Capital Adequacy and Allocation Using Dynamic Financial Analysis

1. Capital Adequacy and Allocation Using Dynamic Financial Analysis Don Mango - American Re John Mulvey - Princeton University

2. Overview • Risk Measures and Required Capital • Capital Allocation • Initial Board Presentation • Follow-Up Meetings • The Reference Binder • Conclusions • Q & A

3. Risk Measures and Required Capital

4. So Many Open Issues... • No consensus definition of “Required Capital” • Which risk measure is best? • Probability of Ruin • What is the right level for that best risk measure? • 1% ? 0.4% ? 0.1% ? • Over what time horizon?

5. So Many Open Issues... • This issue is not limited to insurance • Value-at-Risk (VaR) in securities firms • What time horizon? (30 day) • What probability level? (95%) • Varies firm to firm • Rating agencies are not sure • We need consensus without collusion

6. Alternative Risk Measures • Probability of Ruin • Variance/Std Dev of Surplus • Expected Policyholder Deficit • Expected Default Loss Rate on Surplus

7. Advantages Easy to explain Easy to calculate Support from regulators/rating agencies Translates well to capital market framework (somewhat like VaR) Disadvantages Binary measure Ignores “gradations of solvency” (Philbrick) Associates “risk” with a single point Marginal impacts can be misstated Probability of Ruin

8. Advantages Well known statistical parameters Translate well to capital market framework (from CAPM) Variation captured in a single number Disadvantages Similar to Probability of Ruin No distinction made between upside and downside Variance/Std Dev of Surplus

9. Advantages Reflects the whole tail of the distribution rather than a single point Rating Agency support (AM Best BCAR has ties to EPD) Regulatory support (RBC - Butsic) Disadvantages More difficult to explain and calculate Expected loss may not be an appropriate base for required capital calculation Difficult capital market parallel (“Conditional VaR”) Expected Policyholder Deficit (EPD)

10. Advantages Reflects the whole tail of the distribution rather than a single point Capital market comparisons are immediate - bond default loss rate Easy explanation to financial audience Disadvantages Not (yet) well known Many are uncomfortable with its utility focus Expected Default Loss Rate of Surplus

11. Risk Measure Standards • On what basis should capital adequacy be assessed - economic, GAAP, stat? • Probability of economic ruin (zero NPV) is much lower than Probability of accounting ruin • Company with positive NPV can be accounting bankrupt • That’s why there are Loss Portfolio Transfers

12. Risk Measure Standards • What is the right probability standard? • 1% • 0.4% • 0.1% • All look good to me • Same issues in catastrophe modeling • Consensus / relative measures will emerge, similar to cat models

13. Risk Measure Standards • What is the right time horizon? • One year? • Two years? • Three years? • All look good to me • Could tie it to a planning horizon • The farther out you project, the more forecast error

14. Capital Adequacy Questions • What is the safety level of my current capital? • What is my capital redundancy/(deficiency) relative to other safety levels? • Give answers using many different risk measures

15. Capital Redundancy/(Deficiency)

16. Capital Redundancy/(Deficiency) • Emphasizes that there is no single “correct” answer to this question • Gives translations between the measures • e.g., 1% EPD = 2% EDLR • Sensitivity testing • How much additional capital to move from 0.4% to 0.2% ?

17. Risk and Safety Trade-off

18. Risk and Safety Trade-off • Where on this curve is the “right” place to be? • Probably are additional factors beyond this (e.g., variability) • Demonstrates marginal impact of capital changes

19. Capital Allocation

20. Allocation Actuarial Style • “Swap-in-and-out” • Marginal impact • See Glenn’s paper • For those probabilistic risk measures that we love, sum of marginal impacts will not equal portfolio total • “Diversification benefit” • “Rebalance”

21. Allocation Game Theory Style • Study of well-behaved allocation schemes • Additivity • Fairness • Stability • Order-independence

22. Allocation Game Theory Style • Cooperative games with transferable utilities: • Participants have something to share (benefit or penalty) • Valued the same by everyone ($) • Must be allocated to the players • Everyone wants the most benefit / least penalty

23. Allocation Game Theory Style • Valid allocation schemes • Additive: sum of allocations = total • Order-independent: shouldn’t matter the order in which I consider a participant • Fair: no systematic penalizing of sub-group • Stable: belief in the fairness of the allocation, no formation of factions

24. Allocation Game Theory Style • Shapley Value • Named for Lloyd Shapley, early leader of game theory field • Additive • Order-independent • Stable • Average Marginal impact over all possible entry permutations

25. Allocation Game Theory Style • Shapley Value • If you are using variance, it reduces to Var[division] + Cov[division, Rest of Company] • Manageable calculation • Support from other approaches taken by Gogol, Halliwell, Clark, Bault, ….

26. Initial Board Presentation

27. Board Presentation • Capital adequacy exhibits • Implied safety levels of current capital • Redundancy/(deficiency) relative to other safety levels • GAAP Balance sheets and income statements • Median values and Standard deviations shown

28. Board Presentation • Capital allocation • Absolute amounts of capital • % of total capital • Issues of fairness arise • Divisional loyalties • Nobody wants the penalty • Stability, fairness all lead to BUY-IN

29. Board Presentation • Return on Risk Adjusted Capital • Political hot potato • You had better be confident in your parameterization !! • Especially relative levels of variability which drive allocations

30. Board Presentation • Context • Important to provide familiar parallels for unfamiliar concepts and terms • Assets Needed Ratio = [ Premium + Capital ] / Expected Loss • Premium to Surplus Ratios • Divisional share of Expected Loss • Loss Ratio

31. Follow-Up Meetings

32. Follow-Up Meetings • Digging deeper into questions • Intuitive uneasiness of Board members • One capital adequacy measure was “out of whack” • Probability of achieving a target ROE was too high • These hunches are essential to identifying errors • How else to debug models like this

33. Follow-Up Meetings • Details behind 20 Worst scenarios • Compounded effect of several bad events coinciding • Can span several years • Splitting Runoff from Ongoing capital • Another unanswered question • Can be allocated… • …but should it be?

34. The Reference Binder

35. Reference Binder • Executive Summary • Intro to the DFA Model • Overview of Findings • Economic Modeling • Asset Modeling • Liability Modeling • Reinsurance Modeling

36. ARMS, American Re’s DFA Model

37. Conclusions

38. Conclusions • DFA Models = actuarial equivalent of advanced experimental apparatus • Allows us to pose (and answer) hypothetical questions that previously could not have been asked • No surprise that there are so many unanswered questions in this paper !!

39. Conclusions • Simplify your communications • Philbrick: DFA will prove its value when it recommends a different approach than a traditional analysis • Be open to criticisms, suggestions • Engage our capital market quantitative counterparts. They struggle with many of the same issues.

40. Conclusions • DFA system development has outpaced the theory and understanding • We created this beast, we need to tame it and put it to use

41. Q & A