Class 1: Introduction Insurance and Risk Management

1
Class 1 Introduction Insurance and
RiskManagement

• George D. Krempley
• Bus. Fin. 640
• Autumn 2007

2
Expected value rule

• Holds that
• In an uncertain situation, human beings will
  select the alternative with the highest expected
  value.
• Does it work?
• Does it account for human behavior?
• Can we use it to predict our decisions under
  conditions of uncertainty?

3
Expected Value

• EV ? P X
• Where
• EV the expected value of the outcome
• P the probability of outcome, X
• X the outcome in money value
• ? the sum of

4
Expected Value Rule Prediction

• Everyone will always and everywhere invest in the
  stock market.
• Why? In an uncertain situation, human beings
  will select the alternative with the highest
  expected value.
• Does this hold?

5
Petersburg Paradox

• 18th century Swiss mathematician and physicist,
  Daniel Bernoulli
• Showed how the expected value rule regularly
  breaks down.

6
Consider the following

• One player flips a fair coin
• If coin lands heads, the player will pay the
  other player 2.00.
• If the coin lands tails, it is tossed again.
• If the second toss heads, the first player plays
  the second player (2.00) and the game is over.

2
7
Consider(cont.)

• The game is continued until the first head
  appears.
• The first player pays the second player (2.00)i
• Where i equals the number of tosses required to
  get the first head.
• How much will the second player being willing to
  pay to enter the game?

8
Consider

• Seldom is anyone willing to pay more than 10.00.
• But, the game has an infinite value
• ?Pii Xii (2)(½) (2)²(½)² (2)³(½)³
• 1 1 1 Infinity

9
The Question

• Why will people only pay a few dollars to enter a
  game that has an infinite value?
• Risk matters!

10
Implication

• Risk is present
• Whenever circumstances give rise to an outcome
  that cannot be predicted with certainty
• Not knowing the future creates risk.

11
Definition of Risk

• Risk is defined as uncertainty concerning the
  occurrence of a loss

12
Items To Be Discussed

• Meaning of Risk
• Chance of Loss
• Peril and Hazard
• Basic Categories of Risk
• Types of Pure Risk
• Burden of Risk on Society
• Methods of Handling Risk
• Standard Deviation
• Pooling

13
Meaning of Risk

• Risk Uncertainty concerning the occurrence of a
  loss
• Objective Risk vs. Subjective Risk
• Objective risk is defined as the relative
  variation of actual loss from expected loss
• It can be statistically calculated using a
  measure of dispersion, such as the standard
  deviation
• Subjective risk is defined as uncertainty based
  on a persons mental condition or state of mind
• Two persons in the same situation may have
  different perceptions of risk
• High subjective risk often results in
  conservative behavior

14
Chance of Loss

• Chance of loss The probability that an event
  will occur
• Objective Probability vs. Subjective Probability
• Objective probability refers to the long-run
  relative frequency of an event assuming an
  infinite number of observations and no change in
  the underlying conditions
• It can be determined by deductive or inductive
  reasoning
• Subjective probability is the individuals
  personal estimate of the chance of loss
• A persons perception of the chance of loss may
  differ from the objective probability

15
Peril and Hazard

• A peril is defined as the cause of the loss
• In an auto accident, the collision is the peril
• A hazard is a condition that increases the chance
  of loss
• Physical hazards are physical conditions that
  increase the chance of loss (icy roads, defective
  wiring)
• Moral hazard is dishonesty or character defects
  in an individual, that increase the chance of
  loss (faking accidents, inflating claim amounts)
• Morale Hazard is carelessness or indifference to
  a loss because of the existence of insurance
  (leaving keys in an unlocked car)
• Legal Hazard refers to characteristics of the
  legal system or regulatory environment that
  increase the chance of loss (large damage awards
  in liability lawsuits)

16
Basic Categories of Risk

• Pure and Speculative Risk
• A pure risk is one in which there are only the
  possibilities of loss or no loss (earthquake)
• A speculative risk is one in which both profit or
  loss are possible (gambling)
• Fundamental and Particular Risk
• A fundamental risk affects the entire economy or
  large numbers of persons or groups (hurricane)
• A particular risk affects only the individual
  (car theft)
• Enterprise Risk
• Enterprise risk encompasses all major risks faced
  by a business firm, which include pure risk,
  speculative risk, strategic risk, operational
  risk, and financial risk

17
Types of Pure Risks

• Personal risks involve the possibility of a loss
  or reduction in income, extra expenses or
  depletion of financial assets
• Premature death of family head
• Insufficient income during retirement
• Most workers are not saving enough for a
  comfortable retirement
• Poor health (catastrophic medical bills and loss
  of earned income)
• Involuntary unemployment

18
Types of Pure Risks

• Property risks involve the possibility of losses
  associated with the destruction or theft of
  property
• Physical damage to home and personal property
  from fire, tornado, vandalism, or other causes
• Direct loss vs. indirect loss
• A direct loss is a financial loss that results
  from the physical damage, destruction, or theft
  of the property, such as fire damage to a
  restaurant
• An indirect loss results indirectly from the
  occurrence of a direct physical damage or theft
  loss, such as lost profits due to inability to
  operate after a fire

19
Types of Pure Risks

• Liability risks involve the possibility of being
  held liable for bodily injury or property damage
  to someone else
• There is no maximum upper limit with respect to
  the amount of the loss
• A lien can be placed on your income and financial
  assets
• Defense costs can be enormous

20
Burden of Risk on Society

• The presence of risk results in three major
  burdens on society
• In the absence of insurance, individuals would
  have to maintain large emergency funds
• The risk of a liability lawsuit may discourage
  innovation, depriving society of certain goods
  and services
• Risk causes worry and fear

21
Methods of Handling Risk

• Avoidance
• Loss control
• Loss prevention refers to activities to reduce
  the frequency of losses
• Loss reduction refers to activities to reduce the
  severity of losses
• Retention
• An individual or firm retains all or part of a
  loss
• Loss retention may be active or passive
• Noninsurance transfers
• A risk may be transferred to another party
  through contracts, hedging, or incorporation
• Insurance

22
Chance of Loss Vs.Objective Risk

• Key Distinction
• Chance of loss Probability that a loss will
  occur
• Chance involves probability
• Risk involves variation

23
Pure Risk versus Speculative Risk

• Pure risk situation in which the only
  possibilities are loss or no loss
• Speculative risk situation in which either gain
  or loss is possible

24
Speculative and Pure Risk Examples

• Speculative Risk
• Starting a business
• Introducing a new product/entering a new market
• Investing in a security
• Change in government regulation
• Social change

• Pure Risk
• Property destruction
• Injury to employees on the job
• Illness or death
• Injury to customers and third parties
• Damage to the property of others

25
Diversifiable and Non-diversifiable Risk

• A risk is diversifiable if it is possible to
  reduce a risk through pooling or risk sharing
  agreements.
• Risk is non-diversifiable if pooling agreements
  are ineffective in reducing risk for the
  participants in the pool.

26
Fundamental and Particular Risk

• Risk that cannot be eliminated by diversification
  is called fundamental risk.
• Fundamental risk is risk that belongs to the
  group it also is known as fundamental risk.
• Risk that can be eliminated by diversification is
  called non-systematic risk.
• Non-systematic risk is also known as unique risk
  or particular risk.

27
Standard Deviation and Variance

• Standard deviation indicates the expected
  magnitude of the error from using the expected
  value as a predictor of the outcome
• Variance (standard deviation) 2
• Standard deviation (variance) is higher when
• when the outcomes have a greater deviation from
  the expected value
• probabilities of the extreme outcomes increase

28
Variance and Standard Deviation

• Variance Spi(xi - ?)2
• Standard Deviation Square Root of the Variance
  

N
i1
29
Standard Deviation and Variance

• Comparing standard deviation for three discrete
  distributions
• Distribution 1 Distribution 2 Distribution 3
• Outcome Prob Outcome Prob Outcome Prob
• 250 0.33 0 0.33 0 0.4
• 500 0.34 500 0.34 500 0.2
• 750 0.33 1000 0.33 1000 0.4

30
Standard Deviation - Distribution 1

• Calculate difference between each outcome and
  expected value
• 250-500-250
• 500-500 0
• 750-500 250
• Square the results
• 62,500
• 0
• 62,500

31
Standard Deviation Distr. 1 (cont.)

• Multiply by results of step 2 by the respective
  probabilities
• (0.33)(62,500) 20,833
• (0.34)(0) 0
• (0.33)(62500) 20,833
• Sum the results
• 20,833 0 20,833 41,666
• This is the Variance
• Take the Square Root 204.12

32
Standard Deviation - Distribution 2

• Calculate difference between each outcome and
  expected value
• 0-500-500
• 500-500 0
• 1000-500 500
• Square the results
• 250,000
• 0
• 250,000

33
Standard Deviation Distr. 2

• Multiply by results of step 2 by the respective
  probabilities
• (0.33)(250,000) 82,500
• (0.34)(0) 0
• (0.33)(250,000) 82,500
• Sum the results
• 82,500 0 82,500 165,000
• This is the Variance
• Take the Square Root 406.20

34
Methods of Handling Risk

• Avoidance
• Loss control
• Retention
• Non-insurance transfers
• Insurance

35
Peril

• A peril is defined as a cause of loss.
• If your house burns because of fire, the peril or
  cause of loss is fire.
• If your car is damaged in a collision with
  another vehicle, the peril is collision.
• Insurance policies frequently package coverage
  for various perils
• Known as multi-peril policies

36
Example of Perils
37
Pooling

• Spreading losses incurred by the few over the
  entire group so that the average loss is
  substituted for actual loss.
• Example of 10 Boats on the Yangtze.
• The role of underwriters and actuaries.

38
Two Assumptions Regarding Pooling

• The Pool consists of a group of risks that are
• Relatively homogenous
• Losses to which the group is subjected are
  accidental, not intentional

39
Risk Pooling Example with 2 People

• Two people with same distribution
• Outcome Probability
• 2,500 0.20
• Loss
• 0 0.80
• Assume losses are uncorrelated
• Expected value 500
• Standard deviation 1000

40
Risk Pooling Example with 2 People

• Pooling Arrangement changes distribution of
  accident costs for each individual
• Outcome Probability
• 0 (.8)(.8) .64
• Cost 1,250 (.2)(.8)(2) .32
• 2,500 (.2)(.2) .04
• Expected Cost 500

41
Risk Pooling Example with 2 People

• Effect on Expected Loss
• w/o pooling, expected loss 500
• with pooling, expected loss 500
• Effect on Standard Deviation
• w/o pooling, standard. deviation 1000
• with pooling, standard. deviation 707

42
Risk Pooling with 4 People

• Pooling Arrangement between 4 people
• Outcome Probability
• 10,000 0.000006
• 7,500 0.000475
• Loss 5,000 0.014
• 2,500 0.171
• 0 0.815
• Expected Loss 500
• Variance 1,089
• Standard Deviation 33

43
Risk Pooling with 20 People
44
Risk Pooling of Uncorrelated Losses

• Main Points
• Pooling arrangements
• do not change expected loss
• reduce uncertainty (variance decreases, losses
  become more predictable, maximum probable loss
  declines)
• distribution of costs becomes more symmetric
  (less skewness)

45
Effect of Correlated Losses

• Now allow correlation in losses
• Result uncertainty is not reduced as much
• Intuition
• What happens to one person happens to others
• One persons large loss does not tend to be
  offset by others small losses
• Therefore pooling does not reduce risk as much

46
Effect of Positive Correlation on Risk Reduction
47
Main Points about Risk Pooling

• Main Points
• Pooling reduces each participants risk
• i.e., costs from loss exposure become more
  predictable
• Predictability increases with the number of
  participants
• Predictability decreases with correlation in
  losses