Insurance and Risk Finance 640

1
Insurance and RiskFinance 640

• Class 4
• October 4, 2004

2
Overview

• Revisit Objective of Risk Management
• Review Threshold Point, Confidence Interval and
  Joint Probability
• Homework
• Insurer Ownership, Financial and Operation
  Structure
• Insurance Regulation

3
Risk Management Objective

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

4
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
5
Risk Management Objective Classic Definition

• 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

7
Risk Management Goals Classic Definition (cont.)

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

8
Risk Management Decision Framework Classic Goals
9
Normal Distribution Selected Threshold Points
10
Number of Exposure Units Formula

• Formula exists to estimate the number of exposure
  units for a given degree of accuracy.
• Assumes loss population is normally distributed
• Estimates the occurrence of a loss, not the size
  of the loss
• Formula is based on the fact that known
  percentages of losses will fall within 1, 2 or 3
  standard deviations of the expected value.
• Should be used with great caution

11
Formula (cont.)

• N S2p(1- p)/E2
• Where
• N Number of exposure units required for the
  degree of accuracy desired
• S the number of standard deviations
• p probability of loss
• E the degree of accuracy desired
• Expressed as a ratio of the actual losses to the
  total number in the sample

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Example 1

• 30 Probability of Loss
• 95 Desired Confidence
• That the actual loss ratio will not differ from
  the expected probability by more than 2
  percentage points
• ( the range will be 28 to 32).

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Example 1 (cont.)

• N S2p(1- p)/E2
• N 22(.3)(1- .3)/(.02)2
• N 4(.3)(.7)/(.0004)
• N 4(.21)/(.0004)
• N .84/(.0004)
• N 2,100

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Example 2

• Probability of loss p 5.0
• Degree of accuracy 0.5
• Degree of confidence 95 2 std. Dev.
• Exposure units needed N
• N S2p(1- p)/E2
• N 22(0.05)(0.95)/(0.005)2
• N 7,600

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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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Important Properties of the Normal Distribution

• Often analysts use the following properties of
  the normal distribution to calculate VAR
• Assume X is normally distributed with mean ? and
  standard deviation ?. Then
• Prob (X gt ? -2.33?) 0.01
• Prob (X gt ? -1.645?) 0.05

17
Confidence Interval Versus Threshold Level

• Confidence level expresses
• The probability that the unknown mean of the
  population falls within the sample mean and some
  interval

18
Threshold Level

• The probability that the actual value will be
  lower than some maximum level
• Used in
• Maximum Probable Loss
• Value at Risk

19
The 68-95-99.7 Rule

• In any normal distribution,
• 68 of the observations will fall within one
  standard deviations of the mean
• 95 fall within 2 standard deviations of the
  mean
• 99.7 fall within 3 standard deviations of the
  mean
• What is this an example of? Confidence interval
  or threshold limit?

20
Joint Probability

• Joint probability is the probability that two or
  more event will happen within a given period.
• Also, often called Compound Probability

21
Calculating Joint Probability

• If two or more events are independent,
• The joint probability that all events will occur
  is
• The product of their separate probabilities.

22
Joint Probability Example

• Two buildings located in distinct areas have
  separate probabilities of a fire in a year
• P(bldg. 1) .02
• P (bldg.2) .03
• The joint probability of both buildings having a
  fire in a given year is
• Joint probability (.02)(.03) .0006

23
Free Throw Example, p. 56 Harrington and Niehaus

• Assume
• Alan Iversons probability of making a free throw
  is .8
• And, that each free throw is independent.
• Then, the probability of him making two in a row
  is
• (0.8)(0.8) .64
• The probability that he will make one and miss
  one is
• (0.8)(.0.2) .32

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Question 1a., p. 67 Expected Value of
Individual Loss Distributions

• 50,000 x .005 250.00
• 20,000 x .010 200.00
• 10,000 x .020 200.00
• 0 x .965 0.00
• Total 650.00

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Question 1a., p. 67 Standard Deviation of
Individual Distributions

• (0 650)2 422,500 x .965
  407,712.50
• (50,000 650)2 24,354,422,500 x .03
  730,626,750
• (20,000 650)2 3,744,225,000 x .01
  37,442,250
• (10,000 650)2 87,422,500 x .02
  1,748,450
• Variance
  770,225,162.50
• Standard Deviation is the
• Square Root of Variance
  27,752.9307

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Question 1a., p. 67 Probability Distribution
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Expected Loss for Each Participant Pooled
Distribution

• 0 x .931225 0.00
• 5,000 x .0386 193.00
• 10,000 x .0193 193.00
• 25,000 x .00965 241.25
• 15,000 x .0004 6.00
• 30,000 x .0002 6.00
• 35,000 x .0001 3.50
• 10,000 x .0004 4.00
• 20,000 x .0001 2.00
• 50,000 x .000025 1.25
• Total 650.00

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Standard Deviation

• (0 650)2 422,500 x .931225
  393,442.56
• (500 650)2 22500 x .0386
  8685.00
• (10,000-650)2 87422500 x.0193
  1,687,254.20
• (25000 650)2 592922500 x .00965
  5,721,702.125
• (15000 650)2 205922500 x .0004
  82,369.00
• (30000 650)2 861422500 x.0002
  172,284.50
• (35,000 650)2 1179922500 x .0001
  117,992.25
• (10,000 650)2 87422500x .0004
  34969.00
• (20,000 650)2 374422500 x .0001
  37442.25
• (50,000 650)2 2435422500 x .000025
  60,885.5625
• Variance
  8,317,026.45
• Standard Deviation
• Square Root of Variance
  2,883.925527

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Homework Exercise 2

• Share your top driver and top hazard for Scooper
  Dooper.

30
Insolvency Risk and the Role of Capital

• Insolvency risk is reduced by insurer capital
• Capital provides a cushion
• Greater capital reduces the likelihood of
  insolvency, all else equal

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Definition of Insurer Capital

• Definitions
• Capital Assets - Policyholder Liabilities
• Economic value Difference between market value
  of assets and market value of liabilities
• Economic values not accounting values
• Assets market value of securities, etc.
• Liabilities present value of expected payments
  on policies already sold
• Surplus is another name for capital

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Example to Illustrate the Role of Insurer Capital

• Example
• Insurer initially has assets of 1million no
  liabilities
• Surplus 1 million
• It sells 10,000 one-year policies at beginning of
  the year
• expected claim cost 1,000 per policy
• claims paid at end of year
• ignore non-claim costs and the time value of
  money
• Liabilities at beginning of year 10 million

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Example to Illustrate the Role of Insurer Capital

• Assume premiums 11 m, all paid at beginning
  of the year
• Then assets at beginning of year 12 million
• Surplus (Capital) at beginning of year 2
  million
• surplus/assets 2/12 16.7
• surplus/liabilities 2/10 20.0

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Example to Illustrate the Role of Insurer Capital

• Although expected claim cost 10 million,
  actual claim costs are uncertain
• Assume total claim cost distribution is as
  follows. What is the probability of insolvency?

Claim cost
10m 12m
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Example to Illustrate the Role of Insurer Capital

• Main Points
• Capital reduces Probability of Insolvency
• Capital acts as a cushion
• More capital gt lower probability of insolvency

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Example to Illustrate the Role of Insurer Capital

• What if the correlation in losses increased?
• Distribution of claim costs would have greater
  variance
• Holding capital constant, probability of
  insolvency would increase with the correlation in
  losses
• Holding probability of insolvency constant,
  amount of capital needed increases with the
  correlation in losses

37
Most Common Forms of Insurer Ownership

• Two main types of ownership
• Mutuals
• Policyholders are the residual claimants
• Policyholders usually have limited liability
  they cannot be assessed
• Cannot raise capital by issuing equity
• Stock Companies
• Investors are the residual claimants
• Investors have limited liability

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Lloyds of London

• Marketplace where insurance business is
  transacted
• most business is commercial insurance,
  reinsurance, and automobile insurance
• Owners are called names
• Names contribute capital to syndicates
• Individual names have unlimited liability
• Corporate names have limited liability

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Factors Affecting Insurer Capital Decisions

• How much capital should an insurer hold?
• Difficult question for insurers
• Difficult question for regulators
• Regulatory factors in Chapter 6 7
• Our objective
• Identify factors that influence insurers choice
  in an unregulated environment

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Approach for Examining Insurer Capital Decisions

• Perspective of an owner
• Assume the insurer has some level of capital,
• Identify the benefits of adding additional
  capital
• Identify the costs of adding additional capital?

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Benefits of Capital

• Additional capital lowers the probability of
  insolvency
• Why is this a good thing for owners?
• Improves the terms of contracts
• especially with commercial policyholders
• Protects insurers franchise value

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Costs of Insurer Capital

• What is the cost of adding capital?
• There is an opportunity cost - owners cannot
  invest elsewhere.
• If investment in insurer has disadvantages
  compared with alternatives, then investors
  require additional compensation
• What are the differences between giving funds to
  an insurer versus putting them in a mutual fund?

43
Costs of Insurer Capital

• Differences between investment in an insurer and
  a mutual fund
• Insurer has liabilities, which
• can lead to lower returns
• but also can lead to higher returns
• Thus there is additional risk in giving capital
  to an insurer
• If liabilities are not correlated with investors
  other assets, then the net effect of the
  liabilities on the additional return demanded by
  investors should be zero

44
Cost of Insurer Capital

• Differences between investment in an insurer and
  a mutual fund (continued)
• Insurers investment returns are taxed twice
• Insurer might have greater agency costs
• Thus, investors will demand higher before-tax
  returns to invest in an insurer

45
Cost of Insurer Capital

• The costs of raising capital also limits the
  amount of capital that insurers hold
• Cost of raising capital
• issuance costs
• underpricing costs

46
Amount of Capital Held by Insurers
47
Diversification of Underwriting Risk

• Insolvency risk depends on variability of claim
  costs
• Variability can be reduced by
• diversifying across geographical areas
• diversifying across lines of business

48
Reinsurance

• Reinsurance is insurance for insurers
• Primary roles of reinsurance
• Reduce variance in claim costs by
• diversification
• reducing exposure to very high claims
• Reduce amount of capital needed to achieve a
  given probability of insolvency

49
Types of Reinsurance

• Types of policies
• proportional (pro-rata)
• excess
• treaty
• facultative

50
Largest Reinsurers in 2000
51
Asset Choices and Insolvency Risk

• Insolvency risk also depends on
• risk of assets
• correlation of assets and liabilities

52
Assets Held by Property-Liability Insurers
53
Assets Held by Life-Health Insurers
54
State Regulation of Insurance

• State insurance department or commission
• State insurance commissioner
• elected
• appointed
• National Association of Insurance Commissioners
  (NAIC)
• Model laws
• State insurance code

55
Regulated Activities

• Licensing of insurers and agents/brokers
• Insurer solvency
• Rates
• Residual markets
• Content of policy forms
• Contract interpretation and enforcement
• Sales practices and information disclosure
• Compulsory insurance coverage

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History of State Regulation

• State charters
• 1st state insurance department - NH, 1851
• Paul v. Virginia, 1868 - Insurance is not
  commerce
• Development of rating bureaus, 1870s
• Antitrust Acts, 1890s
• Southeastern Underwriters Association Case, 1942
• Insurance is commerce subject to antitrust laws
• McCarran -Ferguson Act, 1945

57
McCarran-Ferguson Act

• Regulation and taxation by states is in the
  public interest
• Exempt from federal antitrust law, provided
  activities are subject to state law, and do not
  involve boycott, coercion, or intimidation
• Response of many states
• Encouraged insurers to use rating bureaus
• Prior approval rate regulation
• eliminated by many during 1960s

58
Challenges to McCarran-Ferguson

• Some argue it promotes collusion and increases
  prices
• Counter arguments
• Industry has a competitive structure
• Rating bureaus help smaller insurers compete
• Some argue federal solvency regulation would be
  better

59
Arguments in Favor of Federal Regulation

• Lack of uniformity across states increases
  insurers compliance costs
• Lower costs
• Economies in scale
• Avoids costly duplication
• Quality would be uniform
• Weak regulation in one state can hurt people and
  insurers in other states
• Some states free ride on other states

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Arguments in Favor of State Regulation

• Can be tailored to local needs
• Facilitates experimentation
• NAIC coordination is sufficient to
• achieve economies of scale
• reduce costly duplication
• encourage uniformity
• reduce free riding
• Track record of federal regulation of financial
  institutions is not good

61
Public Interest View of Regulation

• Regulate if
• Industry conduct and performance deviates from
  what would occur in a competitive market
• Characteristics of a competitive market
• large number of sellers
• low entry costs
• low cost of information about prices and quality
• Costs and limitations of regulation are
  relatively low

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Example Costly and Imperfect Information

• Costly for consumers to be informed about product
  quality
• Regulations that deal with this problem
• licensing
• solvency
• contract language
• sales practices
• Legal system also deals with the problem

63
Regulation and Political Pressure

• Difference between what regulation should do and
  what it actually does
• Alternative to public interest view
• Economic theory of regulation
• Legislators and regulators act in their own
  interest
• I.e., they maximize political support
• Regulations reflect this objective, not public
  interest

64
Economic Theory of Regulation

• General prediction
• Small groups (organization costs are low)
• with large per capita stakes (potentially large
  benefits)
• will benefit at the expense of large groups with
  low per capita stakes
• gt producers might be beneficiaries of
  regulation
• (capture theory)

65
Economic Theory of Regulation

• Application to insurance
• Insurers benefit at expense of consumers
• Some think this was true of prior approval rate
  regulation in 1950s and 1960s
• Certainly not true of rate regulation in past two
  decades
• rates often have been suppressed and compressed