Skip to main content

Portfolio analysis with a nonnormal multi-index return-generating process

Abstract

This article analyzes the investor's optimum portfolio problem when security returns follow a linear return-generating process with factors that are not normally distributed and that are not replicable with traded assets. It provides a set of decision rules that allows the construction of the investor's optimum portfolio. The article then derives the equilibrium model with heterogeneous expectations that results from all investors acting in the manner described in the first section.

This is a preview of subscription content, access via your institution.

References

  • ArdittiFred and HaimLevy, “Portfolio Efficiency Analysis in Three Moments: The Multiperiod Case,” Journal of Finance 30 (3), 797–809 (June 1975).

    Google Scholar 

  • BawaVijay, “Safety First, Stochastic Dominance and Optimal Portfolio Choice,” Journal of Financial and Quantitative Analysis 13 (2), 255–271 (June 1978).

    Google Scholar 

  • BawaVijay, Edwin J.Elton, and Martin J.Gruber, “Simple Rules for Optimal Portfolio Selection in a Stable Paretian Market,” Journal of Finance 34 (2), 1041–1047 (June 1979).

    Google Scholar 

  • Burmeister, Edwin and Marjorie McElroy, “APT and Multifactor Asset Pricing with Measured and Unobserved Factors: Theoretical and Unobserved Issues,” discussion paper, Department of Economics, University of Virginia and Duke University (1989).

  • BurmeisterEdwin and MarjorieMcElroy, “Joint Estimation of Factor Sensitivities and Risk Premia for the Arbitrage Pricing Theory,” Journal of Finance 43 (3), 721–733 (July 1988).

    Google Scholar 

  • BurmeisterEdwin and KentWall, “The Arbitrage Pricing Theory and Macroeconomic Factor Measures,” The Financial Review27(1), 1–20 (February 1986).

    Google Scholar 

  • ChenNai-fu, RichardRoll, and StephenRoss, “Economic Forces and the Stock Market,” Journal of Business 59, 383–403 (July 1986).

    Google Scholar 

  • EltonEdwin J. and Martin J.Gruber, “A. Multi-Index Risk Model of the Japanese Stock Market,” Japan and the World Economy 1 (1), 21–44 (1988).

    Google Scholar 

  • EltonEdwin J. and Martin J.Gruber, Modern Portfolio Theory and Investment Analysis, 3rd edition, New York: John Wiley and Sons, 1987.

    Google Scholar 

  • EltonEdwin J. and Martin J.Gruber, “Porfolio Theory When Investment Relatives are Lognormally Distributed,” Journal of Finance 24, 1265 (September 1974).

    Google Scholar 

  • Elton, Edwin, J. and Martin J. Gruber, “An Algorithm for Maximizing the Geometric Mean,” Management Science, 483–488 (December 1974).

  • EltonEdwin J. and Martin J.Gruber, “Estimating the Dependence Structure of Share Prices—Implications for Portfolio Selection,” Journal of Finance 8 (5), 1203–1232 (December 1973).

    Google Scholar 

  • FamaEugene, “Risk Return and Equilibrium: Some Clarifying Comments,” Journal of Finance, 23 (1), 29–40 (March 1968).

    Google Scholar 

  • FamaEugene, “The Behavior of Stock Market Prices,” Journal of Business 38, 34–105 (January 1965).

    Google Scholar 

  • FarrellJames, “Analysis Covariation of Returns to Determine Homogeneous Stock Grouping,” Journal of Business 47 (2), 186–207 (April 1974).

    Google Scholar 

  • FishburnPeter, “Mean Risk Analysis with Risk Associated Below Target Returns” American Economic Review 67 (2), 116–126 (March 1977).

    Google Scholar 

  • Gibbons, Michael, “Empirical Examination of the Return-Generating Process of the Arbitrage Pricing Theory,” working paper, Stanford University (1989).

  • Hamao, Yasushi, “An Empirical Examination of the Arbitrage Pricing Theory: Using Japanese Data,” unpublished manuscript, Yale University (1989).

  • IngersollJonathan, Theory of Financial Decision Making. Totowa, NJ: Rowman and Littlefield, 1987.

    Google Scholar 

  • KingBenjamin, “Market and Stock Price Factors in Stock Price Behavior,” Journal of Business 39, 139–140. (June 1966).

    Google Scholar 

  • MarkowitzHarry, Portfolio Selection: Efficient Diversification of Investments New York: John Wiley and Sons 1959.

    Google Scholar 

  • RollRichard and StephenRoss, “An Empirical Investigation of the Arbitrage Pricing Theory”, Journal of Finance 35 (5), 1073–1103 (December 1980).

    Google Scholar 

  • Ross, Stephen, “Mutual Fund Separation in Financial Theory-The Separating Distribution,” Journal of Economic Theory 17, (April 1978)

  • Rothschild, Michael and Joseph Stiglitz, “Increasing Risk: A Definition”, Journal of Economic Theory 2, 225–243 (September??).

  • TreynorJack and FischerBlack, “How to Use Security Analysis to Improve Portfolio Selection,” Journal of Business 46, 66–86, (January 1973).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Elton, E.J., Gruber, M.J. Portfolio analysis with a nonnormal multi-index return-generating process. Rev Quant Finan Acc 2, 5–16 (1992). https://doi.org/10.1007/BF00243981

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00243981

Key words

  • portfolio analysis
  • return-generating process
  • multi-index process