Lecture 5 - Risk Sharing and Insurance

Characteristics of insurance

- The pooling of losses - Payment of fortuitous losses - Risk transfer - Indemnification

The six characteristics of an (ideally) insurable risk - Determinable and measurable loss

- determinable: the loss should be definite as to cause, time, place and size. - measurable: to determine how much should be paid.

The six characteristics of an (ideally) insurable risk

1. Large number of exposure units 2. Accidental and unintentional loss 3. Determinable and measurable loss 4. No catastrophic loss/ limited loss size 5. Calculable probability of loss 6. Economically feasible premium

Two people, Marcia and Karen, are exposed to the possibility of an accident in the upcoming year. The table summarizes the possible outcomes for each and their attached probability. For each person: Outcome Cost Probabiltiy No accident $0 .60 Accident $4,000 .40 a) Calculate the expected loss and standard deviation for the risk. b) When Marcia and Karen's accident losses are independent (uncorrelated), what is the expected cost for each person and what is the standard deviation? c) Donna joins the risk pooling arrangement, what is the expected cost for each person and what is the standard deviation?

a) Expected cost = 0.4 * 4000 = 1,600 and STD = 1959.59 b) Outcome Costs/person Probability Both no loss $0 .6 * .6 = .36 Loss M, no loss K $2,000 .4 * .6 = .24 Loss K, no loss M $2,000 .6 * .4 = .24 Both loss $4,000 .4 * .4 = .16 Expected cost for each person = 0 * 0.36 + 2,000 * 0.24 * 2 + 4,000 * 0.16 = 1,600 *Note that the pooling arrangement changes the probability distribution of accident cost for each person. *Note: Pooling reduced the probably of the extreme outcome. w/o pooling => extreme is having an accident w/ pooling => extreme is both having an accident. c) Expected cost for each person = 1600 Standard Deviation for each person: 1131.38 e)

Basic characteristics of insurance: Payment of fortuitous losses

A loss that is unforeseen, unexpected, and occurs as a random result of chance.

Basic characteristics of insurance: Risk transfer

A pure risk is transferred from the insured to the insurer, who typically is in a stronger financial position.

All of the following are social costs associated with insurance EXCEPT A) insurance company operating expenses. B) fraudulent claims. C) inflated claims. D) increased cost of capital.

A) insurance company operating expenses.

Which of the following is a characteristic of insurance? A) pooling of losses B) avoidance of risk C) payment of intentional losses D) certainty about specific losses that will occur

A) pooling of losses

A pooling arrangement is less effective at reducing participants' risk exposure if the losses are A) positively correlated. B) negatively correlated. C) uncorrelated. D) independent from another.

A) positively correlated.

The six characteristics of an (ideally) insurable risk - Accidental and unintentional loss

Accidental and unintentional loss because the law of large numbers is based on the random occurrence of events.

Basic characteristics of insurance: Pooling of risks

Additional loss can be obtained by adding further individuals into the pooling agreement. First mutual insurance agreements evolved from this idea. Enables the policyholder to replace uncertain loss payments with certain payments - insurance premiums. 1/n x var(x)

From the insurer's viewpoint, all following are characteristics of an ideally insurable risk EXCEPT A) The loss must be accidental. B) The loss should be catastrophic. C) The premium must be economically feasible. D) There must be a large number of exposure units.

B) The loss should be catastrophic.

Which of the following types of risks best meets the requirements for being insurable by private insurers? A) market risks B) property risks C) financial risks D) political risks

B) property risks

Which of the following pairs of random variables are likely to be uncorrelated? A) total health care costs in NYC for 1997; total health care costs in NYC for 1998 B) total property damage due to wildfires in Colorado in 1997; total property damage due to landslides in California in 1998. C) number of people who die from cancer in the US in 1997; number of people who die from cancer in the US in 1998. D) worker injuries at a shoe manufacturing plant owned/managed by Exodus Inc.; worker injuries at a different shoe manufacturing plant owned/managed by Exodus Inc.

B) total property damage due to wildfires in Colorado in 1997; total property damage due to landslides in California in 1998.

According to the law of large numbers, what should happen as an insurer increases the number of units insured? A) The amount the insurer expects to pay in claims should decrease. B) Underwriting expenses should decrease. C) Actual results will more closely approach expected results. D) The insurer's profitability should become more variable.

C) Actual results will more closely approach expected results.

Suppose the original distribution of James's loss is the same as that of John's. They agree to share whatever loss anyone of them suffers. If James's loss is independent of John's (i.e., whatever happens to James has nothing to do with what happens to John), which statement is correct? A) Expected loss for each with the loss sharing agreement is smaller than without the agreement. B) Expected loss for each with the loss sharing agreement is the same as without the agreement. C) John's standard deviation of shared loss will be smaller than the original standard deviation. D) John's standard deviation of shared loss will be the same as the original standard deviation.

C) John's standard deviation of shared loss will be smaller than the original standard deviation.

The six characteristics of an (ideally) insurable risk - Calculable probability of loss

Calculable probability of loss to establish a premium that is sufficient to pay all claims and expenses and yields a profit during the policy period.

Why is a large number of exposure units generally required before a pure risk is insurable? A) It prevents the insurer from losing money. B) It eliminates intentional losses. C) It minimizes moral hazard. D) It enables the insurer to predict losses more accurately.

D) It enables the insurer to predict losses more accurately.

The tendency for unhealthy people to seek life or health insurance at standard rates is an example of A) moral hazard. B) fundamental risk. C) attitudinal hazard. D) adverse selection.

D) adverse selection.

Moral hazard

Describes insurance-induced behavioral changes of insured which affect the overall outcome. Insured may be less precautious than if they didn't have insurance.

The six characteristics of an (ideally) insurable risk - Economically feasible premium

Economically feasible premium - so people can afford to purchase the policy. - For insurance to be an attractive purchase, the premiums paid must be substantially less than the face value, or amount, of the policy.

The six characteristics of an (ideally) insurable risk - Large number of exposure units

Large number of exposure units is necessary to predict the average loss based on the law of large numbers.

The six characteristics of an (ideally) insurable risk - No catastrophic loss/ limited loss size

No catastrophic loss / limited loss size - to allow the pooling technique to work - exposures to catastrophic loss can be managed by using reinsurance, dispersing coverage over a large geographic area, or using financial instruments, such as catastrophe bonds.

Law of Large numbers

States that for any small number greater than 0, if the number of risks in the portfolio tends to infinity, the probability that the average outcome differs from the expected value is positive tends to 0.

The Central Limit Theorum

States that under the same assumption as the Law of Large Numbers, the average outcome approaches a normal distribution with mean (mu) and standard deviation (standard deviation/ square root of n) as n gets very large.

Basic characteristics of insurance: Indemnification

The insured is restored to his or her approximate financial position prior to the occurrence of the loss.

American Risk and Insurance Association (ARIA)

The pooling of

American Risk and Insurance Association (ARIA) definition of Insurance

The pooling of fortuitous losses by transfer of such risks to insurers, who agree to indemnify for such losses, to provide other pecuniary benefits on their occurrence, or to render services connected with the risk.

Adverse selection

The tendency of persons with a higher-than-average chance of loss (bad risk) to seek insurance at standard rates. Adverse selection is controlled by underwriting, policy provisions, and coinsurance.

In a box are 10 globes, one of them is red, the rest are black. "Nature" takes three times one globe and puts it back into the box. When, by chance, a red globe is taken this means a 10,000 $ loss. a) Write down the loss distribution for the example above. b) Calculate the minimum premium (without any cost, etc.) of an insurance policy that fully compensates for the loss. c) Would you buy this insurance policy? Why?

a) The loss distribution is 0 $ with probability 0.729 10.000 $ with probability 0.243 20.000 $ with probability 0.027 30.000 $ with probability 0.001 b) The premium must be as least as high as the expected value. The EV equals 3.000$. c) As a result, every risk-averse person (almost anybody) will purchase insurance at this (fair) price!