Chapter 4 Pooling Arrangements and the Diversification of Risk

Chapter 4 Pooling Arrangements and the Diversification of Risk I. Multiple Choice 1. Which of the following is not a type of contracting cost associated with the creation and operation of pooling arrangements: a. b. c. d. distribution costs underwriting expenses premiums loss adjustment expenses Answer: c Type: K 2. Insurers that rely, to some degree, on exclusive agents to sell their policies are known as: a. b. c. d. mutuals direct writers independents brokers Answer: b Type: K 3. The process of identifying (or estimating) a potential insurance buyer’s expected loss is known as: a. b. c. d. underwriting risk management loss adjusting insurance distribution Answer: a Type: K 4. Insurance distribution costs may include all of the following except: a. b. c. d. advertising and marketing expenses agent commissions mailing costs underwriting expenses 146 Answer: d Type: A 5. Under what circumstance will a pooling arrangement result in reduced risk (standard deviation) to the participants in the pool? a. b. c. d. only when losses are perfectly positively correlated when losses are high only when losses are negatively correlated whenever losses are less than perfectly positively correlated Answer: d Type: K 6. According to the effect of the law of large numbers on a pooling arrangement, the greater the number of participants in the risk pool, a. the less likely the actual average loss will approach the expected (per participant) loss the more closely the actual average loss will approach the expected (per participant) loss the greater will be the skewness of the pool’s loss distribution the greater will be the pool’s correlation b. c. d. Answer: b Type: K 7. Bilbo has just purchased an insurance policy (and thereby joined a risk-pool). Bilbo paid an ex ante premium and did not give the insurer ex post assessment rights. These means a. b. Bilbo does not have the right to collect losses greater than his ex ante premium The insurer does not have the right to deny claims that are less than the agreed upon ex post amount. Bilbo is not required to assess the insurer. The insurer cannot request further premium from Bilbo should the risk-pool experience a bad loss. c. d. Answer: d Type: K 8. Risk-pooling arrangements a. b. c. reduce the risk faced by each member of the risk-pool increase the likelihood of small loss events are used only for liability exposures 147 d. will decrease expected loss for members of the risk pool Answer: a Type: K Dresden and Morgan both have the following loss distribution. Use this information to answer questions 9 through 11. Loss Possibility $0 $4,000 Loss Probability .90 .10 9. If Dresden and Morgan form a pooling arrangement to share losses, what is the expected loss for each of them after the pool is formed? a. b. c. d. $500 $450 $400 $360 Answer: c Type: A 10. If Dresden and Morgan form a pooling arrangement to share losses, what is the variance of expected losses for each of them after the pool is formed? a. b. c. d. $28 $280 $800 $4000 Answer: c Type: A 11. Which one of the following effects occurs when Dresden and Morgan form a riskpool to share losses? a. b. c. d. Their individual expected loss decreases, while the variance increases Their individual expected loss increases, while the variance decreases Their individual expected loss stays the same, while the variance increases Their individual expected loss stays the same, while the variance decreases Answer: d Type: A 148 12. The formation of risk pools by insurers is the same, in principle, as: a. b. c. d. reducing expected losses through the use of safety equipment creating a well-diversified portfolio of stock shares using the futures markets to hedge against fluctuations in the exchange rate of a particular foreign currency agreeing to an assessment premium Answer: b Type: A 13. Pooling arrangements are less effective when the participant’s losses are positively correlated. Which one of the following loss exposure examples will have the greatest positive correlation? a. b. c. d. Flood damage to homes in southern Louisiana Fire damage to homes in the metropolitan area of Houston Automobile property damage in Omaha Personal injury liability lawsuits filed in Minnesota Answer: a Type: A 14. The main (economic) reason for the existence of insurance companies is: a. b. c. d. individuals need to diversify risk insurers’ ability to predict individual losses insurers’ ability to form efficient risk pools with minimal contracting costs individuals inability to determine expected loss Answer: c Type: K 15. The contracting costs incurred when an insurer investigates and attempts to determine the value of loss claim made against the risk-pool are called a. b. c. d. distribution costs premiums underwriting expenses loss adjustment expenses Answer: d Type: K 149 II. Fill-Ins 1. The process of estimating a potential insured’s expected loss is known as underwriting . 2. Insurers that rely on exclusive agents, employees, or direct response methods are known as direct writers . 3. A pooling arrangement is less effective at reducing participants risk exposure if the participant losses are ___positively____ correlated. 4. Their ability to operate with an efficient level of __contracting ___ costs are the main reason that insurers exist and specialize in the formation of pooling arrangements. 5. The amount of risk reduction ___increases___ as more participants are added to a pooling arrangement, provided the losses are uncorrelated across participants. III Problems and Short Answer Questions 1. Explain the main economic functions of insurance institutions. Answer: The main economic function of insurance institutions is to provide an efficient mechanism for economizing on contracting costs associated with pooling of losses. Type: K 2. Compare insurer pooling arrangements with a well-diversified portfolios of stock shares. Answer: Insurance pools and well diversified stock portfolios are, in principle, nearly similar. Both are mechanisms for reducing risk. Predicting the outcome of a set of pooled (and uncorrelated) risks can be done more reliably than predicting the outcome of a single risk. The larger the number of risks in the pool, the smaller is the variance of expected outcomes. 3. Use the following table of information. Loss Outcome #1 Loss Outcome #2 Probability of Loss Outcomes Chayanee Yanisa .15 $1,500 $1,000 .85 $0 $100 150 a. b. c. What is Chayanee’s expected loss and standard deviation of expected loss? What is Yanisa’s expected loss and standard deviation of expected loss? Chayanee’s and Yanisa’s outcomes are independent of one another, so they decide to form a risk pool and share the losses equally. Construct a table displaying the Chayanee’s portion of the possible outcomes of the sharing arrangement and the probabilities thereof. What is the expected loss and standard deviation of expected loss for Chayanee’s outcome from the sharing arrangement? Answer: a. For Chayanee: Expected Losses 1,500(.15) 0(.85) Standard Deviation of Losses b. (1,500  225)2 (.15)  (0 225)2 (.85) $535.61 For Yanisa: Expected Losses 1,000(.15) 100(.85) 235 Standard Deviation of Losses c. 225 (1,000  235)2 (.15)  (0 235)2 (.85) $321.36 For the pooling arrangement: Possible Chayanee’s Loss Outcomes of Portion of the Pooling Arrangement Pooled Outcome 0 + 100 = $100 $50 0 + 1000 = $1,000 $500 1,500 + 100 = $1,600 $800 1,500 + 1,000 = $2,500 $1,250 Probabilities of Loss Outcomes (.85)(.85) = .7225 (.85)(.15) = .1275 (.15)(.85) = .1275 (.15)(.15) = .0225 Chayanee’s expected loss from the pooling arrangement: 50(.7225)  500(.1275)  800(.1275) 1,250(.0225) $230 Chayanee’s standard deviation of expected loss from the pooling arrangement: (50 230)  2 (.7225) (500   2(.1275) (800  230) 2  2 (.1275)  230) (1,250 230) (.0225) $312.31 4. Suppose that Peter Piper has a wholesale meat business similar to Jack Sprat and is exposed to an identical loss distribution from meat spoilage as defined in Problem 1. If Jack and Peter enter into a pooling agreement whereby they agree to split the costs of any losses that occur. a. Make a table that shows the possible total loss outcomes that Jack and Peter will have to split, with their associated probabilities. What is the expected value of each person’s loss share? Will the standard deviation of expected losses for each person in the pool be the same? Why or why not? b. c. 151 Answer: a. Possible Outcomes J($0) P($0) J($0) P($100) J($0) P($1,000) J($100) P($0) J($100) P($100) J($100) P($1,000) J($1,000) P($0) J($1,000) P($100) J($1,000) P($1,000) b. c. Probability .2 x .2 = .04 .2 x .6 = .12 .2 x .2 = .04 .6 x .2 = .12 .6 x .6 = .36 .6 x .2 = .12 .2 x .2 = .04 .2 x .6 = .12 .2 x .2 = .04 Total Loss $0 $100 $1,000 $100 $200 $1,100 $1,000 $1,100 $2,000 Loss to Each $0 $50 $500 $50 $100 $550 $500 $550 $1,000 Expected value for each participant = .04(0) + .12(50) + .04(500) + .12(50) + .36(100) + .12(550) + .04(500) + .12(550) + .04(1000) = $260 The standard deviation will be lower than $372 as long as Jack Sprat’s and Peter Pipers loss distributions are not perfectly correlated with each other. Type: A 5. Pooling arrangements are designed to reduce the risk to members of the pool. Explain the impact on risk reduction as the number of participants in the pool increase, all other factors equal. What happens to the expected cost of risk per participant as the pool size increases? Answer: The amount of risk that can be reduced through pooling arrangements increases as the number of participants increases, all other factors equal. The expected cost of risk per participant will stay the same. Type: K 152