On the optimal selection of portfolios under limited diversification |
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| Institution: | 1. Department of Management Science and Information Systems, University of Auckland, Private Bag 92019, Auckland, New Zealand;2. Computervision Corporation, Bedford, MA 01730, USA;1. McCoy College of Business Administration, Texas State University, San Marcos, TX, 78666, United States;2. College of Business, Zayed University, Dubai, 19282, United Arab Emirates;1. LeBow College of Business, Drexel University, 3141 Chestnut Street, Philadelphia, PA 19104, United States;2. IPAG Lab, IPAG Business School, Paris, France;3. School of Management and Technology of Santarém and Center of Statistics and Applications, University of Lisbon, ComplexoAndaluz, Apartado 295, 2001-904 Santarém, Portugal |
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| Abstract: | We address the problem of selecting portfolios which maximize the ratio of the average excess return to the standard deviation, among all those portfolios which comprise at most a pre-specified number, k, of securities. Under the assumptions of constant pairwise correlations and no short-selling, we argue that the simple ranking procedure of Elton, Gruber, and Padberg effectively solves the problem for all values of k, and that as a function of k, the optimal ratio increases at a decreasing rate. We also clarify why further generalization or extension of our results to other situations is improbable. |
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