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					Risk-Adjusted Performance Measurement and Capital Allocation
Risk-Adjusted Performance Measurement and Capital Allocation       09/2002
                                                                   09/2002




          Risk-Adjusted Performance Measurement

                            and Capital Allocation

                               in Insurance Firms


                                      Helmut Gründl
                                      Hato Schmeiser

                    Humboldt-Universität zu Berlin, Germany


Helmut Gründl and Hato Schmeiser
Helmut Gründl and Hato Schmeiser                               1
Risk-Adjusted Performance Measurement and Capital Allocation
Risk-Adjusted Performance Measurement and Capital Allocation       09/2002
                                                                   09/2002




         Introduction

         The Contributions of Merton/Perold and Myers/Read

         Why Allocate Capital?

         The Fallacy of Traditional RAPM and Capital
         Allocation Methods

         Conclusions

Helmut Gründl and Hato Schmeiser
Helmut Gründl and Hato Schmeiser                               2
Risk-Adjusted Performance Measurement and Capital Allocation
Risk-Adjusted Performance Measurement and Capital Allocation       09/2002
                                                                   09/2002




                         Capital Allocation and
                     RAPM in Financial Services Firms


 •     Risk-adjusted performance measurement (RAPM) has been
       widely discussed for several years



 •     Prominent RAPM measures:

       -    RAROC—risk-adjusted return on capital

       -    EVA—economic value added


Helmut Gründl and Hato Schmeiser
Helmut Gründl and Hato Schmeiser                               3
Risk-Adjusted Performance Measurement and Capital Allocation
Risk-Adjusted Performance Measurement and Capital Allocation       09/2002
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        Capital Allocation and RAPM: How Does it Work?


 •     Capital is allocated to the firm as a whole and to business
       segments of the firm


 •     Cost of the (allocated) capital is compared with an earnings
       figure for the firm and the business segments


 •     From that comparison conclusions are drawn with respect to the
       following issues:


Helmut Gründl and Hato Schmeiser
Helmut Gründl and Hato Schmeiser                               4
Risk-Adjusted Performance Measurement and Capital Allocation
Risk-Adjusted Performance Measurement and Capital Allocation       09/2002
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     Fields of Application for Capital Allocation and RAPM


  1. Often not at all clear

  2. Decisions on future business policy,
     e.g. on restructuring lines of business or setting reservation
     prices for products

  3. Risk management in business segments

  4. Performance evaluation of business segment management


Helmut Gründl and Hato Schmeiser
Helmut Gründl and Hato Schmeiser                               5
Risk-Adjusted Performance Measurement and Capital Allocation
Risk-Adjusted Performance Measurement and Capital Allocation          09/2002
                                                                      09/2002



              Assumptions of Capital Allocation Methods

 •    Most capital allocation and RAPM concepts are claimed to be in
      accordance with the shareholder value (SHV) approach

 •    SHV approach rational only in the context of an arbitrage-free
      capital market

 •    Capital allocation approaches implicitly assume that it is possible
      to earn positive net present values (NPVs)
      Economic reasons for positive NPVs: Market imperfections such
      as taxes, bankruptcy costs, extremely risk-averse behaviour of
      policyholders etc. (see e.g., Doherty/Tinic [1981], Froot/Stein
      [1998], Myers/Read [2001])

Helmut Gründl and Hato Schmeiser
Helmut Gründl and Hato Schmeiser                                  6
Risk-Adjusted Performance Measurement and Capital Allocation
Risk-Adjusted Performance Measurement and Capital Allocation       09/2002
                                                                   09/2002




         Introduction


         The Contributions of
         Merton/Perold and Myers/Read
         Why Allocate Capital?

         The Fallacy of Traditional RAPM and Capital
         Allocation Methods

         Conclusions

Helmut Gründl and Hato Schmeiser
Helmut Gründl and Hato Schmeiser                               7
Risk-Adjusted Performance Measurement and Capital Allocation
Risk-Adjusted Performance Measurement and Capital Allocation            09/2002
                                                                        09/2002



           Contingent Claims Approach: Basic Formulas

 •    Premiums, equity capital and safety level of the initial portfolio


       Pold = ϕ (min[Sold , (E 0 + Pold )(1 + r )])


       ϕ (dpo old ) = ϕ (max[Sold − (E 0 + Pold )(1 + r ), 0])


       Pold + ϕ (dpo old ) = P             *
                                           old   = ϕ (Sold )

Helmut Gründl and Hato Schmeiser
Helmut Gründl and Hato Schmeiser                                    8
Risk-Adjusted Performance Measurement and Capital Allocation
Risk-Adjusted Performance Measurement and Capital Allocation                 09/2002
                                                                             09/2002



            Contingent Claims Approach: Basic Formulas

•     New contract/new line of business

      Keeping the same safety level of the firm
      (in terms of the “dpo-ratio” = ϕ(dpo) / Pold), hence:

                        Pold
      Pnew = P   *
                 new   ⋅ *
                        Pold

      Pold + Pnew = ϕ (min[Sold + Snew , (E 0 + E new + Pold + Pnew )(1 + r )])

      => Enew

Helmut Gründl and Hato Schmeiser
Helmut Gründl and Hato Schmeiser                                         9
Risk-Adjusted Performance Measurement and Capital Allocation
Risk-Adjusted Performance Measurement and Capital Allocation        09/2002
                                                                    09/2002


                          Contingent Claims Approach

                      P

         ϕ(dponew)
 *
Pnew           Pnew
                  Pold




                                                                       E
                                    Eold
                                                    Enew
Helmut Gründl and Hato Schmeiser
Helmut Gründl and Hato Schmeiser                               10
Risk-Adjusted Performance Measurement and Capital Allocation
Risk-Adjusted Performance Measurement and Capital Allocation                                             09/2002
                                                                                                         09/2002


                              Merton/Perold [1993] Approach

 •        Inframarginal changes
          (e.g. closing lines of business)

 •        Again: fixed safety level of the company
          (measured by the “dpo-ratio”)

                     Line 1    Line 2   Line 3   Total       Required     Reduction of default value     default ratio
                       P         P        P       P             E             E           ϕ (dpo)         ϕ (dpo)/P
 Initial situation   £ 100     £ 100    £ 100    £ 300         £ 150                       £ 0.93          0.31 %

 Closing line 1       £0       £ 100    £ 100    £ 200         £ 115           £ 35        £ 0.62          0.31 %

 Closing line 2      £ 100      £0      £ 100    £ 200         £ 104           £ 46        £ 0.62          0.31 %

 Closing line 3      £ 100     £ 100     £0      £ 200          £ 92           £ 58        £ 0.62          0.31 %


                                                         Sum of allocated E:   £ 139



Helmut Gründl and Hato Schmeiser
Helmut Gründl and Hato Schmeiser                                                                    11
Risk-Adjusted Performance Measurement and Capital Allocation
Risk-Adjusted Performance Measurement and Capital Allocation        09/2002
                                                                    09/2002



                      Merton/Perold [1993] Approach

              P



       Pnew
          Pold



                                                               E
                            Eold           Εnew
Helmut Gründl and Hato Schmeiser
Helmut Gründl and Hato Schmeiser                               12
Risk-Adjusted Performance Measurement and Capital Allocation
Risk-Adjusted Performance Measurement and Capital Allocation        09/2002
                                                                    09/2002




                        Myers/Read [2001] Approach


 • Marginal changes (e.g., writing one contract)

 • Again: fixed safety level of the company
   (measured by the “dpo-ratio”)

 • Determine change of the equity capital if the premium income of a
   single line (with homogeneous risks) changes marginally

 • Multiply d E / d P by the premium incomes of the single lines


Helmut Gründl and Hato Schmeiser
Helmut Gründl and Hato Schmeiser                               13
Risk-Adjusted Performance Measurement and Capital Allocation
Risk-Adjusted Performance Measurement and Capital Allocation                                   09/2002
                                                                                               09/2002



                                 Myers/Read [2001] Approach

                        Line 1      Line 2   Line 3   Total    Required   default value   default ratio
                          P           P        P       P          E          ϕ (dpo)       ϕ (dpo)/P
    Initial situation   £ 100       £ 100    £ 100    £ 300     £ 150        £ 0.93         0.31 %
     Marginal E
                        38 %        49 %     63 %
     Requirement
     E allocation       £ 38        £ 49     £ 63               £ 150




•       In contrast to the Merton/Perold approach

        “The resulting marginal surplus requirements … “add up” to the
        overall surplus held by the firm.” (Myers/Read (2001), p. 549)

Helmut Gründl and Hato Schmeiser
Helmut Gründl and Hato Schmeiser                                                          14
Risk-Adjusted Performance Measurement and Capital Allocation
Risk-Adjusted Performance Measurement and Capital Allocation        09/2002
                                                                    09/2002



         Introduction

         The Contributions of Merton/Perold and Myers/Read


         Why Allocate Capital?
         The Fallacy of Traditional RAPM and Capital
         Allocation Methods

         Conclusions

Helmut Gründl and Hato Schmeiser
Helmut Gründl and Hato Schmeiser                               15
Risk-Adjusted Performance Measurement and Capital Allocation
Risk-Adjusted Performance Measurement and Capital Allocation        09/2002
                                                                    09/2002




                               Why Allocate Capital?


 • For what type of decision are these two approaches used?

            Calculating minimum prices

     -      for a contract (Myers/Read)

            or

     -      a line of business (Merton/Perold)


Helmut Gründl and Hato Schmeiser
Helmut Gründl and Hato Schmeiser                               16
Risk-Adjusted Performance Measurement and Capital Allocation
Risk-Adjusted Performance Measurement and Capital Allocation             09/2002
                                                                         09/2002


                               Why Allocate Capital?
 •   But:
 1) For pricing decisions it is not necessary to allocate capital first, but
    instead to price by:
                        Pold
      Pnew = P   *
                 new   ⋅ *
                        Pold
     Then to maintain the desired safety level for the firm specific risk
     management measures become necessary (e.g., additional equity
     capital (Enew)), ––depending on the risk interdependencies of the
     whole firm
 2) For decision making, however, the “adding up” question is of no
    economic importance
Helmut Gründl and Hato Schmeiser
Helmut Gründl and Hato Schmeiser                                    17
Risk-Adjusted Performance Measurement and Capital Allocation
Risk-Adjusted Performance Measurement and Capital Allocation        09/2002
                                                                    09/2002



                                 Further Problems

 •    Furthermore:

      Neither allocation method (and net present values based on them)
      provides information about an efficient future business policy

 •    For example:

      Will the SHV be lowered or increased if line 1 expands or
      contracts?

      What is the optimal (SHV-maximal) business mix?


Helmut Gründl and Hato Schmeiser
Helmut Gründl and Hato Schmeiser                               18
Risk-Adjusted Performance Measurement and Capital Allocation
Risk-Adjusted Performance Measurement and Capital Allocation           09/2002
                                                                       09/2002




                              Future Business Policy



 •    How is the optimal (SHV-maximal) business policy determined?

      -     Definition of alternatives (closing line 1, etc.)

      -     All interrelations and consequences must be considered (cor-
            relations, cross-selling effects, joint distributions, demand
            for insurance depending on the firm’s safety level, etc.)



Helmut Gründl and Hato Schmeiser
Helmut Gründl and Hato Schmeiser                                  19
Risk-Adjusted Performance Measurement and Capital Allocation
Risk-Adjusted Performance Measurement and Capital Allocation            09/2002
                                                                        09/2002




                              Future Business Policy


 •    In general, optimisation leads to

      -     a change in the optimal equity capital (for the whole firm)

            and

      -     possibly a new safety level for the firm (measured, e.g., by
            the “dpo-ratio”)


Helmut Gründl and Hato Schmeiser
Helmut Gründl and Hato Schmeiser                                   20
Risk-Adjusted Performance Measurement and Capital Allocation
Risk-Adjusted Performance Measurement and Capital Allocation        09/2002
                                                                    09/2002



         Introduction

         The Contributions of Merton/Perold and Myers/Read

         Why Allocate Capital?

         The Fallacy of Traditional
         RAPM and Capital Allocation
         Methods
         Conclusions

Helmut Gründl and Hato Schmeiser
Helmut Gründl and Hato Schmeiser                               21
Risk-Adjusted Performance Measurement and Capital Allocation
Risk-Adjusted Performance Measurement and Capital Allocation           09/2002
                                                                       09/2002



        Traditional RAPM and Capital Allocation Methods

 •    Equity capital is allocated to the firm as a whole (e.g., on a
      value-at-risk basis)

 •    Then, typically the equity capital is allocated across the lines of
      business (e.g., by using concepts such as “internal beta”, “indi-
      vidual capital at risk”, etc.)

 •    The cost of the allocated capital is compared with earnings
      figures for the firm and the lines of business (by using RAPM
      concepts such as RAROC or EVA)

Helmut Gründl and Hato Schmeiser
Helmut Gründl and Hato Schmeiser                                  22
Risk-Adjusted Performance Measurement and Capital Allocation
Risk-Adjusted Performance Measurement and Capital Allocation        09/2002
                                                                    09/2002



                           Three Important Problems

 1) RAPM concepts are generally not consistent with the SHV
    approach

      Example: RAROC

            E + E[G ] − R
      NPV =               −E
               1 + rf

                                                     
              1       E[G ] − R                      
      NPV =        E⋅           − rf                 
            1 + rf      4E 3
                     1 24                            
                      RAROC                          

Helmut Gründl and Hato Schmeiser
Helmut Gründl and Hato Schmeiser                               23
Risk-Adjusted Performance Measurement and Capital Allocation
Risk-Adjusted Performance Measurement and Capital Allocation           09/2002
                                                                       09/2002



                           Three Important Problems

      Differences to usual descriptions of RAROC (e.g., Matten
      [1996])

 -    Expected gain accruing from the risk-neutral distribution instead
      of gain observed over one (e.g., the last) period

 -    “Hurdle rate” that RAROC must exceed is rf (therefore, the
      hurdle rate is not a decision variable of the firm); deviation from
      rf => leads to problems of under- or over-investment

 -    Maximizing RAROC maximizes the NPV only, if E is not a
      decision variable (a very strong assumption!)

Helmut Gründl and Hato Schmeiser
Helmut Gründl and Hato Schmeiser                                  24
Risk-Adjusted Performance Measurement and Capital Allocation
Risk-Adjusted Performance Measurement and Capital Allocation        09/2002
                                                                    09/2002




                           Three Important Problems



 2) Allocation methods are largely arbitrary (“joint cost problem”)



 3) For inframarginal changes it is usually impossible to draw
    conclusions on the basis of the firm’s existing structure (e.g.,
    expanding the “best” line of business)




Helmut Gründl and Hato Schmeiser
Helmut Gründl and Hato Schmeiser                               25
Risk-Adjusted Performance Measurement and Capital Allocation
Risk-Adjusted Performance Measurement and Capital Allocation        09/2002
                                                                    09/2002



 Traditional RAPM and Capital Allocation Methods: Results

 1) Calculating minimum prices on the basis of traditional RAPM
    and capital allocation methods leads to mistakes

 2) No information is provided for an optimal future business policy

 3) It is not possible to derive any credible information that would
    help in making decisions about the future direction of the firm
    (e.g., should line 1 be expanded, should line 2 be abandoned?
    etc.)

 => It seems weird that so many companies either already use or plan
    to implement RAPM and capital allocation methods

Helmut Gründl and Hato Schmeiser
Helmut Gründl and Hato Schmeiser                               26
Risk-Adjusted Performance Measurement and Capital Allocation
Risk-Adjusted Performance Measurement and Capital Allocation        09/2002
                                                                    09/2002




         Introduction

         The Contributions of Merton/Perold and Myers/Read

         Why Allocate Capital?

         The Fallacy of Traditional RAPM and Capital
         Allocation Methods


         Conclusions
Helmut Gründl and Hato Schmeiser
Helmut Gründl and Hato Schmeiser                               27
Risk-Adjusted Performance Measurement and Capital Allocation
Risk-Adjusted Performance Measurement and Capital Allocation        09/2002
                                                                    09/2002




                                      Conclusions


 1) Merton/Perold [1993] and Myers/Read [2001] give correct
    reservation prices (for lines of business or single contracts)

      However, you don’t need a capital allocation procedure for the
      reservation price issue

 2) In the SHV setting, RAPM and traditional capital allocation
    methods are not helpful


Helmut Gründl and Hato Schmeiser
Helmut Gründl and Hato Schmeiser                               28
Risk-Adjusted Performance Measurement and Capital Allocation
Risk-Adjusted Performance Measurement and Capital Allocation        09/2002
                                                                    09/2002




                                       Conclusions

 3) To determine a firm’s future business policy we propose a direct
    SHV optimisation calculus (taking into account all of the firm’s
    alternatives)


      In summary:

                 We see no reason for allocating capital
                       (and RAPM based on it)

Helmut Gründl and Hato Schmeiser
Helmut Gründl and Hato Schmeiser                               29

				
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Description: Capital allocation refers to the private equity fund investors, the return is minus expenses and liabilities, the income earned on investments and capital. Limited partners to recover the capital investment costs to obtain the actual distribution of profits. Limited partnership agreement provides for the right partner to obtain a timetable for capital allocation, also provides for limited partners and general partner of their profits.