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Mean Lower Partial Moment Valuation and Lognormally Distributed Returns

Author

Listed:
  • 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)

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.

Suggested Citation

  • Wayne Y. Lee & Ramesh K. S. Rao, 1988. "Mean Lower Partial Moment Valuation and Lognormally Distributed Returns," Management Science, INFORMS, vol. 34(4), pages 446-453, April.
    • Handle: RePEc:inm:ormnsc:v:34:y:1988:i:4:p:446-453
    DOI: 10.1287/mnsc.34.4.446
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    Cited by:

    1. Franke, Günter & Weber, Martin, 1997. "Risk-value efficient portfolios and asset pricing," Discussion Papers, Series II 354, University of Konstanz, Collaborative Research Centre (SFB) 178 "Internationalization of the Economy".
    2. Knoke, Thomas, 2008. "Mixed forests and finance -- Methodological approaches," Ecological Economics, Elsevier, vol. 65(3), pages 590-601, April.
    3. 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.
    4. Dipankar Mondal & N. Selvaraju, 2022. "Convexity, two-fund separation and asset ranking in a mean-LPM portfolio selection framework," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(1), pages 225-248, March.
    5. Rui Pedro Brito & Hélder Sebastião & Pedro Godinho, 2016. "Efficient skewness/semivariance portfolios," Journal of Asset Management, Palgrave Macmillan, vol. 17(5), pages 331-346, September.
    6. 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.
    7. 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.
    8. Lien, Donald & Tse, Yiu Kuen, 2001. "Hedging downside risk: futures vs. options," International Review of Economics & Finance, Elsevier, vol. 10(2), pages 159-169.
    9. John Cotter & Jim Hanly, 2012. "Hedging effectiveness under conditions of asymmetry," The European Journal of Finance, Taylor & Francis Journals, vol. 18(2), pages 135-147, February.
    10. 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).
    11. 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.
    12. Yao, Haixiang & Huang, Jinbo & Li, Yong & Humphrey, Jacquelyn E., 2021. "A general approach to smooth and convex portfolio optimization using lower partial moments," Journal of Banking & Finance, Elsevier, vol. 129(C).
    13. Hildebrandt, Patrick & Knoke, Thomas, 2011. "Investment decisions under uncertainty--A methodological review on forest science studies," Forest Policy and Economics, Elsevier, vol. 13(1), pages 1-15, January.
    14. 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.
    15. Rui Pedro Brito & Hélder Sebastião & Pedro Godinho, 2015. "Efficient Skewness/Semivariance Portfolios," GEMF Working Papers 2015-05, GEMF, Faculty of Economics, University of Coimbra.
    16. Dragicevic, Arnaud Z., 2019. "Rethinking the forestry in the Aquitaine massif through portfolio management," Forest Policy and Economics, Elsevier, vol. 109(C).
    17. Ruili Sun & Tiefeng Ma & Shuangzhe Liu & Milind Sathye, 2019. "Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review," JRFM, MDPI, vol. 12(1), pages 1-34, March.
    18. Huang, Jinbo & Li, Yong & Yao, Haixiang, 2022. "Partial moments and indexation investment strategies," Journal of Empirical Finance, Elsevier, vol. 67(C), pages 39-59.
    19. 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.
    20. 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.
    21. 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 - Leibniz Centre for European Economic Research.
    22. Dai, Jun & Zhou, Haigang & Zhao, Shaoquan, 2017. "Determining the multi-scale hedge ratios of stock index futures using the lower partial moments method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 502-510.
    23. Schröder, Michael, 1996. "Value at risk: proposals on a generalization," ZEW Discussion Papers 96-12, ZEW - Leibniz Centre for European Economic Research.
    24. Li, Xiang & Qin, Zhongfeng, 2014. "Interval portfolio selection models within the framework of uncertainty theory," Economic Modelling, Elsevier, vol. 41(C), pages 338-344.
    25. Demirer, Riza & Lien, Donald, 2003. "Downside risk for short and long hedgers," International Review of Economics & Finance, Elsevier, vol. 12(1), pages 25-44.

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    Keywords

    mean; partial; moment; valuation;
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