IDEAS home Printed from https://ideas.repec.org/a/gam/jsusta/v12y2020i17p6756-d401632.html
   My bibliography  Save this article

Downside Risk-Based Six-Factor Capital Asset Pricing Model (CAPM): A New Paradigm in Asset Pricing

Author

Listed:
  • Usman Ayub

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

  • Samaila Kausar

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

  • Umara Noreen

    (College of Business Administration, Prince Sultan University, P.O. Box No. 66833 Rafha Street, Riyadh 11586, Saudi Arabia)

  • Muhammad Zakaria

    (Department of Economics, COMSATS University Islamabad, Islamabad 45550, Pakistan)

  • Imran Abbas Jadoon

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

Abstract

The importance of downside risk cannot be denied. In this study, we have replaced beta in the five-factor model of using downside beta and have added a momentum factor to suggest a new six-factor downside beta capital asset pricing model (CAPM). Two models are tested—a beta- and momentum-based six-factor model and a downside-beta- (proxy of downside risk) and momentum-based six-factor model. Beta and downside beta are highly correlated; therefore, portfolios are double-sorted to disentangle the correlation. Factor loadings, i.e., size, value, momentum, profitability, and investment, are constructed. The standard methodologies are applied. Data for sample stocks from different non-financial sectors listed in the Pakistan Stock Exchange (PSX) are taken from January 2000 to December 2018. The PSX-100 index and three-month T-bills are taken as proxies for market and risk-free returns. The study uses three subsamples for robustness—period of very high volatility, period of stability, and period of stability and growth with volatility. The results show that the value factor is redundant in both models. The momentum factor is rejected in the beta-based six-factor model only. The beta-based six-factor model shows very low R 2 in periods of highly volatility. The R 2 is high for the other periods. In contrast, the downside beta six-factor model captures the downside trend of the market in an effective manner with a relatively high R 2 . The risk–return relationship is stronger for the downside beta model. These reasons lead us to believe that, overall, the downside beta six-factor model is a better option for investors as compared to the beta-based six-factor model in the area of asset pricing models.

Suggested Citation

  • Usman Ayub & Samaila Kausar & Umara Noreen & Muhammad Zakaria & Imran Abbas Jadoon, 2020. "Downside Risk-Based Six-Factor Capital Asset Pricing Model (CAPM): A New Paradigm in Asset Pricing," Sustainability, MDPI, vol. 12(17), pages 1-16, August.
    • Handle: RePEc:gam:jsusta:v:12:y:2020:i:17:p:6756-:d:401632
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2071-1050/12/17/6756/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2071-1050/12/17/6756/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Dirk Brounen & Abe de Jong & Kees Koedijk, 2004. "Corporate Finance in Europe: Confronting Theory with Practice," Financial Management, Financial Management Association, vol. 33(4), Winter.
    2. Chen, Joseph & Hong, Harrison & Stein, Jeremy C., 2001. "Forecasting crashes: trading volume, past returns, and conditional skewness in stock prices," Journal of Financial Economics, Elsevier, vol. 61(3), pages 345-381, September.
    3. Post, Thierry & van Vliet, Pim, 2006. "Downside risk and asset pricing," Journal of Banking & Finance, Elsevier, vol. 30(3), pages 823-849, March.
    4. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    5. Francisco Barillas & Jay Shanken, 2018. "Comparing Asset Pricing Models," Journal of Finance, American Finance Association, vol. 73(2), pages 715-754, April.
    6. Stephen A. Ross, 2013. "The Arbitrage Theory of Capital Asset Pricing," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 1, pages 11-30, World Scientific Publishing Co. Pte. Ltd..
    7. Harry M. Markowitz, 2010. "Portfolio Theory: As I Still See It," Annual Review of Financial Economics, Annual Reviews, vol. 2(1), pages 1-23, December.
    8. Ingersoll, Jonathan, 1975. "Multidimensional Security Pricing," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 10(5), pages 785-798, December.
    9. 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.
    10. Chang, Tsangyao & Nieh, Chien-Chung & Yang, Ming Jing & Yang, Tse-Yu, 2006. "Are stock market returns related to the weather effects? Empirical evidence from Taiwan," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 343-354.
    11. Fama, Eugene F. & French, Kenneth R., 2015. "A five-factor asset pricing model," Journal of Financial Economics, Elsevier, vol. 116(1), pages 1-22.
    12. 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.
    13. Kraus, Alan & Litzenberger, Robert H, 1976. "Skewness Preference and the Valuation of Risk Assets," Journal of Finance, American Finance Association, vol. 31(4), pages 1085-1100, September.
    14. Estrada, Javier, 2002. "Systematic risk in emerging markets: the," Emerging Markets Review, Elsevier, vol. 3(4), pages 365-379, December.
    15. 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.
    16. Fishburn, Peter C, 1977. "Mean-Risk Analysis with Risk Associated with Below-Target Returns," American Economic Review, American Economic Association, vol. 67(2), pages 116-126, March.
    17. Roll, Richard, 1977. "A critique of the asset pricing theory's tests Part I: On past and potential testability of the theory," Journal of Financial Economics, Elsevier, vol. 4(2), pages 129-176, March.
    18. Carhart, Mark M, 1997. "On Persistence in Mutual Fund Performance," Journal of Finance, American Finance Association, vol. 52(1), pages 57-82, March.
    19. Bali, Turan G. & Demirtas, K. Ozgur & Levy, Haim, 2009. "Is There an Intertemporal Relation between Downside Risk and Expected Returns?," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 44(4), pages 883-909, August.
    20. Graham, John R. & Harvey, Campbell R., 2001. "The theory and practice of corporate finance: evidence from the field," Journal of Financial Economics, Elsevier, vol. 60(2-3), pages 187-243, May.
    21. Bawa, Vijay S., 1975. "Optimal rules for ordering uncertain prospects," Journal of Financial Economics, Elsevier, vol. 2(1), pages 95-121, March.
    22. Ross, Stephen A, 1977. "The Capital Asset Pricing Model (CAPM), Short-Sale Restrictions and Related Issues," Journal of Finance, American Finance Association, vol. 32(1), pages 177-183, March.
    23. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
    24. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    25. Gibbons, Michael R., 1982. "Multivariate tests of financial models : A new approach," Journal of Financial Economics, Elsevier, vol. 10(1), pages 3-27, March.
    26. Harlow, W. V. & Rao, Ramesh K. S., 1989. "Asset Pricing in a Generalized Mean-Lower Partial Moment Framework: Theory and Evidence," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(3), pages 285-311, September.
    27. 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.
    28. Brounen, D. & de Jong, A. & Koedijk, C.G., 2004. "Corporate Finance In Europe Confronting Theory With Practice," ERIM Report Series Research in Management ERS-2004-002-F&A, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    29. Eugene F. Fama & Kenneth R. French, 2016. "Dissecting Anomalies with a Five-Factor Model," The Review of Financial Studies, Society for Financial Studies, vol. 29(1), pages 69-103.
    30. Black, Fischer, 1972. "Capital Market Equilibrium with Restricted Borrowing," The Journal of Business, University of Chicago Press, vol. 45(3), pages 444-455, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Rutkowska-Ziarko, Anna & Markowski, Lesław & Pyke, Christopher & Amin, Saqib, 2022. "Conventional and downside CAPM: The case of London stock exchange," Global Finance Journal, Elsevier, vol. 54(C).
    2. Claudia Florensia & Neneng Susanti, 2020. "How does the six-factor model do in explaining the relationship between return and risk on the Indonesia stock exchange?," International Journal of Research in Business and Social Science (2147-4478), Center for the Strategic Studies in Business and Finance, vol. 9(7), pages 93-107, December.
    3. Hosun Ryou & Han Hee Bae & Hee Soo Lee & Kyong Joo Oh, 2020. "Momentum Investment Strategy Using a Hidden Markov Model," Sustainability, MDPI, vol. 12(17), pages 1-16, August.
    4. Luigi Dolores & Maria Macchiaroli & Gianluigi De Mare, 2022. "Financial Impacts of the Energy Transition in Housing," Sustainability, MDPI, vol. 14(9), pages 1-17, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Philip A. Horvath & Amit K. Sinha, 2017. "Asymmetric reaction is rational behavior," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 41(1), pages 160-179, January.
    2. González-Sánchez, Mariano, 2022. "Factorial asset pricing models using statistical anomalies," Research in International Business and Finance, Elsevier, vol. 60(C).
    3. Shafiqur Rahman & Matthew J. Schneider, 2019. "Tests of Alternative Asset Pricing Models Using Individual Security Returns and a New Multivariate F-Test," Review of Pacific Basin Financial Markets and Policies (RPBFMP), World Scientific Publishing Co. Pte. Ltd., vol. 22(01), pages 1-34, March.
    4. Houda Hafsa & Dorra Hmaied, 2012. "Are Downside Higher Order Co-Moments Priced? : Evidence From The French Market," The International Journal of Business and Finance Research, The Institute for Business and Finance Research, vol. 6(1), pages 65-81.
    5. Chabi-Yo, Fousseni & Ruenzi, Stefan & Weigert, Florian, 2018. "Crash Sensitivity and the Cross Section of Expected Stock Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 53(3), pages 1059-1100, June.
    6. Rocciolo, Francesco & Gheno, Andrea & Brooks, Chris, 2022. "Explaining abnormal returns in stock markets: An alpha-neutral version of the CAPM," International Review of Financial Analysis, Elsevier, vol. 82(C).
    7. Sonntag, Dominik, 2018. "Die Theorie der fairen geometrischen Rendite [The Theory of Fair Geometric Returns]," MPRA Paper 87082, University Library of Munich, Germany.
    8. Javed Iqbal & Sara Azher, 2014. "Value-at-Risk and Expected Stock Returns: Evidence from Pakistan," Lahore Journal of Economics, Department of Economics, The Lahore School of Economics, vol. 19(2), pages 71-100, July-Dec.
    9. Anthonisz, Sean A., 2012. "Asset pricing with partial-moments," Journal of Banking & Finance, Elsevier, vol. 36(7), pages 2122-2135.
    10. Bollerslev, Tim & Patton, Andrew J. & Quaedvlieg, Rogier, 2022. "Realized semibetas: Disentangling “good” and “bad” downside risks," Journal of Financial Economics, Elsevier, vol. 144(1), pages 227-246.
    11. Gilles Boevi Koumou, 2020. "Diversification and portfolio theory: a review," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 34(3), pages 267-312, September.
    12. Lu Zhang, 2017. "The Investment CAPM," European Financial Management, European Financial Management Association, vol. 23(4), pages 545-603, September.
    13. Penaranda, Francisco, 2007. "Portfolio choice beyond the traditional approach," LSE Research Online Documents on Economics 24481, London School of Economics and Political Science, LSE Library.
    14. Botshekan, Mahmoud & Kraeussl, Roman & Lucas, Andre, 2012. "Cash Flow and Discount Rate Risk in Up and Down Markets: What Is Actually Priced?," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 47(6), pages 1279-1301, December.
    15. Tamara Ajrapetova, 2018. "Cross-Section of Asset Returns: Emerging Markets and Market Integration," European Financial and Accounting Journal, Prague University of Economics and Business, vol. 2018(1), pages 41-60.
    16. Fernando Rubio, 2005. "Eficiencia De Mercado, Administracion De Carteras De Fondos Y Behavioural Finance," Finance 0503028, University Library of Munich, Germany, revised 23 Jul 2005.
    17. Asgar Ali & K. N. Badhani, 2023. "Downside risk matters once the lottery effect is controlled: explaining risk–return relationship in the Indian equity market," Journal of Asset Management, Palgrave Macmillan, vol. 24(1), pages 27-43, February.
    18. Sean A. Anthonisz & Tālis J. Putniņš, 2017. "Asset Pricing with Downside Liquidity Risks," Management Science, INFORMS, vol. 63(8), pages 2549-2572, August.
    19. Rutkowska-Ziarko, Anna & Markowski, Lesław & Pyke, Christopher & Amin, Saqib, 2022. "Conventional and downside CAPM: The case of London stock exchange," Global Finance Journal, Elsevier, vol. 54(C).
    20. Liu, Jinjing, 2023. "A novel downside beta and expected stock returns," International Review of Financial Analysis, Elsevier, vol. 85(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jsusta:v:12:y:2020:i:17:p:6756-:d:401632. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.