Multivariate location-scale mixtures of normals and mean-variance-skewness portfolio allocation
AbstractWe 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.
Download InfoIf 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.
Bibliographic InfoPaper provided by Banco de Espa�a in its series Banco de Espa�a Working Papers with number 0909.
Length: 50 pages
Date of creation: Jun 2009
Date of revision:
Generalised Hyperbolic Distribution; Maximum Likelihood; Portfolio Frontiers; Sortino Ratio; Spanning Tests; Tail Dependence;
Other versions of this item:
- Mencía, Javier & Sentana, Enrique, 2009. "Multivariate location-scale mixtures of normals and mean-variance-skewness portfolio allocation," Journal of Econometrics, Elsevier, vol. 153(2), pages 105-121, December.
- Enrique Sentana & Javier Mencía, 2008. "Multivariate Location-Scale Mixtures Of Normals And Mean-Variance-Skwness Portfolio Allocation," Working Papers wp2008_0805, CEMFI.
- C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-06-10 (All new papers)
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.:
- Robert F. Engle & Sharon Kozicki, 1990.
"Testing For Common Features,"
NBER Technical Working Papers
0091, National Bureau of Economic Research, Inc.
- Walter Briec & Kristiaan Kerstens & Octave Jokung, 2005.
"Mean-Variance-Skewness Portfolio Performance Gauging: A General Shortage Function and Dual Approach,"
2005-ECO-05, IESEG School of Management.
- Walter Briec & Kristiaan Kerstens & Octave Jokung, 2007. "Mean-Variance-Skewness Portfolio Performance Gauging: A General Shortage Function and Dual Approach," Management Science, INFORMS, vol. 53(1), pages 135-149, January.
- Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Normal modified stable processes," Economics Papers 2001-W6, Economics Group, Nuffield College, University of Oxford.
- Berk, Jonathan B., 1997. "Necessary Conditions for the CAPM," Journal of Economic Theory, Elsevier, vol. 73(1), pages 245-257, March.
- 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.
- Sentana, E., 2000.
"Factor Representing Portfolios in Large Asset Markets,"
0001, Centro de Estudios Monetarios Y Financieros-.
- Sentana, Enrique, 2004. "Factor representing portfolios in large asset markets," Journal of Econometrics, Elsevier, vol. 119(2), pages 257-289, April.
- Sentana,E., 1995.
"Quadratic Arch Models,"
9517, Centro de Estudios Monetarios Y Financieros-.
- François Longin, 2001. "Extreme Correlation of International Equity Markets," Journal of Finance, American Finance Association, vol. 56(2), pages 649-676, 04.
- Enrique Sentana & Javier Mencía, 2008.
"Distributional Tests In Multivariate Dynamic Models With Normal And Student T Innovations,"
- 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.
- Javier Mencía & Enrique Sentana, 2009. "Distributional tests in multivariate dynamic models with Normal and Student t innovations," Banco de Espaï¿½a Working Papers 0929, Banco de Espa�a.
- Gallant, A. Ronald & Tauchen, George, 1996.
"Which Moments to Match?,"
Cambridge University Press, vol. 12(04), pages 657-681, October.
- 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.
- Guidolin, Massimo & Timmermann, Allan, 2007.
"Asset allocation under multivariate regime switching,"
Journal of Economic Dynamics and Control,
Elsevier, vol. 31(11), pages 3503-3544, November.
- Massimo Guidolin & Allan Timmerman, 2006. "Asset allocation under multivariate regime switching," Working Papers 2005-002, Federal Reserve Bank of St. Louis.
- Jondeau, E. & Rockinger, M., 2004.
"Optimal Portfolio Allocation Under Higher Moments,"
108, Banque de France.
- Bauwens, Luc & Laurent, Sebastien, 2005.
"A New Class of Multivariate Skew Densities, With Application to Generalized Autoregressive Conditional Heteroscedasticity Models,"
Journal of Business & Economic Statistics,
American Statistical Association, vol. 23, pages 346-354, July.
- Tom Doan, . "LOGMVSKEWT: RATS procedure to compute function for log density of multivariate skew-t distribution," Statistical Software Components RTS00107, Boston College Department of Economics.
- 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).
- Dilip B. Madan & Frank Milne, 1991.
"Option Pricing With V. G. Martingale Components,"
Wiley Blackwell, vol. 1(4), pages 39-55.
- 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.
- Chen, Ying & HÃ¤rdle, 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.
- Ying Chen & Wolfgang Härdle & Seok-Oh Jeong, 2004. "Nonparametric Risk Management with Generalized Hyperbolic Distributions," SFB 649 Discussion Papers SFB649DP2005-001, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany, revised Aug 2005.
- Andrew J. Patton, 2004. "On the Out-of-Sample Importance of Skewness and Asymmetric Dependence for Asset Allocation," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(1), pages 130-168.
- Mervyn King & Enrique Sentana & Sushil Wadhwani, 1990.
"Volatiltiy and Links Between National Stock Markets,"
NBER Working Papers
3357, National Bureau of Economic Research, Inc.
- King, Mervyn & Sentana, Enrique & Wadhwani, Sushil, 1994. "Volatility and Links between National Stock Markets," Econometrica, Econometric Society, vol. 62(4), pages 901-33, July.
- 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.
- 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.
- Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
- Kenneth R. French & James M. Poterba, 1991.
"Investor Diversification and International Equity Markets,"
NBER Working Papers
3609, National Bureau of Economic Research, Inc.
- 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.
- 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.
- 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.
- Paul A. Ruud., 1988.
"Extensions of Estimation Methods Using the EM Algorithm.,"
Economics Working Papers
8899, University of California at Berkeley.
- Ruud, Paul A., 1991. "Extensions of estimation methods using the EM algorithm," Journal of Econometrics, Elsevier, vol. 49(3), pages 305-341, September.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
This item has more than 25 citations. To prevent cluttering this page, these citations are listed on a separate page. reading list or among the top items on IDEAS.Access and download statisticsgeneral 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: (Mar�a Beiro. Electronic Dissemination of Information Unit. Research Department. Banco de Espa�a).
If references are entirely missing, you can add them using this form.