Capital Allocation in Financial Firms, by uzw14922

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									  Capital Adequacy and
Allocation Using Dynamic
    Financial Analysis

   Don Mango - American Re
John Mulvey - Princeton University
                Overview

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

12/3/2010                                2
Risk Measures and
 Required Capital
             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?


12/3/2010                                        4
            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


12/3/2010                                     5
            Alternative Risk Measures

   Probability of Ruin
   Variance/Std Dev of Surplus
   Expected Policyholder Deficit
   Expected Default Loss Rate on Surplus




12/3/2010                                   6
               Probability of Ruin

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


12/3/2010                                                7
            Variance/Std Dev of Surplus

   Advantages                      Disadvantages
       Well known                    Similar to Probability
        statistical parameters         of Ruin
       Translate well to             No distinction made
        capital market                 between upside and
        framework (from                downside
        CAPM)
       Variation captured in
        a single number



12/3/2010                                                       8
 Expected Policyholder Deficit (EPD)

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

12/3/2010                                                    9
            Expected Default Loss Rate of
                      Surplus
   Advantages                        Disadvantages
       Reflects the whole              Not (yet) well known
        tail of the distribution        Many are
        rather than a single             uncomfortable with
        point                            its utility focus
       Capital market
        comparisons are
        immediate - bond
        default loss rate
       Easy explanation to
        financial audience

12/3/2010                                                   10
              Risk Measure Standards

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



12/3/2010                                                     11
              Risk Measure Standards

   What is the right probability standard?
       1%
       0.4%
       0.1%
          look good to me
       All
       Same issues in catastrophe modeling
       Consensus / relative measures will
        emerge, similar to cat models

12/3/2010                                     12
            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

12/3/2010                                       13
            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


12/3/2010                                   14
      Capital Redundancy/(Deficiency)
                                                          Excess/
                        Risk                 Capital     (Deficit)
                      Measure                  Need       Capital
            1 in 100 probability of ruin   $ 800        $300
            1 in 250 probability of ruin   $1,000       $100
            1 in 500 probability of ruin   $1,400      ($300)
            2% EPD                         $ 900        $200
            1% EPD                         $1,200      ($100)
            0.5% EPD                       $1,700      ($600)
            2.0% EDLR                      $1,000      ($100)
            1.0% EDLR                      $2,000      ($900)
            0.5% EDLR                      $3,000      ($1,900)




12/3/2010                                                            15
      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% ?

12/3/2010                                              16
                            Risk and Safety Trade-off
                                                          Profitability Versus Safety
      30.0%                                                                            99.60%   99.80%   100.00%
                                                           99.00%           99.25%
                25.0%                      98.00%
      25.0%                                                                                              98.00%
                              21.0%
                              96.00%
      20.0%                               18.0%                                                          96.00%




                                                                                                                   Safety
                                                          15.0%
ROE




      15.0%                                                                                              94.00%
                 93.00%                                                12.0%
                                                                                     10.0%
      10.0%                                                                                     9.0%     92.00%


      5.0%                                                                                               90.00%


      0.0%                                                                                               88.00%
                     (300      (200         (100           -                100       200       300
                                                  Additional Capital ($s)


                            50th Percentile ROE                               1-EPD Ratio

         12/3/2010                                                                                         17
            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



12/3/2010                                  18
Capital Allocation
            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”
12/3/2010                                   20
            Allocation Game Theory Style

   Study of well-behaved allocation
    schemes
   Additivity
   Fairness
   Stability
   Order-independence



12/3/2010                                  21
            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


12/3/2010                                         22
            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



12/3/2010                                         23
            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

12/3/2010                                            24
            Allocation Game Theory Style

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



12/3/2010                                        25
Initial Board Presentation
                    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

12/3/2010                                            27
               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




12/3/2010                                        28
               Board Presentation

   Return on Risk Adjusted Capital
                hot potato
       Political
       You had better be confident in your
        parameterization !!
       Especially relative levels of variability
        which drive allocations




12/3/2010                                           29
               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



12/3/2010                                              30
Follow-Up Meetings
               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
12/3/2010                                       32
             Follow-Up Meetings

   Details behind 20 Worst scenarios
       Compounded   effect of several bad events
        coinciding
       Can span several years

   Splitting Runoff from Ongoing capital
       Anotherunanswered question
       Can be allocated…
       …but should it be?


12/3/2010                                           33
The Reference Binder
            Reference Binder

   Executive Summary
   Intro to the DFA Model
   Overview of Findings
   Economic Modeling
   Asset Modeling
   Liability Modeling
   Reinsurance Modeling

12/3/2010                      35
    ARMS, American Re’s DFA Model
ARMS Structure
        Input                                     Model Calibration & Optimization




     Financial




                                                                                                      Accounting Framework
      Market                                         Asset
                                                     Model




                                                                                     Business Model
                  Economic Model)
                                    GEM (Global

     Economic



   Underwriting
     Liability                                    Liability &
                                                       Re-
                                                  Insurance
     Insurance
                                                     Model
       Market




12/3/2010                                                                                                                    36
Conclusions
                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 !!


12/3/2010                                    38
                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.

12/3/2010                                      39
               Conclusions

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




12/3/2010                                40
Q&A

								
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