A Bayesian Non-Parametric Approach to Asymmetric Dynamic Conditional Correlation Model With Application to Portfolio Selection
We propose a Bayesian non-parametric approach for modeling the distribution of multiple returns. In particular, we use an asymmetric dynamic conditional correlation (ADCC) model to estimate the time-varying correlations of financial returns where the individual volatilities are driven by GJR-GARCH models. The ADCC-GJR-GARCH model takes into consideration the asymmetries in individual assets' volatilities, as well as in the correlations. The errors are modeled using a Dirichlet location-scale mixture of multivariate Gaussian distributions allowing for a great flexibility in the return distribution in terms of skewness and kurtosis. Model estimation and prediction are developed using MCMC methods based on slice sampling techniques. We carry out a simulation study to illustrate the flexibility of the proposed approach. We find that the proposed DPM model is able to adapt to several frequently used distribution models and also accurately estimates the posterior distribution of the volatilities of the returns, without assuming any underlying distribution. Finally, we present a financial application using Apple and NASDAQ Industrial index data to solve a portfolio allocation problem. We find that imposing a restrictive parametric distribution can result into underestimation of the portfolio variance, whereas DPM model is able to overcome this problem.
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.:
- Cecchetti, Stephen G & Cumby, Robert E & Figlewski, Stephen, 1988.
"Estimation of the Optimal Futures Hedge,"
The Review of Economics and Statistics,
MIT Press, vol. 70(4), pages 623-30, November.
- Mark J. Jensen & John M. Maheu, 2012.
"Bayesian semiparametric multivariate GARCH modeling,"
FRB Atlanta Working Paper
2012-09, Federal Reserve Bank of Atlanta.
- Jensen, Mark J. & Maheu, John M., 2013. "Bayesian semiparametric multivariate GARCH modeling," Journal of Econometrics, Elsevier, vol. 176(1), pages 3-17.
- Mark J. Jensen & John M. Maheu, 2012. "Bayesian Semiparametric Multivariate GARCH Modeling," Working Paper Series 48_12, The Rimini Centre for Economic Analysis.
- Mark J Jensen & John M Maheu, 2012. "Bayesian semiparametric multivariate GARCH modeling," Working Papers tecipa-458, University of Toronto, Department of Economics.
- Lawrence R. Glosten & Ravi Jagannathan & David E. Runkle, 1993.
"On the relation between the expected value and the volatility of the nominal excess return on stocks,"
157, Federal Reserve Bank of Minneapolis.
- Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. " On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
- Sheppard, Kevin & Cappiello, Lorenzo & Engle, Robert F., 2003.
"Asymmetric dynamics in the correlations of global equity and bond returns,"
Working Paper Series
0204, European Central Bank.
- Lorenzo Cappiello & Robert F. Engle & Kevin Sheppard, 2006. "Asymmetric Dynamics in the Correlations of Global Equity and Bond Returns," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(4), pages 537-572.
- Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
- Silvennoinen, Annastiina & Teräsvirta, Timo, 2007.
"Multivariate GARCH models,"
SSE/EFI Working Paper Series in Economics and Finance
669, Stockholm School of Economics, revised 18 Jan 2008.
- Hun Y. Park & Anil K. Bera, 1987. "Interest-Rate Volatility, Basis Risk and Heteroscedasticity in Hedging Mortgages," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 15(2), pages 79-97.
- David Ardia & Lennart F. Hoogerheide, 2010.
"Efficient Bayesian Estimation and Combination of GARCH-Type Models,"
Tinbergen Institute Discussion Papers
10-046/4, Tinbergen Institute.
- Ardia, David & Hoogerheide, Lennart F., 2010. "Efficient Bayesian estimation and combination of GARCH-type models," MPRA Paper 22919, University Library of Munich, Germany.
- Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
- Eduardo Rossi & Claudio Zucca, 2002. "Hedging interest rate risk with multivariate GARCH," Applied Financial Economics, Taylor & Francis Journals, vol. 12(4), pages 241-251.
- Omiros Papaspiliopoulos & Gareth O. Roberts, 2008. "Retrospective Markov chain Monte Carlo methods for Dirichlet process hierarchical models," Biometrika, Biometrika Trust, vol. 95(1), pages 169-186.
- Kroner, Kenneth F. & Sultan, Jahangir, 1993. "Time-Varying Distributions and Dynamic Hedging with Foreign Currency Futures," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(04), pages 535-551, December.
- Giamouridis, Daniel & Vrontos, Ioannis D., 2007. "Hedge fund portfolio construction: A comparison of static and dynamic approaches," Journal of Banking & Finance, Elsevier, vol. 31(1), pages 199-217, January.
When requesting a correction, please mention this item's handle: RePEc:arx:papers:1301.5129. 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.