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On the inefficiency of portfolio insurance and caveats to the mean/downside-risk framework

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  • Lucas, Andr‚

    (Vrije Universiteit Amsterdam, Faculteit der Economische Wetenschappen en Econometrie (Free University Amsterdam, Faculty of Economics Sciences, Business Administration and Economitrics)

  • Dert, Cees L.

Abstract

Portfolio insurance strategies based on options typically treat the investment in the risky asset, e.g., stock, as fixed. We show in a mean/downside-risk framework that such a strategy is inefficient. Using at the money put options, expected returns can be increased by more than 250 basis points without taking on more risk. Gains can become arbitrarily large when one uses options with extremely high strike prices. This is due to a serious caveat to the mean/downside-risk framework that is typically adopted in the literature by substituting downside-risk measures for standard risk measures such as the variance of returns. These pathologic results vanish when one maximizes an appropriately chosen HARA utility function. In this framework, fixing the holding of the risky asset in advance leads to efficiency losses that vary between 250 and 650 basis points depending on the degree of risk aversion.

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Bibliographic Info

Paper provided by VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics in its series Serie Research Memoranda with number 0057.

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Date of creation: 1998
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Handle: RePEc:dgr:vuarem:1998-57

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Web page: http://www.feweb.vu.nl

Related research

Keywords: mean/downside-risk efficiency; option strategies; optimal portfolio choice; portfolio insurance; downside-risk.;

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  1. Philip H. Dybvig, 1987. "Inefficient Dynamic Portfolio Strategies or How to Throw Away a Million Dollars in the Stock Market," Cowles Foundation Discussion Papers 826R, Cowles Foundation for Research in Economics, Yale University, revised Jan 1988.
  2. Hayne E. Leland., 1996. "Beyond Mean-Variance: Performance Measurement of Portfolios Using Options or Dynamic Strategies," Research Program in Finance Working Papers RPF-263-rev, University of California at Berkeley.
  3. Merton, Robert C & Scholes, Myron S & Gladstein, Mathew L, 1982. "The Returns and Risks of Alternative Put-Option Portfolio Investment Strategies," The Journal of Business, University of Chicago Press, vol. 55(1), pages 1-55, January.
  4. Dert, Cees & Oldenkamp, Bart, 1997. "Optimal guaranteed return portfolios and the casino effect," Serie Research Memoranda 0025, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  5. Merton, Robert C & Scholes, Myron S & Gladstein, Mathew L, 1978. "The Returns and Risk of Alternative Call Option Portfolio Investment Strategies," The Journal of Business, University of Chicago Press, vol. 51(2), pages 183-242, April.
  6. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  7. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
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