Casualty Actuarial Society
March 13, 2006
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
Question - Is it a good deal?
2
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?
3
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?
4
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?
5
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?
6
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
7
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?
8
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
9
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
10
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
11
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?
12
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
13
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
14
"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
15
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
16
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
17
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
18
$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
20
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
21
Equity Option Comparison
Put Option on Microsoft
Stock price = $25 per share
Put option to sell stock at
$22.5
expiring January, 2006
Option price on March 11 = $2.25
Option price for $20 strike = $1.35
22
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
23
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
24
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
25
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
26
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
27
Step 1
Calculate the expected losses (the mean)
at alternative retentions
$8.123M
- $7.795M
.328M
28
Step 2
Calculate the difference between the
99% confidence interval and the mean
$10.902M
- $9.912M
.990M
29
Step 3
Multiply the difference times a hurdle rate for an
investment with a similar risk profile ("risk margin")
$.990M
* 10%
$.099M
30
Step 4
Add the expected increase plus the risk margin
to calculate the value of the retention
$.328M
+ .099M
$.427M
31
Step 5
Present value to take into account claim
payment and tax deduction timing
$.418M
* .78%
$.333M
32
Step 6
Compare to premium difference
$548,000
- $358,000
$190,000
33
Step 6
Compare to premium difference
$548,000
- $358,000
$190,000
Not Good Enough! Must be at Least $333,000
34
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?
35
Question
If you have a very profitable organization
with numerous investment possibilities,
should you retain more or less risk?
36
Question
Should you set higher retentions
in a soft market?
37
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
38
The Efficient Frontier
Another Look at the Same Concept
Figure 3 - The Efficient Frontier and Preference Indifference (Utility)
25%
Return = Mean Value of Return Distribution
20%
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
15%
10%
5%
0%
0%
1%
2%
3%
4%
5%
6%
7%
8%
9%
Risk = Standard Deviation of Return Distribution
Return = Savings from
Guaranteed Cost
39
10%
The Efficient Frontier
Another Look at the Same Concept
Figure 3 - A portfolio of risk transfer mechanisms and optionson risk retention
25%
Return = Mean Value of Return Distribution
20%
C
A
15%
D
B
10%
5%
0%
0%
1%
2%
3%
4%
5%
6%
7%
Risk = Standard Deviation of Return Distribution
40
8%
9%
10%
The Efficient Frontier
Another Look at the Same Concept
- Company Risk/Return Indifference (Utility)
25%
Return = Mean Value of Return Distribution
20%
C
A
15%
D
B
10%
5%
0%
0%
1%
2%
3%
4%
5%
6%
7%
Risk = Standard Deviation of Return Distribution
41
8%
9%
10%
The Efficient Frontier
Another Look at the Same Concept
Figure 3 - The Efficient Frontier and Preference Indifference (Utility)
25%
Return = Mean Value of Return Distribution
20%
15%
10%
5%
0%
0%
1%
2%
3%
4%
5%
6%
7%
Risk = Standard Deviation of Return Distribution
42
8%
9%
10%
The Efficient Frontier
Another Look at the Same Concept
Figure 3 - The Efficient Frontier and Preference Indifference (Utility)
25%
til
it
y
Cu
rv
e
15%
Optimum
Portfolio
10%
U
Return = Mean Value of Return Distribution
20%
5%
0%
0%
1%
2%
3%
4%
5%
6%
7%
Risk = Standard Deviation of Return Distribution
43
8%
9%
10%
The Efficient Frontier
Another Look at the Same Concept
Figure 3 - The Efficient Frontier and Preference Indifference (Utility)
25%
Cu
rv
e
y
til
it
U
Return = Mean Value of Return Distribution
20%
15%
Optimum
Portfolio
10%
5%
0%
0%
1%
2%
3%
4%
5%
6%
7%
Risk = Standard Deviation of Return Distribution
44
8%
9%
10%
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
45
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
46
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.
47