Capital Allocation under Regret and Kataoka Criteria

  • Günter Bamberg
  • Gregor Dorfleitner
Part of the International Centre for Mechanical Sciences book series (CISM, volume 472)


The paper analyzes the allocation of a given initial capital between a risk-free and a risky alternative. Typically, the risky alternative is the investment into the stock market or into a stock market index. Under expected utility the optimal fraction a * to invest into the stock market depends on the initial capital, on the distribution of stock returns, on the planning horizon, and of course on the von Neumann/Morgenstern utility function. Moreover, the optimal a * can only be evaluated by numerical integration. In order to get explicit formulas and to avoid the problematic assessment of the utility function NEU (non expected utility) approaches are discussed. The maxmin and the minmax regret criterion select only corner solutions (i.e. a * = 0 or a * = 1). The following Kataoka variant of these criteria is considered: Fix a (small) probability α and discard all the extremal events (which have althogether the probability α) from the planning procedure; i.e. define the worst case by exclusion of these extremal events. Obviously, this idea is also the basis of the well-known value-at-risk approach. The optimal fraction a * is no longer a corner solution. Moreover, it allows explicit formulas. These are studied in the Black/Scholes world (i.e. normally distributed log returns). Under realistic parameter values a * increases with the length of the planning horizon.


Stock Market Stock Return Planning Horizon Initial Capital Corner Solution 
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  1. G. Bamberg, G. Dorfleitner, and R. Lasch, Does the Planning Horizon Affect the Portfolio Structure? In W. Gaul and H. Locarek-Junge, editors, Classification in the Information Age, Springer-Verlag, Berlin et al., 100–114, 1999CrossRefGoogle Scholar
  2. G. Bamberg and G. Dorfleitner, Is Traditional Capital Market Theory Consistent with Fat-Tailed Log Returns? Zeitschrift für Betriebswirtschaft 72: 865–878, 2002.Google Scholar
  3. D. Bell, Regret in Decision Making Under Uncertainty, Operations Research 30: 961–981, 1982.CrossRefMATHGoogle Scholar
  4. D. Bell, Disappointment in Decision Making Under Uncertainty, Operations Research 33: 1–27, 1985.MathSciNetCrossRefGoogle Scholar
  5. F. Gul, A Theory of Disappointment Aversion, Econometrica 59: 667–686, 1991.MathSciNetCrossRefMATHGoogle Scholar
  6. S. Kataoka, A Stochastic Programming Model, Econometrica 31: 181–196, 1963.MathSciNetCrossRefMATHGoogle Scholar
  7. W. Krämer and R. Runde, Stochastic Properties of German Stock Returns, Empirical Economics 21: 281–306, 1996.CrossRefGoogle Scholar
  8. A. Lo and C. MacKinlay, Stumbling Block for the Random Walk, In Financial Times, editor, Mastering Finance, London, 185–191, 1998.Google Scholar
  9. G. Loomes and R. Sugden, Regret Theory: An Alternative Theory of Rational Choice Under Uncertainty, Economic Journal 92: 805–824, 1982.CrossRefGoogle Scholar
  10. G. Loomes and R. Sugden. Disappointment and Dynamic Consistency in Choice Under Uncertainty, Review of Economic Studies 53: 271–282, 1986.MathSciNetCrossRefMATHGoogle Scholar
  11. S.T. Rachev and S. Mittnik, Stable Paretian Models in Finance, Chichester et al., 2000.Google Scholar
  12. H.-J. Wolter, Shortfall-Risiko und Zeithorizonteffekte, Finanzmarkt und Portfolio Management 7: 330–338, 2000.MathSciNetGoogle Scholar
  13. H. Zimmermann, Zeithorizont, Risiko und Performance: Eine Ubersicht, Finanzmarkt und Portfolio Management 5: 164–181, 1991.Google Scholar

Copyright information

© Springer-Verlag Wien 2003

Authors and Affiliations

  • Günter Bamberg
    • 1
  • Gregor Dorfleitner
    • 1
  1. 1.Wirtschaftswissenschaftliche FakultätUniversität AugsburgAugsburgGermany

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