The Real World: Dealing With Parameter Risk. Alice Underwood Senior Vice President, Willis Re March 29, 2007

Transcription

1 The Real World: Dealing With Parameter Risk Alice Underwood Senior Vice President, Willis Re March 29, 2007

2 Agenda 1. What is Parameter Risk? 2. Practical Observations 3. Quantifying Parameter Risk 4. ERM Case Study 5. Q&A

3 Types of Risk Process Risk inherent variability in random process fluctuation about the mean Parameter Risk possibility that parameters are misestimated e.g., incorrect mean Model Risk possibility that the mathematical model of the process is inappropriate

4 Types of Risk: Considerations Process Risk diversifiable foundation of the insurance business Parameter Risk systemic affects all estimates using this parameter may be correlated across years / companies Model Risk a type of operational risk

5 Agenda 1. What is Parameter Risk? 2. Practical Observations 3. Quantifying Parameter Risk 4. ERM Case Study 5. Q&A

6 Company Level Observations General Liability Loss Model Based on standard actuarial analysis of several lines of business Balanced to company s plan loss ratio Cumulative Probability 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% process error very unlikely to produce result more than 10 points under plan Plan LR 60% process error also unlikely to produce result more than 10 points over plan 0% 50% 55% 60% 65% 70% 75% Modeled Loss Ratio

7 Company Level Observations Comparison of Model to Historical Data 100% Cumulative Probability 90% 80% 70% 60% 50% 40% 30% 20% 10% not likely to be driven by process error alone Modeled Historical AY Booked LR (at 12 mos) Historical Booked AY LR (at 12/31/05) 0% 50% 60% 70% 80% 90% 100% 110% Plan LR 60% Loss Ratio

8 Industry Level Observations General Liability: OLR vs. ULR Loss Ratio Industry OLR Industry ULR 160% 140% 120% 100% 80% 60% 40% Accident Year Clearly some error is not diversifying away Magnitude and direction of industry error change over time

9 Agenda 1. What is Parameter Risk? 2. Practical Observations 3. Quantifying Parameter Risk 4. ERM Case Study 5. Q&A

10 Sources of Parameter Risk in Actuarial Analysis Data issues finite sample flawed data Projection ( as if ) issues loss trend & development premium on-level Judgment factors development method selected inclusion of soft factors External influences law changes, coverage changes

11 Quantifying Parameter Risk: Top-Down Approach Industry OLR Industry ULR Loss Ratio 160% 140% 120% 100% 80% Time series analysis Simulation 60% 40% Accident Year 7% Result of 10,000 Simulations Distribution of forecast average 2007 parameter error is skew to the right Median is below 1.0 But significant chance of large upward deviation Probability Density 6% 5% 4% 3% 2% 1% 0% Industry Average ULR/OLR

12 Agenda 1. What is Parameter Risk? 2. Practical Observations 3. Quantifying Parameter Risk 4. ERM Case Study 5. Q&A

13 Including Parameter Risk in ERM Ignore it not recommended Two-stage analysis 1: base case without parameter risk 2: stress test / adverse scenarios Blended parameter / process risk analysis incorporate diffuse prior into the model

14 Case Study Monoline GL company 100M premium, 50M capital 60% ELR, 30% expense ratio Loss model large loss frequency: Poisson, n = 20 large loss severity: Pareto, α = 2 [mean 1M] attritional losses: Lognormal Parameter error 20% chance that ELR is really 69% (factor 1.15) driven by increased severity of large losses

15 Case Study Reinsurance structure 500K xs 500K, swing rated (min 4%, max 8%, load 100/80) 1M xs 1M, 3% rate, 10M AAL 3M xs 2M, 2% rate, 1 free reinstatement 5M xs 5M, 1% rate, 1 free reinstatement Strategies considered A: 9.5M xs 0.5M B: 9M xs 1M C: 8M xs 2M D: 5M xs 5M

16 Modeling Using Willis ifm

17 Large Loss Distribution: Base Case 2%-5% chance of observing 4 or more losses in excess of 2M in a given simulated year Base Case E[Freq] = 20 E[Sev] = 1M Graphic shows result of 10,000 simulated years Color indicates the probability of observing certain # of losses larger than the indicated severity in a given simulated year

18 Large Loss Distributions Base Case Freq = 20 Sev = 1M Blended p(base) = 80% p(adverse) = 20% Adverse Freq = 20 Sev = 2M

19 SD Efficient Frontier: Base Case Reinsurance Efficient Frontier UW Result vs. Std. Deviation BASE CASE 12 Gross *A - xs 500K *B - xs 1M *C - xs 2M *D - xs 5M Expected Underwriting Result ($M) preference among B, C, D, and Gross a matter of risk appetite? Standard Deviation of Underwriting Result

20 Variability of Net UW Result: Base Case In the base case, much of the reduction in standard deviation is driven by reduced upside

21 99% VaR Efficient Frontier: Base Case Reinsurance Efficient Frontier UW Result vs. VaR BASE CASE 12 Gross *A - xs 500K *B - xs 1M *C - xs 2M *D - xs 5M Expected Underwriting Result ($M) %ile VaR ($M)

22 EP Efficient Frontier: Base Case Reinsurance Efficient Frontier UW Result: EP BASE CASE 12 Expected Underwriting Result these other risk metrics suggest company should not buy reinsurance at all Gross *A - xs 500K *B - xs 1M *C - xs 2M *D - xs 5M % 11.00% 12.00% 13.00% 14.00% 15.00% 16.00% 17.00% 18.00% 19.00% 20.00% Probability That Net Underwriting Result is Worse Than $-5M

23 Variability of Net UW Result: Adverse Scenario In adverse scenario, purchase of reinsurance is a clear benefit

24 SD Efficient Frontier: Adverse Scenario 6 Reinsurance Efficient Frontier UW Result vs. Std. Deviation: ADVERSE SCENARIO Gross *A - xs 500K *B - xs 1M *C - xs 2M *D - xs 5M Expected Underwriting Result ($M) (2) (4) (6) (8) (10) Standard Deviation of Underwriting Result

25 99% VaR Efficient Frontier: Base Case Reinsurance Efficient Frontier UW Result vs. VaR ADVERSE SCENARIO Gross *A - xs 500K *B - xs 1M *C - xs 2M *D - xs 5M 6 Expected Underwriting Result ($M) (2) (4) (6) (8) (10) 99%ile VaR

26 EP Efficient Frontier: Adverse Scenario Reinsurance Efficient Frontier UW: EP ADVERSE SCENARIO Expected Underwriting Result Gross *A - xs 500K *B - xs 1M *C - xs 2M *D - xs 5M % 10.00% 20.00% 30.00% 40.00% 50.00% 60.00% (2) (4) (6) (8) (10) Probability That Net UW Result is Worse Than $-5M in adverse scenario, the more reinsurance the better: consistent across risk metrics

27 Variability of Net UW Result: Blended Model the blended model offers guidance on how much credence to give the adverse scenario

28 SD Efficient Frontier: Blended Model Reinsurance Efficient Frontier UW Result vs. Std. Deviation: BLENDED MODEL 9 Gross *A - xs 500K *B - xs 1M *C - xs 2M *D - xs 5M Expected Underwriting Result Standard Deviation of Underwriting Result

29 99% VaR Efficient Frontier: Base Case Reinsurance Efficient Frontier UW Result vs. VaR BLENDED MODEL Gross *A - xs 500K *B - xs 1M *C - xs 2M *D - xs 5M Expected Underwriting Result ($M) %ile VaR ($M)

30 EP Efficient Frontier: Blended Model Reinsurance Efficient Frontier UW: EP BLENDED MODEL Gross *A - xs 500K *B - xs 1M *C - xs 2M *D - xs 5M Expected Underwriting Result % 12.00% 14.00% 16.00% 18.00% 20.00% 22.00% Probability That Net UW Result is Worse Than $-5M blended model suggests that option B may be best

31 Including Parameter Risk in ERM Ignore Parameter Risk Two-Stage Analysis Blended Parameter / Process Risk Analysis Advantages model will balance to plan illustrates parameter and process risk separately helps assess the magnitude of each may help in formulating strategies to address these separate issues offers guidance in dealing with holistic risk picture Disadvantages ignores a real source of risk each stand-alone analysis insufficient selection of only one (or a few) adverse scenarios is limiting co-mingles effects of different risks in general, mean will NOT balance to plan

32 Agenda 1. What is Parameter Risk? 2. Practical Observations 3. Quantifying Parameter Risk 4. Case Study 5. Q&A

33 Legal Disclaimers In preparing this Presentation, Willis Re has relied upon data provided by external data sources. No attempt has been made to independently verify the accuracy of this data. Willis Re does not represent or otherwise guarantee the accuracy or completeness of such data, nor assume responsibility for the result of any error or omission in the data or other materials gathered from any source in the preparation of this Presentation. Willis Re shall have no liability in connection with results stemming from the analysis including but not limited to any errors, omissions, inaccuracies, or inadequacies associated with the data. Willis Re expressly disclaims any and all liability to any third party in connection with this Presentation. In preparing this Presentation, Willis Re has used procedures and assumptions that Willis Re believes are reasonable and appropriate. However, there are many uncertainties inherent in actuarial analyses. These include, but are not limited to, issues such as limitations in the available data, reliance on client data and outside data sources, the underlying volatility of loss and other random processes, uncertainties that characterize the application of professional judgment in estimates and assumptions, reinsurance collectability, etc. Ultimate losses, liabilities and claims depend upon future contingent events, including, but not limited to, unanticipated changes in inflation, laws, and regulations. As a result of these uncertainties, the actual outcomes could vary significantly from Willis Re s estimates in either direction. Willis Re makes no representation about and does not guarantee the outcome, results, success, or profitability of any insurance or reinsurance program or venture, whether or not such program or venture applies the analysis or conclusions contained herein. Please consult your own independent professional advisors before making any decisions related to any information contained herein. This Presentation is provided for informational purposes only; it is not intended to be relied upon, and is not intended to be a complete actuarial communication. A complete communication can be provided upon request. Willis Re actuaries are available to answer questions about this Presentation.

34 The Real World: Dealing With Parameter Risk Alice Underwood Senior Vice President, Willis Re March 29, 2007

35 Credit Analysis in an ERM World Athula Alwis Willis Re Inc. March 29, 2007

36 Agenda ERM Framework Credit and Financial Products Credit Analytics Correlation Portfolio, Profit Center, Enterprise Q&A

37 ERM Risk Identification Risk Assessment Risk Management ERM Framework

38 ERM Risk Identification Risk Assessment Risk Management Asset Risk Operational Risk U/W Risk Credit Risk ERM Framework

39 ERM Risk Identification Risk Assessment Risk Management Asset Risk Operational Risk U/W Risk Credit Risk Property Casualty WC & other Financial Pdts ERM Framework

40 ERM Financial Products Trade Credit Structured Credit Political Risk Surety D&O Credit and Finance Products

41 Frequency Severity Pair-wise Correlation Credit Model Loss and Counts Distribution Portfolio Analysis Dynamic Financial Analysis Reinsurance and Capital Markets Structured Solutions Credit Model

42 Frequency Severity Pair-wise Correlation Credit Model Loss and Counts Distribution Frequency Module

43 Credit Rating Credit Spreads Country Risk Rating Sovereign Spreads Credit Default Rates Political Risk Default Rates Frequency Frequency Module: Surety, Trade Credit, Structured Credit and Political Risk

44 Credit Rating Credit Spreads Credit Spread Movement Volatility of Financial Metrics Stock Price Movement Underwriting Factors Large Institutional Investor IPO M & A Regulatory Investigation Frequency Frequency Module: D&O

45 Frequency Severity Pair-wise Correlation Credit Model Loss and Counts Distribution Severity Module

46 Frequency Severity Pair-wise Correlation Willis Re D & O Model Loss and Counts Distribution Correlation Module

47 Proven investment banking methodology used in advanced credit modeling Innovative application for portfolio risk modeling Allows quantification of the value at risk (VaR) and tail value at risk (TVaR) Critical for capital allocation Pair-wise Correlation

48 Option Pricing Theory S & P 500 Sector Indices Asset Correlation Default Correlation Copula Normal, t, Archimedean Pair-wise Correlation Pair-wise Correlation

49 Create a correlation table for simulation Project material correlation within and between industry sectors Project material correlation within and between regions Recognize potential for correlated loss events when generating aggregate losses Application of Pair-wise Correlation

50 Consumer Discretionary Consumer Discretionary Consumer Staples Energy Consumer Staples Energy Financials Healthcare Industrials Information Technology Materials Telecom Services Utilities Correlation within Sectors Financials Healthcare Correlation between Sectors Industrials Information Technology Materials Telecom Services Utilities Event Correlation Table Sample Table

51 For each iteration, apply the methodology to an entire portfolio of correlated risks Create a correlated multivariate default distribution to model losses and counts Simulation Process W

52 Frequency Severity Pair-wise Correlation Willis Re D & O Model Loss and Counts Distribution Correlated Multi-variate Loss Distribution

53 ERM Financial Products Trade Credit Structured Credit Political Risk Surety D&O Credit and Financial Products

54 ERM Risk Identification Risk Assessment Risk Management Asset Risk Operational Risk U/W Risk Credit Risk Property Casualty WC & other Financial Pdts ERM Framework

55 Why do we need to incorporate correlation at every level? Credit defaults, D&O, surety and trade credit losses following a collapse of a large corporation (Enron, etc ) Potential workers compensation losses following an earthquake Asset declines, underwriting losses and reinsurer failures at the same time due to systemic financial crisis Portfolio, Profit Center, Enterprise

56 Why do we need to incorporate correlation at every level? It is not sufficient to consider correlated events within a line of business (i.e. bad things happening at the same time within a single line) It is not sufficient to consider correlated events within a profit center (i.e. several lines of business being affected by a single event a natural CAT event or a severe financial crisis) Portfolio, Profit Center, Enterprise

57 Why do we need to incorporate correlation at every level? ERM practitioners must consider correlated events for the entire enterprise when risk reward profiles or the performance measurements are considered Then, the evaluation of reward per unit of risk will be truly meaningful Portfolio, Profit Center, Enterprise

58 In preparing this presentation, Willis Re has relied upon data provided by external data sources. No attempt has been made to independently verify the accuracy of this data. Willis Re does not represent or otherwise guarantee the accuracy or completeness of such data, nor assume responsibility for the result of any error or omission in the data or other materials gathered from any source in the preparation of this Presentation. Willis Re shall have no liability in connection with results stemming from the analysis including but not limited to any errors, omissions, inaccuracies, or inadequacies associated with the data. Willis Re expressly disclaims any and all liability to any third party in connection with this presentation. In preparing this presentation, Willis Re has used procedures and assumptions that Willis Re believes are reasonable and appropriate. However, there are many uncertainties inherent in actuarial analyses. These include, but are not limited to, issues such as limitations in the available data, reliance on client data and outside data sources, the underlying volatility of loss and other random processes, uncertainties that characterize the application of professional judgment in estimates and assumptions, reinsurance collectability, etc. Ultimate losses, liabilities and claims depend upon future contingent events, including, but not limited to, unanticipated changes in inflation, laws, and regulations. As a result of these uncertainties, the actual outcomes could vary significantly from Willis Re s estimates in either direction. Willis Re makes no representation about and does not guarantee the outcome, results, success, or profitability of any insurance or reinsurance program or venture, whether or not such program or venture applies the analysis or conclusions contained herein. Please consult your own independent professional advisors before making any decisions related to any information contained herein. This presentation is provided for informational purposes only; it is not intended to be relied upon, and is not intended to be a complete actuarial communication. A complete communication can be provided upon request. Willis Re actuaries are available to answer questions about this presentation. The statements and opinions included in this presentation are those of the individual speakers and do not necessarily represent the views of Willis Re or its management. Disclaimer

59 Credit Analysis in an ERM World Athula Alwis Willis Re Inc March 29, 2007