Abstract
We propose a portfolio-selection model that maximizes expected returns subject to a time-varying 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 an 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 a risky portfolio. An empirical application illustrates in an out-of-sample context which models are preferred from a statistical and economic point of view.
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References
Artzner, P., Delbaen, F., Eber, J. and Heath, D. (1999) “Coherent Measures of Risk,” Mathematical Finance, 9 (3): 203–228.
Bollerslev, T. (1986) “Generalized Autoregressive Conditional Heteroskedasticity,” Journal of Econometrics, 52 (4): 5–59.
Campbell, R., Huisman, R. and Koedijk, K. (2001) “Optimal Portfolio Selection in a Value-at-Risk Framework,” Journal of Banking and Finance, 25 (9): 1789–1804.
Consigli, G. (2002), G. (2002) “Tail Estimation and Mean-VaR Portfolio Selection in Markets Subject to Financial Inestability,” Journal of Banking and Finance, 26 (7): 1355–1382.
Ding, Z., Granger, C. and Engle, R. (1993) “A Long Memory Property of Stock Market Returns and a New Model,” Journal of Empirical Finance, 1 (1): 83–106.
Engle, R. and Manganelli, S. (2004) “CAViaR: Conditional Autoregressive Value at Risk by Regression Quantile,” Journal of Business and Economic Statistics, 22 (4): 367–381.
Fleming, J., Kirby, C. and Ostdiek, B. (2001) “The Economic Value of Volatility Timing,” Journal of Finance, 56 (1): 329–352.
Frey, R. and McNeil, A. (2002) “VaR and Expected Shorfall in Portfolios of Dependent Credit Risks: Conceptual and Practical Insights,” Journal of Banking and Finance, 26 (7): 1317–1334.
Giot, P. and Laurent, S. (2003) “Value-at-Risk for Long and Short Trading Positions,” Journal of Applied Econometrics, 18 (6): 641–663.
Giot, P. and Laurent, S. (2004) “Modelling Daily Value-at-Risk Using Realized Volatility and ARCH Type Models,” Journal of Empirical Finance, 11 (3): 379–398.
Gourieroux, C., Laurent, J. and Scaillet, O. (2000) “Sensitivity Analysis of Values at Risk,” Journal of Empirical Finance, 7 (3–4): 225–245.
Guermat, C. and Harris, D. (2002) “Forecasting Value at Risk Allowing for Time Variation in the Variance and Kurtosis of Portfolio Returns,” International Journal of Forecasting, 18 (3): 409–419.
Hansen, B. (1994) “Autoregressive Conditional Density Estimation,” International Economic Review, 35 (3): 705–730.
Jondeau, E. and Rockinger, M. (2003) “Conditional Volatility, Skewness, and Kurtosis: Existence, Persistence, and Comovements,” Journal of Economic Dynamics and Control, 27 (10): 1699–1737.
Jorion, P. (1997) Value-at-Risk: The New Benchmark for Controlling Market Risk. New York: McGraw-Hill.
Kupiec, P. (1995) “Techniques for Verifying the Accuracy of Risk Measurement Models,” The Journal of Derivatives, 3 (2): 174–184.
Lambert, P. and Laurent, S. (2001) “Modelling Financial Time Series using GARCHtype Models with a Skewed Student Distribution for the Innovations,” Working Paper 0125, Institut de Statistique, Université Catholique de Louvain, Louvainla-Neuve, Belgium.
Markowitz, H.M. (1952) “Portfolio Selection,” Journal of Finance, 7 (1): 77–91.
Merton, R. (1980) “On Estimating the Expected Return on the Market: An Exploratory Investigation,” Journal of Financial Economics, 8 (4): 323–361.
Mittnik, S. and Paolella, M. (2000) “Conditional Density and Value-at-Risk Prediction of Asian Currency Exchange Rates,” Journal of Forecasting, 19 (4): 313–333.
Patton, A. (2004) “On the Out-of-sample Importance of Skewness and Asymmetric Dependence for Asset Allocation,” Journal of Financial Econometrics, 2 (1): 130–168.
Szegö, G. (2002) “Measures of Risk,” Journal of Banking and Finance, 26 (7): 1253–1272.
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© 2011 Erick W. Rengifo and Jeroen V.K. Rombouts
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Rengifo, E.W., Rombouts, J.V.K. (2011). Portfolio Selection with Time-Varying Value-at-Risk. In: Gregoriou, G.N., Pascalau, R. (eds) Financial Econometrics Modeling: Market Microstructure, Factor Models and Financial Risk Measures. Palgrave Macmillan, London. https://doi.org/10.1057/9780230298101_9
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DOI: https://doi.org/10.1057/9780230298101_9
Publisher Name: Palgrave Macmillan, London
Print ISBN: 978-1-349-32890-1
Online ISBN: 978-0-230-29810-1
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