Advertisement

Portfolio Selection Theory in Discrete-Time

  • Jia-An Yan
Chapter
Part of the Universitext book series (UTX)

Abstract

When a broker (economic agent) invests in a stock market, he must select an appropriate portfolio. As a saying goes: do not put all your eggs in one basket. A core issue of portfolio selection is the trade-off between profit and risk. To tackle this issue, Harry M. Markowitz (1952) developed a mean-variance analysis, which was the first quantitative treatment of portfolio selection under uncertainty. This approach was further developed by James Tobin (1958). In the mid-1960s, based on Markowitz’s mean-variance analysis and Tobin’s two-fund separation theorem, William F. Sharpe (1964), John Lintner (v), and Jan Mossin (1966) independently observed that there exists a linear relation among expected rates of return on portfolios; in a competitive equilibrium market, the coefficients of the linear relation are related to the so-called betas of rates of return on portfolios with respect to the rate of return on the market portfolio. This relation is the so-called capital asset pricing model (CAPM). CAPM implicitly assumes that the returns on risky assets depend on a single market factor. Ross (1976) proposed a multifactor model for the behavior of asset prices in capital markets, which is called the arbitrage pricing theory (APT).

References

  1. Arrow, K.: Aspects of the Theory of Risk-Bearing. Yrjö Hahnsson Foundation, Helsinki (1965)Google Scholar
  2. Black, F.: Capital market equilibrium with restricted borrowing. J. Bus. 45, 444–454 (1972)CrossRefGoogle Scholar
  3. Chamberlain, G.: A characterization of the distributions that imply mean-variance utility functions. J. Econ. Theory 29, 185–201 (1983)MathSciNetCrossRefGoogle Scholar
  4. Cui, X., Li, D., Yan, J.A.: Classical mean-variance model revisited: pseudo efficiency. J. Oper. Res. Soc. 66, 1646–1655 (2015)CrossRefGoogle Scholar
  5. Dobin, J.: Liquidity preference as behavior towards risk. Rev. Econ. Stud. 25, 65–86 (1958)CrossRefGoogle Scholar
  6. Fishburn, P.: Utility Theory for Decision Making. Publications in Operations Research, vol. 18. Wiley, New York (1970)Google Scholar
  7. Föllmer, H., Schied, A.: Stochastic Finance, an Introduction in Discrete Time, 2nd revised and extended edition. Welter de Gruyter, Berlin, New York (2004)Google Scholar
  8. Huang, C.F., Litzenberger, R.H.: Foundations for Financial Economics. North-Holland, New York (1988)zbMATHGoogle Scholar
  9. Huberman, G.: A simplified approach to arbitrage pricing theory. J. Econ. Theory 28, 1983–1991 (1983)Google Scholar
  10. Jin, H., Markowitz, H.M., Zhou, X.Y.: A note on semivariance. Math. Financ. 16, 53–61 (2006)MathSciNetCrossRefGoogle Scholar
  11. Li, D., Ng, W.-L.: Optimal dynamic portfolio selection: multiperiod mean-variance formulation. Math. Financ. 10(3), 387–406 (2000)MathSciNetCrossRefGoogle Scholar
  12. Lintner, J.: The valuation of risky assets and the selection of risky investments in stock portfolios and capital budgets. Rev. Econ. Stat. 47, 13–37 (1965)CrossRefGoogle Scholar
  13. Markowitz, H.M.: Portfolio selection. J. Financ. 7, 77–91 (1952)Google Scholar
  14. Markowitz, H.M.: Portfolio Selection: Efficient Diversification of Investments. Wiley, New York (1959)Google Scholar
  15. Mehra, R., Prescott, E.C.: The equity premium: a puzzle. J. Monet. Econ. 15(2), 145–161 (1985)CrossRefGoogle Scholar
  16. Mossin, J.: Equilibrium in capital assets markets. Econometrica 34, 261–276 (1966)CrossRefGoogle Scholar
  17. Pratt, J.: Risk aversion in the small and in the large. Econometrica 32, 122–36 (1964)CrossRefGoogle Scholar
  18. Ross, S.A.: The arbitrage theory of capital asset pricing. J. Econ. Theory 13(3), 341–60 (1976)MathSciNetCrossRefGoogle Scholar
  19. Sharpe, W.F.: Capital asset prices: a theory of market equilibrium under conditions of risk. J. Financ. 19, 425–442 (1964)Google Scholar
  20. Tobin, J.: The theory of portfolio selection. In: Hahn, F.H., Brechling, F.P.R. (eds.) The Theory of Interest Rates, pp. 3–51. Macmillan, London (1965)Google Scholar
  21. von Neumann, J., Morgenstern, O.: Theory of Games and Economic Behavior. Princeton University Press, Princeton (1944)zbMATHGoogle Scholar
  22. Wang, J.: Financial Economics. Chinese Renming University Press, Beijing (2006, in Chinese)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. and Science Press 2018

Authors and Affiliations

  • Jia-An Yan
    • 1
  1. 1.Academy of Mathematics and System ScienceChineses Academy of SciencesBeijingChina

Personalised recommendations