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Downside Beta and Downside Gamma: In Search for a Better Capital Asset Pricing Model

Author

Listed:
  • Madiha Kazmi

    (Department of Management Sciences, COMSATS University Islamabad, Islamabad 45550, Pakistan)

  • Umara Noreen

    (College of Business Administration, Prince Sultan University, Riyadh 11586, Saudi Arabia)

  • Imran Abbas Jadoon

    (Department of Management Sciences, COMSATS University Islamabad, Islamabad 45550, Pakistan)

  • Attayah Shafique

    (Department of Management Sciences, COMSATS University Islamabad, Islamabad 45550, Pakistan)

Abstract

In the financial world, the importance of “downside risk” and “higher moments” has been emphasized, predominantly in developing countries such as Pakistan, for a substantial period. Consequently, this study tests four models for a suitable capital asset pricing model. These models are CAPM’s beta, beta replaced by skewness (gamma), CAPM’s beta with gamma, downside beta CAPM (DCAPM), downside beta replaced by downside gamma, and CAPM with downside gamma. The problems of the high correlation between the beta and downside beta models from a regressand point of view is resolved by constructing a double-sorted portfolio of each factor loading. The problem of the high correlation between the beta and gamma, and, similarly, between the downside beta and downside gamma, is resolved by orthogonalizing each risk measure in a two-factor setting. Standard two-pass regression is applied, and the results are reported and analyzed in terms of R 2 , the significance of the factor loadings, and the risk–return relationship in each model. The risk proxies of the downside beta/gamma are based on Hogan and Warren, Harlow and Rao, and Estrada. The results indicate that the single factor models based on the beta/downside beta or even gamma/downside gamma are not a better choice among all the risk proxies. However, the beta and gamma factors are rejected at a 5% and 1% significance level for different risk proxies. The obvious choice based on the results is an asset pricing model with two risk measures.

Suggested Citation

  • Madiha Kazmi & Umara Noreen & Imran Abbas Jadoon & Attayah Shafique, 2021. "Downside Beta and Downside Gamma: In Search for a Better Capital Asset Pricing Model," Risks, MDPI, vol. 9(12), pages 1-14, December.
    • Handle: RePEc:gam:jrisks:v:9:y:2021:i:12:p:223-:d:695922
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    References listed on IDEAS

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    1. Bawa, Vijay S., 1975. "Optimal rules for ordering uncertain prospects," Journal of Financial Economics, Elsevier, vol. 2(1), pages 95-121, March.
    2. Fama, Eugene F & French, Kenneth R, 1992. "The Cross-Section of Expected Stock Returns," Journal of Finance, American Finance Association, vol. 47(2), pages 427-465, June.
    3. Marshall E. Blume & Irwin Friend, "undated". "A New Look at the Capital Asset Pricing Model," Rodney L. White Center for Financial Research Working Papers 01-71, Wharton School Rodney L. White Center for Financial Research.
    4. Basu, S, 1977. "Investment Performance of Common Stocks in Relation to Their Price-Earnings Ratios: A Test of the Efficient Market Hypothesis," Journal of Finance, American Finance Association, vol. 32(3), pages 663-682, June.
    5. Blume, Marshall E & Friend, Irwin, 1973. "A New Look at the Capital Asset Pricing Model," Journal of Finance, American Finance Association, vol. 28(1), pages 19-33, March.
    6. Ang, James S. & Chua, Jess H., 1979. "Composite Measures for the Evaluation of Investment Performance," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 14(2), pages 361-384, June.
    7. Kandel, Shmuel & Stambaugh, Robert F., 1987. "On correlations and inferences about mean-variance efficiency," Journal of Financial Economics, Elsevier, vol. 18(1), pages 61-90, March.
    8. Hogan, William W. & Warren, James M., 1974. "Toward the Development of an Equilibrium Capital-Market Model Based on Semivariance," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 9(1), pages 1-11, January.
    9. John Lintner, 1965. "Security Prices, Risk, And Maximal Gains From Diversification," Journal of Finance, American Finance Association, vol. 20(4), pages 587-615, December.
    10. Fama, Eugene F & MacBeth, James D, 1973. "Risk, Return, and Equilibrium: Empirical Tests," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 607-636, May-June.
    11. Ayub, Usman & Shah, Syed Zulfiqar Ali & Abbas, Qaisar, 2015. "Robust analysis for downside risk in portfolio management for a volatile stock market," Economic Modelling, Elsevier, vol. 44(C), pages 86-96.
    12. Fama, Eugene F. & French, Kenneth R., 2015. "A five-factor asset pricing model," Journal of Financial Economics, Elsevier, vol. 116(1), pages 1-22.
    13. Basu, Sanjoy, 1983. "The relationship between earnings' yield, market value and return for NYSE common stocks : Further evidence," Journal of Financial Economics, Elsevier, vol. 12(1), pages 129-156, June.
    14. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    15. Estrada, Javier, 2007. "Mean-semivariance behavior: Downside risk and capital asset pricing," International Review of Economics & Finance, Elsevier, vol. 16(2), pages 169-185.
    16. Andrew Ang & Robert J. Hodrick & Yuhang Xing & Xiaoyan Zhang, 2006. "The Cross‐Section of Volatility and Expected Returns," Journal of Finance, American Finance Association, vol. 61(1), pages 259-299, February.
    17. Javid, Attiya Yasmin, 2009. "Test of Higher Moment Capital Asset Pricing Model in Case of Pakistani Equity Market," MPRA Paper 38059, University Library of Munich, Germany.
    18. Reinganum, Marc R., 1981. "Misspecification of capital asset pricing : Empirical anomalies based on earnings' yields and market values," Journal of Financial Economics, Elsevier, vol. 9(1), pages 19-46, March.
    19. Chen, Gongmeng & Kwok, Chuck C. Y. & Rui, Oliver M., 2001. "The day-of-the-week regularity in the stock markets of China," Journal of Multinational Financial Management, Elsevier, vol. 11(2), pages 139-163, April.
    20. Banz, Rolf W., 1981. "The relationship between return and market value of common stocks," Journal of Financial Economics, Elsevier, vol. 9(1), pages 3-18, March.
    21. Thierry Post & Haim Levy, 2005. "Does Risk Seeking Drive Stock Prices? A Stochastic Dominance Analysis of Aggregate Investor Preferences and Beliefs," The Review of Financial Studies, Society for Financial Studies, vol. 18(3), pages 925-953.
    22. Black, Fischer, 1972. "Capital Market Equilibrium with Restricted Borrowing," The Journal of Business, University of Chicago Press, vol. 45(3), pages 444-455, July.
    23. Bawa, Vijay S. & Lindenberg, Eric B., 1977. "Capital market equilibrium in a mean-lower partial moment framework," Journal of Financial Economics, Elsevier, vol. 5(2), pages 189-200, November.
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