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Portfolio Management and the Shrinking Knapsack Algorithm

Published online by Cambridge University Press:  06 April 2009

Bernell K. Stone  and
Ned C. Hill
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Extract

Since the formulation of the portfolio selection problem by Markowitz [12] as a parametric quadratic programming problem, considerable effort has been devoted to obtaining operational portfolio management models. Research has involved: (1) characterizing the return generating process in terms of index models; (2) specifying special-purpose algorithms such as the critical-line method of Markowitz [13] or the solution procedure of Jucker and de Faro [11]; (3) using linear programming formulations to approximate solutions to the nonlinear programming problems such as Sharpe [20, 22] and Stone [25]; and (4) converting portfolio selection models into portfolio management models designed to revise an existing protfolio subject to transaction costs using heuristics such as Smith [24] or revision formulations such as Pogue [16, 17] and Stone and Reback [27].

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 14 , Issue 5 , December 1979 , pp. 1071 - 1083
Copyright
Copyright © School of Business Administration, University of Washington 1979

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References

REFERENCES

[1]Aber, John W.Beta Coefficients and Models of Security Return. Lexington, Mass.: D. C. Heath (1973).Google Scholar
[2]Aber, John W. “Industry Effects and Multivariate Stock Price Behavior”. Journal of Financial and Quantitative Analysis, Vol. 11 (11 1976), pp. 617–624.CrossRefGoogle Scholar
[3]Ahlers, David M.A New Look at Portfolio Management. Greenwich, Conn.: Johnson Associates Inc. (1977).Google Scholar
[4]Bradley, Stephen P., and Crane, Dwight B.. “A Dynamic Model for Bond Portfolio Management”. Management Science, Vol. 19 (10 1972), pp. 139–151.CrossRefGoogle Scholar
[5]Cohen, Kalman J., and Pogue, Jerry A.. “An Empirical Evaluation of Alternative Portfolio Selection Models”. Journal of Business, Vol. 40 (04 1967), pp. 166–193.CrossRefGoogle Scholar
[6]Conway, Richard, and Gries, David. An Introduction to Programming. Cambridge, Mass.: Winthrop Publishers, Inc. (1973).Google Scholar
[7]Dantzig, George B. “Upper Bounds, Block Triangularity, and Secondary Constraints”. Econometrica, Vol. 23 (01 1955), pp. 174–183.CrossRefGoogle Scholar
[8]Francis, Jack Clark, and Archer, Stephen H.. Portfolio Analysis. Englewood Cliffs, N. J.: Prentice-Hall Inc. (1971).Google Scholar
[9]Garfinkel, R. S., and Nemhauser, G. L.. Integer Programming. New York: John Wiley & Sons (1972).Google Scholar
[10]Jensen, M. C. “Capital Markets: Theory and Evidence”. The Bell Journal of Economics and Management Science, Vol. 3 (Autmun 1972), pp. 357–398.CrossRefGoogle Scholar
[11]Jucker, James V., and de Faro, Clovis. “A Simple Algorithm for Stone's Version of the Portfolio Selection Problem”. Journal of Financial and Quantitative Analysis, Vol. 10 (12 1975), pp. 859–870.CrossRefGoogle Scholar
[12]Markowitz, Harry M. “Portfolio Selection”. The Journal of Finance, Vol. 7 (03 1952), pp. 77–91.Google Scholar
[13]Markowitz, Harry M. “The Optimization of a Quadratic Function Subject to Linear Constraints.” Naval Research Logistics Quarterly, Vol. 3 (03-06 1956), pp. 111–133.CrossRefGoogle Scholar
[14]Markowitz, Harry M.Portfolio Selection: The Efficient Diversification of Investments. New York: John Wiley and Sons, Inc. (1959).Google Scholar
[15]Modigliani, Franco, and Pogue, Gerald A.. “An Introduction to Risk and Return.” Financial Analysts Journal, Vol. 30, No. 2 and 3, (03-04 1974) and (May–June 1974), pp. 68–80 and pp. 69–86.CrossRefGoogle Scholar
[16]Pogue, Gerald A. “An Intertemporal Model for Investment Management”. Journal of Bank Research, Vol. 1 (Spring 1970), pp. 17–33.Google Scholar
[17]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 (12 1970), pp. 1005–1027.CrossRefGoogle Scholar
[18]Rosenberg, Barr “Extra-Market Components of Covariance in Security Returns”. Journal of Financial and Quantitative Analysis, Vol. 9 (03 1974), pp. 263–274.CrossRefGoogle Scholar
[19]Sharpe, William F. “A Simplified Model for Portfolio Analysis”. Management Science, Vol. 9 (01 1963), pp. 277–293.CrossRefGoogle Scholar
[20]Sharpe, William F. “A Linear Programming Algorithm for Mutual Fund Portfolio Selection”. Management Science, Vol. 13 (03 1967) pp. 449–510.CrossRefGoogle Scholar
[21]Sharpe, William F.Portfolio Theory and Capital Markets. New York: Mc Graw-Hill Book Co. (1970).Google Scholar
[22]Sharpe, William F. “A Linear Programming Approximation for the General Portfolio Problem”. Journal of Financial and Quantitative Analysis, Vol. 6 (12 1971), pp. 1263–1275.CrossRefGoogle Scholar
[23]Sharpe, William F. “The Capital Asset Pricing Model: A ‘Multi-Beta’ Interpretation”. In Financial Decision Making Under Uncertainty, edited by Haim Levy and Marshall Sarnat. New York: Academic Press, Inc. (1977). pp. 127–135.CrossRefGoogle Scholar
[24]Smith, Keith V. “Alternative Procedures for Revising Investment Portfolios”. Journal of Financial and Quantitative Analysis, Vol. 3 (12 1968), pp. 371–403.CrossRefGoogle Scholar
[25]Stone, Bernell K. “A Linear Programming Formulation of the General Portfolio Selection Problem”. Journal of Financial and Quantitative Analysis, Vol. 8 (09 1973), pp. 621–636.CrossRefGoogle Scholar
[26]Stone, Bernell K. “Systematic Interest-Rate Risk in a Two-Index Model of Returns”. Journal of Financial and Quantitative Analysis, Vol. 9 (11 1974), pp. 709–721.CrossRefGoogle Scholar
[27]Stone, Bernell K. and Reback, Robert. “Linear Programming Models for Managing Portfolio Revisions” Journal of Bank Research, Vol. 6 (Spring 1975), pp. 48–60.Google Scholar
[28]Wagner, Harvey M.Principles of Operations Research. Englewood Cliffs, N. J.: Prentice-Hall, Inc. (1969).Google Scholar