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Chapter 2: The Insurance Mechanism
Agenda
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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
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
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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:
Expected loss  0.90 * $0  0.10 * $50,000  $5,000
Standard deviation  0.900  $5,000   0.10$50,000  $5,000 
2
2
 $15,000
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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:
Expected loss  0.81* $0  0.09 * $25,000  0.09 * $25,000  0.01* $50,000
 $5,000
Standard deviation  0.810  $5,000   (2)(0.09)$25,000  $5,000   0.01($50,000  $5,000) 2
2
2
 $10,607
– As additional individuals are added to the pooling arrangement,
the standard deviation continues to decline while the expected
value of the loss remains unchanged
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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
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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.
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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.
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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.
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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
2-9
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, 2003-06-26.
– 荷里活「差額保險」失敗的啟示, 香港《太陽報》, 2003-07-16,
p. B5
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Exhibit 2.1 Risk of Fire as an Insurable Risk
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Exhibit 2.2 Risk of Unemployment as an
Insurable Risk
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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?
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Insurance vs. Gambling
Insurance
Gambling
• Insurance is a technique
for handing an already
existing pure risk
• Gambling creates a new
speculative risk
• Insurance is socially
productive:
• Gambling is not socially
productive
– both parties have a
common interest in the
prevention of a loss
– The winner’s gain comes
at the expense of the
loser
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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
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Credit Default Swap (CDS) in five minutes: BBC
…everyone in my road buying insurance on my house in the hope that it collapses…
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Types of Insurance
• Private Insurance
– Life and Health
– Property and Liability
• Government Insurance
– Social Insurance
– Other Government Insurance
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Private Insurance
• Life and Health
– 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
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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
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Exhibit 2.3 Property and Casualty Insurance
Coverages
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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
– Examples:
• Federal flood insurance, state health insurance pools
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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
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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
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Chapter 2
Appendix
Basic Statistics
and the Law of
Large Numbers
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
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Probability and Statistics
• The mean or expected value is:
 or EV   X i Pi
Amount of
Loss (Xi)
Probability
of Loss (Pi)
X iP i
$ 0
X
0.30
=
$ 0
$360
X
0.50
=
$180
$600
X
0.20
=
$120
X P
=
$300
i i
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Probability and Statistics
• The variance of a probability distribution is:
 2   Pi  X i  EV 2
• For the previous loss distribution,
 2  0.30(0  300) 2  0.50(360  300) 2
0.20(600  300) 2
 27,000  1,800  1,800
 46,800
• The standard deviation =
 2    216.33
• Higher standard deviations, relative to the mean, are
associated with greater uncertainty of loss; therefore, the risk
is greater
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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
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Exhibit A2.1 Sampling Distribution
Versus Sample Size
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Exhibit A2.2 Standard Error of the Sampling
Distribution Versus Sample Size
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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!
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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.
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Normal Distribution
0.15%
-3
-2
-1
mean
+1S.D.
+2
+3
68.3%
95.5%
99.7%
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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?
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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?
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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.
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