Risk-Adjusted Performance Measurement. and Capital Allocation. in Insurance Firms

Transcription

1 Risk-Adjusted erformance Measurement and Capital Allocation in Insurance Firms Helmut Gründl Hato Schmeiser Humboldt-Universität zu Berlin, Germany 1

2 Introduction The Contributions of Merton/erold and Myers/Read Why Allocate Capital? The Fallacy of Traditional RAM and Capital Allocation Methods Conclusions 2

3 Capital Allocation and RAM in Financial Services Firms Risk-adjusted performance measurement (RAM) has been widely discussed for several years rominent RAM measures: - RAROC risk-adjusted return on capital - EVA economic value added 3

4 Capital Allocation and RAM: 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: 4

5 Fields of Application for Capital Allocation and RAM 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. erformance evaluation of business segment management 5

6 Assumptions of Capital Allocation Methods Most capital allocation and RAM 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 (NVs) Economic reasons for positive NVs: 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]) 6

7 Introduction The Contributions of Merton/erold and Myers/Read Why Allocate Capital? The Fallacy of Traditional RAM and Capital Allocation Methods Conclusions 7

8 Contingent Claims Approach: Basic Formulas remiums, equity capital and safety level of the initial portfolio ϕ ( min[ S,( E + ) ( 1 r) ]) old = ϕ old 0 old + ( dpo ) = ϕ( max[ S ( E + )( 1 r),0]) old old 0 old + old + ϕ ( ) * dpo = = ϕ( S ) old old old 8

9 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)/ old ), hence: new = * new old * old ( min[ S + S,( E + E + + )( 1 r) ]) old + new = ϕ old new 0 new old new + => E new 9

10 Contingent Claims Approach ϕ(dpo new ) * new new old E old E new E 10

11 Merton/erold [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 E Reduction of E default value ϕ (dpo) default ratio ϕ (dpo)/ Initial situation % Closing line % Closing line % Closing line % Sum of allocated E:

12 Merton/erold [1993] Approach new old E old Ε new E 12

13 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 by the premium incomes of the single lines 13

14 Myers/Read [2001] Approach Line 1 Line 2 Line 3 Total Required E default value ϕ (dpo) default ratio ϕ (dpo)/ Initial situation % Marginal E Requirement 38 % 49 % 63 % E allocation In contrast to the Merton/erold approach The resulting marginal surplus requirements add up to the overall surplus held by the firm. (Myers/Read (2001), p. 549) 14

15 Introduction The Contributions of Merton/erold and Myers/Read Why Allocate Capital? The Fallacy of Traditional RAM and Capital Allocation Methods Conclusions 15

16 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/erold) 16

17 Why Allocate Capital? But: 1) For pricing decisions it is not necessary to allocate capital first, but instead to price by: new = * new old * old Then to maintain the desired safety level for the firm specific risk management measures become necessary (e.g., additional equity capital (E new )), depending on the risk interdependencies of the whole firm 2) For decision making, however, the adding up question is of no economic importance 17

18 Further roblems 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? 18

19 Future Business olicy How is the optimal (SHV-maximal) business policy determined? - Definition of alternatives (closing line 1, etc.) - All interrelations and consequences must be considered (correlations, cross-selling effects, joint distributions, demand for insurance depending on the firm s safety level, etc.) 19

20 Future Business olicy 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 ) 20

21 Introduction The Contributions of Merton/erold and Myers/Read Why Allocate Capital? The Fallacy of Traditional RAM and Capital Allocation Methods Conclusions 21

22 Traditional RAM 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, individual 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 RAM concepts such as RAROC or EVA) 22

23 Three Important roblems 1) RAM concepts are generally not consistent with the SHV approach Example: RAROC NV = E [ ] + E G 1+ r f R E NV 1 1+ r E[ G] R E E RAROC = rf f 23

24 Three Important roblems 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 r f (therefore, the hurdle rate is not a decision variable of the firm); deviation from r f => leads to problems of under- or over-investment - Maximizing RAROC maximizes the NV only, if E is not a decision variable (a very strong assumption!) 24

25 Three Important roblems 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) 25

26 Traditional RAM and Capital Allocation Methods: Results 1) Calculating minimum prices on the basis of traditional RAM 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 RAM and capital allocation methods 26

27 Introduction The Contributions of Merton/erold and Myers/Read Why Allocate Capital? The Fallacy of Traditional RAM and Capital Allocation Methods Conclusions 27

28 Conclusions 1) Merton/erold [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, RAM and traditional capital allocation methods are not helpful 28

29 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 RAM based on it) 29