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Mean-variance vs. full-scale optimization: broad evidence for the U.K

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  • Björn Hagströmer
  • Richard G. Anderson
  • Jane M. Binner
  • Thomas Elger
  • Birger Nilsson

Abstract

In the Full-Scale Optimization approach the complete empirical financial return probability distribution is considered, and the utility maximising solution is found through numerical optimization. Earlier studies have shown that this approach is useful for investors following non-linear utility functions (such as bilinear and S-shaped utility) and choosing between highly non-normally distributed assets, such as hedge funds. We clarify the role of (mathematical) smoothness and differentiability of the utility function in the relative performance of FSO among a broad class of utility functions. Using a portfolio choice setting of three common assets (FTSE 100, FTSE 250 and FTSE Emerging Market Index), we identify several utility functions under which Full-Scale Optimization is a substantially better approach than the mean variance approach is. Hence, the robustness of the technique is illustrated with regard to asset type as well as to utility function specification.

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Bibliographic Info

Paper provided by Federal Reserve Bank of St. Louis in its series Working Papers with number 2007-016.

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Date of creation: 2007
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Handle: RePEc:fip:fedlwp:2007-016

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Keywords: Great Britain;

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References

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  1. Arditti, Fred D, 1969. "A Utility Function Depending on the First Three Moments: Reply," Journal of Finance, American Finance Association, vol. 24(4), pages 720, September.
  2. Levy, H & Markowtiz, H M, 1979. "Approximating Expected Utility by a Function of Mean and Variance," American Economic Review, American Economic Association, vol. 69(3), pages 308-17, June.
  3. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-91, March.
  4. Samuelson, Paul A, 1970. "The Fundamental Approximation Theorem of Portfolio Analysis in terms of Means, Variances, and Higher Moments," Review of Economic Studies, Wiley Blackwell, vol. 37(4), pages 537-42, October.
  5. Gourieroux, C. & Monfort, A., 2005. "The econometrics of efficient portfolios," Journal of Empirical Finance, Elsevier, vol. 12(1), pages 1-41, January.
  6. Scott, Robert C & Horvath, Philip A, 1980. " On the Direction of Preference for Moments of Higher Order Than the Variance," Journal of Finance, American Finance Association, vol. 35(4), pages 915-19, September.
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Cited by:
  1. George Yungchih Wang, 2012. "Evaluating an Investment Project in an Incomplete Market," The Review of Finance and Banking, Academia de Studii Economice din Bucuresti, Romania / Facultatea de Finante, Asigurari, Banci si Burse de Valori / Catedra de Finante, vol. 4(1), pages 055-073, June.
  2. de Farias Neto, Joao Jose, 2008. "S-shaped utility, subprime crash and the black swan," MPRA Paper 12122, University Library of Munich, Germany.
  3. David Johnstone & Dennis Lindley, 2013. "Mean-Variance and Expected Utility: The Borch Paradox," Papers 1306.2728, arXiv.org.

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