1. Chapter 2: The Insurance Mechanism
Agenda
Definition and Basic Characteristics of Insurance
Characteristics of An Ideally Insurable Risk
Adverse Selection and Insurance
Insurance vs. Gambling
Insurance vs. Hedging
Types of Insurance
Benefits and Costs of Insurance to Society

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

3. Basic Characteristics of Insurance
Transparency Master 1.2
Basic Characteristics of Insurance
Pooling of losses
Spreading losses incurred by the few over the entire group
Risk reduction based on the Law of Large Numbers
Example:
Two business owners own identical buildings valued at $50,000
There is a 10 percent chance each building will be destroyed by a peril in any year; loss to either building is an independent event
Expected value and standard deviation of the loss for each owner is:

4. Basic Characteristics of Insurance
Example, continued:
If the owners instead pool (combine) their loss exposures, and each agrees to pay an equal share of any loss that might occur:
As additional individuals are added to the pooling arrangement, the standard deviation continues to decline while the expected value of the loss remains unchanged

5. Pooling of Losses
… spreading of losses incurred by the few over the entire group, so that in the process, average loss is substituted for actual loss.
do not change expected loss
reduce uncertainty (variance decreases, costs from loss exposure become more predictable)
Distribution becomes more symmetric (less skewed)
Predictability increases with the number of participants
Predictability decreases with correlation in losses

6. Basic Characteristics of Insurance
Payment of fortuitous losses
Insurance pays for losses that are unforeseen, unexpected, and occur as a result of chance
Risk transfer
A pure risk is transferred from the insured to the insurer, who typically is in a stronger financial position
Indemnification
The insured is restored to his or her approximate financial position prior to the occurrence of the loss
Q: All of the following are characteristics of insurance EXCEPT
(A) risk avoidance.
(B) pooling of losses.
(C) payment of fortuitous losses.
(D) indemnification.

7. Case Application
Based on the definition of insurance stated above, indicates which of the following is considered insurance.
a. A TV set is guaranteed by the manufacturer against defects for 90 days.
b. A new set of radial tires is guaranteed by the manufacturer against road defects for 50,000 miles.
c. A builder of new homes gives a 10-year guarantee against structural defects in the home.
d. A cosigner of a note agrees to pay the loan balance if the original debtor defaults on the payments.
e. A large group of homeowners agrees to pay for losses to homes that burn during the year because of fire.

8. Characteristics of an Ideally Insurable Risk
Transparency Master 1.2
Characteristics of an Ideally Insurable Risk
Large number of exposure units
to predict average loss
Accidental and unintentional loss
to control moral hazard
to assure randomness
Determinable and measurable loss
to facilitate loss adjustment
insurer must be able to determine if the loss is covered and if so, how much should be paid.

9. Requirements of an Insurable Risk
No catastrophic loss
to allow the pooling technique to work
exposures to catastrophic loss can be managed by:
dispersing coverage over a large geographic area
using reinsurance
catastrophe bonds
Calculable chance of loss
to establish an adequate premium

10. Requirements of an Insurable Risk
Economically feasible premium
so people can afford to buy
Premium must be substantially less than the face value of the policy
Based on these requirements:
Most personal, property and liability risks can be insured
Market risks, financial risks, production risks and political risks are difficult to insure
Why “Gap Insurance” fails?
AXA Sees Red, FORTUNE,
荷里活「差額保險」失敗的啟示, 香港《太陽報》, , p. B5

11. Exhibit 2.1 Risk of Fire as an Insurable Risk

12. Exhibit 2.2 Risk of Unemployment as an Insurable Risk

13. Adverse Selection and Insurance
Adverse selection is the tendency of persons with a higher-than-average chance of loss to seek insurance at standard rates
If not controlled, adverse selection result in higher-than-expected loss levels
Adverse selection can be controlled by:
careful underwriting (selection and classification of applicants for insurance)
policy provisions (e.g., suicide clause in life insurance)
Advantageous Selection: Risk averse people are more willing to buy insurance, and… they are of low risk type.
HK life insurance market: adverse selection or advantageous selection?

14. Insurance vs. Gambling Insurance
Insurance is a technique for handing an already existing pure risk
Insurance is socially productive:
both parties have a common interest in the prevention of a loss
Gambling
Gambling creates a new speculative risk
Gambling is not socially productive
The winner’s gain comes at the expense of the loser

15. Insurance vs. Hedging Insurance Risk is transferred by a contract
Insurance involves the transfer of insurable risks
Insurance can reduce the objective risk of an insurer through the Law of Large Numbers
Hedging
Risk is transferred by a contract
Hedging involves risks that are typically uninsurable
Hedging does not result in reduced risk

16. Credit Default Swap (CDS) in five minutes: BBC
…everyone in my road buying insurance on my house in the hope that it collapses…

17. Types of Insurance Private Insurance Government Insurance
Life and Health
Property and Liability
Government Insurance
Social Insurance
Other Government Insurance

18. Private Insurance Life and Health Property and Liability
Life insurance pays death benefits to beneficiaries when the insured dies
Health insurance covers medical expenses because of sickness or injury
Disability plans pay income benefits
Property and Liability
Property insurance indemnifies property owners against the loss or damage of real or personal property
Liability insurance covers the insured’s legal liability arising out of property damage or bodily injury to others
Casualty insurance refers to insurance that covers whatever is not covered by fire, marine, and life insurance

19. Private Insurance
Private insurance coverages can be grouped into two major categories
Personal lines
coverages that insure the real estate and personal property of individuals and families or provide protection against legal liability
Commercial lines
coverages for business firms, nonprofit organizations, and government agencies

20. Exhibit 2.3 Property and Casualty Insurance Coverages

21. Government Insurance Social Insurance Programs
Financed entirely or in large part by contributions from employers and/or employees
Benefits are heavily weighted in favor of low-income groups
Eligibility and benefits are prescribed by statute
Examples:
Social Security, Unemployment, Workers Comp
Other Government Insurance Programs
Found at both the federal and state level
Federal flood insurance, state health insurance pools

22. Social Benefits of Insurance
Indemnification for Loss
Contributes to family and business stability
Reduction of Worry and Fear
Insureds are less worried about losses
Source of Investment Funds
Premiums may be invested, promoting economic growth
Loss Prevention
Insurers support loss-prevention activities that reduce direct and indirect losses
Enhancement of Credit
Insured individuals are better credit risks than individuals without insurance

23. Social Costs of Insurance
Cost of Doing Business
Insurers consume resources in providing insurance to society
An expense loading is the amount needed to pay all expenses, including commissions, general administrative expenses, state premium taxes, acquisition expenses, and an allowance for contingencies and profit
Cost of Fraudulent and Inflated Claims
Payment of fraudulent or inflated claims results in higher premiums to all insureds, thus reducing disposable income and consumption of other goods and services

24. Basic Statistics and the Law of Large Numbers
Chapter 2 Appendix
Basic Statistics and the Law of Large Numbers

25. Probability and Statistics
The probability of an event is the long-run relative frequency of the event, given an infinite number of trials with no changes in the underlying conditions.
Events and probabilities can be summarized through a probability distribution
Distributions may be discrete or continuous
A probability distribution is characterized by:
A mean, or measure of central tendency
A variance, or measure of dispersion

26. Probability and Statistics
The mean or expected value is:
Amount of Loss (Xi)
Probability of Loss (Pi)
XiPi
$ 0 X
0.30 =
$360
0.50
$180
$600
0.20
$120
$300

27. Probability and Statistics
The variance of a probability distribution is:
For the previous loss distribution,
The standard deviation =
Higher standard deviations, relative to the mean, are associated with greater uncertainty of loss; therefore, the risk is greater

28. Law of Large Numbers
The law of large numbers is the mathematical foundation of insurance.
Average losses for a random sample of n exposure units will follow a normal distribution because of the Central Limit Theorem.
Regardless of the population distribution, the distribution of sample means will approach the normal distribution as the sample size increases.
The standard error of the sampling distribution can be reduced by simply increasing the sample size

29. Exhibit A2.1 Sampling Distribution Versus Sample Size

30. Exhibit A2.2 Standard Error of the Sampling Distribution Versus Sample Size

31. Law of Large Numbers
When an insurer increases the size of the sample of insureds:
Underwriting risk increases, because more insured units could suffer a loss.
But, underwriting risk does not increase proportionately. It increases by the square root of the increase in the sample size.
There is “safety in numbers” for insurers!

32. An Example: The Law of Large Number
Suppose you are in charge of an insurance company and you have a pool of insureds. Historical information on this pool of insureds include the following: (assuming normal distribution)
50 individuals are members of this pool.
The annual expected total number of loss incidents generated by this pool is 60.
The standard deviation associated with the expected number of loss incidents above is 10.
The average expected loss per incident is $1,000.

33. Normal Distribution
0.15% -3 -2 -1
mean
+1S.D. +2 +3
68.3%
95.5%
99.7%

34. An Example: The Law of Large Number
Given that there can be variation regarding the actual annual total number of losses incurred by this pool, what premium would you charge each member of this group if you wanted to be 99.85% sure you will generate enough premium revenue to cover losses for this group?
What is the premium loading for the above case?

35. An Example: The Law of Large Number
Now suppose your pool size were to increase to 5,000 individuals with similar risk characteristics to the smaller group. What is the new annual expected number of loss incidents for this pool? What is the new standard deviation?
Given this new larger pool of insureds, what premium would you charge each person if you wanted to be 99.85% sure you will generate enough premium revenue to cover losses?

36. An Example: The Law of Large Number
What do we learn from the example?
When N = 50, the insurance company needs to charge ______ to maintain 99.85% solvency!!
When N = 5,000, the insurance company needs only ______ to maintain the same level of solvency.