Stochastic Dominance and Diversification

  • Haim Levy
Part of the Studies in Risk and Uncertainty book series (SIRU, volume 12)


Stochastic dominance (SD) rules are applicable in selection between mutually exclusive investments but, unlike the mean-variance rule, they cannot identify all possible efficient diversification strategies. Thus, SD rules can tell us whether investment F dominates investment G, or investment G dominates H, but they cannot provide us with the set of combinations of these three assets that dominate all other sets of combinations. Moreover, for two investments F and G, even if it is given that F dominates G, say by SSD, when diversification is considered, one cannot tell unequivocally whether this SSD implies that more than 50% of the wealth should be invested by all risk averters in the superior investment F. Analysis of SD and diversification has been attempted but much still has to be accomplished in this area of research. In this chapter we first discuss some published results obtained in this area, and then we will report some new results.


Risky Asset Stochastic Dominance Absolute Risk Aversion Diversification Strategy Risky Investment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Arrow, J.K., Essays in the Theory of Risk Bearing, Markam Publishing Company, Chicago, 1971.Google Scholar
  2. 2.
    Tobin, J., “Liquidity Preferences as Behavior Toward Risk,” Review of Economic Studies, 25, 1958, pp. 65–86.CrossRefGoogle Scholar
  3. 3.
    Levy, H., “The Demand for Assets Under Conditions of Risk,” Journal of Finance, 28, March 1973, pp. 79–96.CrossRefGoogle Scholar
  4. 4.
    Fishburn, P.C., and R.B. Porter, “Optimal Portfolios with One Safe and One Risky Asset: Effects of Changes in Rates of Return and Risk,” Management Science, 22, 1976, pp. 1064–1073.CrossRefGoogle Scholar
  5. 5.
    Kira, D. and W.T. Ziemba, “The Demand for Risky Assets,” Management Science, 26, 1980, pp. 1158–1165.CrossRefGoogle Scholar
  6. 6.
    Hadar, J. and T.K. Seo, “Asset Proportions in Optimal Portfolios,” Review Economic Studies, 55, 1988, pp. 459–468.CrossRefGoogle Scholar
  7. 7.
    Hadar, J. and T.K. Seo, “The Effects of Shifts in a Return Distribution on Optimal Portfolio,” International Economic Review, 31, 1990, pp. 721–736.CrossRefGoogle Scholar
  8. 8.
    Landsberger, M. and I. Meilijson, “Demand for Risky Financial Assets: A Portfolio Analysis,” Journal Economic Theory, 12, 1976, pp. 483–487.CrossRefGoogle Scholar
  9. 9.
    Levy, H., and Markowitz, H.M., “Approximating Expected Utility by a Function of Mean and Variance,” American Economic Review, 69, No. 3, June 1979, pp. 308–317.Google Scholar

Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Haim Levy
    • 1
  1. 1.The Hebrew University of JerusalemIsrael

Personalised recommendations