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Dynamic optimal portfolio selection in a VaR framework

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  • RENGIFO, Erick
  • ROMBOUTS, Jeroen

Abstract

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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Bibliographic Info

Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2004057.

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Date of creation: 00 Jul 2004
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Handle: RePEc:cor:louvco:2004057

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Keywords: portfolio selection; Value-at-Risk; skewed-t distribution; weighted maximum likelihood;

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References

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  1. 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.
  2. GIOT, Pierre & LAURENT, Sébastien, . "Value-at-Risk for long and short trading positions," CORE Discussion Papers RP -1707, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Gourieroux, C. & Laurent, J. P. & Scaillet, O., 2000. "Sensitivity analysis of Values at Risk," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 225-245, November.
  4. Giot,Pierre & Laurent,Sebastien, 2001. "Modelling daily value-at-risk using realized volatility and arch type models," Research Memorandum 014, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  5. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
  6. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-30, August.
  7. 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.
  8. 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.
  9. 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.).
  10. Pierre Giot and S»bastien Laurent, 2001. "Value-At-Risk For Long And Short Trading Positions," Computing in Economics and Finance 2001 94, Society for Computational Economics.
  11. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  12. 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.
  13. 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.
  14. Jeff Fleming, 2001. "The Economic Value of Volatility Timing," Journal of Finance, American Finance Association, vol. 56(1), pages 329-352, 02.
  15. 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.
  16. 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.
  17. 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.
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Cited by:
  1. Luc, BAUWENS & Walid, BEN OMRANE & Erick, Rengifo, 2006. "Intra-Daily FX Optimal Portfolio Allocation," Discussion Papers (ECON - Département des Sciences Economiques) 2006005, Université catholique de Louvain, Département des Sciences Economiques.

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