Chapter 3 Risk Identification and Measurement

Chapter 3 Risk Identification and Measurement I. Multiple Choice 1. A listing of a random variable’s possible outcomes and the respective probabilities of those outcomes is called the: a. b. c. d. expected value standard deviation probability distribution correlation Answer: c Type: K 2. Multiplying each possible outcome of a random variable by its probability of occurrence, and then adding up these results will be equal to the random variable’s: a. b. c. d. expected value standard deviation probability distribution correlation Answer: a Type: K Probability B A Loss 3. The graph above depicts the probability distributions for risks A and B. Based on the graph, which of the following statements is true? a. The expected value of loss for risk A is larger than the expected value of loss for risk B. 138 b. c. d. The expected value of loss for risk B is larger than the expected value of loss for risk A. The standard deviation of expected losses for risk A is larger than the standard deviation of losses for risk B. The standard deviation of expected losses for risk B is larger than the standard deviation of losses for risk A. Answer: a Type: A Use this table to answer questions 4 through 7: Loss Distribution X Outcome Probability $0 .60 $1,000 .25 $5,000 .15 Loss Distribution Y Outcome Probability $0 .40 $1,000 .50 $5,000 .10 4. Which distribution has the highest expected value? a. b. c. d. Distribution X Distribution Y Both have the same expected value There is not enough information to answer this question. Answer: c Type: A 5. All other factors equal, which distribution is the most risky? a. b. c. d. Distribution X Distribution Y Both distributions have equivalent risk Both distributions have zero risk. Answer: a Type: A 6. In which distribution is there a higher likelihood that the outcome will be close to the expected value of $1,000? a. b. c. Distribution X Distribution Y The likelihood that outcomes will be close to the expected value is the same for both distributions. 139 d. There is not enough information to answer this question. Answer: b Type: A 7. Which distribution(s) exhibit(s) skewness? a. b. c. d. Distribution X only Distribution Y only Both X and Y are skewed. Neither distribution is skewed. Answer: c Type: A 8. Which type of risk would you expect to have the most skewed probability distribution? (Assume a time period of one year.) a. b. c. d. product liability claims for a drug manufacturer shoplifting losses for a small bookstore collision damage to vehicles for a delivery service employee injuries in a grocery store Answer: a Type: A 9. Which of the following pairs of random variables are likely to be uncorrelated? a. total health care costs in New York City for 1997; total health care costs in New York City for 1998 total property damage due to wildfires in Colorado in 1997; total property damage due to wildfires in California in 1998. number of people who die from cancer in the US in 1997; number of people who die from cancer in the US in 1998. worker injuries at a shoe manufacturing plant owned and managed by Exodus Incorporated; worker injuries at a different shoe manufacturing plant owned and managed by Exodus Incorporated. b. c. d. Answer: b Type: A 10. Unidentified risk exposures will result in: a. b. c. reduced insurance premiums increased insurance premiums implicit retention 140 d. purchasing too much insurance Answer: c Type: K 11. When estimating property loss exposure, which of the following methods for valuing property is the least relevant measure for risk managers? a. b. c. d. book value market value firm specific value replacement cost Answer: a Type: K 12. The number of losses in a given period of time is known as: a. b. c. d. loss severity loss frequency total losses the loss distribution Answer: b Type: K 13. The magnitude of loss per occurrence is known as: a. b. c. d. loss severity loss frequency total losses the loss distribution Answer: a Type: K 14. The expected loss per exposure is: a. b. c. d. the expected frequency per exposure. the expected severity per occurrence. the expected frequency per exposure times the expected severity per occurrence all divided by the number of exposures. the expected frequency per exposure times the expected severity per occurrence. Answer: d Type: K 141 15. Darunee Inc. has estimated that ½ of their twenty workers will be injured in the coming year. The expected severity per occurrence is $1,000. What is the expected loss per exposure? a. b. c. d. $1,000 $10 $10,000 $500 Answer: d Type: K 16. Which of the following is not a key feature of loss distributions that would be considered by risk managers? a. b. c. d. expected value standard deviation maximum probable loss least probable loss Answer: d Type: K II. Fill-Ins 1. A random variable is a variable whose outcome is uncertain. 2. A probability distribution identifies all the possible outcomes for a random variable and the probability of each outcome. 3. A common statistical measure of the risk of a random variable is the ___standard deviation (or variance)___. 4. If a probability distribution is not symmetrical, as in the case of liability losses, the distribution is said to be skewed . 5. A firm that is concerned about losses due to temporary shut-down of its manufacturing facility following a fire can purchase ___business interruption___ insurance. III Problems and Short Answer Questions 1. Jack Sprat Wholesale Meats, Inc. is faced with the following probability distribution for losses due to meat spoilage: 142 Possible Losses $0 $100 $1000 a. b. c. Probability .20 .60 .20 What is Jack Sprat’s expected loss due to meat spoilage? What is the standard deviation of expected losses due to meat spoilage? Draw a probability distribution for Jack Sprat’s meat spoilage losses. Answer: a. Expected loss due to meat spoilage = (.2)($0) + (.6)($100) + (.2)($1000) = $260 b. Standard deviation of expected loss due to meat spoilage = [(.2)(0-260)2 + (.6)(100-260)2 + (.2)(1000-260)2]1/2 = 37 0.7 0.6 0.5 0.4 Probability 0.3 0.2 0.1 0 c. Type: A 2. Trumpet Manufacturing owns real estate valued at $500,000. They estimate that their property losses have the following distribution: Loss Equals a. b. $500,000 $100,000 $25,000 $1,000 $0 with probability .001 with probability .010 with probability .050 with probability .100 with probability .839 What is the expected value of Trumpet Manufacturing’s losses? If insurance for this loss were available for a price of $3,000 per year, do you think that Trumpet would want to buy it? Why or why not? 143 Answer: a. The expected cost is: ($500,000)(.001) + ($100,000)(.010) + ($25,000)(.050) + ($1,000)(.1) + (0)(.839) = $2,850. b. If insurance were available for $3,000, the company would probably want to buy it. Although it is slightly more expensive than the expected cost of the loss, since the firm is exposed to very high potential losses, they will probably be willing to incur a little higher cost to reduce this risk. Type: A 3. Skewness measures what characteristic of a loss distribution? Why are skewed distributions relevant to risk managers? Answer: Skewness measures the symmetry of a distribution. The normal distribution is symmetrical so it has zero skewness. Skewed distributions are very relevant to risk managers simply because many individual businesses face skewed loss distributions. A skewed loss distribution has a higher probability of very low losses, and a lower probability of very large losses. During a given year, most businesses experience relatively small losses, if any, while a small number of firms will experience large losses. Type: A 4. Over the last 7 years, East Eagle Company has averaged 10,000 employees per year, 641 worker injuries (on the job) at an annual average cost of $134,369. Using this data a. b. c. Compute the probability of a worker suffering an on-the-job injury Compute the average injury severity Compute the expected loss per worker Answer:  641   6.41% a.  10,000  $134,369   $209.62 b.   641  c. (.0641)($209.62)=$13.44 Type: K 144 5. Fill-in the second column of the following table to indicate if the specific variables, or exposures, for the identified group(s) or context are most likely positively correlated, negatively correlated, or uncorrelated. Variables or Exposure Unemployment amongst a group of factory workers The number of auto accidents, in a given year, for each resident of Omaha Natural gas demand and winter temperatures in Minnesota Total damage from house fires in South Dakota and total damage from house fires in Arizona Number of days with rainfall and volume of paying customers at a public outdoor swimming pool. Flood damages to homes in Southern Louisiana. Correlation Answer: Variables or Exposure Unemployment amongst a group of factory workers The number of auto accidents, in a given year, for each resident of Omaha Natural gas demand and winter temperatures in Minnesota Total damage from house fires in South Dakota and total damage from house fires in Arizona Number of days with rainfall and volume of paying customers at a public outdoor swimming pool. Flood damages to homes in Southern Louisiana. Type: A 145 Correlation positive uncorrelated positive uncorrelated negative positive