored. b. For liability losses, the data should relate to past claims that are substantially the same as the potential future claims being assessed. c. Data to analyze personnel loss exposures must relate to personnel with similar experience and expertise as those being considered as future loss exposures. d. The appropriate data for considering net income loss exposures would depend on the type of loss exposure being analyzed. The data should involve similar reductions in revenue and similar additional expenses as would those loss exposures under consideration.

1-3. Describe how an organization uses the following documents to identify loss exposures. a. Financial Statements b. Contracts c. Insurance policies d. Organizational policies and records e. Flowcharts and organizational charts f. Loss histories

a. Risk management professionals sometimes begin the loss exposure identification process by reviewing an organization's financial statements, including the balance sheet, income statement, statement of cash flows, and supporting statements because it identifies current loss exposures and can be used to identify any future plans that could lead to new loss exposures. For example, asset entries on a balance sheet indicate property values that could be reduced by loss. b. Analyzing an organization's contracts may help identify its property and liability loss exposures and can help determine who has assumed responsibility for which loss exposures. c. Analyzing insurance policies reveals many of the insurable loss exposures that an organization faces. d. Corporate by-laws, board minutes, employee manuals, procedure manuals, mission statements, and risk management policies may identify existing loss exposures and indicate impending changes that may create new loss exposures. e. An organization can use flowcharts to show the nature and use of the resources involved in its operations as well as the sequence of and relationships between those operations. Flowcharts can help identify loss exposures/critical loss exposures. They may also reveal bottlenecks where losses could have substantial effects on business operations. An organizational chart helps identify key personnel for whom the organization may have a personnel loss exposure. f. Loss history analysis, that is, reviewing an organization's own losses or those suffered by comparable organizations, can help a risk management or an insurance professional to both identify and analyze current or future loss exposures .

2-4. The risk management professional of ABC Manufacturing has the following data for losses that have occurred during 2009: a. If the risk management professional of ABC Manufacturing were trying to analyze employee injuries for workers compensation purposes, what data are relevant? b. Are the data provided complete? c. Are the data consistent? d. Organize the employee injury data into an array.

a. The relevant data are the 3/17 sales rep injury, the 5/21 assembly line worker injury, and the 8/11 office worker injury. b. The data are not complete; they do not list the specific cause, time of loss, or treatments used. c. Because all the data are 2009 data, they are consistent. d. An array of losses are amounts of losses listed in increasing or decreasing value and could reveal clusters of losses by severity and could focus attention on large losses 8/11/09; $500 3/17/09; $800 5/21/09; $7000