Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-08T00:34:31.319Z Has data issue: false hasContentIssue false

A Linear Programming Formulation of the General Portfolio Selection Problem

Published online by Cambridge University Press:  19 October 2009

Extract

Almost two decades ago, Markowitz [12] formulated the portfolio selection problem as a parametric quadratic programming problem. The crux of his formulation was the mean-variance assumption which asserted that a portfolio is efficient if (and only if): (1) it has less variance than any other feasible portfolio with the same return and (2) it has more return than any other feasible portfolio with the same variance.

Type
Research Article
Copyright
Copyright © School of Business Administration, University of Washington 1973

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Alderfer, Clayton P., and Bierman, Harold Jr.Choices with Risk: Beyond the Mean and Variance.” Journal of Business, vol. 43, July 1970.Google Scholar
[2]Arditti, Fred D. “Risk and the Required Rate of Return.” Journal of Finance, March 1967.CrossRefGoogle Scholar
[3]Arditti, Fred D. “Another Look at Mutual Fund Performance.” Journal of Financial and Quantitative Analysis, June 1971.CrossRefGoogle Scholar
[4]Bierman, Harold Jr., and Rao, V. R.. “Portfolio Analysis and Higher Moments.” Working Paper, July 1971.Google Scholar
[5]Cohen, Kalman J., and Hammer, Frederick S.. “Editorial Comment on ‘A Simplified Model for Portfolio Analysis.’” In Analytical Methods in Banking. Homewood, Ill.: Richard D. Irwin, 1966.Google Scholar
[6]Cohen, Kalman J., and Pogue, J. A.. “An Empirical Evaluation of Alternative Portfolio Selection Models.” The Journal of Business, April 1967.CrossRefGoogle Scholar
[7]Dantzig, George B.Upper Bounds, Block Triangularity, and Secondary Constraints.” Econometrica, vol. 23, January 1955.CrossRefGoogle Scholar
[8]Frankfurter, George M.; Phillips, Herbert E.; and Seagle, John P.. “Portfolio Selection: The Effects of Uncertain Means, Variances, and Covariances.” Journal of Financial and Quantitative Analysis, December 1971.CrossRefGoogle Scholar
[9]Hanoch, G., and Levy, H.. “The Efficiency Analysis of Choices Involving Risk.” The Review of Economic Studies, July 1969.CrossRefGoogle Scholar
[10]Hanoch, G., and Levy, H.. “Efficient Portfolio Selection with Quadratic and Cubic Utility.” Journal of Business, April 1970.CrossRefGoogle Scholar
[11]Levy, Haim. “A Utility Function Depending on the First Three Moments.’ Journal of Finance, September 1969.CrossRefGoogle Scholar
[12]Markowitz, Harry. “Portfolio Selection.” Journal of Finance, March 1952.CrossRefGoogle Scholar
[13]Markowitz, Harry. Portfolio Selection: The Efficient Diversification of Investments. New York: John Wiley and Sons, Inc., 1959.Google Scholar
[14]Pogue, Gerald A. “An Intertemporal Model for Investment Management.’ Journal of Bank Research, Spring 1970.Google Scholar
[15]Pogue, Gerald A.An Extension of the Markowitz Portfolio Selection Model to Include Variable Transaction Costs, Short Sales, Leverage Policies, and Taxes.” Journal of Finance, vol. 25, December 1970.CrossRefGoogle Scholar
[16]Sharpe, William F. “A Simplified Model for Portfolio Analysis.” Management Science, January 1963.CrossRefGoogle Scholar
[17]Sharpe, William F. “A Linear Programming Algorithm for Mutual Fund Portfolio Selection.” Management Science, March 1967.CrossRefGoogle Scholar
[18]Sharpe, William F.Portfolio Theory and Capital Markets. New York: McGraw-Hill, 1970.Google Scholar
[19]Sharpe, William F.A Linear Programming Approximation for the General Portfolio Analysis Problem.” Journal of Financial and Quantitative Analysis, December 1971.CrossRefGoogle Scholar
[20]Stone, Bernell K.Risk, Return, and Equilibrium: A General Single Period Theory of Asset Selection and Capital Market Equilibrium. Cambridge, Mass.: M.I.T. Press, 1970.Google Scholar
[21]Stone, Bernell K. “The Inclusion of Skewness in Asset Pricing Models.’ Working Paper, April 1972.Google Scholar
[22]Stone, Bernell K., and Reback, Robert. “A Linear Programming Model for Portfolio Management,” May 1971.Google Scholar
[23]Tsiang, S. C. “The Rationale of the Mean-Standard Deviation Analysis, Skewness Preference, and the Demand for Money.” Working Paper, April 1971.Google Scholar
[24]Tobin, James.Liquidity Preference as Behavior Toward Risk.” Review of Economics and Statistics, vol. 25, February 1958.Google Scholar