# Two dimensions of pure risk

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1 What is Insurance? Insurance is protection against risks. We face many risks in our lives: Car accident Theft Disability Heart attack Etc. Consumers buy insurance to pay for the costs associated with some of these risks if they do occur. 1 2 What should you insure -Types of risks Risks can be categorized into two types: pure risks and speculative risks Pure risks: Risks in which only a loss can result if the risk occurs Examples: car accident, illness Speculative risks: Risks in which the results can be either a loss or a gain Examples: gambling, investments In this unit we study pure risks. Speculative risks will be studied in the Investment chapter. Two dimensions of pure risk Severity of the potential loss Death has the highest severity of loss Frequency of occurrence a pencil has the highest frequency of loss Severity of loss Killed in accident property in fire shirt Loss of property from theft Death from disease or illness Disability from disease or illness Damage to car from accident Injury in combat Death from jumping the Grand Canyon on motocycle pencil Frequncy of occurance 3 4 What to Do about Pure Risks Avoid risk You can choose not to jump off the Grand Canyon on a motorcycle. By doing that you avoid the risk completely. Reduce risk Take a defensive driving course and drive defensively reduces your risk of a car accident. Self-insure If it s a small severity of loss, then you can self-insure. For example, most consumers do not buy insurance for lost pencils or lost shirts. If a pencil is lost most people just buy another one from their own funds. Transfer risk (buy insurance) This is advisable for items that have high severity of loss, like a house, a car, an illness, etc. Insurance on what? A simple rule to use to decide where to best spend your insurance money is to use expected loss Expected loss = Sum of (frequency of occurrence i * severity of loss i ) 5 6 1

2 An example of expected loss car accident possibilities for six months Frequency of occurrence Severity of loss Expected loss Light auto damage 10% \$500 \$50 Medium auto damage 5% \$1,500 \$75 Light personal injury 5% \$2,000 \$100 Heavy auto damage 1% \$5,000 \$50 Medium personal injury 1% \$5,000 \$50 Total expected loss = \$325 In the table on previous slide, for this person, we are estimating that the person has a 10% chance of getting into a small car accident that can cause a damage of about \$500. In this case usually there is no personal injury. A medium auto damage is probably coupled with a light personal injury, with a 5% probability and an average of \$1,500 for auto damage and \$2,000 for personal injury. A heavy auto damage is usually coupled with a medium personal injury, with a 1% probability and an average of \$5,000 of auto damage and \$5,000 of personal injury. Expected Loss = (10%*500)+(5%*1500)+5%*2000+1%*5000+1%*5000 =325 Note this is just a simplified example. 7 8 The concept of diminishing marginal utility again Remember in Unit 1 we talked about diminishing marginal value or diminishing marginal utility of consumption? The is, the value of the first hamburger to a hungry consumer is a lot more than the value of the fifth hamburger. The same concept applies to income. The value of the first \$10,000 of income is a lot more than the value of the fifth \$10,000 of income. Why? An increase of income from \$0 to \$10,000 makes a world of difference from not being able to eat to have something to survive. An increase from \$50,000 of income to \$60,000 of income is nice, but not nearly as life-changing as an increase from \$0 to \$10,000. Util, and Diminishing marginal utility in loss situations The expected loss usually is computed in consumer value of loss or util a measure of utility, instead of just dollar values. The rule of diminishing marginal value in loss situations implies that The last \$1000 loss cause more suffering than the first \$1000 loss. So the last \$1000 loss may have 5000 utils, whereas the first \$1000 loss may only have 1000 utils How does utilaffect insurance priority? Large but infrequent losses will be more important to insure compared to small but frequent losses, because large losses have more disastrous effect on the consumer, and thus cause more loss of utils. Car accident vs. disability expected loss in dollar values: Expected loss of car accident = 10%*5000=500 Expected loss of disability =0.5%*50000=250 But measured in utils, it might be: Expected loss of car accident =10%*5000=500 Expected loss of disability=0.5%*130000=650 So measured in value to consumers, disability insurance is more important than car insurance in the above example. What kinds of insurance to buy? Buy insurance on those pure risks that have the highest expected loss in utils. Suggested priority for insuring pure risks Death (if have dependents) - Life insurance Disability - Disability insurance Medical costs Health insurance Liability Both Home and Auto have liability coverage Property damage to home (if homeowner) Property damage to possessions Property damage to car

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