Insurance Risk Study. Fifth Edition Capital Access Advocacy Innovation

Transcription

1 Insurance Risk Study Fifth Edition 2010 redefining Capital Access Advocacy Innovation

2 Contents 3 Foreword 4 Global Risk Parameters 6 Evaluating Solvency II Factors 8 U.S. Risk Parameters 10 Best of Times, Worst of Times 12 Correlation and the Pricing Cycle 16 Modeling Dependence 17 Size and Correlation 18 Macroeconomic Correlation 19 Managing Inflation Risk 21 Global Market Review 25 Afterword: The Greatest Risk About the Study Rating agencies, regulators and investors today are demanding that insurers provide detailed assessments of their risk tolerance and quantify the adequacy of their economic capital. To complete such assessments requires a credible baseline for underwriting volatility. The Insurance Risk Study provides our clients with an objective and data-driven set of underwriting volatility benchmarks by line of business and country as well as correlations by line and country. These benchmarks are a valuable resource to CROs, actuaries and other economic capital modeling professionals who seek reliable parameters for their models. Modern portfolio theory for assets teaches that increasing the number of stocks in a portfolio will diversify and reduce the portfolio s risk, but will not eliminate risk completely; the systemic market risk remains. This is illustrated in the left chart below. In the same way, insurers can reduce underwriting volatility by increasing portfolio volume, but they cannot reduce their volatility to zero. A certain level of systemic insurance risk will always remain, due to factors such as the underwriting cycle, macroeconomic factors, legal changes and weather (right chart below). The Study calculates this systemic risk by line of business and country. The Naïve Model on the right chart shows the relationship between risk and volume using a Poisson assumption for claim count a textbook actuarial approach. The Study clearly shows that this assumption does not fit with empirical data for any line of business in any country. It will underestimate underwriting risk if used in an ERM model. Asset Portfolio Risk Insurance Portfolio Risk Portfolio Risk Portfolio Risk Insurance Risk Systemic Market Risk Systemic Insurance Risk Number of Stocks Volume Naïve Model

3 Foreword Since the first internal Aon Benfield Insurance Risk Study in 2003, the insurance world has been shaken by mega-catastrophes and threatened by financial market turmoil. Industry best practice in enterprise risk management has evolved almost beyond recognition, and techniques for risk quantification and capital modeling have advanced from nascent specialties into mainstream core competencies. Yet despite change and progress, much remains constant. Risk quantification still relies fundamentally on accurate parameterization and realistic stochastic models. An incorrectly specified model is often worse than no model at all. Bad models can lead the user astray, as was shown by numerous examples during the financial crisis. Aon Benfield has consistently focused on the need to provide our clients the robust data and fact-based parameters published in this Study to complement state-of-the-art financial modeling tools such as our ReMetrica software. The Study is a cornerstone of Aon Benfield Analytics integrated and comprehensive risk modeling and risk assessment capabilities. > Our reinsurance optimization framework, linking reinsurance to capital, relies on the Study for a credible assessment of baseline frequency and severity volatility > Our global risk and capital strategy practice, providing ERM and economic capital services, uses the Study to benchmark risk, quantify capital adequacy and allocate capital to risk drivers > Our ReMetrica risk evaluation and capital modeling software provides easy access to the Study parameters and risk insights 2010 s Fifth Edition has again expanded in scope and coverage from previous editions. It includes: > Results from 46 countries, comprising more than 90 percent of global premium > A global market review showing premium, historical loss ratio and volatility parameters for the top 50 countries > A new approach to loss ratio volatility that measures year-over-year changes illustrating the magnitude of historical planning misses > A focus on the potential impact of inflation on P&C companies The massive database underlying the Study is supported by more than 450 professionals within the global Analytics team who are available to work with you to customize the basic parameters reported here to answer your specific, pressing business questions. Aon Benfield s Insurance Risk Study, now in its fifth edition, continues to be the industry s leading publicly available set of risk parameters for modeling and benchmarking underwriting risk. We are pleased to offer the Study for the advancement of risk management within our industry. For convenient reference, you can find earlier editions of the Study at aonbenfield.com. I welcome your thoughts and suggestions, which you can share with an to stephen.mildenhall@aonbenfield.com. Stephen Mildenhall CEO, Aon Benfield Analytics 3

4 Insurance Risk Study Global Risk Parameters The 2010 Insurance Risk Study quantifies the systemic risk by line for 46 countries worldwide, up from 26 last year. Systemic risk in the Study is the coefficient of variation of loss ratio for a large book of business. Coefficient of variation (CV) is a commonly used normalized measure of risk defined as the standard deviation divided by the mean. Systemic risk typically comes from non-diversifiable risk sources such as changing market rate adequacy, unknown prospective frequency and severity trend, weather-related losses, legal reforms and court decisions, the level of economic activity, and other macroeconomic factors. It also includes the risk to smaller and specialty lines of business caused by a lack of credible data. For many lines of business systemic risk is the major component of underwriting volatility. The systemic risk factors for major lines by region appear on the next page. Detailed charts comparing motor and property risk by country appear below. The factors measure the volatility of gross loss ratios. If gross loss ratios are not available the net loss ratio is used. Coefficient of Variation of Gross Loss Ratio by Country Motor Property Hungary 4% Israel 8% 5% South Africa 6% Australia 7% Italy 7% Switzerland 7% Germany 8% Austria 8% Spain 8% Panama 9% U.K. 9% Denmark 9% Chile 9% Canada 9% China 9% Malaysia 10% Japan 10% India 11% Turkey 11% France 11% Venezuela 12% Uruguay 12% El Salvador 12% Vietnam 13% Bolivia 15% 15% Hungary 15% South Korea 16% Poland 16% Netherlands 18% Slovakia 18% U.S. 18% Ecuador 18% Dominican Republic 18% Argentina 21% Brazil 23% Romania 24% Colombia 25% Honduras 25% Indonesia 25% Nicaragua 27% Hong Kong 29% Singapore 35% Greece 43% Peru 46% Mexico 64% Taiwan Japan Turkey Taiwan South Korea Israel Australia Austria Czech Republic Switzerland Germany Mexico France Argentina Spain Italy Bolivia U.K. China Netherlands Chile India Brazil Uruguay Malaysia Colombia Poland U.S. Peru Vietnam Canada Venezuela El Salvador Honduras Ecuador Romania Denmark South Africa Slovakia Dominican Republic Singapore Indonesia Panama Hong Kong Greece Nicaragua 13% 16% 17% 18% 18% 18% 19% 21% 22% 22% 25% 26% 27% 28% 28% 31% 31% 32% 36% 37% 38% 38% 38% 40% 42% 42% 43% 44% 45% 46% 51% 51% 53% 54% 54% 58% 58% 62% 67% 71% 73% 91% 92% 98% Americas Asia Pacific Europe, Middle East & Africa 4

5 Aon Benfield Underwriting Volatility for Major Lines by Country, Coefficient of Variation of Loss Ratio for Each Line Motor Motor - Personal Motor - Commercial Property Property - Personal Property - Commercial General Liability Accident & Health Marine, Aviation & Transit Workers Compensation Credit Fidelity & Surety Americas Argentina 9% 51% 61% 116% 164% Bolivia 10% 38% 18% Brazil 12% 53% 48% 60% 57% 45% 43% 58% Canada 18% 26% 18% 41% 37% 43% 72% 110% 116% Chile 12% 25% 51% 65% Colombia 15% 54% 55% 57% 71% Dominican Republic 25% 51% 120% 64% Ecuador 21% 46% 49% 178% El Salvador 18% 38% 21% 100% Honduras 18% 58% 5% 193% Mexico 9% 92% 65% 43% Nicaragua 64% 62% 91% 107% Panama 35% 21% 24% 103% Peru 16% 91% 60% 7% 21% 68% 77% Uruguay 13% 37% 124% U.S. 16% 14% 24% 45% 51% 34% 37% 52% 39% 28% 70% Venezuela 18% 36% 23% 160% Asia Pacific Australia 8% 16% 23% 32% 54% 10% 30% China 11% 11% 27% 31% 19% 16% 113% Hong Kong 43% 44% 67% 82% 24% 60% 81% India 12% 12% 31% 14% 31% Indonesia 29% 29% 58% 124% 56% 72% 55% 92% Japan 5% 28% 10% 8% 17% 7% Malaysia 15% 28% 126% 30% 40% 88% Singapore 27% 71% 52% 57% 46% South Korea 7% 7% 42% 32% 55% Taiwan 7% 7% 98% 53% 33% 71% 44% Vietnam 18% 38% 41% 11% 38% Europe, Middle East & Africa Austria 8% 18% 12% 52% 21% 13% 21% 51% Czech Republic 8% Denmark 24% 22% 18% 33% 18% 16% 39% 23% France 9% 32% 35% 26% 30% 25% 57% Germany 9% 18% 20% 31% 29% 14% 22% 43% Greece 46% 73% 81% 81% Hungary 4% 40% Israel 7% 8% 53% Italy 10% 17% 25% 12% 46% 40% 72% Netherlands 11% 43% 26% 49% 54% 41% Poland 15% 42% Romania 23% 54% Slovakia 25% 44% South Africa 25% 13% 61% 33% 46% Spain 9% 19% 10% 23% 30% 13% 34% 48% 97% Switzerland 9% 18% 21% 7% 50% 73% Turkey 6% 10% 31% 44% 36% 15% 93% 52% U.K. 11% 10% 18% 22% 21% 26% 30% 8% 67% Reported CVs are of gross loss ratios, except for Argentina, Australia, Bolivia, Chile, Ecuador, India, Malaysia, Singapore, Uruguay, and Venezuela, which are of net loss ratios. Accident & Health is defined differently in each country; it may include pure accident A&H coverage, credit A&H, and individual or group A&H. In the U.S., A&H comprises about 80 percent of the Other line of business with the balance of the line being primarily credit insurance. 5

6 Insurance Risk Study Evaluating Solvency II Factors Solvency II is scheduled to take effect no later than January 1, The fifth quantitative impact study (QIS 5) is in progress with a deadline of October 2010 for individual insurers and mid-november 2010 for groups. QIS 5 is likely the key test for most insurers across Europe. The Standard Formula factors were designed to be appropriate for the entire market meaning a typical company of average size so larger insurers with greater diversification will find the formula generates conservative capital requirements. Moreover, in QIS 5, the formula reflects added concerns that emerged from the 2008 financial crisis. Insurers now have heightened incentives to develop full or partial internal models as an alternative to the Solvency II Standard Formula. At this stage, the most important aspect of preparing for Solvency II is correct parameterization, driven by access to data. Insurers may face serious challenges to their IT systems. They will need some reference point as they undertake the various Solvency II tests: evaluating the statistical quality of the data, calibrating and validating the models they are using. The non-life Solvency Capital Requirement (SCR) is predominantly driven by premium risk, reserve risk and catastrophe risk. Since many companies with catastrophe exposure purchase excess of loss reinsurance, premium and reserve risk will be the key drivers of capital. Solvency II vs. Insurance Risk Study There are four key differences between the Solvency II factors and those in the Insurance Risk Study. Key Differences Solvency II Standard deviations of gross loss ratios Based on loss ratios at end of first year Excludes catastrophe risk Average-sized company, parameter and process risk Insurance Risk Study Coefficients of variation of gross loss ratios Based on ultimate loss ratios Includes catastrophe risk Large company, parameter risk only Standard Deviations vs. Coefficients of Variation In Solvency II, the premium risk factors are calculated as standard deviations of historical loss ratios. Within the Standard Formula, these standard deviations are applied on the total volume of premium rather than to the premium net of loadings for costs, commissions and profit. Whether this overestimates the risk, and thus the capital requirement, depends on the company and the line of business. Certainly the Regulator has made some conservative assumptions: expenses are assumed to have the same volatility as the losses, and no profit is assumed over the cycle. If insurers disagree with these assumptions they must apply for a partial internal model. One-Year Emergence vs. View of Ultimate The Standard Formula premium risk factors and the corresponding Insurance Risk Study factors appear below. For ease of comparison, we have restated our factors as standard deviations rather than coefficients of variation. Non-Life Premium Risk, Gross of Reinsurance QIS 5 CEIOPS Risk Study Line StDev StDev # Obs StDev # Obs Motor TPL 10.0% 11.5% % 4,631 Motor Other 7.0% 8.5% 107 n/a n/a Marine, Aviation & Transit 17.0% 23.0% % 2,623 Fire 10.0% 15.0% % 4,751 General Liability 15.0% 17.5% % 3,443 Credit 21.5% 28.0% % 570 The factors proposed by CEIOPS and those used in the QIS 5 exercise can be made comparable with the factors in this Study through appropriate adjustments. If we use Motor TPL as an example, the CV in this Study corresponds to a standard deviation of 12.0 percent. The Study standard deviation is calculated from an ultimate perspective. We can use the same dataset that was used in our analysis to recalculate it from a one-year perspective, producing a standard deviation of 8.7 percent. Finally, the Study parameter reflects the non-diversifiable premium risk for a large insurance company whereas the QIS 5 parameters used in the Standard Formula represent an averagesized insurance company. As expected the QIS 5 parameter, 10.0 percent, is higher than systemic-only parameter of 8.7 percent for motor TPL. 6

7 Aon Benfield Solvency II Correlation Coefficients Not surprisingly, correlation will be an important determinant of capital requirements. Solvency II Correlation Coefficients Motor - TPL Motor - Other Marine, Aviation & Transit These coefficients are more conservative than we would derive from calculating linear correlation since they must consider nonlinear tail correlation. The factors applied were derived mainly from an analysis of German market data for the years 1998 through As an example, for the correlation between motor TPL and general liability, the average correlation was 28 percent using the data of 89 firms and 1,269 observations. The final coefficient selected was 50 percent, as seen above. In this case, we find that the Solvency II correlations are significantly higher than many of the observed correlations for European insurers. The correlation matrix for Germany appears below, and corresponds to the larger matrix on page 13 of this Study. Insurance Risk Study Germany Fire General Liability Motor TPL 50% 50% 25% 50% 25% Motor Other 50% 25% 25% 25% 25% Marine, Aviation & Transit Credit 50% 25% 25% 25% 25% Fire 25% 25% 25% 25% 25% General Liability 50% 25% 25% 25% 50% Credit 25% 25% 25% 25% 50% S2Metrica: ReMetrica Modeling for Proposed Solvency II Developing an internal model can be a significant investment of time and resources. To assist our clients, Aon Benfield has developed S2Metrica SM, a standalone tool built on ReMetrica technology. S2Metrica builds a simplified internal model from QIS 5 inputs, supplemented with details about large losses, cat losses, reinsurance, and the asset portfolio. It also has a built-in economic scenario generator. Standard output reports include: > Profit and loss accounts for different return periods > Year-end balance sheets > Comparisons between Standard Formula capital requirements and those generated by the S2Metrica internal model Using S2Metrica, clients can quickly construct a competent baseline model, freeing them to focus on critical tasks such as parameterization and appropriate customization. ReMetrica is Aon Benfield s innovative financial modeling tool and the engine of S2Metrica. Insurers increasingly turn to financial modeling to help them achieve their corporate objectives. Each insurer has its own distinct objectives, risks, corporate structure, and reinsurance strategy. Using the ReMetrica software platform, insurers can build adaptable and flexible models that capture their risks better than the Solvency II Standard Formula and fully recognize their risk mitigation strategies. In particular, ReMetrica allows insurers to: Motor Marine, Aviation & Transit Property General Liability Credit > Create off-the-shelf internal models that cover both assets and liabilities Motor 20% 7% 6% 26% Marine, Aviation 20% 22% 10% 45% & Transit Property 7% 22% 0% 31% General Liability 6% 10% 0% -3% Credit 26% 45% 31% -3% > Use customizable templates to monitor internal metrics and Solvency II requirements such as Fair Value and SCR > Model highly customized reinsurance structures > Integrate partial models, such as non-life and health lines, in a full internal model covering all aspects of the balance sheet The combination of the Insurance Risk Study with ReMetrica allows our clients to parameterize their models in an optimal way and to make informed decisions about risk transfer through reinsurance or the capital markets. 7

8 Insurance Risk Study U.S. Risk Parameters The U.S. portion of the Insurance Risk Study uses data from nine years of NAIC annual statements for 2,265 individual groups and companies. The database covers all 22 Schedule P lines of business and contains 1.4 million records of individual company observations from accident years The charts below show the loss ratio volatility for each Schedule P line, with and without the effect of the underwriting cycle. The effect of the underwriting cycle is removed by normalizing loss ratios by accident year prior to computing volatility. This adjustment decomposes loss ratio volatility into its loss and premium components. Coefficient of Variation of Gross Loss Ratio All Risk No Underwriting Cycle Risk Private Passenger Auto 14% 13% Auto Physical Damage Commercial Auto Workers Compensation Warranty Medical PL Occurrence Commercial Multi Peril Other Liability Occurrence Special Liability Medical PL Claims-Made Other Liability Claims-Made Products Liability Occurrence Homeowners Other Reinsurance Liability International Fidelity & Surety Reinsurance Property Reinsurance Financial Products Liability Claims-Made Special Property Financial Guaranty 17% 24% 28% 31% 32% 34% 37% 39% 40% 43% 47% 51% 52% 67% 68% 70% 85% 91% 102% 104% 163% 15% 17% 19% 31% 32% 27% 25% 29% 28% 29% 32% 43% 49% 45% 54% 54% 54% 59% 47% 62% 106% The U.S. Underwriting Cycle Volatility for most lines of business is increased by the insurance underwriting and pricing cycle. The underwriting cycle acts simultaneously across many lines of business, driving correlation between the results of different lines and amplifying the effect of underwriting risk to primary insurers and reinsurers. Our analysis demonstrates that the cycle increases volatility substantially for all major commercial lines, as shown in the table. For example, the underwriting volatility of other liability increases by 47 percent, workers compensation by 46 percent, medical professional liability by 43 percent, and commercial auto liability by 42 percent. Impact of the Pricing Cycle Line Impact of the Pricing Cycle Reinsurance Liability 50% Other Liability Occurrence 47% Other Liability Claims-Made 47% Workers Compensation 46% Medical PL Claims-Made 43% Commercial Auto 42% Special Liability 33% Commercial Multi Peril 24% Homeowners 21% Private Passenger Auto 9% 8

9 Aon Benfield Industry Reserve Adequacy: How Long Can Favorable Development Continue? U.S. P&C industry reserves continue to show redundancy at the end of Standard actuarial reserving methods applied to the industry Schedule P indicate that there is approximately $22 billion of excess reserves across all lines of business. The market is unlikely to harden again as long as the industry has more than adequate reserves according to these metrics. Calendar years 2007, 2008 and 2009 saw favorable reserve development, helping to prolong soft market conditions. We estimate that reserve redundancies will be depleted in two to three years if favorable development continues at the pace it has from 2007 to A summary of adequacy by major market segments appears below. U.S. Reserve Estimated Adequacy ($B) Line Estimated Booked Favorable/(Adverse) Development Remaining Years at Reserves Reserves Average Redundancy Run Rate Personal Lines Commercial Property Commercial Liability Workers Compensation (0.5) 0.6 (0.8) n/a Total Excl. Financial Guaranty Financial Guaranty (1.2) (12.6) 7.0 (2.3) (1.4) n/a Total Reserve Risk and Leverage Insurers face two sources of risk from reserves. The first source is volatility of reserve values over time to settlement. The second source comes from leverage. The longer the average duration of the claim payout, the larger the reserve balance becomes relative to the premium base. As reserve leverage increases, the sensitivity of calendar year combined ratio results compared to changes in reserve balances magnifies. The first source of volatility has traditionally been measured with methods such as the Mack method, which calculates the volatility of the link ratio estimate of ultimate losses coming from a loss triangle. More recently, Merz and Wuthrich have published a methodology that calculates the same estimate, but over a one-year time horizon to be consistent with Solvency II. Using these methods, we can estimate the total reserve volatility and how much of that volatility is expected to emerge in the next 12 months. We can also estimate the potential impact of reserve volatility on next year s combined ratio. Using the U.S industry aggregate workers compensation paid triangle as an example, the total reserve volatility is estimated at 3.3 percent based on an adjusted Mack method. The one-year reserve volatility is 2.2 percent based on an adjusted Merz Wuthrich method, meaning that 66 percent of the triangle s volatility emerges in one development year. The Mack and Merz Wuthrich methods were both adjusted to account for reserves more than 10 years old. With reserves levered at 3.4 times premium, the impact on combined ratio of a one standard deviation change is 7.5 points. For a normal distribution a one standard deviation move, up or down, is a one in three year event. U.S. Reserve Volatility by Line Line Reserve to Premium Ratio % Reserves Over 10 Yrs Old Ultimate Reserve CV One Year Reserve CV % CV Emerging in One Year One Year Combined Ratio Impact Homeowners % 5.1% 4.8% 94.0% 1.5% Private Passenger Auto % 2.1% 1.7% 79.1% 1.5% Commercial Auto % 2.5% 1.8% 69.4% 2.6% Commercial Multi Peril % 4.6% 3.8% 81.4% 4.6% Workers Compensation % 3.3% 2.2% 66.0% 7.5% Medical PL - CM % 5.1% 4.0% 78.9% 10.0% Other Liability - Occ % 5.2% 3.2% 62.1% 10.8% Other Liability - CM % 6.3% 5.1% 79.7% 12.8% Products Liability - Occ % 9.9% 5.0% 50.9% 35.1% Ultimate reserve CV calculated using the Mack method applied to industry paid triangles by line. One-year reserve CV uses the Merz Wuthrich method. Both methods adjusted to account for reserves more than 10 years old. 9

10 Insurance Risk Study Best of Times, Worst of Times In economic capital modeling, the systemic volatility of each insurance line is a vital input to ensure that the parameters reflect an appropriate level of risk. As a result, we have always focused on quantifying this systemic volatility by measuring the CV. However, the CV offers guidance only on the variance of the resulting loss distribution; it does not offer a clear view of the distribution s shape. Two insurance lines may have similar CVs but one may have a much thicker tail than the other. To expand our view of insurance risk beyond the CV, we have studied the largest deviations in loss ratio between successive accident years. The 18 accident years in our dataset give us 17 years of changes, and with this data we selected the biggest increase and decrease in ultimate accident year loss ratio for each company. For example, on the following page commercial auto insurers showed on average a biggest increase (deteriorating results) of 18.3 loss ratio points and a biggest decrease (improving results) of 25.1 loss ratio points from one accident year to the next. The chart below shows mean changes for all U.S. lines. Overall this analysis is consistent with the analysis of CVs. Personal and commercial auto show the smallest fluctuation in results, followed by the other commercial lines. The catastrophe-exposed lines homeowners, special property, reinsurance property, and financial guaranty comprise the top end of the range, with a mean worst increase of 60 loss ratio points or higher on a gross basis. For most lines, the increases are significant. Among the commercial lines, the results show a mean increase of 44 percent for other liability claims-made, 39 percent for other liability occurrence, 36 percent for commercial multi-peril, 29 percent for medical professional liability claims-made, 23 percent for workers compensation, and 18 percent for commercial auto. The following page shows detailed results for commercial auto, other liability occurrence and workers compensation. The impact of the underwriting cycle is clearly visible in all three lines, as insurers suffered their biggest increases from 1998 to 2000 and their biggest decreases in 2002 after the market hardened. Differences in volatility between lines are also visible. At 39.5 percent, the mean increase for other liability occurrence is double that of commercial auto; moreover, its distribution is more positively skewed with a 90th percentile of 78.4 loss ratio points compared with 32.5 points for commercial auto. In planning, insurers may implicitly assume that loss ratios will be within two or three points of best estimates. But the evidence shows that results are not infrequently off by 20 points or more, on both the hard and soft sides of the cycle. This deviation is further exacerbated because initial booked loss ratios are generally near plan and vary little from year to year. The output from any financial modeling should reflect a realistic view of outcomes that can deviate from plan. The results of this extreme value analysis can serve as useful benchmarks for evaluating model results. Mean Year-Over-Year Change in Loss Ratio Biggest Increase (Deteriorating Results) 125% 170% 499% 9% 14% 18% 23% 29% 36% 38% 39% 42% 44% 45% 48% 51% 56% 66% 67% 73% 78% Auto Phys. Damage Private Auto Commercial Auto Workers Comp Medical PL - CM Commercial Multi Peril Medical PL - Occ Other Liability - Occ Fidelity & Surety Other Liability - CM Reinsurance - Liability Products Liability - Occ Special Liability Products Liability - CM Reinsurance - Financial Homeowners Special Property International Reinsurance - Property Financial Guaranty Other -12% -18% -25% -25% -41% -46% -52% Biggest Decrease (Improving Results) -41% -32% -72% -64% -67% -67% -93% -123% -79% -262% -81% -185% -87% -41% 10

11 Aon Benfield Year-Over-Year Change in Gross Loss Ratio Commercial Auto Probability Density Biggest Increase Biggest Decrease Frequency by Accident Year % -100% -50% 0% 50% 100% 150% 0.3 Biggest Increase Mean 18.3% Median 15.1% 90th %ile 32.5% Biggest Decrease Mean -25.1% Median -20.1% 90th %ile -45.2% Other Liability - Occurrence Probability Density 0.6 Frequency by Accident Year % -100% -50% 0% 0 50% 100% 150% Biggest Increase Mean 39.5% Median 24.8% 90th %ile 78.4% Biggest Decrease Mean -40.8% Median -27.4% 90th %ile -71.5% Workers Compensation Probability Density 0.3 Frequency by Accident Year % -100% -50% 0% 0 50% 100% 150% 0.3 Biggest Increase Mean 23.1% Median 20.1% 90th %ile 38.9% Biggest Decrease Mean -25.0% Median -20.5% 90th %ile -46.0% 11

12 Insurance Risk Study Correlation and the Pricing Cycle Correlation of Underwriting Results Correlation between different lines of business is central to a realistic assessment of aggregate portfolio risk, and, in fact, becomes increasingly significant as companies grow in size. Modeling is invariably performed using an analysis-synthesis paradigm: analysis is carried out at the product or business unit level and then aggregated to the company level. In most applications, results are more significantly impacted by the correlation and dependency assumptions made during the synthesis step than by all the detailed assumptions made during the analysis step. The Study determines correlations between lines within each country and also between countries. Although not shown here, we have also calculated confidence intervals for each correlation coefficient. Correlation between Lines Correlation between lines is computed by examining the results from larger companies that write pairs of lines in the same country. The following tables show a sampling of the results available for Australia, China, Germany, Japan, the U.K., and the U.S. Australia General Liability Marine, Aviation & Transit China Accident & Health Motor Agriculture Property Credit Engineering General Liability Marine, Aviation & Transit Motor Property Workers Comp General Liability 19% 21% -24% 21% Marine, Aviation & Transit 19% 31% -3% 21% Motor 21% 31% 25% 14% Property -24% -3% 25% -6% Workers Comp 21% 21% 14% -6% Correlation is a measure of association between two random quantities. It varies between -1 and +1, with +1 indicating a perfect increasing linear relationship and -1 a perfect decreasing relationship. The closer the coefficient is to either +1 or -1 the stronger the linear association between the two variables. A value of 0 indicates no linear relationship whatsoever. All correlations in the Study are estimated using the Pearson sample correlation coefficient. In each table the correlations shown in bold are statistically different from zero at the 90 percent confidence level. Accident & Health 24% 31% 39% 53% 38% 59% 56% Agriculture 24% 53% n/a 29% 9% 16% -4% Credit 31% 53% n/a 18% 18% 34% 25% Engineering 39% n/a n/a 68% 38% 64% 28% General Liability 53% 29% 18% 68% 29% 62% 54% Marine, Aviation & Transit 38% 9% 18% 38% 29% 41% 24% Motor 59% 16% 34% 64% 62% 41% 59% Property 56% -4% 25% 28% 54% 24% 59% 12

13 Aon Benfield Germany Japan U.K. U.S. Commercial Auto Commercial Multi Peril Homeowners Medical Malpractice CM Other Liability CM Other Liability Occ Personal Auto Liability Products Liability Occ Workers Comp Accident & Health Commercial Lines Liability Commercial Motor Commercial Property Financial Loss Household & Domestic Private Motor Accident & Health General Liability Marine, Aviation & Transit Motor Property Workers Comp Accident & Health Assistance Credit General Liability Legal Protection Marine, Aviation & Transit Motor Property Accident & Health 62% -37% 10% -13% -13% -12% -3% Assistance 62% n/a -40% 39% 83% -6% -40% Credit -37% n/a -3% -24% 45% 26% 31% General Liability 10% -40% -3% -10% 10% 6% 0% Legal Protection -13% 39% -24% -10% -48% 20% -21% Marine, Aviation & Transit -13% 83% 45% 10% -48% 20% 22% Motor -12% -6% 26% 6% 20% 20% 7% Property -3% -40% 31% 0% -21% 22% 7% Accident & Health 27% 1% 50% 42% 53% General Liability 27% 0% 3% 32% 28% Marine, Aviation & Transit 1% 0% 16% 33% -4% Motor 50% 3% 16% 61% 43% Property 42% 32% 33% 61% 32% Workers Comp 53% 28% -4% 43% 32% Accident & Health 47% n/a 55% -49% 15% 55% Commercial Lines Liability 47% 72% 40% 69% 49% 56% Commercial Motor n/a 72% 51% -9% -14% 61% Commercial Property 55% 40% 51% 33% 57% 39% Financial Loss -49% 69% -9% 33% 16% -15% Household & Domestic 15% 49% -14% 57% 16% 30% Private Motor 55% 56% 61% 39% -15% 30% Commercial Auto 53% 8% 73% 44% 67% 28% 72% 63% Commercial Multi Peril 53% 21% 56% 41% 48% 28% 40% 42% Homeowners 8% 21% 1% -2% -1% 8% 14% -7% Medical Malpractice CM 73% 56% 1% 72% 78% 58% 76% 71% Other Liability CM 44% 41% -2% 72% 57% 42% 29% 62% Other Liability Occ 67% 48% -1% 78% 57% 33% 66% 63% Personal Auto Liability 28% 28% 8% 58% 42% 33% 42% 33% Products Liability Occ 72% 40% 14% 76% 29% 66% 42% 63% Workers Comp 63% 42% -7% 71% 62% 63% 33% 63% 13

14 Insurance Risk Study Correlation between Countries In addition to correlation between lines of business, global insurers must also consider the correlation of business written in different countries. We estimated these correlation coefficients based on country-level loss ratios by line by year. The following tables show results by region for motor and liability lines. Americas - Motor Asia Pacific - Motor Europe - Motor Austria Belgium France Germany Italy Netherlands Norway Spain Switzerland United Kingdom Australia China Hong Kong India Japan Malaysia Russia Singapore South Korea Taiwan Argentina Brazil Canada Chile Colombia Mexico Peru Puerto Rico United States Venezuela Argentina 49% -62% -71% -14% 23% 10% -13% -14% -28% Brazil 49% -18% -5% -26% -3% -51% 34% 34% 32% Canada -62% -18% 61% 22% -24% -27% 10% 85% 43% Chile -71% -5% 61% 14% -13% -31% 14% 20% -4% Colombia -14% -26% 22% 14% -28% 16% 37% 34% -5% Mexico 23% -3% -24% -13% -28% 6% -47% -24% -58% Peru 10% -51% -27% -31% 16% 6% -18% -21% -32% Puerto Rico -13% 34% 10% 14% 37% -47% -18% 41% 7% United States -14% 34% 85% 20% 34% -24% -21% 41% 41% Venezuela -28% 32% 43% -4% -5% -58% -32% 7% 41% Australia 63% 54% 44% -35% -49% 82% 8% -34% 21% China 63% 24% -3% -7% 14% -30% -10% -20% 12% Hong Kong 54% 24% 55% -46% -46% 5% 37% -67% -23% India 44% -3% 55% -45% -32% 97% 13% -34% 33% Japan -35% -7% -46% -45% 50% 85% -2% 68% -3% Malaysia -49% 14% -46% -32% 50% 72% -8% 41% 33% Russia 82% -30% 5% 97% 85% 72% 14% -35% -81% Singapore 8% -10% 37% 13% -2% -8% 14% -35% -37% South Korea -34% -20% -67% -34% 68% 41% -35% -35% 34% Taiwan 21% 12% -23% 33% -3% 33% -81% -37% 34% Austria 52% 64% 65% 38% 87% 44% -12% 82% 12% Belgium 52% 63% 79% 63% 45% 61% -41% 7% 34% France 64% 63% 59% 41% 54% 45% -33% 49% 23% Germany 65% 79% 59% 7% 54% 35% -29% 23% 10% Italy 38% 63% 41% 7% -5% 71% -41% 17% 62% Netherlands 87% 45% 54% 54% -5% 37% 1% 80% -19% Norway 44% 61% 45% 35% 71% 37% -47% 41% 32% Spain -12% -41% -33% -29% -41% 1% -47% 30% 7% Switzerland 82% 7% 49% 23% 17% 80% 41% 30% -2% United Kingdom 12% 34% 23% 10% 62% -19% 32% 7% -2% 14

15 Aon Benfield Americas - Liability Asia Pacific - Liability Europe - Liability Austria Belgium Denmark France Germany Italy Norway Spain Switzerland United Kingdom Australia China Hong Kong Japan Malaysia Russia Singapore South Korea Taiwan Argentina Brazil Canada Chile Colombia Mexico Peru Puerto Rico United States Venezuela Argentina 33% 18% -5% -67% 6% 3% 49% 30% 2% Brazil 33% 33% 18% -59% 22% 15% 75% 72% -7% Canada 18% 33% -17% -32% 25% 24% 26% 81% 5% Chile -5% 18% -17% -28% 44% -12% 26% -1% 31% Colombia -67% -59% -32% -28% -18% -26% -76% -67% -23% Mexico 6% 22% 25% 44% -18% -3% 14% 23% -20% Peru 3% 15% 24% -12% -26% -3% 0% 44% -18% Puerto Rico 49% 75% 26% 26% -76% 14% 0% 69% 2% United States 30% 72% 81% -1% -67% 23% 44% 69% 18% Venezuela 2% -7% 5% 31% -23% -20% -18% 2% 18% Australia 81% 46% -33% -11% -15% -30% 6% 32% China 81% 36% -13% 22% 36% 91% -28% 17% Hong Kong 46% 36% 1% -9% 2% -31% -15% -28% Japan -33% -13% 1% 45% 7% 72% -3% 20% Malaysia -11% 22% -9% 45% -57% 70% -35% 26% Russia -15% 36% 2% 7% -57% -60% 65% 47% Singapore -30% 91% -31% 72% 70% -60% -74% 10% South Korea 6% -28% -15% -3% -35% 65% -74% 6% Taiwan 32% 17% -28% 20% 26% 47% 10% 6% Austria -46% 55% 86% 88% 49% 19% -36% 29% 65% Belgium -46% -29% -54% -35% -43% 21% -81% 13% -31% Denmark 55% -29% 65% 60% 71% 16% 10% 29% 36% France 86% -54% 65% 90% 61% 16% -26% 32% 59% Germany 88% -35% 60% 90% 54% 5% -41% 27% 65% Italy 49% -43% 71% 61% 54% 20% 15% 26% 5% Norway 19% 21% 16% 16% 5% 20% -39% 3% 4% Spain -36% -81% 10% -26% -41% 15% -39% -24% 12% Switzerland 29% 13% 29% 32% 27% 26% 3% -24% 10% United Kingdom 65% -31% 36% 59% 65% 5% 4% 12% 10% 15

16 Insurance Risk Study Modeling Dependence Dependence is a core component of economic capital modeling. Risk managers frequently discuss correlation, and this Study includes numerous correlation matrices. But correlation alone does not fully describe dependence. There are many ways to combine two variables to have the same linear correlation coefficient. For example, the familiar symmetric, elliptical contours of the normal copula can have the same linear correlation as a more pinched distribution, and pinching can occur either on the left, the right or both sides. The impact of dependence is most clearly seen in the distribution of the sum (or portfolio return) of the two variables, with extreme tail correlation producing an aggregate distribution with much fatter tails. Variables in financial markets often exhibit such extreme tail correlation, as seen in the left chart below. In this plot, the outliers at the 10.0 percent and 1.0 percent significance levels assuming a multivariate normal distribution comprise 11.9 percent and 2.1 percent of the observations. This kind of behavior has led many analysts to reject the normal distribution as a model for dependence. Academics and risk managers have introduced many different copulas as means of modeling dependence with flexible tail behavior. But the appropriateness of different copulas for insurance losses has been less well tested. Daily Stock Returns of Two Financial Stocks Through the Crisis Our study of U.S. data shows that apart from correlation driven by property catastrophe events there is little evidence of multi-line extreme correlation. The right chart below compares results for other liability occurrence and workers compensation. In this case, the outliers at the 10.0 percent and 1.0 percent significance levels assuming multivariate normal distribution represent 10.9 percent and 1.0 percent of the observations well within expectations. Analysis of other U.S. lines shows similar results. There is still the possibility that events with long return periods are not shown in our 18-year data sample for example, the impact of asbestos on other liability occurrence and products liability. We may yet observe extreme tail correlation in insurance results. But its absence during the past 18 years suggests that it is not nearly as commonplace as in financial markets. We conclude that while the traditional approach to modeling dependence using the normal copula has known limitations, it is not rejected by the data as a model for correlation between non-catastrophe insurance lines. Catastrophe simulation models address this issue for catastrophe lines by including correlation as a model output. Products Liability Occurrence vs. Workers Compensation 3.0 Normal Transformed Data 3.0 Normal Transformed Data

17 Aon Benfield Size and Correlation Insurers of different sizes face different levels of correlation across their portfolios. For small insurers, the process risk in each line of business may keep the correlation observed between lines relatively low. In contrast, large insurers are exposed primarily to the systemic risk in each line, but correlation in systemic risk will drive observed correlations across the portfolio. The U.S. correlation coefficients published earlier in the Study represent an average level of correlation for companies with premium volume above a threshold Workers Compensation vs. Other Liability Occurrence of $100 million. We selected this threshold as representative of the size of a typical product division within a medium to large insurance company. The observed level of correlation varies within this threshold, as shown below for several pairs of lines. Companies with volume exceeding $100 million will observe an increasing level of correlation between lines. For example, between workers compensation and other liability occurrence, the correlation at $100 million is 63 percent, at $500 million it is 72 percent, and at $1 billion it is 80 percent. Commercial Auto vs. Other Liability Occurrence Correlation Above Threshold Correlation Risk Study Coefficient Correlation Above Threshold Correlation Risk Study Coefficient ,000 10,000 Size Threshold, $M ,000 10,000 Size Threshold, $M The table below shows the measured correlation coefficients at different premium thresholds between U.S. Schedule P lines. In each case, both premium amounts exceed the threshold. Line of Business Correlation by Premium Size Threshold Line A Line B $25M $50M $100M $250M $500M $1,000M Homeowners Private Passenger Auto 10% 11% 8% 17% 33% 33% Commercial Multi Peril Commercial Auto 33% 37% 53% 55% 73% 58% Commercial Multi Peril Workers Compensation 27% 31% 42% 48% 48% 59% Commercial Multi Peril Other Liability Occ 22% 27% 48% 46% 53% 53% Commercial Auto Workers Compensation 49% 60% 63% 71% 73% 85% Commercial Auto Other Liability Occ 51% 54% 67% 78% 82% 78% Workers Compensation Other Liability Occ 44% 51% 63% 67% 72% 80% Other Liability Occ Other Liability CM 45% 50% 57% 55% 59% 65% Medical PL CM Other Liability CM 65% 72% 72% 64% 68% n/a Medical PL CM Workers Compensation 47% 72% 71% 73% 77% n/a The larger the company, the more important correlation becomes for the company. Regulators and rating agencies scrutinize correlation assumptions in their evaluations of capital adequacy. Aon Benfield Analytics can help companies understand the sensitivity of their model results to correlation assumptions and guide them during the rating agency review process. 17

18 Insurance Risk Study Macroeconomic Correlation Correlation among macroeconomic factors is a very important consideration in risk modeling. The interaction of inflation and GDP growth with loss ratios and investment returns has a profound effect on insurer financial health and stability. The matrix below shows correlation coefficients for various macroeconomic variables that impact an insurer s balance sheet. The Consumer Price Index (CPI-U) and Producer Price Index (PPI) are highly correlated, but they do not show particularly strong correlation with other factors. This may be because inflation has been relatively tame for the last 25 years. GDP growth shows strong negative correlation with changes in unemployment. When GDP drops or unemployment increases credit spreads tend to increase, property values fall and the VIX increases. We were surprised not to see stronger correlation between GDP and stock returns without a lag. Treasury yields and corporate bond spreads are inversely correlated; financial market fears may push investors to flee corporates for the safety of treasuries, causing corporate yields to rise and treasury yields to fall. Stock volatility measured by the VIX Index is sensitive to fear and directionally has the appropriate signs: positive correlation with spreads and unemployment, negative correlation with GDP and stock returns. These coefficients represent only the beginning of an analysis of macroeconomic dependency. Lags may be appropriate among certain variables. For example, GDP and stock returns show the strongest correlation when stock returns lead GDP by two quarters, suggesting that stock prices adjust as soon as expectations for GDP change. It is also important to consider values that shift over time. In successive eight-quarter periods, stock returns and property returns showed zero or negative correlations until the recent financial crisis when correlations turned strongly positive. This fact alone suggests that a simplistic view of correlation across the balance sheet will expose insurers to significant risks. Model output is only as good as the assumptions used, and with the prevalence of DFA modeling and economic scenario generators there is potential for naïve assumptions to drive decision making. In the next section, we look more closely at the potential impact of inflation on insurer balance sheets. Macroeconomic Correlations Inflation (CPI-U) Inflation (PPI) GDP Growth Unemployment Change 3-Month T-Bill Rate 1-3 Year T-Bill AAA-AA 3-5 Year Spread BBB 3-5 Year Spread S&P 500 Returns VIX Property Returns Inflation (CPI-U) 78% -3% -2% 32% 26% -11% -25% -12% -23% 13% Inflation (PPI) 78% 4% -7% 30% 11% -4% -20% -7% -22% 14% GDP Growth -3% 4% -70% -4% 25% -64% -69% 5% -44% 52% Unemployment Change -2% -7% -70% -3% -27% 62% 77% -1% 57% -51% 3-Month T-Bill Rate 32% 30% -4% -3% 98% -34% -58% -6% -25% 13% 1-3 Year T-Bill 26% 11% 25% -27% 98% -39% -61% 19% -28% 10% AAA-AA 3-5 Year Spread -11% -4% -64% 62% -34% -39% 85% -43% 62% -66% BBB 3-5 Year Spread -25% -20% -69% 77% -58% -61% 85% -36% 67% -53% S&P 500 Returns -12% -7% 5% -1% -6% 19% -43% -36% -51% 17% Stock Volatility Index, VIX -23% -22% -44% 57% -25% -28% 62% 67% -51% -32% Property Returns 13% 14% 52% -51% 13% 10% -66% -53% 17% -32% 18

19 Aon Benfield Managing Inflation Risk Risk managers today recognize inflation as a potential threat in the years ahead, but struggle to quantify the risk and identify ways to mitigate it. The historical record reminds us that periods of high inflation have occurred repeatedly in virtually every economy. But during the last 25 years, inflation has been contained at low levels in the U.S. and other developed economies. As a result, the time series available to measure inflation s impact on the current insurance industry will not serve us well in anticipating the next potential inflation shock. Inflation % 15% 10% 5% 0% -5% -10% -15% 1910 Impact on Insurers Periods of high inflation, and high inflation volatility in particular, have generally preceded periods of rising accident year combined ratios. Inflation and Combined Ratio 14% 12% 10% 8% 6% 4% 2% 0% This lagged relationship between inflation and combined ratios is driven by three factors: > Lags between the incidence of inflation rate changes and recognition in loss reserving systems and rate indications > Lags between attempts to raise rates and actual rate changes due to regulatory and competitive limitations > Immediate impact on balance sheets 1990 Combined Ratio Inflation % 120% 115% 110% 105% 100% 95% 90% Industry Balance Sheet Impact In the table below we demonstrate the last of these three effects for U.S. insurers using the 2009 industry balance sheet and the sensitivity of bond holdings, equity holdings and nominal loss reserves to changes in inflation. We show that a 200 basis point increase in inflation could result in a $70.9 billion impact on surplus, a 13.7 percent decrease. Impact of Inflation Increase on Industry Balance Sheet Assets Balance ($B) Pre-tax Sensitivity % After-Tax Sensitivity % After- Tax Impact ($B) Bonds % -4.7% Stocks % -3.9% -8.9 Other Assets % 0.0% Total Assets 1, % -3.3% Liabilities Net Loss Reserves % 3.8% 21.2 Other Liabilities % 0.0% Total Liabilitites % 2.2% 21.2 Surplus % -13.7% The primary drivers of these changes are bonds, stocks and loss reserves. Bonds Changes in inflation affect bond yields differently for bonds of different maturities. Overall, a 200 basis point increase in inflation would be expected to decrease the value of the industry bond portfolio by 7.3 percent. Stocks Stock portfolios are often assumed to have a high sensitivity to changes in bond yields. However, since empirically 80 percent of changes in inflation expectations ultimately flow through the S&P 500 as higher nominal dividends, this significantly offsets the effect of discounting these dividends at higher yields. The overall affect is approximately a 6.0 percent decline in the value of a diversified equity portfolio for a 200 basis point change in inflation. Loss Reserves The impact of inflation, particularly when measured as changes in the broad CPI-U, varies by line of business. Many short-tailed lines are impacted directly, though modestly, as a result of their quick settlement. In contrast, long-tailed lines are impacted more significantly by components of the CPI-U, which results in a more muted relationship to general inflation. Overall, for the industry reserves, we estimate a 5.8 percent increase in undiscounted loss reserves for a 200 basis point increase in inflation. 19

20 Insurance Risk Study Managing Inflation Risk Insurers can seek to manage this risk in several ways. Inflation CPI-U, % Interest Rate Risk Management An interest rate risk management process should distinguish between inflation duration and real interest rate duration, thus enhancing an asset-liability management framework. It is often assumed that asset and liability portfolios with equal present values and with the same duration will respond similarly on a discounted basis to changes in bond yields. However, this may not be the case if the changes are driven by changes in inflation rates. In the previous balance sheet example, a 200 basis point increase in inflation caused a $21.2 billion increase in the undiscounted loss reserves, and if interest rates rose as well, then there would also have been an increase in the amount of discounting leaving discounted reserves approximately unchanged. 10% 5% 0% S&P 500 Year 1-Year Change 40% 20% 0% -20% -40% On the asset side, a bond portfolio of comparable size and duration would have decreased by $17.9 billion as a result of the same change in interest rates. Despite being matched, the net effect would be a three percent decrease in surplus. Asset Allocation Several asset classes, including inflation-indexed bonds (TIPS), commodities and real estate, offer varying degrees of inflation hedging and can be considered as a natural part of insurers asset portfolios. However, careful consideration must be given to the impact on expected investment returns in the case of TIPS especially and to the additional volatility and portfolio management skills needed for these asset classes. Equity Allocations The conventional wisdom is that equities are a natural hedge against inflation, since companies can pass rising costs along to consumers. But over short horizons, equities have not always outperformed inflation. In the 1970s, inflation soared well above 10 percent even as real equity returns were negative. An investment in the S&P 500 made in 1973 would only have broken even in real dollar terms in When operating performance is measured over a five-year or ten-year period, these results suggest that insurers holding equities may face flat or even negative investment returns while their liabilities increase in value. S&P 500 Cumulative Real Index Value vs. CPI-U 4% 3% 2% 1% 0% 1970 Base Year = The experience of the 1970 s suggests that a broad index such as the S&P 500 may be less effective than a more carefully constructed equity portfolio. Sectors such as energy, medical services and defense offer a greater degree of inflation hedging than other sectors; value stocks also tend to perform better in inflationary environments than growth stocks. Equities do offer a degree of natural inflation hedging, but history suggests that risk managers should pay careful attention to sector and style allocations. Reinsurance Inflation is just one of many sources of volatility for liabilities. Rather than isolate and manage this risk separately, an alternative could be to incorporate aggregate stop loss or adverse development covers into reinsurance programs with coverage terms selected to respond appropriately to adverse inflation impacts on current or prior accident year claims. 20