Optimal long term investment in a jump diffusion setting : a large deviation approach
Chu, Ba M., Knight, John L. and Satchell, S. (Stephen) (2006) Optimal long term investment in a jump diffusion setting : a large deviation approach. Working Paper. University of Warwick: Warwick Business School Financial Econometrics Research Centre. (Working Papers Series).
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Official URL: http://www2.warwick.ac.uk/fac/soc/wbs/research/wfr...
In this study, we propose a new method based on the large deviations theory to select an optimal investment for a large portfolio such that the risk, which is defined as the probability that the portfolio return underperforms an investable benchmark, is minimal. As a particular case, we examine the effect of two types of asymmetric dependence; 1) asymmetry in a portfolio return distribution, and 2) asymmetric dependence between asset returns, on the optimal portfolio invested in two risky assets. Furthermore, since our analysis is based on a parametric framework, this allows us to formulate a close-form relationship between the measures of correlation and the optimal portfolio. Finally, we calibrate our method with equity data, namely S&P 500 and Bangkok SET. The empirical evidences confirm that there is a significant impact of asymmetric dependence on optimal portfolio and risk.
|Item Type:||Working or Discussion Paper (Working Paper)|
|Subjects:||H Social Sciences > HG Finance|
|Divisions:||Faculty of Social Sciences > Warwick Business School > Financial Econometrics Research Centre
Faculty of Social Sciences > Warwick Business School
|Library of Congress Subject Headings (LCSH):||Large deviations, Portfolio management, Risk-return relationships|
|Series Name:||Working Papers Series|
|Publisher:||Warwick Business School Financial Econometrics Research Centre|
|Place of Publication:||University of Warwick|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
|References:||Bawa, V. S. (1978). Safety-first, stochastic dominance, and optimal portfolio choice, Journal of Financial and Quantitative Analysis 13: 255–271. Burden, R. and Fairs, J. (1997). Numerical Analysis, Brooks/Cole Publishing Company, California. Cramer, H. (1946). Mathematical Methods of Statistics, Princeton University Press, Princeton. Dembo, A. and Zeitouni, O. (1999). Large Deviations Techniques and Applications, Jones and Bartlett Publishers, Boston, London. Fan, J. and Gu, J. (2003). Semiparametric estimation of Value at Risk, Econometrics Journal 6: 261–290. Harlow, W. and Rao, K. S. (1989). Asset pricing in a generalized mean-lower partial moment framework: theory and evidence, Journal of Financial and Quantitative Analysis 24(3): 285– 311. Harvey, C. R. and Siddique, A. (2000). Conditional skewness in asset pricing tests, Journal of Finance 3: 1263–1295. Ingersoll, J. E. (1987). Theory of Financial Decision Making, Rowman & Littlefield, New York. Jondeau, E. and Rockinger, M. (1999). Estimating Gram-Charlier expansions with positivity constraints, working paper, Banque de France . Jondeau, E. and Rockinger, M. (2003). Conditional volatility, skewness, and kurtosis: Existence, persistence, and comovement, Journal of Economic Dynamics and Control 27: 1699–1737. Kane, A. (1982). Skewness preference and portfolio choice, Journal of Financial and Quatitative Analysis 17(1): 15–25. Knight, J. L., Satchell, S. and Tran, K. (1995). Statistical modelling of asymmetric risk in asset returns, Applied Mathematical Finance 3: 155–172. Malevergne, Y. and Sornette, D. (2002). Multi-moments methods for portfolio management: Generalized CAPM in homogeneous and heterogeneous markets, working paper . Markowitz, H. (1952). Portfolio selection, Journal of Finance 7(1): 77–91. Menezes, C., Geiss, C. and Tressler, J. (1980). Increasing downside risk, American Economic Review 70(5): 921–932. Parthasarathy, K. R. (1977). Introduction to Probability and Measure, The MacMillan Company of India Ltd, Calcutta. Patton, A. J. (2004). On the importance of skewness and asymmetric dependence in stock returns for asset allocation, Journal of Financial Econometrics 2: 130–168. Rao, C. R. (1973). Linear Statistical Inference and Its Applications, John Wiley & Sons, New York. Scales, L. E. (1985). Introduction to Nonlinear Optimization, MacMillan Publishers Ltd, London. Shiryaev, A. N. (1995). Probability, Vol. 95 of Graduate text in mathematics, 2 edn, Springer- Verlag, New York Berlin Heidelberg. Stutzer, M. (2000). A portfolio performance index, Financial Analysts Journal 56. Stutzer, M. (2001a). A large deviation approach to portfolio analysis, working paper, University of Iowa . Stutzer, M. (2001b). Optimal asset allocation for endowments: A large deviation approach, working paper, University of Iowa . Stutzer, M. (2003). Portfolio choice with endogeneous utility: A large deviation approach, Journal of Econometrics 116: 365–386. Stutzer, M. (2004). Asset allocation without unobservable parameters, Financial Analysts Journal 60(5): 38–51. Wong, C. M. and So, M. K. P. (2004). On conditional moments of GARCH models, with applications to multiple period value, Statistica Sinica 13: 1015–1044. Zhulenev, S. V. (1997). On the large deviation, Theory of Probability and Its Applications 44(1): 75–92.|
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