Transcript Risk-Based Capital Case Study for General Insurance Glenn Meyers Insurance Services Office, Inc. CAS Spring Meeting May 18, 2004

Risk-Based Capital Case Study
for
General Insurance
Glenn Meyers
Insurance Services Office, Inc.
CAS Spring Meeting
May 18, 2004
General Insurance Case Study
Proposal for “Standardized Approach”
Illustrative “Internal Model”
Desirable Properties of a
Standard Formula
Simplicity – The formula fits on a spreadsheet.
This may allow for some complexity in the formulas,
as long as the objective of the formulas is clear.
Input Availability – The inputs needed for the
formula are either readily available, or can be
reasonably estimated with the help of the appointed
actuary.
Conservative – When there is uncertainty in the
values of the parameters, the parameters should be
chosen to yield a conservative estimate of the
required capital
A Proposal for a Standard Formula
The formula is sensitive to:
The volume of business in each line of
business;
The overall volatility of each line of
insurance;
The reinsurance provisions; and
The correlation, or dependency structure,
between each line of business.
Correlation Generated by
Multiple Line Parameter Uncertainty
A model where losses tend to move together
Select b from a distribution with E[b] = 1 and
Var[b] = b.
For each line h, multiply each loss by b.
Correlation Generated by
Multiple Line Parameter Uncertainty
A simple, but nontrivial example
b1  1  3b , b 2  1, b3  1  3b
Pr b  b1  Pr b  b3   1/ 6 and Pr b  b 2   2 / 3
E[b] = 1 and Var[b] = b
Low Volatility
b = 0.01 r = 0.50
Chart 3.3
4,000
3,500
Y 2 = bX 2
3,000
2,500
2,000
1,500
1,000
500
0
0
1,000
2,000
Y 1 = bX 1
3,000
4,000
Low Volatility
b = 0.03 r = 0.75
Chart 3.3
4,000
3,500
Y 2 = bX 2
3,000
2,500
2,000
1,500
1,000
500
0
0
1,000
2,000
Y 1 = bX 1
3,000
4,000
High Volatility
b = 0.01 r = 0.25
Chart 3.3
4,000
3,500
Y 2 = bX 2
3,000
2,500
2,000
1,500
1,000
500
0
0
1,000
2,000
Y 1 = bX 1
3,000
4,000
High Volatility
b = 0.03 r = 0.45
Chart 3.3
4,000
3,500
Y 2 = bX 2
3,000
2,500
2,000
1,500
1,000
500
0
0
1,000
2,000
Y 1 = bX 1
3,000
4,000
Dependency Analyses are Directed
Toward Goal of Evaluating
Insurer Capital Costs
If bad things happen at the same time,
your need more capital.
Volatility Determines Capital Needs
Low Volatility
Size of Loss
Chart 3.1
Random Loss
Needed Assets
Expected Loss
Volatility Determines Capital Needs
High Volatility
Size of Loss
Chart 3.1
Random Loss
Needed Assets
Expected Loss
Correlation and Capital
b = 0.00
Chart 3.4
Correlated Losses
Sum of Random Losses
7,000
6,000
5,000
4,000
3,000
2,000
1,000
0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
Random Multiplier
Low correlation implies lower capital
1.0
1.0
1.0
1.0
1.0
Correlation and Capital
b = 0.03
Chart 3.4
Correlated Losses
Sum of Random Losses
7,000
6,000
5,000
4,000
3,000
2,000
1,000
0
0.7
1.3
1.3
1.0
1.0
0.7
1.0
0.7
1.3
1.3
0.7
1.3
1.3
1.0
0.7
0.7
1.0
1.3
0.7
1.0
1.3
Random Multiplier
High correlation implies higher capital
1.0
0.7
0.7
1.0
Features of the Formula
Input for insurance losses
– Expected losses for current business
– Loss Reserves (at expected values of payout)
Parameters - Specified by regulator (??)
– Claim severity distribution by line of business
– Claim count distribution
– Dependency model parameters (see next slide)
Calculates first two moments of aggregate loss
distribution. Using lognormal approximation:
Capital = TVaR99% – Expected Loss
Dependency Model Parameters
Common shock model
– Uncertainty in trend affects all lines simultaneously
– Magnitude of shock varies by line of business
Catastrophes treated separately
Capital = TVaR99% – Expected Loss + Cat PML
Calculate Cat PML with a catastrophe model
Example on Spreadsheet
Big Insurer – ABC Insurance Company
Small Insurer – XYZ Insurance Company
ABC Volume = 10 times XYZ Volume
– Otherwise they are identical
Spreadsheet on CAS website for this
session
ABC with no
Reinsurance
ABC with
Reinsurance
XYZ with no
Reinsurance
XYZ with
Reinsurance
Standard Formula Example
Capital ($Millions)
1,000
100
With Reinsurance
No Reinsurance
10
1
ABC
XYX
Diversification effect of size – ABC < 10×XYZ
Reinsurance has proportionally greater effect on XYZ
Moving Toward an Internal Model
Recall WP recommendations
– That the “Standard Model” be deliberately
conservative.
Several modifications to the “Standard
Model” are possible.
Insurer internal models are to be subject to
standards for risk-based capital formulas.
Possible Improvements
with Internal Model
More realistic claim severity distributions
– Tailored to the individual insurer
Richer dependency structure
– Parameter uncertainty in claim frequency as
well as claim severity
– Parameter uncertainty in claim frequency
applied across groups of lines.
Possible Improvements
with Internal Model
Calculate aggregate loss distribution
directly rather than by moments
Include catastrophe model directly in
aggregate loss calculation, rather than add
PML.
Allow for more flexible reinsurance
arrangements.
– e.g. varying participation by layer
Standand and Internal Model Example
Capital ($Millions)
1,000
100
With Reinsurance
No Reinsurance
10
1
ABC Std
ABC Internal
XYX Std
XYZ Internal
Diversification effect of size – ABC < 10×XYZ
Internal model is less conservative
Requirements for Internal Models
The insurer should have an independent
internal risk management unit, responsible for
the design and implementation of the risk-based
capital model.
The insurer’s Board and senior management
should be actively involved in the risk control
process, which should be demonstrated as a
key aspect of business management.
Requirements for Internal Models
The model should be closely integrated with
the day-to-day management processes of the
insurer.
An independent review of the model should be
carried out on a regular basis. (Amongst other
considerations, it should be recognised that
evolution of the modelling capabilities is to be
encouraged)
Operational risks should be fully considered
Requirements for Internal Models
The model should be closely integrated
with the day-to-day management
processes of the insurer.
Examples using an internal model:
– Reinsurance analysis
– Allocating Capital and Underwriting Targets
– Evaluating growth strategies
Cost of Financing Insurance
Net Cost of Reins
Cost of Capital
No Re
Cat Re
All Re
Cat Reinsurance is the best strategy
Target Analysis by Source of Cost
Target Combined Ratio
105%
95%
Reinsurance
Capital
Other
85%
75%
65%
CMP
HO
Auto
Cat
Total
Note: Cats are analyzed separately from other HO and CMP
Required Capital
Growing the Business
Prospect 1
Prospect 2
Existing
Standalone
Standalone
Standalone
Total
Total
Prospect 2 is the best growth decision for the insurer
Summary
Simple factor-based models for capital
requirements are available that reflect:
– Volatility by line and size of insurer
– Reinsurance
– Correlation
Working party proposal is to allow insurer
to use internal models to justify capital
– Subject to standards