Class 1: Introduction Insurance and Risk Management

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Class 1 Introduction Insurance and
RiskManagement

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

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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?

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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

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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?

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Petersburg Paradox

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

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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.

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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?

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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

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The Question

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

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Implication

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

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Definition of Risk

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

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Objective Risk

• Objective risk is the relative variation of
  actual loss from expected loss
• One situation is riskier than another when
• There is greater variance in outcomes relative to
  the expected loss

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Objective Vs. Subjective Risk

• Objective Risk Relative variation of the actual
  loss from the expected loss
• Subjective risk the mental state of uncertainty
  of the individual
• Subjective risk is
• Personal
• Not easily measured
• Remember Ben Krempleys Bike

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Chance of Loss Vs.Objective Risk

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

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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

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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

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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.

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Systematic and Non-systematic Risk

• Risk that cannot be eliminated by diversification
  is called systematic risk.
• Systematic risk is risk that belongs to the
  group also 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.

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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

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Variance and Standard Deviation

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

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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

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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

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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

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Standard Deviation - Distribution 2

• Calculate difference between each outcome and
  expected value
• 0-500-500
• 500-500 0
• 100-500 500
• Square the results
• 250,000
• 0
• 250,000

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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

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Skewness

• Skewness measures the symmetry of the
  distribution
• No skewness gt symmetric
• Most loss distributions exhibit skewness
• Skewered by the skewness

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Maximum Probable Loss

• Maximum Probable Loss at the 95 level is the
  number, MPL, that satisfies the equation
• Probability (Loss lt MPL) lt 0.95
• Losses will be less than MPL 95 percent of the
  time

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Risk Is Costly

• Greater risk imposes costs (reduces value)
• Identical properties subject to damage
• Greater expected property loss lowers value of
  property, all else equal
• Greater uncertainty about property loss often
  lowers value of property, all else equal

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Risk Management

• A process that identifies loss exposures faced by
  an organization or individual and selects the
  most appropriate techniques for treating such
  exposures.
• Traditional risk management focuses on pure risks.

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Enterprise Risk

• Encompasses all major risks faced by a business
  firm, which include
• pure risk
• speculative risk
• strategic risk
• operational risk
• financial risk

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Enterprise Risk Management

• Broadly defined, risk management is a method for
  making decisions
• Regarding how to treat exposures to loss in value
  from any source.

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The Risk Management Process

• Identification of risks
• Evaluation of frequency and severity of losses
• Choosing risk management methods
• Implementation of the chosen methods
• Monitoring the performance and suitability of the
  methods.

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Methods of Handling Risk

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

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Definition of Insurance

• Pooling of fortuitous losses
• by transfer to an insurer,
• who agrees to indemnify insureds for such losses,
  and
• render services connected with the risk.

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Risk Management Vs. Insurance

• Risk management is a decision process insurance
  is a method of risk transfer
• Risk management focuses on identifying and
  measuring risks to select the most appropriate
  technique.
• Insurance is only one of several options to treat
  pure loss exposures.

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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

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Example of Perils
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Major Pure Risks - Personal

• Premature death of family head
• Insufficient income during retirement
• Poor health (catastrophic medical bills and loss
  of earned income)
• Involuntary unemployment
• Physical damage to home and personal property
  from fire, tornado, or other causes
• Legal liability

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EXHIBIT 1.2 Total Accumulated for Retirement, by
Age Group
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Property and Casualty Insurance Coverages
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How Does Insurance Reduce Objective Risk?

• Pooling of a group of risks
• So, that the accidental losses to which the group
  is subjected
• Become predictable within narrow limits.

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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.

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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

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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

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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

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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

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Risk Pooling with 20 People
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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)

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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

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Effect of Positive Correlation on Risk Reduction
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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

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Costs of Pooling Arrangements

• Pooling arrangements reduce risk, but they
  involve costs
• Adding Participants
• marketing
• underwriting
• Verifying Losses
• Collecting Assessments

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Requirements of an 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
• No catastrophic loss
• to allow the pooling technique to work
• Calculable chance of loss
• to determine the premium need
• Economically feasible premium
• so people can afford to buy

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EXHIBIT 2.1 Risk of Fire as an Insurable Risk
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Risk of Unemployment as an Insurable Risk