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Viewing Risk Through theEyes of the Insured
March 13, 2006
Casualty Actuarial Society
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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
General Liability$750k Attachment
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
General Liability$250k Attachment
Forecasted retained losses (limited) =
$3,000,000
Premium = $1,000,000
General Liability$750k Attachment
Forecasted retained losses (limited) =
$4,000,000
Premium = $500,000
Which is the better deal?
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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?
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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
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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
Compare to premium difference
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Step 6
$548,000- $358,000 $190,000
Not Good Enough! Must be at Least $333,000
Compare to premium difference
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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?
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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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The Efficient FrontierAnother Look at the Same Concept
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%
Risk = Standard Deviation of Return Distribution
Retu
rn =
Mean V
alue of Return D
istribution
A
B
C
D
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The Efficient FrontierAnother Look at the Same Concept
- Company Risk/Return Indifference (Utility)
XYZ Cor
p Indiff
eren
ce C
urve
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
C
DB
A
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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
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The Efficient FrontierAnother Look at the Same Concept
Figure 3 - The Efficient Frontier and Preference Indifference (Utility)
Optimum Portfolio
Utility
Curv
e
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
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The Efficient FrontierAnother Look at the Same Concept
Figure 3 - The Efficient Frontier and Preference Indifference (Utility)
Optimum Portfolio
Utility
Curv
e
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
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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.