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Mean Lower Partial Moment Valuation and Lognormally Distributed Returns

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Author Info

  • Wayne Y. Lee

    (Leavey School of Business Administration, Santa Clara University, Santa Clara, California 95053)

  • Ramesh K. S. Rao

    (Graduate School of Business, University of Texas, Austin, Texas 78712)

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    Abstract

    In this paper we develop a capital asset pricing model in a mean lower partial moment framework. Specifically, we show that when partial moments are computed about the expected risky portfolio return, optimal portfolio choice in a mean lower partial framework permits a two-fund portfolio separation between a riskless asset and a "market" portfolio of risky assets. In this new framework, risk is measured as semideviation (for second degree stochastic dominance), and semivariance (for third degree stochastic dominance). Further, when security returns are lognormally distributed and "small risk," this new mean lower partial moment valuation specializes to the mean-logarithmic variance capital asset pricing model.

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    File URL: http://dx.doi.org/10.1287/mnsc.34.4.446
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 34 (1988)
    Issue (Month): 4 (April)
    Pages: 446-453

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    Handle: RePEc:inm:ormnsc:v:34:y:1988:i:4:p:446-453

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    Keywords: mean; partial; moment; valuation;

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    Cited by:
    1. Lien, Donald & Tse, Yiu Kuen, 2001. "Hedging downside risk: futures vs. options," International Review of Economics & Finance, Elsevier, vol. 10(2), pages 159-169.
    2. Clasen, Christian & Griess, Verena C. & Knoke, Thomas, 2011. "Financial consequences of losing admixed tree species: A new approach to value increased financial risks by ungulate browsing," Forest Policy and Economics, Elsevier, vol. 13(6), pages 503-511, July.
    3. Schröder, Michael, 1996. "Value at risk: proposals on a generalization," ZEW Discussion Papers 96-12, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
    4. Ba Chu, 2012. "Large deviations estimation of the windfall and shortfall probabilities for optimal diversified portfolios," Annals of Finance, Springer, vol. 8(1), pages 97-122, February.
    5. S. M. Sunoj & S. S. Maya, 2008. "The role of lower partial moments in stochastic modeling," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 223-242.
    6. Demirer, Riza & Lien, Donald & Shaffer, David R., 2005. "Comparisons of short and long hedge performance: the case of Taiwan," Journal of Multinational Financial Management, Elsevier, vol. 15(1), pages 51-66, February.
    7. Cotter, John & Hanly, James, 2007. "Hedging Effectiveness under Conditions of Asymmetry," MPRA Paper 3501, University Library of Munich, Germany.
    8. Hildebrandt, Patrick & Knoke, Thomas, 2009. "Optimizing the shares of native tree species in forest plantations with biased financial parameters," Ecological Economics, Elsevier, vol. 68(11), pages 2825-2833, September.
    9. Demirer, Riza, 2013. "Can advanced markets help diversify risks in frontier stock markets? Evidence from Gulf Arab stock markets," Research in International Business and Finance, Elsevier, vol. 29(C), pages 77-98.
    10. Korn, Olaf & Schröder, Michael & Szczesny, Andrea & Winschel, Viktor, 1996. "Risikomessung mit Shortfall-Maßen: Das Programm MAMBA - Metzler Asset Management Benchmark Analyser," ZEW Dokumentationen 96-09, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
    11. Demirer, Riza & Lien, Donald, 2003. "Downside risk for short and long hedgers," International Review of Economics & Finance, Elsevier, vol. 12(1), pages 25-44.
    12. Lee, Sang-Hak & Yang, Seung-Ryong, 2000. "The Minimum Semi-Variance Hedge For Food Manufacturers In Korea," 2000 Annual meeting, July 30-August 2, Tampa, FL 21867, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    13. Grootveld, Henk & Hallerbach, Winfried, 1999. "Variance vs downside risk: Is there really that much difference?," European Journal of Operational Research, Elsevier, vol. 114(2), pages 304-319, April.

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