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Capital Consumption

Capital Consumption. Don Mango, FCAS, MAAA Director of R&D GE Insurance Solutions 2004 CAS Annual Meeting.

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Capital Consumption

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  1. Capital Consumption Don Mango, FCAS, MAAA Director of R&D GE Insurance Solutions 2004 CAS Annual Meeting

  2. GE Insurance Solutions protects people, property and reputations. With over $50bn in combined assets, the GE Insurance Solutions group of companies is one of the world’s leading providers of commercial insurance, reinsurance and risk management services. PROPRIETARY INFORMATION NOTICE The information contained in this document is the property of Employers Reinsurance Corporation, a member of the GE Insurance Solutions group of companies. It should not be reprinted, redistributed or disclosed to others without the express written consent of ERC.

  3. Goals for Today Demonstrate: alternative evaluation framework to capital allocation/release/IRR Shared Asset: unifying it with capital allocation (PCAS submission) Portfolio: two methods to allocate a portfolio risk charge to segment

  4. Demonstrate

  5. Allocation vs Consumption • Three questions: What do you do with the total capital? How do you evaluate business segments? What does it mean to be in a portfolio?

  6. Allocation vs Consumption Simultaneous, Overlapping Rights to a Single Capital Pool

  7. Allocation vs Consumption Decentralized vs Centralized Capital Management

  8. This is THE CRITICAL SLIDE! Allocation vs Consumption The difference between having a kiddie pool in your backyard and joining a swim club

  9. Scenario analysis and capital consumption Default-free discounting Capital Call Cost Function Details of the Framework

  10. Experience fund From Finite Reinsurance Fund into which goes all revenue, from which comes all payments Reflects investment income When the fund is exhausted, but further payments still need to be made, exercise the Call Option for capital That capital gets spent  CONSUMED 1. Scenario Analysis and Capital Consumption

  11. Experience Fund Long-Tailed LOB

  12. Experience FundShort-Tailed LOB

  13. Property Cat Example

  14. Conditional on its occurrence, a given scenario’s outcome is certain  discount at the default-free rate Risk-adjusted discounting is too clumsy Overloaded operator Try splitting out default probability from price of risk in risky debt spreads Reflect uncertainty between scenarios, not within 2. Default-Free Discounting

  15. Risk-based overhead expense loading Pricing decision variable Application of utility theory Borch (1961):To introduce a utility function which the company seeks to maximize, means only that such consistency requirements (in the various subjective judgments made by an insurance company) are put into mathematical form. 3. Capital Call Cost Function Transparent, Explicit Formulation of Risk-Reward Appetite

  16. Make the implicit explicit Express your preferences explicitly, in mathematical form, and apply them via a utility function The mythical “Risk Appetite” Enforce consistency in the many judgments being made 3. Capital Call Cost Function

  17. Preferences buried in Kreps’ “Marginal Standard Deviation” risk load approach: The marginal impact on the portfolio standard deviation is our chosen functional form for transforming a given distribution of outcomes to a single risk measure. Risk is completely reflected, properly measured and valued by this transform. Upward deviations are treated the same as downward deviations. Implicit Preferences

  18. Shared Asset

  19. Capital Allocation is necessary The best way to make risk-based portfolio composition decisions Critical element of financial product pricing Standard language of management Capital Allocation makes no sense All of the company’s capital is available to support each policy No capital is transferred at policy inception Capital is transferred via reserve strengthening Problem Statement How can we resolve this paradox and move forward?

  20. 2. Earmarking Categorizing, bucketing, setting aside This applies to balances We earmark assets all the time, a.k.a. reserves Allocation Has Two Definitions • 1. Transfer • Distributing, moving • This applies to flows • We transfer assets all the time, a.k.a. claims payments Resolution May Lie in the Theory of Shared Assets

  21. Shared Asset Usage Shared AssetReservoir, Golf Course,Pasture, Forest, … User Community Access Users have their own interests, often cannot see larger picture Asset owners control access rights to preserve asset, control against over-use Uses are classified as either CONSUMPTIVE or NON-CONSUMPTIVE

  22. Consumptive Permanent transfer of control of a portion of the asset to the user Aggregation risk from over-depletion Examples: Water from reservoir Fisheries Timber Non-Consumptive Temporary partial transfer of control of a portion of the asset to the user Aggregation risk from exceeding capacity Examples: Golf course Campsites Hotel Consumptive and Non-Consumptive

  23. Written Premium Reserves @ t=2 @ t=3 Required Capital @ t=1 @ t=4 @ t=2 @ t=5 @ t=3 @ t=4 @ t=5 Required Capital Formula Typical Insurance Capital Allocation Changes in Required Capital are attributed to imputed capital transfers to and from the Owner But no such transfers ever take place!

  24. Must We Assume a Capital Transfer? • Changes in the level of required capital are attributable to changes in the balancesthat generate required capital • Not to transfers of required capital • Technically a mis-imputation • Amounts of required capital could be thought of as generated balances, like the amount of rooms rented in a hotel • Occupancy of the firm’s finite capacity

  25. The Capital Hotel • Occupancyhas a time dimension and an amount dimension • Return is equivalent of rental fees  should also be linear with time and amount • There are also clearly opportunity costs, since occupancy of capacity (rooms) precludes it from use by others

  26. The Bi-Polar Capital Hotel • Two distinct different types of insurance capital usage: • Non-Consumptive or “Rental”> Returns are at or above expectation> Capital is occupied, then returned undamaged> A.k.a. Benign room occupancy • Consumptive>Results deteriorate> Reserve strengthening is needed > A.k.a. Destroy your room, your floor, the entire hotel

  27. Different types of capital usage at different parts of the spectrum Better Outcomes Worse Outcomes

  28. Advantages of Shared Asset Approach • Clear demonstration of dual modes of insurance capital usage • Handles simultaneous claim of any policy to lay claim to all the company’s assets • Inclusive not divisive: from slicing the pie to simultaneous, competing usage of a common capital pool

  29. Portfolio Allocation

  30. Capital Consumption

  31. Shared Asset Portfolio Mix ModelKey Inputs • Plan Expected Loss • Plan Profit Margin, expressed as percent of expected loss • Mean Loss and Margin (ex expenses) gives you Plan Premium • Actual Profit Margin (will be changed by Solver) • Demand Curve (see below) • Max Required Capital = input constraint • Capital Usage Charges (aka Hotel charges)

  32. Shared Asset Portfolio Mix ModelKey Calculations • Actual/Plan Profit Margin = Price Deviation off Plan (feeds Volume Impact formula) • Assumes Plan [ Profit Margin, Premium Volume ] is achievable • Volume Impact = based on Demand Curve • Increase or decrease in Exposure Units as a function of deviation of Actual price deviation off Plan • Actual Premium = Exp Loss * Actual Profit Margin * Volume Impact

  33. Shared Asset Portfolio Mix ModelKey Calculations • Required Capital = X% * Actual Premium (simplified approximation of rating agency formula) • Hotel formula is calculated using Loss Distribution only (excluding Profit Margin), scaled for Volume Impact as well • Capital Usage Charges are therefore Required Profit Margin, which can be expressed as % of Expected Loss

  34. Shared Asset AllocationCalculation • Given: Scenarios of underwriting income by product segment • Capital rental charge(Example uses 7% of allocated capital) • Charge for damage within your allocationExample uses 14% of underwriting result • Charge for damage beyond your allocationExample uses 112% of underwriting result beyond capital alloc

  35. Shared Asset AllocationCalculation Example • Capital Allocation = $5M • Underwriting ResultCapital Usage Cost • +$2M $5M*7% = $350K • -$3M $350K + $3M*14% = $770K • -$8M $350K + $5M*14% + $3M*112% = $4,050K • Steepness of penalty depends on relative difference in charges between “within capital” and “beyond capital” usages

  36. Shared Asset Portfolio Mix ModelKey Calculations • Solver minimizes sum of squared differences between Actual and Required Profit Margin by modifying the price changes, which impact volume • Constraints: • Required Capital cannot exceed maximum required capital; • Actual profit margin must not be less than Required profit margin for all Products.

  37. References • Shared Asset – working paper draft and Excel demo model, send me an email: don.mango@ge.com • Capital Consumption Allocation – see Appendix B of www.casact.org/pubs/forum/03wforum/03wf351.pdf

  38. Thank YouQuestions?

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