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Theory and Decision

, Volume 80, Issue 2, pp 227–243 | Cite as

Risk aversion, prudence, and asset allocation: a review and some new developments

  • Michel M. Denuit
  • Louis Eeckhoudt
Article
  • 489 Downloads

Abstract

In this paper, we consider the composition of an optimal portfolio made of two dependent risky assets. The investor is first assumed to be a risk-averse expected utility maximizer, and we recover the existing conditions under which all these investors hold at least some percentage of their portfolio in one of the assets. Then, we assume that the decision maker is not only risk-averse, but also prudent and we obtain new minimum demand conditions as well as intuitively appealing interpretations for them. Finally, we consider the general case of investor’s preferences exhibiting risk apportionment of any order and we derive the corresponding minimum demand conditions. As a byproduct, we obtain conditions such that an investor holds either a positive quantity of one of the assets (positive demand condition) or a proportion greater than 50 % (i.e., the “50 % rule”).

Keywords

Optimal portfolio Diversification Risk aversion  Downside risk Prudence Risk apportionment 

Notes

Acknowledgments

The financial support of PARC “Stochastic Modelling of Dependence” 2012–2017 awarded by the Communauté française de Belgique is gratefully acknowledged by Michel Denuit.

References

  1. Chiu, W. H. (2005). Degree of downside risk aversion and self-protection. Insurance: Mathematics and Economics, 36, 93–101.Google Scholar
  2. Clark, E., & Jokung, O. (1999). A note on asset proportions, stochastic dominance, and the 50 % rule. Management Science, 45, 1724–1727.CrossRefGoogle Scholar
  3. Denuit, M., Huang, R., & Tzeng, L. (2015). Almost expectation and excess dependence notions. Theory and Decision, in press.Google Scholar
  4. Denuit, M., & Rey, B. (2010). Prudence, temperance, edginess, and risk apportionment as decreasing sensitivity to detrimental changes. Mathematical Social Sciences, 60, 137–143.CrossRefGoogle Scholar
  5. Dionne, G., Li, J., & Okou, C. (2012). An extension of the consumption-based CAPM model. Available at SSRN: http://ssrn.com/abstract=2018476.
  6. Drèze, J., & Modigliani, F. (1972). Consumption decision under uncertainty. Journal of Economic Theory, 5, 308–335.CrossRefGoogle Scholar
  7. Eeckhoudt, L., & Schlesinger, H. (2006). Putting risk in its proper place. American Economic Review, 96, 280–289.CrossRefGoogle Scholar
  8. Fagart, M. C., & Sinclair-Desgagné, B. (2007). Ranking contingent monitoring systems. Management Science, 53, 1501–1509.CrossRefGoogle Scholar
  9. Hadar, J., & Seo, T. K. (1988). Asset proportions in optimal portfolios. Review of Economic Studies, 55, 459–468.CrossRefGoogle Scholar
  10. Leland, H. (1968). Saving and uncertainty: The precautionary demand for saving. Quarterly Journal of Economics, 82, 465–473.CrossRefGoogle Scholar
  11. Kimball, M. S. (1990). Precautionary savings in the small and in the large. Econometrica, 58, 53–73.CrossRefGoogle Scholar
  12. Li, J. (2011). The demand for a risky asset in the presence of a background risk. Journal of Economic Theory, 146, 372–391.CrossRefGoogle Scholar
  13. Sandmo, A. (1970). The effect of uncertainty on saving decisions. Review of Economic Studies, 37, 353–360.CrossRefGoogle Scholar
  14. Shalit, H., & Yitzhaki, S. (1994). Marginal conditional stochastic dominance. Management Science, 40, 670–684.CrossRefGoogle Scholar
  15. Wright, R. (1987). Expectation dependence of random variables, with an application in portfolio theory. Theory and Decision, 22, 111–124.CrossRefGoogle Scholar
  16. Yitzhaki, S., & Olkin, I. (1991). Concentration indices and concentration curves. In: Stochastic Orders and Decision under Risk, AMS Lecture Notes-Monograph Series, 19 (pp. 380–392).Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Institut de Statistique, Biostatistique et Sciences Actuarielles (ISBA)Université Catholique de LouvainLouvain-la-NeuveBelgium
  2. 2.IESEG School of Management LEMLilleFrance
  3. 3.CORE Université Catholique de LouvainLouvain-la-NeuveBelgium

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