Skip to main content

Capital Allocation under Regret and Kataoka Criteria

  • Chapter
Planning Based on Decision Theory

Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 472))

  • 190 Accesses

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

Bibliography

  • 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, 1999

    Chapter  Google Scholar 

  • 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 

  • D. Bell, Regret in Decision Making Under Uncertainty, Operations Research 30: 961–981, 1982.

    Article  MATH  Google Scholar 

  • D. Bell, Disappointment in Decision Making Under Uncertainty, Operations Research 33: 1–27, 1985.

    Article  MathSciNet  Google Scholar 

  • F. Gul, A Theory of Disappointment Aversion, Econometrica 59: 667–686, 1991.

    Article  MathSciNet  MATH  Google Scholar 

  • S. Kataoka, A Stochastic Programming Model, Econometrica 31: 181–196, 1963.

    Article  MathSciNet  MATH  Google Scholar 

  • W. Krämer and R. Runde, Stochastic Properties of German Stock Returns, Empirical Economics 21: 281–306, 1996.

    Article  Google Scholar 

  • A. Lo and C. MacKinlay, Stumbling Block for the Random Walk, In Financial Times, editor, Mastering Finance, London, 185–191, 1998.

    Google Scholar 

  • G. Loomes and R. Sugden, Regret Theory: An Alternative Theory of Rational Choice Under Uncertainty, Economic Journal 92: 805–824, 1982.

    Article  Google Scholar 

  • G. Loomes and R. Sugden. Disappointment and Dynamic Consistency in Choice Under Uncertainty, Review of Economic Studies 53: 271–282, 1986.

    Article  MathSciNet  MATH  Google Scholar 

  • S.T. Rachev and S. Mittnik, Stable Paretian Models in Finance, Chichester et al., 2000.

    Google Scholar 

  • H.-J. Wolter, Shortfall-Risiko und Zeithorizonteffekte, Finanzmarkt und Portfolio Management 7: 330–338, 2000.

    MathSciNet  Google Scholar 

  • H. Zimmermann, Zeithorizont, Risiko und Performance: Eine Ubersicht, Finanzmarkt und Portfolio Management 5: 164–181, 1991.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Wien

About this chapter

Cite this chapter

Bamberg, G., Dorfleitner, G. (2003). Capital Allocation under Regret and Kataoka Criteria. In: Della Riccia, G., Dubois, D., Kruse, R., Lenz, HJ. (eds) Planning Based on Decision Theory. International Centre for Mechanical Sciences, vol 472. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2530-4_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-7091-2530-4_10

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-40756-1

  • Online ISBN: 978-3-7091-2530-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics