Abstract
This paper deals with the portfolio selection problem of risky assets with a diagonal covariance matrix, upper bounds on all assets and transactions costs. An algorithm for its solution is formulated which terminates in a number of iterations that is at most three times the number of assets. The efficient portfolios, under appropriate assumptions, are shown to have the following structure. As the risk tolerance parameter increases, an asset's holdings increases to its target, then stays there for a while, then increases to its upper bound, reaches it and stays there. Then the holdings of the asset with the next highest expected return proceeds in a similar way and so on.
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References
M.J. Best and N. Chakravarti, “An O(n 2) active set method for solving a certain parametric quadratic program,” Journal of Optimization Theory and Applications, vol. 72, no. 2, pp. 213–224, 1992.
M.J. Best and R.R. Grauer, “The efficient set mathematics when mean-variance problems are subject to general linear constraints,” Journal of Economics and Business, vol. 42, pp. 105–120, 1990.
M.J. Best and R.R. Grauer, “Sensitivity analysis for mean-variance portfolio problems,” Management Science, vol. 37, pp. 980–989, 1991.
M.J. Best and J. Hlouskova, “The efficient frontier for bounded assets,” Mathematical Methods of Operations Research, vol. 52, no. 2, pp. 195–212, 2000.
M.J. Best and J.K. Kale, “Quadratic programming for large-scale portfolio optimization,” in Financial Services Information Systems, Jessica Keyes (Ed.), CRC Press: Boca Raton, FL, 2000, pp. 513–529.
O.L. Mangasarian, Nonlinear Programming, McGraw-Hill: New York, 1969.
H. Markowitz, “The optimization of a quadratic function subject to linear constraints,” Naval Research Logistics Quarterly, March–June, 1956, pp. 111–133.
H. Markowitz, Portfolio Selection: Efficient Diversification of Investment, John Wiley: New York, Yale University Press: New Haven, 1959.
K.G. Murty, Linear Programming, John Wiley and Sons: New York, 1983.
K. Ritter, “A method for solving nonlinear maximum-problems depending on parameters,” Naval Research Logistics Quarterly, vol. 14, pp. 147–162, 1967.
J.B. Schattman, “Portfolio selection under nonconvex transaction costs and capital gains taxes,” Ph.D. Thesis, Rutgers Center for Operations Research, Rutgers University, USA, 2000.
W.F. Sharpe, Portfolio Theory and Capital Markets, McGraw-Hill: New York, 1970.
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Best, M.J., Hlouskova, J. Portfolio Selection and Transactions Costs. Computational Optimization and Applications 24, 95–116 (2003). https://doi.org/10.1023/A:1021806200854
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DOI: https://doi.org/10.1023/A:1021806200854