Chapter 9 Risk Aversion and Risk Management by Individuals and Corporations

Chapter 9 Risk Aversion and Risk Management by Individuals and Corporations I. Multiple Choice 1. The major underlying force that motivates individuals to purchase insurance even though insurance premiums exceed expected claim costs is: a. b. c. d. profit risk aversion expected losses premium loadings Answer: b Type: K 2. An individual’s demand for insurance depends on all of the following factors except: a. b. c. d. income wealth premium loading portfolio return Answer: d Type: K 3. Suppose that you have $20,000 in wealth and face a 20% chance of losing $10,000. Without insurance, your possible wealth outcomes are: a. b. c. d. $20,000, $18,000 $20,000, $10,000 $10,000, $2,000 $20,000, $18,000 Answer: b Type: A 4. Using the same scenario in Question #3, what is the expected value of your wealth without insurance? a. b. c. d. $20,000 $10,000 $18,000 $16,000 153 Answer: c Type: A 5. Using the same scenario in Question #3, if you purchase $10,000 in insurance coverage for a price of $2,500, what are your possible wealth outcomes? (Assume that the premium would be paid at the end of the year and that the loss would occur at the end of the year so that you can ignore the time value of money.) a. b. c. d. $20,000, $10,000 $17,500 $17,500, $7,500 $18,000 Answer: b Type: A 6. An example of a non-monetary loss is: a. b. c. d. children’s funeral costs damage to your automobile which isn’t covered by your insurance pain and suffering loss of time at work Answer: c Type: A 7. Suppose that an insurance company views Jennifer as having the following distribution for the present value of losses: Loss = $10,000 $2,000 $500 $0 with probability .10 with probability .20 with probability .50 with probability .20 What is the fair premium for full coverage if the insurer’s competitive loading for administrative costs and capital costs is 10% of expected discounted claims? a. b. c. d. $1,815 $1,650 $825 $165 Answer: a Type: A 154 8. (Use information from Question #7) If Jennifer believes that her true probabilities for each possible loss outcome are half as high as the insurer has estimated, what is the percentage loading on the policy from her perspective? (Note: This means Jennifer believes her probability for $0 loss is .60) a. b. c. d. 10% 20% 120% 200% Answer: c Type: A 9. The main reason that diversified shareholders might not want their corporate managers to purchase insurance is that: a. b. c. d. they like risk they have already diversified away the risk that is being insured they are risk averse cash flow variability increases their return on investment Answer: b Type: A 10. The main tax benefit of insurance from a corporate shareholder’s perspective is due to: a. b. c. d. the tax deductibility of insurance payments the different treatment of gains and losses under the tax code the progressive nature of the corporate tax schedule the double taxation of corporate profits Answer: c Type: K 11. What is the risk premium of a gamble whereby the participant has a .55 chance of winning $1,000 or a .45 chance of losing $1,000. a. b. c. d. $10 $15 $100 $150 Answer: c Type: A 155 12. Due to premium loading, people generally pay insurance premiums that are greater than their expected claim costs. A risk adverse individual may be willing to pay this additional amount because insurance reduces risk. This ‘additional amount’ that a person is willing to pay to reduce risk is an example of a a. b. c. d. gamble risk premium down payment risk neutral transaction Answer: b Type: A 13. As a person’s wealth increases it is likely that their degree of risk aversion will a. b. c. d. decline stay the same increase cannot tell since wealth and risk aversion are not related Answer: a Type: K 14. Law of Demand: As price increases, the quantity demanded decreases. In the context of fair insurance premiums, the relevant ‘price’ that determines quantity demanded is a. b. c. d. premium loading present value of expected claims costs expected loss amount discount rate Answer: a Type: A 15. Which one of the following is not a reason for a publicly held, widely traded, business to purchase insurance? a. b. c. d. to provide efficient claims processing and loss control services reduce the expected cost of loss financing reduce expected tax payments reduce the owners’ risk Answer: d Type: K 156 II. Fill-Ins 1. If Mary has a preference for a definite payment of $100 over a risky gamble that has an expected value of $100, she is risk averse . 2. Even a risk averse person may choose not to buy insurance if the loading is too high relative to the expected loss. 3. People who have greater purchase insurance. 4. If Rocky Road, Inc.’s shareholders all have diversified they may not want the firm’s managers to buy insurance. 5. Even if corporate insurance does not reduce the shareholders’ risk, it may provide other benefits such as more efficient claims processing , lower cost financing of losses , and reduced tax payments . (Other answers include: reduced likelihood of financial distress and better contract terms with the firm’s stakeholders.) income (or wealth) premium may be less likely to portfolios, III. Problems and Short Answer Questions 1. “The purchase of insurance is not value-maximizing for firms with well-diversified corporate shareholders.” Explain the logic of this statement. Answer: Diversification of the portfolio is a mechanism whereby a shareholder can reduce the variability of returns due to pure risks. Therefore, since insurance and diversification achieve the same outcome, the use of both may be redundant and may impose unnecessary costs on the shareholders. Type: A 2. Explain why a corporation might still want to purchase insurance despite the fact that its shareholders are well-diversified. Answer: Business insurance purchases can: a) be an efficient method of purchasing claims processing and loss control services; b) reduce the expected cost of financing losses; c) reduce the likelihood that the firm will have to raise costly external capital for new investment projects and thereby increase the likelihood that it will adopt good investment projects; d)reduce the likelihood of financial distress and thereby improve the terms on which the firm contracts with other claimants, such as employees, suppliers, lenders, and customers; and e) reduce expected tax payments. Type: A 157 3. Mary Johnson, the mother of two young children, has a life-threatening health condition, currently has a minimum wage job, and has very little savings. She is considering the purchase of a life insurance policy since she has no other family and her children would have no other source of income if she were to die. It’s Your Life Insurance Co. offers a fairly expensive life insurance policy that does not require any medical information or tests. What are some factors that might cause Mary to opt for this policy despite it’s relatively high premium loading? Answer: Mary’s demand for insurance will depend not only on the premium loading, but also on her income and wealth (both low), her level of information relative to the insurer’s (she has a high expected claims cost), the availability of other sources of indemnity (she has none), and the nature of the loss (she is worried about her children’s future). Type: A 4. Richie Rich, a millionaire, and Penny Poor, a welfare recipient, are both at high risk for automobile accidents. Richie owns a fast sports car and he likes to drag race it with his friends on the weekends. Penny has a small junker that has an extra powerful engine which she regularly tests as she speeds to her part-time job every day. Auto liability insurance is not compulsory in their state. Explain why Penny might have less incentive to purchase liability insurance than Richie. Answer: Wealthier people have more incentive to purchase liability insurance because they have more to lose in the event of a claim against them. Since Penny has little or no assets, it would take a very low claim to bring her wealth to zero, so the cost of the insurance may actually be higher than her expected loss without insurance. Furthermore, Penny may not have sufficient funds to be able to purchase insurance, since her limited income is probably used totally for the purchase of necessities. Type: A 5. Explain why the purchase of insurance may be more beneficial to small businesses than to large publicly-held firms. Answer: Business insurance is beneficial to risk-averse owners of businesses in much the same way the personal insurance is beneficial to risk-averse individuals. Since they are not able to diversify away the risk the way that shareholder-owners can, insurance is likely to be the most cost-efficient method of reducing their risk. Type: K 158