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Mean-Variance Analysis

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Abstract

Mean-variance analysis is concerned with combining risky assets in a way that minimizes the variance of risk at any desired mean return. In the use of mean-variance analysis for actual money management, the issue is how to estimate the large number of required covariances. Many-factor models of covariance are widely used, as are scenario and combined scenario and factor models, and constant correlation models. This simplifies the parameter estimation problem and can accelerate the computation of efficient sets for analyses containing hundreds of securities.

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Bibliography

  • Arrow, K. 1965. Aspects of the theory of risk bearing. Helsinki: Yrjö Jahnsson Foundation.

    Google Scholar 

  • Bellman, R.E. 1957. Dynamic programming. Princeton: Princeton University Press.

    Google Scholar 

  • Black, F. 1972. Capital market equilibrium with restricted borrowing. Journal of Business 45: 444–455.

    Article  Google Scholar 

  • Black, F., and M. Scholes. 1973. The pricing of options and corporate liabilities. Journal of Political Economy 81: 637–654.

    Article  Google Scholar 

  • Cohen, J.K., and J.A. Pogue. 1967. An empirical evaluation of alternative portfolio-selection models. Journal of Business 40: 166–193.

    Article  Google Scholar 

  • Elton, E.J., and M.J. Gruber. 1973. Estimating the dependence structure of share prices. Journal of Finance 28: 1203–1232.

    Google Scholar 

  • Elton, E.J., M.J. Gruber, and M.W. Padberg. 1976. Simple criteria for optimal portfolio selection. Journal of Finance 31: 1341–1357.

    Article  Google Scholar 

  • Elton, E.J., M.J. Gruber, and M.W. Padberg. 1978. Simple criteria for optimal portfolio selection: Tracing out the efficient frontier. Journal of Finance 33: 296–302.

    Article  Google Scholar 

  • King, B.F. 1966. Market and industry factors in stock price behavior. Journal of Business 39: 139–190.

    Article  Google Scholar 

  • Kroll, Y., H. Levy, and H.M. Markowitz. 1984. Mean variance versus direct utility maximization. Journal of Finance 39: 47–61.

    Article  Google Scholar 

  • Levy, H., and H.M. Markowitz. 1979. Approximating expected utility by a function of mean and variance. American Economic Review 69: 308–317.

    Google Scholar 

  • Lintner, J. 1965. The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. Review of Economics and Statistics 47: 13–37.

    Article  Google Scholar 

  • Markowitz, H.M. 1952. Portfolio selection. Journal of Finance 7: 77–91.

    Google Scholar 

  • Markowitz, H.M. 1956. The optimization of a quadratic function subject to linear constraints. Naval Research Logistics Quarterly 3: 111–133.

    Article  Google Scholar 

  • Markowitz, H.M. 1959. Portfolio selection: Efficient diversification of investments. New Haven: Yale University Press. Reprinted, New York: Wiley, 1970.

    Google Scholar 

  • Markowitz, H.M., and A. Perold. 1981. Portfolio analysis with factors and scenarios. Journal of Finance 36: 871–877.

    Article  Google Scholar 

  • Merton, R.C. 1969. Lifetime portfolio selection under uncertainty: The continuous-time case. Review of Economics and Statistics 51 (3): 247–257.

    Article  Google Scholar 

  • Mossin, J. 1966. Equilibrium in a capital asset market. Econometrica 34: 768–783.

    Article  Google Scholar 

  • Mossin, J. 1968. Optimal multiperiod portfolio policies. Journal of Business 41: 215–229.

    Article  Google Scholar 

  • Ohlson, J.A. 1975. The asymptotic validity of quadratic utility as the trading interval approaches zero. In Stochastic optimization models in finance, ed. W.T. Ziemba and R.G. Vickson. New York: Academic Press.

    Google Scholar 

  • Perold, A.F. 1984. Large-scale portfolio optimization. Management Science 30: 1143–1160.

    Article  Google Scholar 

  • Pratt, J.W. 1964. Risk aversion in the small and in the large. Econometrica 32: 122–136.

    Article  Google Scholar 

  • Pulley, L.B. 1981. A general mean-variance approximation to expected utility for short holding periods. Journal of Financial and Quantitative Analysis 16: 361–373.

    Article  Google Scholar 

  • Rosenberg, B. 1974. Extra-market components of covariance in security returns. Journal of Financial and Quantitative Analysis 9 (2): 263–274.

    Article  Google Scholar 

  • Samuelson, P.A. 1969. Lifetime portfolio selection by dynamic stochastic programming. Review of Economics and Statistics 51 (3): 239–246.

    Article  Google Scholar 

  • Samuelson, P.A. 1970. The fundamental approximation theorem of portfolio analysis in terms of means, variances and higher moments. Review of Economic Studies 37: 537–542.

    Article  Google Scholar 

  • Sharpe, W.F. 1963. A simplified model for portfolio analysis. Management Science 9 (2): 277–293.

    Article  Google Scholar 

  • Sharpe, W.F. 1964. Capital asset prices: A theory of market equilibrium under conditions of risk. Journal of Finance 19: 425–442.

    Google Scholar 

  • Tobin, J. 1958. Liquidity preference as behavior toward risk. Review of Economic Studies 25: 65–86.

    Article  Google Scholar 

  • Young, W.E., and R.H. Trent. 1969. Geometric mean approximations of individual security and portfolio performance. Journal of Financial and Quantitative Analysis 4 (2): 179–199.

    Article  Google Scholar 

  • Ziemba, W.T., and R.G. Vickson, eds. 1975. Stochastic optimization models in finance. New York: Academic Press.

    Google Scholar 

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Markowitz, H.M. (2018). Mean-Variance Analysis. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95189-5_1016

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