The Role of ERM in Reinsurance Decisions Abbe S. Bensimon, FCAS, MAAA ERM Symposium Chicago, March 29, 2007 1
Agenda A Different Framework for Reinsurance Decision-Making An ERM Approach for Reinsurance Decision-Making MegaRisk Model Parameter Development MegaRisk Statistical Analysis of Current Reinsurance Program 2
A Different Framework for Reinsurance Decision-Making 3
How Effective is the Reinsurance Structure? Base Case ($000) METRIC Gross Ceded Net Volume 636,000 239,000 397,000 Mean 79,249 37,074 42,176 4
Enterprise Risk Management: Expected profitability needs to be evaluated relative to the risks being assumed Implement an ERM framework to gain: An awareness of risk that is being ceded to the reinsurer The ability to measure that risk against the profit being ceded to the reinsurer An explicit recognition of risk tolerance Assets Liabilities Risk Balance Sheet Business Plan 5
Enterprise Risk Management: The Reason Why Reinsurance is Purchased Gross Business Plan Economic Capital Risk Balance Sheet Risk Tolerance 6
Enterprise Risk Management: Reinsurance is a Capital Source Value Created Risk Balance Sheet Business Plan Economic Capital From Reinsurer Economic Capital From Other Sources Risk Tolerance 7
Enterprise Risk Management: Advantages for Making Reinsurance Decisions Helps us maintain discipline in our decision making Focuses us on evaluating decisions using the framework of our risk tolerance Ensures that this decision is aligned with corporate risk and return objectives If we choose to shift our risk tolerance to increase our net risk to achieve a greater return, we will explicitly know the choice we make Protects us from unknowingly eroding our capital position Increases the likelihood that the business plans we choose will be successful 8
Dynamic Financial Analysis: An ERM Tool used in Reinsurance Decision-Making 9
Enterprise Risk Management: Dynamic Financial Analysis Simulation based The underlying drivers of the simulations are economic and insurance events Encompasses many risks Market risk, credit risk, pricing risk, reserving risk, catastrophe risk Forward looking Recognizes the current book as well as the business plan Considers accumulation/diversification of risk Across the book and across the balance sheet 10
Enterprise Risk Management: A Sample DFA Model Structure E c o n o m i c F a c t o r s Individual Assets Individual Loss Events Catastrophe Event Tables Asset Proxy (Duration/ Convexity/Credit) Fit Frequency and Severity Distributions Aggregated Losses C O R R E L A T I O N S I M U L A T I O N Enterprise Risk/Return Economic Capital Operational Risk Event Tables Aggregated Losses 11
Some Common Measures of Risk Calculated using DFA Model Output Standard Deviation Value at Risk (VaR) Tail Value at Risk (TVaR) 12
Standard Deviation Standard deviation is represented by the sigma (σ). Illustrated below is one standard deviation around the mean. Mean -σ +σ -σ -70% -30% +25% (Mean) +50% % Underwriting Profit/Loss to Premium (=Underwriting Ratio) 13
Value at Risk (VaR) The maximum loss an organization can suffer Under normal market conditions Over a given period of time At a given probability level Measure of downside risk Common measure of risk in the banking sector Ask the question of management: At what point would you start behaving dysfunctionally? 14
Value at Risk (VaR) Defined as Value at Risk, the 20% probability of a 30% negative underwriting ratio is illustrated below. Mean 20% probability of a 30% underwriting loss to premium ratio -70% -30% +25% (Mean) +50% % Underwriting Ratio 15
Tail Value at Risk (TVaR) Both the probability and the cost of tail events are considered. It is the expected value of all events beyond the tail threshold event, not just the shortfall amount. Measures, How bad is bad? 16
Tail Value at Risk (TVaR) The TVaR (5%) shows the average value of underwriting loss ratio beyond the 5% threshold. Mean In the 5% worse scenarios, the average % underwriting loss ratio is 55% -70% -30% +25% (Mean) +50% Underwriting Ratio 17
Risk Metrics: Risks Captured in Simulation Process Risk Monte Carlo simulation models process risk Parameter Risk and Model Risk Monte Carlo simulation models are unable to directly measure either type of risk 18
MegaRisk Model Parameter Development Data Adjustments/assumptions Modifications to analysis Size of Loss Analysis Model Parameterization 19
Enterprise Risk Management: Analytical Process, Modified for MegaRisk E c o n o m i c F a c t o r s Individual Assets Individual Loss Events Catastrophe Event Tables Asset Proxy (Duration/ Convexity/Credit) Fit Frequency and Severity Distributions Aggregated Losses C O R R E L A T I O N S I M U L A T I O N Enterprise Risk/Return Economic Capital Operational Risk Event Tables Aggregated Losses 20
Data for Study 100,000 individual liability claims from 80,000 occurrences; 50,000 property claims Ground up Accident years 1988 through December 31, 2005 Gross and ceded premium by LOB for years 2002-2005 2005 Limits profiles for liability and property 21
Current Reinsurance Program 22
Adjustments and Assumptions Model inputs include large loss severity curves, that generate claims over $1M. Historical MegaRisk large losses, trended annually at 2.5% (and for some alternative models to perform sensitivity testing, at 5%) to 12/31/06, the midpoint of the reinsurance coverage of the upcoming renewal. Loss data excludes IBNR; only data from claims 2002 and prior were used for liability and assumed to be fully developed. Correlation between liability lines is 10%; between liability and property is 20%. 23
Catastrophic Events Table 24
Fitted Severity Curves 25
MegaRisk Statistical Analysis of Current Program Gross/Ceded/Net Simulation Current Assumptions Sensitivity Testing 26
Four Models to Analyze (for Sensitivity Testing) Models Base Case 2.5% Trend with 5% Cat Probability 5% Trend with 7.5% Cat Probability 5% Trend and 5% Cat Probability Trend 2.5% 2.5% 5% 5% Probability of Cat Event 7.5% 5% 7.5% 5% Exhibit Underwriting Gain Perspective Gross, Ceded, Net 27
Gross U/W Gain/Loss Statistical Analysis Model: 2.5% Trend and 7.5% Cat Probability 28
Comparison: Gross Underwriting Results METRIC Trend: 2.5% 7.5% Prob. 5% Prob. 7.5% Prob. Trend: 5% 5% Prob. Mean 79,249 89,182 81,707 91,640 VaR @99% (552,078) (503,154) (541,635) (498,705) TVaR @99% (676,165) (656,439) (668,799) (641,352) Mean/VaR 14.4% 17.7% 15.1% 18.4% Mean/TVaR 11.7% 13.6% 12.2% 14.3% 29
Ceded U/W Gain/Loss Statistical Analysis Model: 2.5% Trend and 7.5% Cat Probability 30
Comparison: Ceded Underwriting Results METRIC Trend: 2.5% 7.5% Prob. 5% Prob. 7.5% Prob. Trend: 5% 5% Prob. Mean 37.074 45,730 21,767 30,410 VaR @99% (509,724) (455,940) (607,997) (585,535) TVaR @99% (611,027) (569,357) (765,380) (747,766) Mean/VaR 7.3% 10.0% 3.6% 5.2% Mean/TVaR 6.1% 8.0% 2.8% 4.1% 31
Net U/W Gain/Loss Statistical Analysis Model: 2.5% Trend and 7.5% Cat Probability 32
Comparison: Net Underwriting Results METRIC Trend: 2.5% 7.5% Prob. 5% Prob. 7.5% Prob. Trend: 5% 5% Prob. Mean 42,176 43,450 59,940 61,229 VaR @99% (101,978) (111,198) (97,640) (94,915) TVaR @99% (129,302) (143,456) (127,601) (124,134) Mean/VaR 41.4% 39.1% 61.4% 64.5% Mean/TVaR 32.6% 30.3% 47.0% 49.3% 33
ERM Symposium March 29, 2007 Reinsurance for Risk and Capital Management Implications for: Capital Needs New York The Impact of Reinsurance
Introduction Getting the structure right Systemic risks Accumulation over time Impact of casualty XOL reinsurance Guy Carpenter 2
Section 1
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. Guy Carpenter 4
!" 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 Are these are captured in the risk model? Guy Carpenter 5
Section 2
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 Guy Carpenter 7
#$ Time Related Risk Trend and Development Parameters. Changing Trends Simultaneously impact new business and accumulated reserves. Market Related Risk Also: Casualty catastrophes Guy Carpenter 8
% Model Structure (one LOB, one AY) Nominal Incremental Paid for accident year i = AY i for a single simulation. Each RV is sampled once per simulation. RV s are mutually independent AY i = A x B x C (F i-e) x D i E : Average date of payment in historical data F i : Average date of payment for period i Guy Carpenter 9
& Process+ Risk AY i = A x B x C (F i-e) x D i 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. Guy Carpenter 10
& Accident Year Deviation AY i = A x B x C (F i-e) x D i 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 Guy Carpenter 11
& Trend/Development Parameter Risk AY i = A x B x C (F i-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,) or C ~ L-N(0,) are reasonable choices. Compounded error factor for each payment is multiplied by the payment Guy Carpenter 12
%'( ) Long-Tail LOB Historical Data Development Short-Tail LOB Trend Future Accident Year Ultimate Guy Carpenter 13
& Future Trend Process Risk AY i = A x B x C (F i-e) x D i 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) Guy Carpenter 14
%) The AR(1) Process X i (i = 1, 2,, n) are independent mean zero Normal random variables drawn from the same distribution. Then define: ρ t 1 = X 1 t ρ + = tk 1 is the autocorrelation coefficient. k X k Annual trend error = e t k Cumulative trend error for year k = D k = k i= 1 t k e i = e i = 1 t i Guy Carpenter 15
% Historical Data Expected Future Trend Future Accident Year Guy Carpenter 16
) $* The estimated trends may be wrong: 2 1.5 1 0.5 0 l----------- Historical Period -----------l l--------- Projected Period ------------l Plus the trends may change: 2 1.5 1 0.5 0 l----------- Historical Period -----------l l--------- Projected Period ------------l Guy Carpenter 17
$+(,)' -$. $+ Probability Density Function Process + Systemic Process Only -60,000-40,000-20,000 0 20,000 40,000 60,000 80,000 100,000 120,000 $ (thousands) Guy Carpenter 18
$+(, ' -$. $+ Cumulative Distribution Functions at Different Retentions 120% with 99th percentiles 100% Probability 80% 60% 40% Process + systemic Process Only 20% 0% -60,000-40,000-20,000 0 20,000 40,000 60,000 80,000 100,000 120,000 Excess Over the Mean Guy Carpenter 19
% Model Structure (multiple lines) A, B, C, D i, E, F i per line A, B, C, D i within lines are independent B s, C s, D i s may be correlated across lines. For D i s, the future random errors (X i s) are correlated across lines for each year; the X i s for different years are mutually independent. The structure may also be used to reflect correlation among different accident years for the same line, or alternatively between the current accident year and reserves for the same line. Guy Carpenter 20
Section 3 (%
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. Guy Carpenter 22
'/ 0 Calendar Year Exposure Drawing Capital 1 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. Guy Carpenter 23
1,2 (& 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. Guy Carpenter 24
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. Guy Carpenter 25
$+(,)' -$. $+ AY Only AY + Accumulation -200,000-150,000-100,000-50,000 0 50,000 100,000 150,000 200,000 250,000 300,000 350,000 Losses vs. Mean (in thousands) Guy Carpenter 26
. $+(, ' -$. $+ 110% 100% 90% Probability 80% 70% 60% 50% 40% 30% 20% 10% AY + Accumulation AY Only AY Process Only 0% -200,000-150,000-100,000-50,000 0 50,000 100,000 150,000 200,000 250,000 300,000 350,000 Losses vs. Mean (in thousands) Guy Carpenter 27
% $+3 $+(, ' 4 56 One Accident Year AY + Accumulation Cumulative Distribution Function with 99th percentiles 120% 100% 80% Probability 60% 40% 20% 0% -400,000-200,000 0 200,000 400,000 600,000 800,000 $ (thousands) Guy Carpenter 28
Section 4 7-
7-' Leveraged Process Risk Leveraged Impact of Trend and Development Uncertainty Longer Payout Pattern creates: A longer trend period More accumulated reserves Guy Carpenter 30
$7- %,, 4 89:-$ Losses Per Claim 8,000 7,000 6,000 5,000 4,000 3,000 2,000 1,000 0 Payments by Layer 0 2 4 6 8 10 12 14 Years $5M $2M $1M $500K $250K Guy Carpenter 31
$7- %,, 4 %'* - Losses Per Claim 1,000 900 800 700 600 500 400 300 200 100 0 Payments by Layer 14 19 24 29 34 39 44 49 Years $5M $2M $1M $500K $250K Guy Carpenter 32
' 4 $+( 120% Cumulative Distribution Function with 99th percentiles $5M $2M 100% $1M $500K 80% Probability 60% 40% 20% 0% -300,000-200,000-100,000 0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 $ (thousands) Guy Carpenter 33
Using ERM to Evaluate Reinsurance Concurrent Session 3 Stephen Lowe, Managing Director 29 March 2007 2007 Towers Perrin
My first topic is retention optimization Retention optimization focuses on answering the following question How do I decide how much risk to retain and how much to transfer? Decision criteria should Maximize value creation Be consistent with actuarial principles Be consistent with corporate finance Apply to all businesses, not just insurers 2007 Towers Perrin 2
For all types of businesses, insurance and other hedges are forms of capital Capital purposes: 1. Operational capital required to produce goods and services such as plant, equipment, patents, staff, inventory, etc. 2. Risk capital required to support inherent volatility in operations such as varying economic conditions; uncertainties in revenues and production costs; catastrophic events (For an insurer, the sum is Economic Capital) Capital resources include both paid-up capital and contingent capital: Paid-Up Capital Equity Debt Preferred Surplus Notes Contingent Capital Line of credit Reinsurance Side-Cars Securitization For an insurer, the value of reinsurance can be assessed by comparing it to the cost of traditional on-balance-sheet sources of capital 2007 Towers Perrin 3
The Standard Model of the Firm Capital High Paid-up Low Senior Debt Priority Hybrid capital Equity Risk Exposure Risk Low Retain High 2007 Towers Perrin 4
The Insurative Model Capital Contingent Paid-up Low Insurance Hedge Senior Debt Hybrid capital Equity Risk Exposure Risk Transfer Retain High 2007 Towers Perrin 5
The Insurative Model Capital Contingent Paid-up Insurance Hedge Committed Capital Senior Debt Hybrid capital Equity Risk-Linked Securities Risk Transfer Retain Transfer 2007 Towers Perrin 6
Our approach is formalized in an ERM Value Framework Maximize value by relating a firm s decisions on the risks it takes to decisions on the capital it uses to finance its business Value Creation Maximize the spread between returns and total capital costs Return on Risk Value Management Capital Costs Minimize the total cost of capital for a given portfolio of enterprise risks Risk Structure Portfolio of Enterprise Risks How much capital do I need? Capital Adequacy Risk and Capital Management What type of capital do I need? Portfolio of Capital Resources Capital Structure Economic Capital 2007 Towers Perrin 7
Application to risk retention Type of capital Value ($) Cost (% Value) Expense ($) Equity E e ee Debt D d dd Paid-up W = E + D w ww = ee +dd Insurance H h hh Total T = E + D + H t tt = ww + hh Impact of change in retention in firm s capital expense is: Δ(tT) = Δ (ww) + Δ (hh) hh will change since insurance coverage has changed ww will change since risk borne by debt and equity has changed W may change if the firm changes the amount of paid-up capital w may change if investors perceive a change in their risk Opportunity to minimize the total expense, tt, due to risk leverage, H/W 2007 Towers Perrin 8
Case Study: United Grain Growers UGG is a grain trader in western Canada Revenue and profits are volatile due to harvest variations High level of working capital required to support volatility of operations Swiss Re offers UGG insurance for risk of poor harvest UGG substantially lowers its working capital requirements UGG s total cost of capital (including insurance) goes down; value of business goes up Volatility of UGG Net Income ALL FIGURES ARE ILLUSTRATIVE Before After Probability After Swiss Re Contract Before Swiss Re Contract Working Capital $400 $100 Cost of Capital 9% 9% Annual $ Capital Cost $36 $9 Insurance Risk Premium $17 Total Capital Cost $36 $26 Unfavorable Favorable 2007 Towers Perrin 9
Step 1 Risk Modeling Conceptual overview of model to generate stochastic pro-forma financial results Projected Financials Economic Scenario Generator Inflation Interest Rates Asset Class Performance Asset Asset Behavior Behavior Model Model Product Product Behavior Behavior Model Model Distribution of Future Financial Results Probability Alternative Strategies Asset Mix Product Mix Financial Leverage Risk Leverage Optimization 2007 Towers Perrin 10
Step 2 Apply decision criteria Choosing Best Retention and Limit for Reinsurance ILLUSTRATIVE 40% 35% 30% Too much "trading of of dollars" Too far "out of of the the money" Cost of Capital 25% 20% 15% 10% 5% 0% Reinsurance Paid-up capital 0 100 200 300 400 500 Retention Retention/Limit Trade-Off ($ Millions) Limit 2007 Towers Perrin 11
Highlights of AIF Study 2007 Towers Perrin
In the event of an active hurricane season in 2007, most claim payments will be funded after-the-fact $90 $80 80.0 $70 Billions of Dollars $60 $50 $40 $30 $20 $10 $0 55.0 49.5 54.2 43.8 35.0 37.4 34.5 25.0 31.4 20.0 24.1 9.9 14.6 25.8 10.1 10.4 10.9 12.4 15.0 17.6 1 in 20 1 in 30 1 in 50 1 in 70 1 in 85 1 in 100 1 in 250 Hurricane Probability Pre-event funding Post-event funding (assessments and bonds) Notes: Pre-event funding includes funds available to Citizens, FHCF, and private carriers, plus contingent funding available through private reinsurance to pay claims in 2007. Post-event funding is on a present-value basis and does not include cumulative financing costs. Probabilities are expressed as odds of a single storm of this magnitude or greater happening in the 2007 season. 2007 Towers Perrin 13
Potential long-term costs of 2007 hurricanes could overshadow 2007 premium savings for consumers Hurricane Probability Savings 1 in 20 1 in 30 1 in 50 1 in 70 1 in 85 1 in 100 265 1,005 721 1,486 1,066 3,503 4,416 4,694 4,956 2,528 3,219 3,497 3,752 This illustration does not contemplate the possibility of multiple hurricanes in 2007 or the possibility of hurricanes beyond 2007, which would further constrain funding and result in additional assessments 1 in 250 7,855 6,116 0 2,000 4,000 6,000 8,000 10,000 12,000 14,000 16,000 Nominal Savings/Cost per Household Savings Direct Costs Indirect Costs Notes: Assumed average homeowners premium per household is $1,300 in 2007. Savings for 2007 premiums reflects 24.3% savings on hurricane costs, which are assumed to be 63% of total premiums. These savings are based on the statewide OIR estimate. Actual savings may be less. Direct costs include assessments paid by policyholders on homeowners and personal auto premiums. Indirect costs include assessments on commercial lines passed onto consumers through higher prices. Amounts expressed here are the nominal costs, or the total cost of borrowing including financing charges paid over the term of the bond. 2007 Towers Perrin 14
Annual assessments per average household would extend out thirty years under various scenarios (here, a 1 in 100 storm in 2007) 600 509 Average Dollar Assessment per Household 500 400 300 200 100 0 377 377 377 377 377 377 377 377 377 377 221 221 221 221 221 221 221 221 221 221 221 221 221 221 221 221 221 221 221 221 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033 2034 2035 2036 2037 Citizens Regular Assessments Citizens Emergency Assessments FHCF Assessments FIGA Regular Assessments FIGA Emergency Assessments This illustration does not contemplate the possibility of multiple hurricanes in 2007 or the possibility of hurricanes beyond 2007, which would further constrain funding and result in additional assessments Note: Number of households is based on 2007 households and is not adjusted for population growth. 2007 Towers Perrin 15