Insurance and Risk Finance 640

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Insurance and RiskFinance 640

• Class 7
• October 13, 2004

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Pricing Question 1 Page 159

• Loss Distribution
• 100,000 with 0.005 probability
• 60,000 with 0.010 probability
• 20,000 with 0.020 probability
• 10,000 with 0.050 probability
• 0 with .915 probability
• Calculate
• Expected claim cost per policy
• Discounted expected claim cost at 6 interest
  rate
• Fair premium if
• Administrative cost is 100 per policy
• Fair Profit Loading is 50

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Question 1 Solution

• Expected claim cost
• (100,000 x .005) (60,000 x .01) (20,000
  x .02) (10,000 x .05)
• 500 600 400 500 2,000
• Present Value of Expected Claim Cost
• 2,000/1.06
• 1,886.79
• Fair Premium
• 1,886.79 100 50
• 2036.79

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Pricing Question 2 P. 159

• Assuming that
• Expected loss adjustment expense equal 12 of
  expected losses
• Loss adjustment expenses are paid at the same
  time that claims are paid
• Recalculate fair premium

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Question 2 Solution

• Expected loss adjustment expenses
• .12 x 2000 240
• Present value of expected loss adjustment
  expenses
• 240/1.06
• 226.42
• Fair premium
• 2036.79 226.42
• 2,263.21

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Principle of SubrogationExpanded Discussion

• Supports the principle of Indemnity
• Substitutes the Insurer in place of the Insured
  for the purpose of claiming indemnity from a
  third party for a loss covered by insurance

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Subrogation Example

• Assume a negligent motorist
• Fails to stop at a red light
• Smashes into the Insureds car
• Causing damages to the Insureds car of 5,000.
• Insured has purchased collision insurance for her
  car.
• The Insureds Insurance Company will
• Pay the physical damage loss (less any
  deductible)
• Then attempt to collect from the negligent
  motorist

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Subrogation Example (cont.)

• Alternatively, the Insured could attempt to
  collect directly from the negligent motorist.
• Subrogation does not apply, if a loss payment is
  not made by the Insureds Insurance Company.
• To the extent that a loss payment is made, the
  Insurer receives the legal right to collect
  damages from the negligent third party.

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Subrogations Purpose

• Subrogation
• Prevents the Insured from collecting twice for
  the same loss.
• Holds the guilty party responsible
• Holds down insurance rates
• Generally, subrogation recoveries are factored
  into the rate-making process

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Important Subrogation Points

• The Insured cannot do anything after the loss
  that impairs the Insurers subrogation rights.
• Subrogation does not apply to life insurance and
  most health insurance contacts.
• Insurer cannot recover against its own Insureds.

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Principle of Utmost Good Faith

• Utmost Good Faith means that
• A higher degree of honesty is imposed on both
  parties to an insurance contract than is imposed
  on parties to other contracts

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Historical Roots Ocean Marine Insurance

• Marine underwriter had to place great faith in
  the statements made by the applicant for
  insurance
• The cargo may not have been able to be visually
  inspected
• The contract may have been issued in a location
  far removed from the cargo or ship
• Thus, a high degree of honesty was imposed on the
  applicant for insurance

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Legal Doctrines Supporting Utmost Good Faith

• Representations Statements made by the applicant
  for insurance
• Concealment Intentional failure of the applicant
  for insurance to reveal a material fact to the
  Insurer

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Representation Legal Significance

• Insurance contract is void able at the Insurers
  option, if representation is
• Material
• False
• Relied on by the Insurer

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Representation (cont.)

• Material means that
• If the Insurer knew the true facts, the policy
  would not have been issued or would have been
  issued on different terms.
• False means that
• The statement is not true or is misleading.
• Reliance means that
• The Insurer relies on the misrepresentation in
  issuing the policy at a specified premium

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Concealment Legal Significance

• Concealment is the same as non-disclosure.
• The applicant for insurance deliberately
  withholds material information from the insurer
• Its legal significance is the same as
  misrepresentation
• The contract is void able at the Insurers
  option.

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Concealment (cont.)

• Concealment generally has two elements
• The concealed fact was known by the Insured to be
  material
• The Insured intended to defraud the Insurer
• However, a harsher standard applies in marine
  insurance
• An ocean marine insurer is not required to prove
  that the concealment is intentional.
• An ocean marine insurer can successfully deny a
  claim if it can be shown that the concealed fact
  is material

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Risk Management Objective - Revisited

• According to Harrington and Niehaus,
• The appropriate criterion for selecting among
  risk management decision options is to
• ? Minimize Cost of Risk

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Maximizing Value by Minimizing Cost of Risk

• Define
• Cost of risk Value without risk Value with
  risk
• Rearrange
• Value with risk Value without risk Cost of
  risk
• Implication
• Maximize Value ? Minimize Cost of Risk

Hypothetical construct
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Classic Definition of Risk Management Objective
- Revisited

• Multiple Goals
• Pre- loss
• Post loss
• Goal Select the option(s) that achieves the best
  balance among the multiple goals

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Classic Definition (cont.)

• Pre-loss goals
• Economical cost
• Fulfill social responsibility
• Reduce anxiety
• Meet externally imposed goals

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Risk Management Goals Classic Definition (cont.)

• Post-loss goals
• Social responsibility
• Financial Goals
• Survival
• Operational continuity
• Earnings Stability
• Sustained Growth

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Risk Management Decision Framework Classic
Goals
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Types of Loss Control

• Loss control
• Expenditures of time, money, or effort to reduce
  expected losses
• Loss Prevention reduce probability of loss
• Loss Reduction reduce severity of loss

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How Loss Control Affects a Probability
Distribution

• How would the probability distribution for
  property losses change if
• Install a sprinkler system?
• Replace old wiring?
• Discrete Distribution
• Property Losses for the coming Year Probability
• 1.000 million 0.01
• 0.500 million 0.05
• 0.250 million 0.10
• 0.100 million 0.20
• Continuous Distribution

Probability density
Losses
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Importance of Indirect Losses

• Recall, large losses can cause indirect losses
• Lost profits
• Clean-up costs
• Costs of raising capital
• Foregone investment opportunities
• Bankruptcy costs
• Thus, reducing probability of large losses (MPL)
  can reduce indirect losses
• Main point need to consider reduction in
  expected indirect losses when making risk
  management decisions
• Diversification does not change expected direct
  losses, but does reduce maximum probable loss and
  therefore reduces expected indirect losses

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Diversification by Segregating Assets

• No segregation
• 1 plant worth 100 million,
• Probability of complete loss 0.05
• Expected direct loss 5 million
• Segregation
• 2 plants each worth 50 million,
• Probability of complete loss at each plant 0.05
• Outcome at each plant are independent of the
  other
• What is the Probability distribution for total
  losses
• 100 million with probability of .05 X .05
  .0025
• 50 million with probability of 2 x .05 x .95
  .095
• 0 with probability of .95 x .95 .9025
• Expected direct loss 5 million

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Diversification by Segregating Assets

• Now assume an indirect loss equal to 10 million
  occurs if a 100 million direct loss occurs
• No segregation ? expected indirect loss
  500,000
• Segregation ? expected indirect loss 25,000
• Main Point diversification that reduces
  probability of high losses, can reduce expected
  indirect losses

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Cost Benefit Analysis

• Should compare costs and benefits of loss control
• Identifying costs and benefits
• Example Safer work environment
• What are the costs?
• What are the benefits?

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Cost Benefit Analysis - Example

• Example
• Average Loss Severity 20,000.
• Total number of employees 5,000

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Cost Benefit Analysis Example (cont.)
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Incorporating Time Dimension

• Often costs and benefits occur over time
• Need to calculate present values
• Example
• Cost 1 million
• Benefit reduction in liability cost of 300,000
  for each of next four years
• Cost of capital 8

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Incorporating Time Dimension

• Map the expected cash flows (in millions)
• Today 1 yr 2 yrs 3 yrs 4yrs
• -1 0.3 0.3 0.3 0.3
• Discount the future cash flows to find net
  present value
• NPV 0.016 million

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Identifying Costs and Benefits in Practice

• Benefits of loss control can be difficult to
  estimate
• Can use historical data on your own firm
• Use industry data
• Hire consultants, brokers
• Get estimates of insurance premium reductions
• Brokers and insurers

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Government Safety Programs

• Examples
• OSHA
• EPA
• CPSC
• Why have safety regulations?
• Firms may not consider all benefits of loss
  control if workers or customers are not fully
  informed
• Avoids duplication of expenditures on safety
  research

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Valuing Life

• Often loss control decisions involve changing the
  probability of death
• How do you value a life?
• One approach Use wage differentials for jobs
  with different probabilities of death (actual
  studies are more complex)
• Example
• Job 1 has .0002 higher probability of death on
  the job per year
• Job 1 has 1,000 wage premium per year, holding
  all else equal
• Employees willing to receive 1,000 for a .0002
  increased chance of dying.
• 1,000 .0002 x (Value of Life)
• ? Value of Life 1,000/.0002 5 million

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Government Safety Regulations

• Estimated costs and benefits of safety regulation
• (source K. Viscusi, Pricing Environmental
  Risks, 1992)
• Cost per life saved
• Regulation Passed Agency (in millions of
  1984)
• Unvented space heaters 1980 CPSC 0.10
• Passive restraints/belts 1984 NHTSA 0.30
• Crane suspended personnel platform 1988 OSHA
  1.20
• Grain dust 1987 OSHA 5.30
• Uranium mill tailings (inactive) 1983 EPA
  27.60
• Asbestos 1989 EPA 104.20
• Arsenic/low-arsenic copper 1986 EPA 764.00
• Formaldehyde 1987 OSHA 72,000.00

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Calculations for Question 1, p. 214
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Solution Question 1, p. 214

• The optimal amount to spend on safety is
• 45,000

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Calculations for Question 3, p. 214
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Present Value Calculations Question 3, p. 214

• (45,000/1.07) 42,056
• (45,000/1.072) 39,305
• 42,056 39,305 - 70,000 11,361
• Since the NPV of this project is positive, the
  firm should undertake the project.