Unraveling Risk Appetite

232 Pages·2012·5.39 MB·English

Unraveling
Risk Appetite
Applications of Decision Theory
in the Evaluation of Organizational Risk Appetite
Arie de Wild
dissertation
Unraveling Risk Appetite
Applications of decision theory in the
evaluation of organizational risk appetite
Het ontrafelen van risicoacceptatiegraad
Toepassingen van besliskunde in de
evaluatie van de risicoacceptatiegraad van organisaties
Proefschrift
ter verkrijging van de graad van doctor aan de
Erasmus Universiteit Rotterdam
op gezag van
de rector magnificus
Prof.dr. H.G. Schmidt
en volgens besluit van het College voor Promoties.
De openbare verdediging zal plaatsvinden op
donderdag 10 januari 2013 om 15.30 uur
Arie Frederik de Wild
geboren te Dordrecht
Promotiecommissie:
Promotor: Prof.dr. G.J. van der Pijl RE
Overige leden: Prof.dr. M. Abdellaoui
Prof.dr. H.R. Commandeur
Prof.dr. P.P. Wakker
“Nobody said it was easy”
The Scientist – Coldplay

Contents
List of tables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9
List of figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15
1.1 The economic problem of organizational risk appetite. . . . . . . . . . . . . . . . . . . .15
1.2 Decision theory and decision analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17
1.3 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20
1.4 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22
2 On the Measurement of Risk Appetite and Risk Attitude. . . . . . . . . . . . . . . . . .25
2.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25
2.2 The measurement of risk appetite in risk management. . . . . . . . . . . . . . . . . . . .26
2.2.1 The formal definition and relevance of risk appetite . . . . . . . . . . . . . . . .26
2.2.2 The practical measurement of risk appetite . . . . . . . . . . . . . . . . . . . . . . .28
2.3 The measurement of risk attitude in decision theory . . . . . . . . . . . . . . . . . . . . .30
2.3.1 The definition of risk attitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30
2.3.2 Decision theories under risk: EV, EU and PT . . . . . . . . . . . . . . . . . . . . .31
2.3.2.1 Expected value theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32
2.3.2.2 Expected utility theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32
2.3.2.3 Prospect theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .34
2.3.3 Willingness-to-accept (WTA) and willingness-to-pay (WTP) . . . . . . . . .35
2.4 Risk measures for organizational risk appetite. . . . . . . . . . . . . . . . . . . . . . . . . . .38
2.4.1 Risk measures and acceptance sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38
2.4.2 The WTA(-) and WTP(+) risk measure continuum . . . . . . . . . . . . . . . .39
2.4.3 Unbiased utility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .40
2.4.4 Utility based shortfall risk (UBSR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .42
2.4.5 The definition of the zero equivalent risk measure . . . . . . . . . . . . . . . . .43
2.4.6 Entropic risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .43
2.5 Decision rules for organizational risk appetite . . . . . . . . . . . . . . . . . . . . . . . . . .44
2.5.1 Derivation of decision rules for organizational risk appetite . . . . . . . . . .44
2.5.2 Examples of the application of the organizational risk
appetite rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .46
2.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .52
2.7 Appendices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .53
2.7.1 Appendix A: Rating scales for financial damages and
frequency in Fine (1971). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .53
2.7.2 Appendix B: Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .55
3 Articulating Risk Attitude in the Risk Matrix using Decision Theory . . . . . . . .57
3.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .57
3.2 The risk matrix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .58
5
3.3 Utility functions and risk measures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60
3.3.1 Utility functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60
3.3.2 Zero equivalent risk measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .62
3.4 Articulation of risk attitude in the risk matrix . . . . . . . . . . . . . . . . . . . . . . . . . .63
3.4.1 Decision rule 1: Risk bearing constraint . . . . . . . . . . . . . . . . . . . . . . . . .63
3.4.2 Decision rule 2: Marginal analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . .64
3.4.3 Implications of the isocontours in the risk matrix
for risk management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .66
3.5 Deriving risk appetite for individual cells. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .67
3.5.1 Linear utility. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .69
3.5.2 Concave exponential utility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .69
3.5.3 TK’92 utility specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .71
3.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .72
3.7 Appendices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .74
3.7.1 Appendix A: Functional specifications of isocontours
with linear scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .74
3.7.2 Appendix B: Functional specifications of isocontours
with logarithmic scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .78
3.7.3 Appendix C: Assigning cells to the acceptable or unacceptable zone . . . .81
3.7.4 Appendix D: Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .82
4 Utility Elicitation in the Context of Organizational Risk Appetite. . . . . . . . . . .87
4.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .87
4.2 Overview of utility elicitation methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .88
4.3 Four-step nonparametric utility elicitation method . . . . . . . . . . . . . . . . . . . . . .90
4.4 Results of trial sessions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .93
4.4.1 Details of the trial sessions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .93
4.4.2 Tailoring the elicitation method to entrepreneurial circumstances. . . . . .93
4.4.3 Weights of the probabilities of being profitable and unprofitable. . . . . . .94
4.4.4 Utility curves in the domain of gains and losses. . . . . . . . . . . . . . . . . . . .96
4.4.5 Issues related to the elicitation procedure. . . . . . . . . . . . . . . . . . . . . . . . .98
4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .99
4.6 Appendices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .101
4.6.1 Appendix A: Overview of utility elicitation methods. . . . . . . . . . . . . . .101
4.6.2 Appendix B: Elicitation procedure. . . . . . . . . . . . . . . . . . . . . . . . . . . . .103
5 Describing Organizational Risk Appetite using Decision Theory...........107
5.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .107
5.2 The case company risk matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .109
5.3 Risk attitude and three decision theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . .110
5.4 Isocontours in the risk matrix under decision theory . . . . . . . . . . . . . . . . . . . .113
5.5 Field study details. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .116
5.5.1 Elicitation of professional risk attitudes. . . . . . . . . . . . . . . . . . . . . . . . .117
5.5.2 Elicitation of introspective judgments of organizational risk appetite. . . . .119
6
5.6 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .121
5.6.1 Professional risk attitudes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .121
5.6.2 Utility functions for financial damages . . . . . . . . . . . . . . . . . . . . . . . . .121
5.6.3 Probability weighting functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .122
5.6.4 Introspective judgment regarding organizational risk appetite. . . . . . . .123
5.6.5 Decision theoretic predictions for organizational risk appetite. . . . . . . .124
5.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .126
6 The Utility and Weight of Verbal Outcome and Probability Expressions:
A Field Experiment ..............................................129
6.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .129
6.2 Scaling methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .130
6.3 Vagueness studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .132
6.3.1 Vagueness, source of uncertainty, and mode of representation. . . . . . . .132
6.3.2 Verbal probability expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .133
6.3.2.1 Mode preference studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .133
6.3.2.2 Mode translation studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .134
6.3.2.3 Mode effectiveness studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .134
6.3.3 Verbal outcome expressions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .135
6.4 Field experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .137
6.4.1 Elicitation of utility and probability weights . . . . . . . . . . . . . . . . . . . . .138
6.4.2 Introspective translation of verbal outcome and
probability expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .140
6.5 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .141
6.5.1 Manipulation and reliability checks. . . . . . . . . . . . . . . . . . . . . . . . . . . .141
6.5.2 Median utility and probability weights . . . . . . . . . . . . . . . . . . . . . . . . .141
6.5.3 Verbal probability expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .142
6.5.4 Verbal outcome expressions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .145
6.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .149
7 Curbing Risk Appetite with Performance-based Incentives. . . . . . . . . . . . . . . .153
7.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .153
7.2 Performance-based incentives and organizational risk appetite . . . . . . . . . . . . .155
7.2.1 The influence of the 2007–2009 financial crisis on
performance-based incentives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .155
7.2.2 The influence of compensation on risk taking. . . . . . . . . . . . . . . . . . . .156
7.3 Risk preference in the domain of losses and organizational risk appetite. . . . . .158
7.4 Experimental design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .160
7.4.1 The experimental task. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .160
7.4.2 Effective and efficient use of risk management resources . . . . . . . . . . . .163
7.4.3 Incentive conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .165
7.4.4 Details of the experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .168
7.5 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .169
7.5.1 General findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .169
7
7.5.2 Analysis of qualitative judgments in relation to the game . . . . . . . . . . .170
7.5.3 The effect of incentive conditions on the expression of risk
appetite in the risk matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .171
7.5.3.1 Independent samples tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .171
7.5.3.2 Paired samples tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .172
7.5.4 The effect of incentive conditions on risk management
efficiency and effectiveness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .174
7.5.4.1 Performance of participants in the experiment . . . . . . . . . . . . . .175
7.5.4.2 Performance of participants on the basis of simulation statistics . .175
7.5.5 Assessment of utility under expected utility using Maximum
Likelihood Estimation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .177
7.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .178
7.7 Appendices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .181
7.7.1 Appendix A: Additional scatter diagrams of simulation results. . . . . . . .181
7.7.2 Appendix B: Proof. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .182
7.7.3 Appendix C: Maximum Likelihood Estimation model and
data fittings in STATA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .182
8 Conclusion ....................................................187
8.1 Decision theory, measure theory, and organizational risk appetite . . . . . . . . . .187
8.2 Utility elicitation and organizational risk appetite . . . . . . . . . . . . . . . . . . . . . .189
8.3 Describing organizational risk appetite using decision theory. . . . . . . . . . . . . .190
8.4 The utility and probability weight of verbal expressions. . . . . . . . . . . . . . . . . .191
8.5 Performance-based incentives and organizational risk appetite . . . . . . . . . . . . .193
8.6 Epilogue. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .194
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .195
Samenvatting .....................................................215
1 Inleiding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .215
2 Onderzoeksvragen. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .217
3 Resultaten . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .219
3.1 Besliskunde, meettheorie en risicoacceptatiegraad . . . . . . . . . . . . . . . . . . . . . .219
3.2 Nutmeting en risicoacceptatiegraad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .221
3.3 Het beschrijven van de risicoacceptatiegraad met besliskunde. . . . . . . . . . . . . .221
3.4 Het nut en de kansweging van verbale uitdrukkingen. . . . . . . . . . . . . . . . . . . .222
3.5 Resultaatgerelateerde prikkels en risicoacceptatiegraad . . . . . . . . . . . . . . . . . . .223
4 Tot slot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .224
Acknowledgements.................................................225
About the author ..................................................227
Colofon..........................................................229
8
List of Tables
Table 2.1 Willingness-to-accept and willingness-to-pay for both X + and X -. . . . . . . . .36
Table 2.2 Zero equivalence and certainty equivalence relationships for
direct elicitation of WTA and WTP for X + and X -. . . . . . . . . . . . . . . . . . . .37
Table 3.1 Risk profile with lotteries A, B, C and D and their expected values
(EV) in a 2 × 2 risk matrix with probability expressed in the columns
with decimal values .25 and .75 and impact expressed in the rows
with present values € -4 and € -12. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .68
Table 3.2 Risk matrix with lotteries A, B, C and D, and their ρze risk measure
under the assumption of expected utility theory and concave
exponential utility (R = 11) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .70
Table 3.3 Risk matrix with lotteries A, B, C and D, and their ρze risk measure
under the assumption of expected utility theory with utility specified
by the power function with TK’92 specifications . . . . . . . . . . . . . . . . . . . . .71
Table 3.4 Risk matrix with lotteries A, B, C and D, and their willingness-to-pay
(WTP) under the assumption of expected utility theory with utility
specifications from TK’92. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .72
Table 4.1 Four-step nonparametric elicitation procedure . . . . . . . . . . . . . . . . . . . . . . .91
Table 4.2 Specifications provided by eight entrepreneurs together with figures
for the personal age of the entrepreneurs and the number of active
years of their companies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .95
Table 4.3 Probabilities, probability weights, and classifications of the participants’
attitude to probability with symbols, +, - and =, respectively indicating
overweighting (w s( p) > p), underweighting (w s( p) < p), and linear
weighting at a significance level of .02 (w s ( p) = p) . . . . . . . . . . . . . . . . . . . .95
Table 4.4 Assessed quantities for which the lottery with the largest spread or
the lottery with the smallest spread in outcomes, indicated by (*),
was preferred in all of the five iterative choices . . . . . . . . . . . . . . . . . . . . . . .98
Table 4.5 Elicitation methods for eliciting indifference between binary
lottery pairs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .102
Table 4.6 Starting, minimum and maximum values of the quantity
that is assessed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .105
9