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Optimal Economic Capital Allocation in Banking on the Basis of Decision Rights

Müller, Jan

Studienreihe der Stiftung Kreditwirtschaft an der Universität Hohenheim, Vol. 52

(2015)

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Abstract

As a regulatory consequence banks today have to provide more equity for the same risk exposure than before the financial crisis. This significantly increases the banks’ need for a strict risk-return driven management. However, the mere neoclassical risk management view appears inadequate in the case of overall bank management. Consistently applying portfolio optimization on an overall bank level requires the consideration of the decision makers’ behavior where portfolios cannot be assumed fix any longer. The current model shows this using a value at risk limit system strictly understanding limits as addressees’ decision rights. Despite the resulting unstable correlations the model shows the overall bank management in the form of a global optimization being the superior approach. The model clearly demonstrates the costliness for banks dispensing with sophisticated limit setting.

Table of Contents

Section Title Page Action Price
FOREWORD 5
CONTENTS 7
FIGURES 11
TABLES 15
ALGORITHMS 17
1 INTRODUCTION 19
1.1 Problem and research question 19
1.2 Organization of the research 21
2 CORPORATE MANAGEMENT BYECONOMIC CAPITALALLOCATION 25
2.1 Properties of economic capital 25
2.2 Required economic capital by downside riskmeasurement 26
2.3 Corporate management by bank-wide VARlimit systems 28
2.4 Economic capital allocation on the basis of riskadjusted performance measurement 31
2.4.1 Introduction to risk adjusted Performance measures 31
2.4.2 Controversial benchmarking on the basis of hurdle rates 32
2.4.3 Implications of limit addressees in the form of decision makers 33
2.5 Economic capital allocation as a situation ofdelegation by decision rights 34
2.5.1 Implications for the risk management process 34
2.5.2 Costs of delegation by decision rights 36
3 IMPLICATIONS OF RELATEDFIELDS OF RESEARCH 41
3.1 Different situations of economic capitalallocation 41
3.2 Risk contribution – a form of economic capitalallocation 42
3.2.1 Risk contribution schemes 42
3.2.2 Particular approaches from the field of risk contribution 44
3.3 Axiomatization of economic capital allocation 46
3.3.1 Axiomatization of risk measures 46
3.3.2 Transfer of the axiomatization framework to economic capitalallocation 48
3.4 Risk assessment over time by dynamic riskmeasures 50
3.5 Economic capital allocation as a means ofcorporate management 53
3.6 Portfolio optimization under a downside riskconstraint 60
3.6.1 Approaches on the basis of traditional methods of optimization 60
3.6.2 Heuristic methods of optimization 62
3.6.2.1 Categorization of the field of heuristic optimization 62
3.6.2.2 Approaches on the basis of heuristic optimization methods 64
4 BASIC MODEL OF OPTIMALECONOMIC CAPITALALLOCATION 69
4.1 Qualitative description of the model 69
4.2 Determination of the underlying stochasticprogram 71
4.3 Valuation of the objective function on the basisof a trading simulation 74
4.3.1 Simulation of the stocks’ returns 74
4.3.2 Simulation of the business units’ profits and losses 76
4.3.3 Simulation of the heterogeneous prospects of success of the businessunits 78
4.4 Out-of-sample backtesting and the role ofimportance sampling 80
5 HEURISTIC OPTIMIZATION OFRISK LIMIT SYSTEMS BYTHRESHOLD ACCEPTING 83
5.1 Visual proof of non-convexity by an exemplarymodel case 83
5.2 Basic algorithm of threshold accepting 87
5.3 Determination of start solutions 89
5.4 Neighborhood function 94
5.4.1 Basic design of the neighborhood function 94
5.4.2 Generation of the transfer value 96
5.4.3 Monitoring of the constraints’ satisfaction 99
5.5 Generation of the threshold sequence 101
5.6 Parallelization of threshold accepting 104
6 PARAMETERIZATION OFTHRESHOLD ACCEPTING 107
6.1 Concept of successive parameterization incontext with the present model 107
6.2 Effective combinations of thresholds andtransfer values 108
6.2.1 Simple parameterization by visual analysis 108
6.2.2 Comprehensive analysis on the basis of detailed grid structures 112
6.2.3 Excursus on the impact of the transfer value generation on theparameterization 115
6.3 Effective combinations of restarts and steps 119
6.3.1 Appropriate coverage of the solution space 119
6.3.2 Particular aspects of parallel computing 121
6.4 Concluding remarks on the parameterizationfor different model cases 123
7 SUPERIORITY OF OPTIMALECONOMIC CAPITALALLOCATION – THE INFORMEDCENTRAL PLANNER 125
7.1 Introduction to the benchmarking of allocationmethods in case of an informed central planner 125
7.2 Benchmarking of allocation methods in case ofan informed central planner 127
7.2.1 Allocation methods’ performances before the background of anarbitrary model bank 127
7.2.2 Precise benchmarking on the basis of particular model settings 132
7.2.2.1 Implementation of a level playing field 132
7.2.2.2 Impact of restrictions through minimum limits 135
7.2.2.3 Relevance of optimal allocation in case ofless privately informed traders 138
7.2.2.4 Influence of higher degrees of diversification in the form of highernumbers of business units 141
7.3 Discussion of the superiority of optimaleconomic capital allocation 143
8 UNINFORMED CENTRALPLANNER – INFORMATION ONTHE BASIS OF BAYESIANLEARNING 147
8.1 Introduction to the case of an uninformedcentral planner 147
8.2 Description of the Bayesian learning algorithm 148
8.3 Bayesian learning central planner in case ofindependently acting decision makers 153
8.3.1 Benchmarking of allocation methods using perfect priorprobabilities 153
8.3.2 Benchmarking under adjusted prior probabilities for the anticipationof risk underestimation 160
8.4 Influence of herding decision makers on optimaleconomic capital allocation 168
8.4.1 Herding and informational cascades in case of economic capitalallocation 168
8.4.2 Modeling of herding tendencies among the decision makers 170
8.4.3 Benchmarking of allocation methods under herding decision makers 176
8.5 Conclusions on optimal allocation before thebackground of an uninformed central planner 187
9 CONCLUSIONS 191
9.1 Summary of results 191
9.2 Closing remarks on the model assumptions andsuggested future research 194
APPENDIX 197
REFERENCES 207
Studienreihe der Stiftung Kreditwirtschaftan der Universität Hohenheim 214