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Optimal guaranteed return portfolios and the casino effect

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Author Info

  • Dert, Cees

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

  • Oldenkamp, Bart
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    Abstract

    In this paper, we address the problem of maximizing expected return subject to a worst case return constraint by composing a portfolio that may consist of cash, holdings in a stock market index and options on the index. We derive properties of optimal and feasible portfolios and present a linear programming model to solve the problem. The optimal portfolios have pay-off functions that reflect a gambling policy. We show that optimal solutions to a large class of portfolio models that maximize expected return subject to downside risk constraints are driven by this casino effect and present tractable conditions under which it occurs in our model. We propose to control the casino effect by using chance constraints. Using results from financial theory we formulate an LP model that maximizes expected return subject to worst case return constraints and chance constraints on achieving prespecified levels of return. The results are illustrated with real life data on the S&P 500 index.

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    File URL: ftp://zappa.ubvu.vu.nl/19970025.pdf
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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 0025.

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    Date of creation: 1997
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    Handle: RePEc:dgr:vuarem:1997-25

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

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    References

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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.
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    Cited by:
    1. Jansen, Dennis W. & Koedijk, Kees G. & de Vries, Casper G., 2000. "Portfolio selection with limited downside risk," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 247-269, November.
    2. Gulpinar, Nalan & Rustem, Berc, 2007. "Robust optimal decisions with imprecise forecasts," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3595-3611, April.
    3. Lucas, André & Dert, Cees L., 1998. "On the inefficiency of portfolio insurance and caveats to the mean/downside-risk framework," Serie Research Memoranda 0057, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    4. Jón Daníelsson & Bjørn Jorgensen & Casper Vries & Xiaoguang Yang, 2008. "Optimal portfolio allocation under the probabilistic VaR constraint and incentives for financial innovation," Annals of Finance, Springer, vol. 4(3), pages 345-367, July.

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