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 PricewaterhouseCoopers LLP (a Delaware limited liability partnership) or, as the context requires, other member firms of PricewaterhouseCoopers International Ltd., each of which is a separate and independent legal entity. *connectedthinking is a trademark of PricewaterhouseCoopers LLP. PwC