CAS Spring Meeting
Solvency Models Compared
June 19, 2007
PwC
Agenda/Contents
Overview
Comparison of Solvency Capital Requirements
Overview
Comparison of Formula Elements
US RBC
PricewaterhouseCoopers
Solvency II – QIS3
June 2007
Slide 3
Overview
Comparison of Formula Elements
US - RBC
2
2
1
 1

2
2
2
RBC  R 0, InsSub  R 1, FI  R 2, EQ   R 3,CR    R 3,CR  R 4, Res   R 5, Prem
2
 2

Solvency II – QIS3
SCR  BSCR  COP
where BSCR 
  C
ij
i
PricewaterhouseCoopers
i
Cj
j
June 2007
Slide 4
Overview
Significant Differences between “Standard” Formulas
Formula Calibration
Components of the QIS3 formula are calibrated to VaR 99.5
Certain components of NAIC formula are calibrated to 1% EPD
Regulatory Capital
QIS3 formula reflects correlations between and within risk categories
Market Risk – Fixed Income
NAIC formula assumes independence between risk categories (with the
exception of credit and reserve risk)
QIS3 formula reflects interest rate risk and spread risk
NAIC formula reflects fixed income default risk
Underwriting Risk - Reserves
Underwriting Risk Catastrophe
QIS3 capital charge applied to the best estimate reserves; the QIS3 balance
sheet reflects fair value reserves
NAIC capital charge applied to US statutory value of reserves discounted
using fixed discount factors by line of business
Considered as an additional shock within the QIS3 formula
Not considered explicitly within the NAIC formula
Underwriting Risk
QIS3 formula combines premium and reserve risk together using assumed
correlations
NAIC formula treats premium and reserve risk independently
Operational Risk
Considered explicitly within the QIS3 formula
Not considered within the NAIC formula
PricewaterhouseCoopers
June 2007
Slide 5
Comparison of Solvency Requirements
Limitations of Model Comparison
The “standard approach” for measuring the solvency capital requirement within the Solvency II framework
continues to be under development. Currently, Quantitative Impact Study 3 (QIS3) is underway, with a request
for companies to review the standard solvency formula and assumptions and respond to CEIOPS with detailed
feedback and commentary by June 30th. The standard approach (Excel model), user instructions, and
background information are all available for review on www.ceiops.org.
For purposes of this session, we have applied the current Solvency II standard approach to the financials of a
hypothetical property and casualty insurance company, and to the extent possible, compared the calculated
solvency capital requirements to those produced by the US NAIC RBC model. The purpose of this exercise is to
provide participants with an overview of the key assumptions and considerations within the current Solvency II
standard approach. It is likely that many of the assumptions currently reflected within QIS3 standard approach
may be modified prior to completion based upon further review, calibration, and feedback from the industry. We
are making no representations as to the appropriateness of the assumptions, the solvency formula, or the
resulting solvency capital presented within the following exhibits.
PricewaterhouseCoopers
June 2007
Slide 6
Comparison of Solvency Requirements
Sample Company
Key Characteristics
• Multi-line writer, personal and commercial
• Net written premium (NWP) $5.9 billion
•
•
•
•
Reserves $7.6 billion
Assets $17.5 billion
Surplus $5.9 billion
Simplifying assumptions:
- No affiliates
- No currency risk
- Diversified asset portfolio
PricewaterhouseCoopers
June 2007
Slide 7
Comparison of Solvency Requirements
Market, Credit and Underwriting Risk – Consistent Categories
Solvency II – QIS3
US RBC
Risk
($Millions)
Risk
Market
$656.9
Market
Credit
131.4
Credit
($Millions)
$1,551.6
111.3
Underwriting
1,337.5
Underwriting
2,754.1
Subtotal
2,125.7
Subtotal
4,417.1
Total RBC
1,495.9
Total BSCR
3,540.4
Key Considerations:
•
QIS3 Market capital excludes interest rate risk
•
QIS3 Underwriting capital excludes CAT risk
•
Total US RBC based upon square root rule without cross terms
•
Total QIS3 BSCR based on the correlation matrix:
PricewaterhouseCoopers
Note: All values subject to Slide 6 limitations.
June 2007
Slide 8
Comparison of Solvency Requirements
QIS3 – Total Solvency Capital Requirement
Solvency II – QIS3
Risk
($Millions)
Market
2,247.3
Credit
111.3
Underwriting
2,930.0
Subtotal
5,288.7
Total BSCR
4,170.3
Operational
151.1
Total SCR
4,321.4
Key Considerations
• Interest rate risk & CAT risk included
• BSCR based on the correlation matrix:
• Operational risk capital added to BSCR
PricewaterhouseCoopers
Note: All values subject to Slide 6 limitations.
June 2007
Slide 9
Comparison of Solvency Requirements
QIS3 – Market Solvency Capital Requirement
Solvency II – QIS3
Risk
($Millions)
Interest Rate
1,440.3
Equity
1,154.3
Property
Spread
Concentration
1.4
786.3
0.0
Subtotal
3,382.3
Market BSCR
2,247.3
Key Considerations
• Interest rate risk reflects shocks to fixed income
investments & liabilities
• Spread risk reflects shock due to change in credit curve
• Market BSCR based on the correlation matrix:
PricewaterhouseCoopers
Note: All values subject Slide 6 limitations.
June 2007
Slide 10
Comparison of Solvency Requirements
QIS3 – Underwriting Solvency Capital Requirement
Solvency II – QIS3
Risk
($Millions)
NWP
1,076.8
Reserves
2,132.6
Pre-Covariance
3,209.4
Subtotal Excl. CAT
2,754.1
CAT
1,000.0
Subtotal
3,754.1
Underwriting BSCR
2,930.0
Key Considerations
• QIS3 aggregates premium and reserve risk in a single step
• Subtotal Excl-CAT based upon X-LoB correlations (not shown)
• CAT & Non-CAT capital aggregated assuming independence
PricewaterhouseCoopers
Note: All values subject to Slide 6 limitations.
June 2007
Slide 11
Comparison of Solvency Requirements
Underwriting Risk - Premium
US RBC
Risk
($Millions)
Risk
Solvency II – QIS3
($Millions)
2006 NWP
5,858
2006 NWP
Growth Factor
x NA
Growth Factor
2007 NWP
5,858
2007 NWP
Implied Capital Charge
x .156
Implied Capital Charge
Pre-Concentration
Concentration
NWP RBC
5,858
x 1.05
6,150
x .262
914
Pre-Covariance
1,612
x .760
Cov. Adjustment
x .668
NWP BSCR
1,077
695
Key Considerations
• QIS3 growth factor is a standard assumption that may be overwritten
• QIS3 implied capital charge reflects credibility weighted average of the standard deviation of company and
industry historical loss ratios
• QIS3 “NWP BSCR” is identified separately from “Reserve BSCR” for purposes of this comparison only
PricewaterhouseCoopers
Note: All values subject to slide 6 limitations.
June 2007
Slide 12
Comparison of Solvency Requirements
Underwriting Risk - Reserves
US RBC
Risk
($Millions)
2006 Reserves
Discount Factor
x
Discounted Reserves
Implied Capital Charge
Pre-Concentration
Concentration
Reserve RBC
7,561
2006 Reserves
.873
Discount Factor
6,603
x
x
Risk
Solvency II – QIS3
($Millions)
.202
x
Best Estimate Reserves
Implied Capital Charge
1,333
Pre-Covariance
.787
Cov. Adjustment
1,049
7,561
.898
6,791
x
.431
2,927
x
Reserve BSCR
.729
2,133
Key Considerations
• QIS3 discount factor is based upon company-specific payout pattern and standard term structure
• QIS3 capital charge reflects a fixed assumption regarding the standard deviation of industry loss reserves
• QIS3 “Reserve BSCR” is identified separately from “NWP BSCR” for purposes of this comparison only
PricewaterhouseCoopers
Note: All values subject to Slide 6 limitations.
June 2007
Slide 13
© 2007 PricewaterhouseCoopers LLP. All rights reserved. "PricewaterhouseCoopers" refers to
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firms of PricewaterhouseCoopers International Ltd., each of which is a separate and independent legal entity.
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