Viewing Risk Through the Eyes of the Insured March 13, 2006 Casualty Actuarial Society

Viewing Risk Through theEyes of the Insured

March 13, 2006

Casualty Actuarial Society

2

Client Considerations on Risk

Traditional, non-analytic approaches

Difference between a claim and a risk are cloudy

Claims in a normal year are a normal expense

Aggregation of annual claims are considered “risk”

Risk is negative variability from expected

Higher retention = higher expected losses retained

Assuming higher levels of retention increases volatility, but it may not be material

Retaining risk and avoiding premium is the reward for accepting the chance of higher claim expense

Question - Is it a good deal?

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Is It Better – in Risk Retention, It Depends

How much premium is saved?

What is the difference in expected losses?

How much volatility is added?

What is the value of the added volatility?

What parts of the financial equation are impacted?

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Example

General Liability$250k Attachment

Forecasted retained losses (unlimited) =

$5,000,000

Premium = $1,000,000


Premium = $500,000

Which is the better deal?

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It Depends

What are the losses expected at $250,000 loss limitation?

What are the losses expected at $750,000 loss limitation

What is the relative timing of the loss payments on the differential?

What is the impact of the tax deduction timing?

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Example


Forecasted retained losses (limited) =

$3,000,000

Premium = $1,000,000


Forecasted retained losses (limited) =

$4,000,000

Premium = $500,000

Which is the better deal?

7

Why Retain Risk?

Avoiding frictional costs

– Premium taxes

– Insurance company profit/overhead

– Risk pooling cost

Risk may be immaterial

Many losses are predictable

Difference in perception of risk

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Conventional Wisdom – Bigger is Better

Higher retentions results in lower cost

Higher retentions improve control

Large retentions are good

Buying risk transfer is bad

Problems

– Based on different times

– Assumes that risk transfer cost avoided results in lower cost

– May be true, but objective analysis is required to know

Test for effectiveness: If the worst case happens, will you still be employed?

9

Most Common Ways an Insured Views Retention and Limits Needed

Ratio rules of thumb

Market driven

Premium too high

Management decision based on feel

"Threshold of pain"

"Not a problem - couldn't happen to us" logic

Peer benchmarks

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Ratio Rules of Thumb

Various ratios to financial statements added provide an overall risk retention capacity in excess of expected

Problems– Aggregate capacity figure has little practical use

– Overly broad

– No relationship to premium avoided

– Ratios are subjectively set

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Market Driven

During hard market, retentions forced up by insurers

Got used to it - the bad thing didn’t happen

No reason for exploring - now used to higher level and management understands

Problems– Not based on rational decision

– Doesn't measure risk reward relationship

– Externally controlled

– Assumes status quo is OK

– Doesn't lead to least cost decision

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Premium Too High

Premium expense not in budget

Quotes too high for perceived benefit

Problems– No objective consideration of risk/reward

– Unanticipated claim isn't in the budget

– Will stockholders consider the premium too high after a loss?

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Management Decision Based on Feel

Decision based on management comfort

Risk Manager can't have a problem based on a directive

Problems– Decision based on reaction rather than objective analysis

– Management looks to risk management for input, shouldn't be forced to decide without information

– No rational decision can result

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Threshold of Pain

Much like decision on feel, just masked as an EPS decision

Same issues as management decision on feel, modified by how the stockholders might react, based on EPS

Problems– Same as prior slide

– Ignores transfer savings or expense in the equation

– Sounds more scientific - it isn’t

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"Not a Problem – Couldn't Happen to Us" Logic

Common human response to unlikely event

Ignores probability of losses

Assumes losses happening to others won't occur to me

Assumes past adverse loss experience will not repeat itself

Problems– Irrational

– Least cost decision by luck only - rolling the dice

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Peer Benchmarks

Blind leading the blind?

Assumes others are efficient

Easy fallback - can't be faulted

Problems– Statistically not comparable

– Assumes your risks are identical

– Accuracy/interpretation of responses

– Doesn't measure risk reward relationship

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Considering Expected Loss Differences

Retained loss expectancy increases as retention levels increase

Retainted Losses @ Alt Retentions

$20,000,000

$22,000,000

$24,000,000

$26,000,000

$28,000,000

$30,000,000

$32,000,000

500k 750k 1m 1.5m 2m

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Considering Expected Loss Differences

Volatility increases as retentions increase

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

$4,6

05

$5,2

42

$5,9

00

$6,5

58

$7,2

16

$7,8

74

$8,5

32

$9,1

90

$9,8

48

$10,5

06

$11,1

64

$11,8

22

$12,4

80

Values in Thousands

PR

OB

AB

ILIT

Y

$250k SIR

$1M SIR

Risk Retention as an Investment Decision

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How Can Retaining Risk Be an Investment?

When risk is retained, capital is contingently exposed

If losses occur beyond expected, income and net worth both decrease

When net worth decreases, there is an impact to ongoing interest expense

Retaining risk results in a immediate reward - the premium saved

Retention decisions impact other investment opportunities

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How Can Retaining Risk Be an Investment?

When risk is retained, capital is contingently exposed

If losses occur beyond expected, income and net worth both decrease

When net worth decreases, there is an impact to ongoing interest expense

Retaining risk results in a immediate reward - the premium saved

Retention decisions impact other investment opportunities

Result – Much like an equity option decision

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Equity Option Comparison

Put Option on Microsoft

Stock price = $25 per sharePut option to sell stock at $22.5 expiring January, 2006

Option price on March 11 = $2.25

Option price for $20 strike = $1.35

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What Happens?

If stock remains the same or increases, put has no value at expiration, buyer loses $2.25

Seller of option makes $2.25

Buyer of option received protection against MSFT decreasing to $20.25 instead of selling it now and losing the upside potential

On the expiration date, coverage expires

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Why is This Like Retention? Decisions

Owner of stock purchased "protection" for a premium

Covers a defined period

If no loss, the premium is lost

If a loss, buyer of coverage is made whole

Seller of the option contingently exposes their capital to gain the premium in the same way as one who retains risk to avoid premium payment

Over time neither buyer or seller "win", as rational pricing models take into account stock volatility

Credit for $20 strike recognizes lower probability of attaching

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Valuing Volatility by Line

Each exposure has its inherent volatility

The more volatile the exposure, the higher the amount of avoided premium needed to assume the exposure

Unlike options, insurance market pricing is individual risk based, and may be more imperfect

Markets may lead to purchasing coverage or avoiding coverage in a non-traditional way

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How do You Calculate the Investment Return on Retention?

Calculate the expected losses (the mean) at alternative retentions

Calculate the difference between the 99% confidence interval and the mean

Multiply the difference times a hurdle rate for an investment with a similar risk profile ("risk margin")

Add the expected increase plus the risk margin to calculate the value of the retention

Present value to take into account claim payment and tax deduction timing

Compare to premium difference

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Example

= $7.795M @ $250k = $8.123M @ $1M 99% Confidence = $9.912M @ $250k 99% Confidence = $10.902M @ $1M Hurdle Rate = 10% (assumed) Premium at $250k retention = $548,000 Premium at $1M retention = $358,000

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Step 1

$8.123M - $7.795M .328M

Calculate the expected losses (the mean) at alternative retentions

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Step 2

$10.902M- $9.912M .990M

Calculate the difference between the 99% confidence interval and the mean

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Step 3

$.990M * 10% $.099M

Multiply the difference times a hurdle rate for an investment with a similar risk profile ("risk margin")

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Step 4

$.328M+ .099M $.427M

Add the expected increase plus the risk margin to calculate the value of the retention

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Step 5

$.418M* .78% $.333M

Present value to take into account claim payment and tax deduction timing

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Step 6

$548,000- $358,000 $190,000


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Step 6

$548,000- $358,000 $190,000

Not Good Enough! Must be at Least $333,000


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What Rate of Return is Needed?

Internal rate of return?

– What if its negative?

– Uncertainty of timing

– Does the business have the same risk profile?

Short term cost of money?

– Borrowing, not investment rate

– Debt has no risk profile

Cost of Capital

Investment decision process

Payback period

Impact on stock price?

36

Question

If you have a very profitable organization with numerous investment possibilities,

should you retain more or less risk?

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Question

Should you set higher retentions in a soft market?

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It Depends Entirely on Risk – Reward Relationship

If premium avoided is more than the additional loss expectation and a risk margin, then yes

If an insurer is willing to put up their capital at a lower price than your firm, then no

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The Efficient FrontierAnother Look at the Same Concept

Figure 3 - The Efficient Frontier and Preference Indifference (Utility)

0%

5%

10%

15%

20%

25%

0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

Risk = Standard Deviation of Return Distribution

Retu

rn =

Mean V

alue of Return D

istribution

Each point represents an alternative portfolio of risk financing/transfer strategies. For example, this point on the risk/return sphere may represent :

•a casualty per occurrence retention of $10.0 Million,•a property retention of 20.0Million •FinPro Retention of $25.0 Million

Return = Savings from Guaranteed Cost

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Figure 3 - A portfolio of risk transfer mechanisms and optionson risk retention

0%

5%

10%

15%

20%

25%

0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%


Retu

rn =

Mean V

alue of Return D

istribution

A

B

C

D

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- Company Risk/Return Indifference (Utility)

XYZ Cor

p Indiff

eren

ce C

urve

0%

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25%

0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%


Retu

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Mean V

alue of Return D

istribution

C

DB

A

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0%

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25%

0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%


Retu

rn =

Mean V

alue of Return D

istribution

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Optimum Portfolio

Utility

Curv

e

0%

5%

10%

15%

20%

25%

0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%


Retu

rn =

Mean V

alue of Return D

istribution

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Optimum Portfolio

Utility

Curv

e

0%

5%

10%

15%

20%

25%

0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%


Retu

rn =

Mean V

alue of Return D

istribution

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Outcome of Efficient Frontier

There is a continuum of efficient alternatives where risk and cost trade-off balance

On the frontier, there may be efficiency, but that does not imply a willingness to accept the higher level of risk

Each point “Southeast” of the frontier is less efficient that points on the line

Each point further to the “Northwest” of the frontier on the map is more efficient, but not available in the market

As markets harden, the frontier moves down and right

As markets soften, they move up and left

Similar to efficient frontier concepts in other financial decisions

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What About Limits Insured?

Much more complex decision

Modeling is less certain in the tail of the distribution

– Less (or no) losses in the extremes

– Modeling less helpful, as the outcomes are random and wide

– Still useful as a guide

Most risk managers revert to the traditional approaches

Most difficult question to answer and may not be answerable in an analytic way

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Summation

Retaining more or less risk is not a qualitative decision, its economic

Contingently exposing corporate resources to volatility without a return is irrational

Care must be taken to avoid losing control or decreasing loss and claim control efforts

Must be willing to accept year to year changes in retentions (inconsistent?)

Limits purchased is also a risk-reward relationship, but with fewer tools to assess, unlikely to occur and more catastrophic if it does

If you don't consider all possibilities, your replacement will.

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Viewing Risk Through the Eyes of the Insured March 13, 2006 Casualty Actuarial Society