Advanced Search
MyIDEAS: Login to save this paper or follow this series

Least quartic Regression Criterion with Application to Finance

Contents:

Author Info

  • Giuseppe arbia
Registered author(s):

    Abstract

    This article proposes a new method for the estimation of the parameters of a simple linear regression model which accounts for the role of co-moments in non-Gaussian distributions being based on the minimization of a quartic loss function. Although the proposed method is very general, we examine its application to finance. In fact, in this field the contribution of the co-moments in explaining the return-generating process is of paramount importance when evaluating the systematic risk of an asset within the framework of the Capital Asset Pricing Model (CAPM). The suggested new method contributes to this literature by showing that, in the presence of non-normality, the regression slope can be expressed as a function of the co-kurtosis between the returns of a risky asset and the market proxy. The paper provides an illustration of the method based on some empirical financial data referring to 40 industrial sector assets rates of the Italian stock market.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL: http://arxiv.org/pdf/1403.4171
    File Function: Latest version
    Download Restriction: no

    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1403.4171.

    as in new window
    Length:
    Date of creation: Mar 2014
    Date of revision:
    Handle: RePEc:arx:papers:1403.4171

    Contact details of provider:
    Web page: http://arxiv.org/

    Related research

    Keywords:

    This paper has been announced in the following NEP Reports:

    References

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
    as in new window
    1. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
    2. Jennifer Conrad & Robert F. Dittmar & Eric Ghysels, 2013. "Ex Ante Skewness and Expected Stock Returns," Journal of Finance, American Finance Association, vol. 68(1), pages 85-124, 02.
    3. Barone-Adesi, Giovanni & Talwar, Prem P, 1983. "Market Models and Heteroscedasticity of Residual Security Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(2), pages 163-68, April.
    4. Robert F. Dittmar, 2002. "Nonlinear Pricing Kernels, Kurtosis Preference, and Evidence from the Cross Section of Equity Returns," Journal of Finance, American Finance Association, vol. 57(1), pages 369-403, 02.
    5. Markus K. Brunnermeier & Jonathan A. Parker & Christian Gollier, 2007. "Optimal Beliefs, Asset Prices, and the Preference for Skewed Returns," American Economic Review, American Economic Association, vol. 97(2), pages 159-165, May.
    6. Nicholas Barberis & Ming Huang, 2008. "Stocks as Lotteries: The Implications of Probability Weighting for Security Prices," American Economic Review, American Economic Association, vol. 98(5), pages 2066-2100, December.
    7. Alberto HOLLY & Alain MONFORT & Michael ROCKINGER, . "Fourth Order Pseudo Maximum Likelihood Methods," Swiss Finance Institute Research Paper Series 09-23, Swiss Finance Institute.
    8. Bargès, Mathieu & Cossette, Hélène & Marceau, Étienne, 2009. "TVaR-based capital allocation with copulas," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 348-361, December.
    9. 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.
    10. Ingersoll, Jonathan, 1975. "Multidimensional Security Pricing," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 10(05), pages 785-798, December.
    11. Todd Mitton & Keith Vorkink, 2007. "Equilibrium Underdiversification and the Preference for Skewness," Review of Financial Studies, Society for Financial Studies, vol. 20(4), pages 1255-1288.
    12. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    13. Fama, Eugene F & French, Kenneth R, 1992. " The Cross-Section of Expected Stock Returns," Journal of Finance, American Finance Association, vol. 47(2), pages 427-65, June.
    14. Chris Brooks, 2005. "Autoregressive Conditional Kurtosis," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(3), pages 399-421.
    15. Brian Boyer & Todd Mitton & Keith Vorkink, 2010. "Expected Idiosyncratic Skewness," Review of Financial Studies, Society for Financial Studies, vol. 23(1), pages 169-202, January.
    16. Campbell R. Harvey & Akhtar Siddique, 2000. "Conditional Skewness in Asset Pricing Tests," Journal of Finance, American Finance Association, vol. 55(3), pages 1263-1295, 06.
    17. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    18. Christie-David, Rohan & Chaudhry, Mukesh, 2001. "Coskewness and cokurtosis in futures markets," Journal of Empirical Finance, Elsevier, vol. 8(1), pages 55-81, March.
    19. Barone-Adesi, Giovanni, 1985. "Arbitrage Equilibrium with Skewed Asset Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 20(03), pages 299-313, September.
    20. Mathieu Bargès & Hélène Cossette & Etienne Marceau, 2009. "TVaR-based capital allocation with copulas," Working Papers hal-00431265, HAL.
    Full references (including those not matched with items on IDEAS)

    Citations

    Lists

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:arx:papers:1403.4171. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators).

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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