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Dynamic Optimal Portfolio Selection in a VaR Framework

We propose a dynamic portfolio selection model that maximizes expected returns subject to a Value-at-Risk constraint. The model allows for time varying skewness and kurtosis of portfolio distributions estimating the model parameters by weighted maximum likelihood in a increasing window setup. We determine the best daily investment recommendations in terms of percentage to borrow or lend and the optimal weights of the assets in the risky portfolio. Two empirical applications illustrate in an out-of-sample context which models are preferred from a statistical and economic point of view. We find that the APARCH(1,1) model outperforms the GARCH(1,1) model. A sensitivity analysis with respect to the distributional innovation hypothesis shows that in general the skewed-t is preferred to the normal and Student-t.

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File URL: http://www.hec.ca/iea/cahiers/2004/iea0405_jrom.pdf
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Paper provided by HEC Montréal, Institut d'économie appliquée in its series Cahiers de recherche with number 04-05.

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Length: 31 pages
Date of creation: Jul 2004
Date of revision:
Handle: RePEc:iea:carech:0405
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  1. Christian Gourieroux & J. P. Laurent & Olivier Scaillet, 2000. "Sensitivity Analysis of Values at Risk," Econometric Society World Congress 2000 Contributed Papers 0162, Econometric Society.
  2. Robert C. Merton, 1980. "On Estimating the Expected Return on the Market: An Exploratory Investigation," NBER Working Papers 0444, National Bureau of Economic Research, Inc.
  3. de Roon, F.A. & Nijman, T.E. & Werker, B.J.M., 2003. "Currency hedging for international stock portfolios : The usefulness of mean variance analysis," Other publications TiSEM ef0968be-f501-4434-bc45-0, Tilburg University, School of Economics and Management.
  4. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
  5. Pierre Giot & Sébastien Laurent, 2003. "Value-at-risk for long and short trading positions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(6), pages 641-663.
  6. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
  7. Hansen, B.E., 1992. "Autoregressive Conditional Density Estimation," RCER Working Papers 322, University of Rochester - Center for Economic Research (RCER).
  8. Pierre Giot & Sébastien Laurent, 2002. "Modelling Daily Value-at-Risk Using Realized Volatility and ARCH Type Models," Computing in Economics and Finance 2002 52, Society for Computational Economics.
  9. Christian Gourieroux & Jean-Paul Laurent & Olivier Scaillet, 2000. "Sensitivity Analysis of Values at Risk," Working Papers 2000-05, Centre de Recherche en Economie et Statistique.
  10. 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.
  11. Guermat, Cherif & Harris, Richard D. F., 2002. "Forecasting value at risk allowing for time variation in the variance and kurtosis of portfolio returns," International Journal of Forecasting, Elsevier, vol. 18(3), pages 409-419.
  12. 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.
  13. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  14. Campbell, Rachel & Huisman, Ronald & Koedijk, Kees, 2001. "Optimal portfolio selection in a Value-at-Risk framework," Journal of Banking & Finance, Elsevier, vol. 25(9), pages 1789-1804, September.
  15. de Roon, Frans A. & Nijman, Theo E. & Werker, Bas J. M., 2003. "Currency hedging for international stock portfolios: The usefulness of mean-variance analysis," Journal of Banking & Finance, Elsevier, vol. 27(2), pages 327-349, February.
  16. Jeff Fleming, 2001. "The Economic Value of Volatility Timing," Journal of Finance, American Finance Association, vol. 56(1), pages 329-352, 02.
  17. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
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