May 7, 2007
CAS Seminar on Reinsurance 2007
Hidden Risks in (Re)Insurance
Systemic Risks and Accumulation:
Spencer M. Gluck, FCAS
New York
Outline
 Section 1: Systemic Risks and Accumulation
A: Introduction - Model Structure
B: Systemic Risks
C: Accumulation
 Section 2: Examples
Impact of Systemic Risks and Accumulation
1
Section 1 – Systemic Risks
and Accumulation
A: Introduction - Model Structure
2
Introduction
 A modeling framework that captures important risks that we
may have been missing.
 Important applications:
–Impact of reinsurance, especially casualty
–Cross-lines correlation and whole company models:
 Capital adequacy and allocation
 ERM
3
Reasons for US P/C Insurer Impairments
1969-2005
2003-2005
Affiliate
Problems
8.6%
Catastrophe
Losses
8.6%
Alleged
Fraud
11.4%
Rapid
Growth
8.6%
1969-2005
Sig. Change
in Business
4.6%
Misc.
9.2%
Deficient
Loss
Reserves/Inadequate
Pricing
62.8%
Reinsurance
Failure
3.5%
Deficient
Loss
Reserves/Inadequate
Pricing
38.2%
Investment
Problems*
7.3%
Affiliate
Problems
5.6%
Catastrophe
Losses
6.5%
Alleged
Fraud
8.6%
Rapid
Growth
16.5%
*Includes overstatement of assets.
Source: A.M. Best: P/C Impairments Hit Near-Term Lows Despite Surging Hurricane Activity, Special Report, Nov. 2005;
4
Getting the Structure Right
 Catastrophe models “understand” the risk that’s being
modeled.
–The most dangerous risks are those that act in a
correlated way on accumulated exposure.
 We require a model structure for other types of
underwriting risk that reflect the impact of correlation and
accumulation.
5
Some Historical Casualty Killers
 Runaway Trends
– WC: 1970 through 1990 (California, Texas, etc.)
– Med Mal: Late 1960’s through early 1980’s (e.g. NY) and then again
in the 1990’s.
– All casualty 1970’s through early 1980’s.
 Extended Downcycles
– E.g., early 1980’s, late 1990’s
 Latent Losses
– E.g. asbestos, environmental, construction defects
For the risk model to be meaningful, these types of risk must be
captured.
6
Section 1 – Systemic Risks
and Accumulation
B: Systemic Risks
Systemic Risks Are Crucial
Systemic Risks:
–Difficult to Measure
–Affect all LOB’s -- but
–Greatest Impact in Casualty
Systemic Risks Accumulate
8
Elements of Systemic Risk
Time Related Risk
–Trend and Development Parameters.
–Changing Trends
–Simultaneously impact new business and
accumulated reserves.
Market Related Risk
Also: Casualty catastrophes
–But we’re not yet modeling these.
9
Casualty Markets are More Volatile
Price is driven by the lowest estimated costs.
Long tails increase:
–Risk of misestimated costs.
–Positive cash flows.
Therefore:
Long tail casualty market cycles are the most
severe.
10
Components of Risk
Other than diversifying process risk
 Limitations of the sample
 Uncertainty in other analysis parameters
– Trend factors
– Loss development factors
– Payment patterns
 Market Risks (pricing / underwriting)
– Imperfect exposure data / on-level process
– Actual prices achieved differ from targets
– Risk quality changes (underwriting selection)
 External Conditions
– Changes in inflation
– Changes in insurance loss trends / social inflation
– Other economic conditions (line specific)
 Differences in exposure between the data and the future period
11
Summarized Elements of Systemic Risk
Time Related Risk (i.e. the tail)
–Trend and Development Parameters.
–Changing Trends
–Simultaneously impact new business and
accumulated reserves.
Market Related Risk (i.e. the cycle)
Also: Casualty catastrophes
12
The Risk Factor Model
Model Structure (one LOB, one AY)
 Nominal Incremental Paid for accident year i = AYi for a single simulation.
 Each RV is sampled once per simulation.
 RV’s are mutually independent
AYi = A x B x C(Fi-E) x Di
E : Average date of payment in historical data
Fi : Average date of payment for period i
13
Risk Factor Model Components:
“Process+” Risk
AYi =
A x B x C(Fi-E) x Di
 Input Loss Distribution
 Reflects both process risk and sample-size related
parameter risk
–The data “sample” in this case is usually claims at
estimated ultimate values, trended to the appropriate
prospective level.
–Reflects risks that typically do not correlate across lines
of business
 Alternatively, A can be a placeholder for output from
another model.
14
Risk Factor Model Components:
Accident Year Deviation
AYi = A x B x C(Fi-E) x Di
 Structured as an independent random variable multiplied by the
overall aggregate losses
 Multiply B by expected frequency in a frequency/severity model.
 Parametric distribution
– Usually mean 1.0
 May be considered to reflect:
– Market risk (pricing / underwriting)
– Non-diversifying frequency risk (contagion)
– Differences between past and future exposures
15
Risk Factor Model Components:
Trend/Development Parameter Risk
AYi = A x B x C(Fi-E) x D
 Structured as an annualized error
 Annual error is compounded from the average date of payment in the
experience data to each future payment
– The period includes both the “development” and “trend” periods
– The structure is appropriate for both trend parameter error and
development parameter error
 C ~ N(1,σ) or C ~ L-N(0,σ) are reasonable choices.
 Compounded error factor for each payment is multiplied by the
payment
16
Trend and Development Parameter Risk
Long-Tail LOB
Historical
Data
Development
Trend
Short-Tail LOB
Future Accident Year
Ultimate
17
Risk Factor Model Components:
Future Trend Process Risk
AYi = A x B x C(Fi-E) x Di
 The result of a time series model
 The dynamic risk component -- reflects unpredictable changes
in future trends / external conditions
 Can also be considered as a reflection of specification error
 Future trend deviation is modeled as a time series:
–First order auto-regressive (AR(1))
–The simplest mean-reverting time series (reverts to mean of
zero)
18
Future Trend Process Risk
The AR(1) Process
 Xi (i = 1, 2, …, n) are independent mean zero Normal
random variables drawn from the same distribution.
 Then define:
t1  X 1
t k    t k 1  X k

is the autocorrelation coefficient.

 Annual trend error =
e
tk
 Cumulative trend error for year k = Dk =
k
k
 ti
i 1
e

e

ti
i 1
19
Changing Trends
Historical
Data
Future Accident Year
Expected Future
Trend
20
Some Pictures from the ERM Book
 The estimated trends
may be wrong:
2
1.5
1
0.5
0
 Plus the trends may
change:
l----------- Historical Period -----------l
l--------- Projected Period ------------l
l----------- Historical Period -----------l
l--------- Projected Period ------------l
2
1.5
1
0.5
0
21
Section 1 – Systemic Risks
and Accumulation
C: Accumulation Over Time
22
Accumulated Risk
 Trend and development risks accumulate over many years
of underwriting.
 Extended down cycles accumulate losses over several
years of underwriting.
 This appears as reserve risk.
 Risk decisions you make now affect reserves for years to
come.
 The business you write this year absorbs capital for years
to come.
23
Drawing Capital for Years to Come
Calendar Year
1
Exposure Drawing Capital
The new AY (Premium)
2
Reserves for one year old AY
3
Reserves for two year old AY
4
Reserves for three year old AY
5
Reserves for four year old AY
6
Reserves for five year old AY
•
•
•
•
•
•
etc.
24
“As-If” Reserves:
An Approach to Accumulated Risk
Reserves “As If” the company had been writing
the business consistently over time.
Equivalent to capital to be allocated in the future.
Can reflect the correlated risks on accumulated
exposure.
Can measure the impact of reinsurance over time.
25
Accumulation of Systemic Risks
 Trend and development parameter risk is identical (100%
correlated) between the new AY and the reserves.
 Risk of changing trends is identical (100% correlated)
between the new AY and the reserves.
 The model for changing trend risk can also be a surrogate
for latent losses and emerging exposures.
 Market risk is partially correlated between successive AY’s.
26
Section 2 - Examples
Impact of Systemic Risk and
Accumulation
27
Effect of Systemic Risk
Direct Private Passenger Auto PDF
Effect of Systemic Risks
Probability Density Functions
Process+ Only
Include Systemic Risks
-300,000
-200,000
-100,000
0
100,000
200,000
300,000
400,000
$ (thousands)
28
Effect of Systemic Risk
Direct Private Passenger Auto CDF
Effects of Systemic Risks and Accumulation
Cumulative Distribution Functions with 99th percentiles
120%
100%
Process+ Only
80%
Probability
Include Systemic Risks
60%
40%
20%
0%
-150,000
-100,000
-50,000
0
50,000
100,000
150,000
Excess Over the Mean
29
Effect of Systemic Risk
Direct Workers Compensation PDF
Effects of Systemic Risks and Accumulation
Probability Density Functions
Process+ Only
Include Systemic Risks
-50,000
-30,000
-10,000
10,000
30,000
50,000
70,000
90,000
$ (thousands)
30
Effect of Systemic Risk
Direct Workers Compensation CDF
Effects of Systemic Risks and Accumulation
Cumulative Distribution Functions with 99th percentiles
120%
Process+ Only
100%
Probability
Include Systemic Risks80%
60%
40%
20%
0%
-50,000
-30,000
-10,000
10,000
30,000
50,000
70,000
90,000
Excess Over the Mean
31
Effect of Systemic Risk
Direct Casualty Multiline PDF
Effect of Systemic Risks
Probability Density Functions
Process+ Only
Include Systemic Risks
-300,000
-200,000
-100,000
0
100,000
200,000
300,000
400,000
$ (thousands)
32
Effect of Systemic Risk
Direct Casualty Multiline CDF
Effect of Systemic Risks
Cumulative Distribution Functions with 99th percentiles
120%
100%
Process+ Only
Probability
Include Systemic Risks
80%
60%
40%
20%
0%
-300,000
-200,000
-100,000
0
100,000
200,000
300,000
400,000
Excess Over the Mean
33
Effect of Systemic Risk
Ceded Casualty PDF
Effects of Systemic Risks
Probability Density Functions
Process+ Only
Include Systemic Risks
-20,000
-10,000
0
10,000
20,000
30,000
40,000
50,000
$ (thousands)
34
Effect of Systemic Risk
Ceded Casualty CDF
Effects of Systemic Risks
Cumulative Distribution Functions with 99th percentiles
120%
Process+ Only
100%
Probability
80%
Include Systemic Risks
60%
40%
20%
0%
-20,000
-10,000
0
10,000
20,000
30,000
40,000
50,000
Excess Over the Mean
35
Effect of Systemic Risk
Ceded Casualty 20 Accounts PDF
Effects of Systemic Risks
Probability Density Functions
Process+ Only
Include Systemic Risks
-500,000
-300,000
-100,000
100,000
300,000
500,000
700,000
900,000
$ (thousands)
36
Effect of Systemic Risk
Ceded Casualty 20 Accounts CDF
Effects of Systemic Risks
Cumulative Distribution Functions with 99th percentiles
120%
Process+ Only
100%
Probability
Include Systemic Risks 80%
60%
40%
20%
0%
-500,000
-300,000
-100,000
100,000
300,000
500,000
700,000
900,000
Excess Over the Mean
37
Effect of Systemic Risk and Accumulation
Direct Private Passenger Auto PDF
Effects of Systemic Risks and Accumulation
Probability Density Functions
Process+ Only
Include Systemic Risks
Include Accumulation
-250,000
-150,000
-50,000
50,000
150,000
250,000
350,000
$ (thousands)
38
Effect of Systemic Risk and Accumulation
Direct Private Passenger Auto CDF
Effects of Systemic Risks and Accumulation
Cumulative Distribution Functions with 99th percentiles
120%
Process+ Only
100%
Include Systemic Risks
Probability
Include Accumulation
80%
60%
40%
20%
0%
-250,000
-150,000
-50,000
50,000
150,000
250,000
350,000
Excess Over the Mean
39
Effect of Systemic Risk and Accumulation
Direct Workers Compensation PDF
Effects of Systemic Risks and Accumulation
Probability Density Functions
Process+ Only
Include Systemic Risks
Include Accumulation
-200,000
-150,000
-100,000
-50,000
0
50,000
100,000
150,000
200,000
250,000
300,000
$ (thousands)
40
Effect of Systemic Risk and Accumulation
Direct Workers Compensation CDF
Effects of Systemic Risks and Accumulation
Cumulative Distribution Functions with 99th percentiles
120%
Process+ Only
100%
Include Systemic Risks
Probability
Include Accumulation
80%
60%
40%
20%
0%
-200,000
-150,000
-100,000
-50,000
0
50,000
100,000
150,000
200,000
250,000
300,000
Excess Over the Mean
41
Effect of Systemic Risk and Accumulation
Direct Casualty Multiline PDF
Effects of Systemic Risks and Accumulation
Probability Density Functions
Process+ Only
Include Systemic Risks
Include Accumulation
-600,000
-400,000
-200,000
0
200,000
400,000
600,000
800,000
$ (thousands)
42
Effect of Systemic Risk and Accumulation
Direct Casualty Multiline CDF
Effects of Systemic Risks and Accumulation
Cumulative Distribution Functions with 99th percentiles
120%
Process+ Only
100%
Include Systemic Risks
Probability
Include Accumulation
80%
60%
40%
20%
0%
-600,000
-400,000
-200,000
0
200,000
400,000
600,000
800,000
Excess Over the Mean
43
Effect of Systemic Risk and Accumulation
Ceded Casualty PDF
Effects of Systemic Risks and Accumulation
Probability Density Functions
Process+ Only
Include Systemic Risks
Include Accumulation
-100,000
-50,000
0
50,000
100,000
150,000
$ (thousands)
44
Effect of Systemic Risk and Accumulation
Ceded Casualty CDF
Effects of Systemic Risks and Accumulation
Cumulative Distribution Functions with 99th percentiles
120%
Process+ Only
100%
Include Systemic Risks
Probability
Include Accumulation
80%
60%
40%
20%
0%
-100,000
-50,000
0
50,000
100,000
150,000
Excess Over the Mean
45
Effect of Systemic Risk and Accumulation
Ceded Casualty 20 Accounts PDF
Effects of Systemic Risks and Accumulation
Probability Density Functions
Process+ Only
Include Systemic Risks
Include Accumulation
-1,500,000
-1,000,000
-500,000
0
500,000
1,000,000
1,500,000
2,000,000
2,500,000
$ (thousands)
46
Effect of Systemic Risk and Accumulation
Ceded Casualty 20 Accounts CDF
Effects of Systemic Risks and Accumulation
Cumulative Distribution Functions with 99th percentiles
120%
Process+ Only
100%
Include Systemic Risks
Probability
Include Accumulation
80%
60%
40%
20%
0%
-1,500,000
-1,000,000
-500,000
0
500,000
1,000,000
1,500,000
2,000,000
2,500,000
Excess Over the Mean
47