The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Portfolio Analysis

  • Nils H. Hakansson
Reference work entry


Many observers trace the beginnings of modern financial investment theory to the pioneering article of Markowitz (1952), published only a third of a century ago. This is not surprising in view of the dominant position that the mean-variance approach to portfolio choice analysed by Markowitz has attained in the last two decades, particularly in empirical studies. Financial investment theory under uncertainty goes well beyond this particular model, however, and somewhat further back in time as well. This entry will first examine the pure portfolio model, both the single-period and the intertemporal varieties. It will then turn to consumptioninvestment formulations.

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  1. Arrow, K. 1965. Aspects of the theory of risk-bearing. Yrjö Jahnsson Saätiö: Helsinki.Google Scholar
  2. Bernoulli, D. 1738. Exposition of a new theory on the measurement of risk. Trans. by L. Sommer. Econometrica 22, January 1954, 23–36.Google Scholar
  3. Breiman, L. 1960. Investment policies for expanding business optimal in a long-run sense. Naval Logistics Quarterly.Google Scholar
  4. Cass, D., and J. Stiglitz. 1972. Risk aversion and wealth effects on portfolios with many assets. Review of Economic Studies 39(3): 331–354.CrossRefGoogle Scholar
  5. Freund, R. 1956. The introduction of risk into a programming model. Econometrica 24: 253–263.CrossRefGoogle Scholar
  6. Hakansson, N. 1970. Optimal investment and consumption strategies under risk for a class of utility functions. Econometrica 38(5): 587–607.CrossRefGoogle Scholar
  7. Hakansson, N. 1971. Optimal entrepreneurial decision in a completely stochastic environment. Management Science: Theory 17(7): 427–449.CrossRefGoogle Scholar
  8. Hakansson, N. 1974. Convergence to isoelastic utility and policy in multiperiod portfolio choice. Journal of Financial Economics 1(3): 20–24.CrossRefGoogle Scholar
  9. Kelly Jr., J.L. 1956. A new interpretation of information rate. Bell System Technical Journal 35: 917–925.CrossRefGoogle Scholar
  10. Latané, H. 1959. Criteria for choice among risky ventures. Journal of Political Economy 67: 144–155.CrossRefGoogle Scholar
  11. Markowitz, H. 1952. Portfolio selection. Journal of Finance 7(1): 77–91.Google Scholar
  12. Marschak, J. 1951. Why ‘should’ statisticians and businessmen maximize ‘moral expectation’? In Proceedings of the second Berkeley symposium on mathematical statistics and probability, ed. J. Neyman. Berkeley: University of California Press.Google Scholar
  13. Merton, R. 1971. Optimum consumption and portfolio rules in a continuous time model. Journal of Economic Theory 3(4): 373–413.CrossRefGoogle Scholar
  14. Mossin, J. 1968. Optimal multiperiod portfolio policies. Journal of Business 41(April): 215–229.CrossRefGoogle Scholar
  15. Ross, S. 1978. Mutual fund separation in financial theory: The separating distributions. Journal of Economic Theory 17(2): 254–286.CrossRefGoogle Scholar
  16. Rothschild, M., and J. Stiglitz. 1971. Increasing risk II: Its economic consequences. Journal of Economic Theory 3(1): 66–84.CrossRefGoogle Scholar
  17. Roy, A. 1952. Safety first and the holding of assets. Econometrica 20: 431–449.CrossRefGoogle Scholar
  18. Samuelson, P.A. 1970. The fundamental approximation theorem of portfolio analysis in terms of means, variances, and higher moments. Review of Economic Studies 37(4): 537–542.CrossRefGoogle Scholar
  19. Tobin, J. 1958. Liquidity preference as behavior towards risk. Review of Economic Studies 25: 65–86.CrossRefGoogle Scholar
  20. von Neumann, J., and O. Morgenstern. 1944. Theory of games and economic behavior. Princeton: Princeton University Press.Google Scholar
  21. Williams, J. 1936. Speculation and the carryover. Quarterly Journal of Economics 50: 436–455.CrossRefGoogle Scholar

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© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Nils H. Hakansson
    • 1
  1. 1.