Casualty Actuarial Society
March 12, 2004
Viewing Risk Through the
Eyes of the Insured
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
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?
3
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?
4
Example
General Liability
$250k Attachment
General Liability
$750k Attachment
Forecasted retained
losses (unlimited) =
$5,000,000
Premium = $1,000,000
Premium = $500,000
Which is the better deal?
5
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?
6
Example
General Liability
$250k Attachment
General Liability
$750k Attachment
Forecasted retained
losses (limited) =
$3,000,000
Forecasted retained
losses (limited) =
$4,000,000
Premium = $1,000,000
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
8
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
10
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
11
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?
13
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
14
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
15
"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
16
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
$32,000,000
$30,000,000
$28,000,000
$26,000,000
$24,000,000
$22,000,000
$20,000,000
500k
750k
1m
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1.5m
2m
Considering Expected Loss Differences
Volatility increases as retentions increase
18%
16%
14%
12%
10%
8%
6%
4%
2%
0%
$250k SIR
Values in Thousands
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$12,480
$11,822
$11,164
$10,506
$9,848
$9,190
$8,532
$7,874
$7,216
$6,558
$5,900
$5,242
$1M SIR
$4,605
PROBABILITY

Risk Retention as an Investment Decision
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
21
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
22
Equity Option Comparison
Put Option on Microsoft
Stock price = $25 per share
Put option to sell stock at
$22.5
expiring January, 2005
Option price on March 11 = $2.25
Option price for $20 strike = $1.35
23
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
24
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
25
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 nontraditional way
26
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







m = $7.795M @ $250k
m = $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
28
Step 1
Calculate the expected losses (the mean)
at alternative retentions
$8.123M
- $7.795M
.328M
29
Step 2
Calculate the difference between the
99% confidence interval and the mean
$10.902M
- $9.912M
.990M
30
Step 3
Multiply the difference times a hurdle rate for an
investment with a similar risk profile ("risk margin")
$.990M
* 10%
$.090M
31
Step 4
Add the expected increase plus the risk margin
to calculate the value of the retention
$.328M
+ .090M
$.418M
32
Step 5
Present value to take into account claim
payment and tax deduction timing
$.418M
* .78%
$.326M
33
Step 6
Compare to premium difference
$548,000
- $358,000
$190,000
34
Step 6
Compare to premium difference
$548,000
- $358,000
$190,000
Not Good Enough! Must be at Least $326,000
35
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?
37
Question
Should you set higher retentions
in a soft market?
38
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
39
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
40
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.
41