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Portfolio Optimization with Many Assets: The Importance of Short-Selling

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  • Levy, Moshe
  • Ritov, Yaacov

Abstract

We investigate the properties of mean-variance efficient portfolios when the number of assets is large. We show analytically and empirically that the proportion of assets held short converges to 50% as the number of assets grows, and the investment proportions are extreme, with several assets held in large positions. The cost of the no-shortselling constraint increases dramatically with the number of assets. For about 100 assets the Sharpe ratio can be more than doubled with the removal of this constraint. These results have profound implications for the theoretical validity of the CAPM, and for policy regarding short-selling limitations.

Suggested Citation

  • Levy, Moshe & Ritov, Yaacov, 2001. "Portfolio Optimization with Many Assets: The Importance of Short-Selling," University of California at Los Angeles, Anderson Graduate School of Management qt41x4t67m, Anderson Graduate School of Management, UCLA.
    • Handle: RePEc:cdl:anderf:qt41x4t67m
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    3. Michael McKenzie & Olan T. Henry, 2007. "The Determinnts of Short Selling in the Hong Kong Equities Market," Department of Economics - Working Papers Series 1001, The University of Melbourne.
    4. Vrinda Dhingra & Shiv Kumar Gupta & Amita Sharma, 2023. "Norm constrained minimum variance portfolios with short selling," Computational Management Science, Springer, vol. 20(1), pages 1-35, December.

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