IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i9p1011-d546290.html
   My bibliography  Save this article

How to Explain the Cross-Section of Equity Returns through Common Principal Components

Author

Listed:
  • José Manuel Cueto

    (Department of Statistics, Universidad Carlos III de Madrid, 28903 Getafe, Spain)

  • Aurea Grané

    (Department of Statistics, Universidad Carlos III de Madrid, 28903 Getafe, Spain)

  • Ignacio Cascos

    (Department of Statistics, Universidad Carlos III de Madrid, 28903 Getafe, Spain)

Abstract

In this paper, we propose a procedure to obtain and test multifactor models based on statistical and financial factors. A major issue in the factor literature is to select the factors included in the model, as well as the construction of the portfolios. We deal with this matter using a dimensionality reduction technique designed to work with several groups of data called Common Principal Components. A block-bootstrap methodology is developed to assess the validity of the model and the significance of the parameters involved. Data come from Reuters, correspond to nearly 1250 EU companies, and span from October 2009 to October 2019. We also compare our bootstrap-based inferential results with those obtained via classical testing proposals. Methods under assessment are time-series regression and cross-sectional regression. The main findings indicate that the multifactor model proposed improves the Capital Asset Pricing Model with regard to the adjusted- R 2 in the time-series regressions. Cross-section regression results reveal that Market and a factor related to Momentum and mean of stocks’ returns have positive risk premia for the analyzed period. Finally, we also observe that tests based on block-bootstrap statistics are more conservative with the null than classical procedures.

Suggested Citation

  • José Manuel Cueto & Aurea Grané & Ignacio Cascos, 2021. "How to Explain the Cross-Section of Equity Returns through Common Principal Components," Mathematics, MDPI, vol. 9(9), pages 1-22, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:9:p:1011-:d:546290
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/9/1011/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/9/1011/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Guanhao Feng & Stefano Giglio & Dacheng Xiu, 2020. "Taming the Factor Zoo: A Test of New Factors," Journal of Finance, American Finance Association, vol. 75(3), pages 1327-1370, June.
    2. Grané, A. & Veiga, H., 2008. "Accurate minimum capital risk requirements: A comparison of several approaches," Journal of Banking & Finance, Elsevier, vol. 32(11), pages 2482-2492, November.
    3. Y. Lempérière & C. Deremble & T. T. Nguyen & P. Seager & M. Potters & J. P. Bouchaud, 2017. "Risk premia: asymmetric tail risks and excess returns," Quantitative Finance, Taylor & Francis Journals, vol. 17(1), pages 1-14, January.
    4. Pin-Huang Chou & Guofu Zhou, 2006. "Using Bootstrap to Test Portfolio Efficiency," Annals of Economics and Finance, Society for AEF, vol. 7(2), pages 217-249, November.
    5. Fama, Eugene F. & French, Kenneth R., 2015. "A five-factor asset pricing model," Journal of Financial Economics, Elsevier, vol. 116(1), pages 1-22.
    6. Gibbons, Michael R & Ross, Stephen A & Shanken, Jay, 1989. "A Test of the Efficiency of a Given Portfolio," Econometrica, Econometric Society, vol. 57(5), pages 1121-1152, September.
    7. José Manuel Cueto & Aurea Grané & Ignacio Cascos, 2020. "Models for Expected Returns with Statistical Factors," JRFM, MDPI, vol. 13(12), pages 1-17, December.
    8. 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.
    9. Viale, Ariel M. & Kolari, James W. & Fraser, Donald R., 2009. "Common risk factors in bank stocks," Journal of Banking & Finance, Elsevier, vol. 33(3), pages 464-472, March.
    10. Elyasiani, Elyas & Gambarelli, Luca & Muzzioli, Silvia, 2020. "Moment risk premia and the cross-section of stock returns in the European stock market," Journal of Banking & Finance, Elsevier, vol. 111(C).
    11. Shanken, Jay, 1992. "On the Estimation of Beta-Pricing Models," The Review of Financial Studies, Society for Financial Studies, vol. 5(1), pages 1-33.
    12. Carhart, Mark M, 1997. "On Persistence in Mutual Fund Performance," Journal of Finance, American Finance Association, vol. 52(1), pages 57-82, March.
    13. 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.
    14. 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.
    Full references (including those not matched with items on IDEAS)

    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. Cueto, José Manuel & Grané Chávez, Aurea & Cascos Fernández, Ignacio, 2021. "How to explain the cross-section of equity returns through Common Principal Components," DES - Working Papers. Statistics and Econometrics. WS 32258, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. José Manuel Cueto & Aurea Grané & Ignacio Cascos, 2020. "Models for Expected Returns with Statistical Factors," JRFM, MDPI, vol. 13(12), pages 1-17, December.
    3. Fletcher, Jonathan, 2018. "Betas V characteristics: Do stock characteristics enhance the investment opportunity set in U.K. stock returns?," The North American Journal of Economics and Finance, Elsevier, vol. 46(C), pages 114-129.
    4. Cueto, José Manuel & Grané Chávez, Aurea & Cascos Fernández, Ignacio, 2019. "Models for expected returns with statistical factors," DES - Working Papers. Statistics and Econometrics. WS 28776, Universidad Carlos III de Madrid. Departamento de Estadística.
    5. Cujean, Julien & Andrei, Daniel & Fournier, Mathieu, 2019. "The Low-Minus-High Portfolio and the Factor Zoo," CEPR Discussion Papers 14153, C.E.P.R. Discussion Papers.
    6. Ma, Tian & Leong, Wen Jun & Jiang, Fuwei, 2023. "A latent factor model for the Chinese stock market," International Review of Financial Analysis, Elsevier, vol. 87(C).
    7. Gagliardini, Patrick & Ossola, Elisa & Scaillet, Olivier, 2019. "Estimation of large dimensional conditional factor models in finance," Working Papers unige:125031, University of Geneva, Geneva School of Economics and Management.
    8. Kim, Soohun & Skoulakis, Georgios, 2018. "Ex-post risk premia estimation and asset pricing tests using large cross sections: The regression-calibration approach," Journal of Econometrics, Elsevier, vol. 204(2), pages 159-188.
    9. Kolari, James W. & Huang, Jianhua Z. & Butt, Hilal Anwar & Liao, Huiling, 2022. "International tests of the ZCAPM asset pricing model," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 79(C).
    10. Venmans, Frank, 2021. "The leverage anomaly in U.S. bank stock returns," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 75(C).
    11. Ciciretti, Rocco & Dalò, Ambrogio & Dam, Lammertjan, 2023. "The contributions of betas versus characteristics to the ESG premium," Journal of Empirical Finance, Elsevier, vol. 71(C), pages 104-124.
    12. Yu Wang & Haicheng Shu, 2019. "Evaluating the Performance of Factor Pricing Models for Different Stock Market Trends: Evidence from China," Working Papers 2019-10-10, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    13. repec:gnv:wpaper:unige:76321 is not listed on IDEAS
    14. Clarke, Charles, 2022. "The level, slope, and curve factor model for stocks," Journal of Financial Economics, Elsevier, vol. 143(1), pages 159-187.
    15. Lu Zhang, 2017. "The Investment CAPM," European Financial Management, European Financial Management Association, vol. 23(4), pages 545-603, September.
    16. Murtazashvili, Irina & Vozlyublennaia, Nadia, 2012. "The role of data limitations, seasonality and frequency in asset pricing models," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 22(3), pages 555-574.
    17. Patrick Gagliardini & Elisa Ossola & Olivier Scaillet, 2016. "Time‐Varying Risk Premium in Large Cross‐Sectional Equity Data Sets," Econometrica, Econometric Society, vol. 84, pages 985-1046, May.
    18. Vendrame, Vasco & Guermat, Cherif & Tucker, Jon, 2018. "A conditional regime switching CAPM," International Review of Financial Analysis, Elsevier, vol. 56(C), pages 1-11.
    19. Jamali, Ibrahim & Yamani, Ehab & Smallwood, Aaron D., 2023. "An investment-based explanation of currency excess returns," Journal of International Money and Finance, Elsevier, vol. 133(C).
    20. Du, Ding & Hu, Ou, 2012. "Foreign exchange volatility and stock returns," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 22(5), pages 1202-1216.
    21. Cakici, Nusret & Zaremba, Adam, 2021. "Who should be afraid of infections? Pandemic exposure and the cross-section of stock returns," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 72(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:jmathe:v:9:y:2021:i:9:p:1011-:d:546290. 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.