IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this article or follow this journal

Multivariate location-scale mixtures of normals and mean-variance-skewness portfolio allocation

  • Mencía, Javier
  • Sentana, Enrique

We show that the distribution of any portfolio whose components jointly follow a location-scale mixture of normals can be characterised solely by its mean, variance and skewness. Under this distributional assumption, we derive the mean-variance-skewness frontier in closed form, and show that it can be spanned by three funds. For practical purposes, we derive a standardised distribution, provide analytical expressions for the log-likelihood score and explain how to evaluate the information matrix. Finally, we present an empirical application in which we obtain the mean-variance-skewness frontier generated by the ten Datastream US sectoral indices, and conduct spanning tests.

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://www.sciencedirect.com/science/article/B6VC0-4W8TW8S-1/2/ba493f2fd28f69fb25e0c3a0a15513c8
Download Restriction: Full text for ScienceDirect subscribers only

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 153 (2009)
Issue (Month): 2 (December)
Pages: 105-121

as
in new window

Handle: RePEc:eee:econom:v:153:y:2009:i:2:p:105-121
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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. Andrew J. Patton, 2002. "On the out-of-sample importance of skewness and asymetric dependence for asset allocation," LSE Research Online Documents on Economics 24951, London School of Economics and Political Science, LSE Library.
  2. BAUWENS, Luc & LAURENT, Sébastien, . "A new class of multivariate skew densities, with application to generalized autoregressive conditional heteroscedasticity models," CORE Discussion Papers RP -1793, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Dilip B. Madan & Frank Milne, 1991. "Option Pricing With V. G. Martingale Components," Mathematical Finance, Wiley Blackwell, vol. 1(4), pages 39-55.
  4. Sentana, Enrique, 1995. "Quadratic ARCH Models," Review of Economic Studies, Wiley Blackwell, vol. 62(4), pages 639-61, October.
  5. Robert F. Engle & Sharon Kozicki, 1990. "Testing For Common Features," NBER Technical Working Papers 0091, National Bureau of Economic Research, Inc.
  6. 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(01), pages 1-11, January.
  7. Ruud, Paul A., 1991. "Extensions of estimation methods using the EM algorithm," Journal of Econometrics, Elsevier, vol. 49(3), pages 305-341, September.
  8. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
  9. Engle, Robert F & Kozicki, Sharon, 1993. "Testing for Common Features: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(4), pages 393-95, October.
  10. Mervyn King & Enrique Sentana & Sushil Wadhwani, 1990. "Volatiltiy and Links Between National Stock Markets," NBER Working Papers 3357, National Bureau of Economic Research, Inc.
  11. Sentana, E., 2000. "Factor Representing Portfolios in Large Asset Markets," Papers 0001, Centro de Estudios Monetarios Y Financieros-.
  12. 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.
  13. Eric Jondeau & Michael Rockinger, 2006. "Optimal Portfolio Allocation under Higher Moments," European Financial Management, European Financial Management Association, vol. 12(1), pages 29-55.
  14. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Normal modified stable processes," Economics Papers 2001-W6, Economics Group, Nuffield College, University of Oxford.
  15. Berk, Jonathan B., 1997. "Necessary Conditions for the CAPM," Journal of Economic Theory, Elsevier, vol. 73(1), pages 245-257, March.
  16. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(04), pages 657-681, October.
  17. Owen, Joel & Rabinovitch, Ramon, 1983. " On the Class of Elliptical Distributions and Their Applications to the Theory of Portfolio Choice," Journal of Finance, American Finance Association, vol. 38(3), pages 745-52, June.
  18. Walter Briec & Kristiaan Kerstens & Octave Jokung, 2005. "Mean-Variance-Skewness Portfolio Performance Gauging: A General Shortage Function and Dual Approach," Working Papers 2005-ECO-05, IESEG School of Management.
  19. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
  20. Jondeau, Eric & Rockinger, Michael, 2003. "Conditional volatility, skewness, and kurtosis: existence, persistence, and comovements," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1699-1737, August.
  21. 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 1121-52, September.
  22. Javier Mencía & Enrique Sentana, 2012. "Distributional Tests in Multivariate Dynamic Models with Normal and Student-t Innovations," The Review of Economics and Statistics, MIT Press, vol. 94(1), pages 133-152, February.
  23. Flavio Pressacco & Patrizia Stucchi, 2000. "Linearity properties of a three-moments portfolio model," Decisions in Economics and Finance, Springer, vol. 23(2), pages 133-150.
  24. 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.
  25. de Athayde, Gustavo M. & Flores, Renato Jr., 2004. "Finding a maximum skewness portfolio--a general solution to three-moments portfolio choice," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1335-1352, April.
  26. French, Kenneth R & Poterba, James M, 1991. "Investor Diversification and International Equity Markets," American Economic Review, American Economic Association, vol. 81(2), pages 222-26, May.
  27. H. D. Vinod & B. D. McCullough, 1999. "The Numerical Reliability of Econometric Software," Journal of Economic Literature, American Economic Association, vol. 37(2), pages 633-665, June.
  28. Andrea Gamba & Francesco Rossi, 1998. "A three-moment based portfolio selection model," Decisions in Economics and Finance, Springer, vol. 21(1), pages 25-48, June.
  29. Christian Pedersen & Stephen Satchell, 2002. "On the foundation of performance measures under asymmetric returns," Quantitative Finance, Taylor & Francis Journals, vol. 2(3), pages 217-223.
  30. Yusif Simaan, 1993. "Portfolio Selection and Asset Pricing---Three-Parameter Framework," Management Science, INFORMS, vol. 39(5), pages 568-577, May.
  31. Lim, Kian-Guan, 1989. "A New Test of the Three-Moment Capital Asset Pricing Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(02), pages 205-216, June.
  32. François Longin, 2001. "Extreme Correlation of International Equity Markets," Journal of Finance, American Finance Association, vol. 56(2), pages 649-676, 04.
  33. Chen, Ying & Härdle, Wolfgang & Jeong, Seok-Oh, 2008. "Nonparametric Risk Management With Generalized Hyperbolic Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 910-923.
  34. Massimo Guidolin & Allan Timmerman, 2006. "Asset allocation under multivariate regime switching," Working Papers 2005-002, Federal Reserve Bank of St. Louis.
  35. Fiorentini, Gabriele & Sentana, Enrique & Calzolari, Giorgio, 2003. "Maximum Likelihood Estimation and Inference in Multivariate Conditionally Heteroscedastic Dynamic Regression Models with Student t Innovations," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(4), pages 532-46, October.
  36. H. D. Vinod & B. D. McCullough, 1999. "Corrigenda: The Numerical Reliability of Econometric Software," Journal of Economic Literature, American Economic Association, vol. 37(4), pages 1565-1565, December.
Full references (including those not matched with items on IDEAS)

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

When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:153:y:2009:i:2:p:105-121. 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: (Zhang, Lei)

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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.