Portfolio Optimization And Sharpe Ratio Based On Copula Approach
Abstract
In this paper we will discuss the allocation problem from the perspective of an asset manager or an investment institution. Investors make decision about efficient allocation of their resources. To utilize their resources efficiently they need to balance high return, higher risk activities with those that have low return and lower risk. But how should they choose the ‘best’ mix of activities? How can a fund manager choose his investments in different assets to optimize the performance of his portfolio? How should he measure the performance of his investments? How should he control the risk of his portfolio? The investors need to use methods that focus on the proper aggregation of risks, taking into account the netting of positions and the correlations between assets and risk factors. Because of these reasons we use copula approach to compute optimal portfolio weight. In this paper we have used the optimization of the portfolio weight based on maximized Generalized Sharpe Ratio. We have also computed Generalized Sharpe Ratio based on Value–at–Risk of our portfolio as a risk measure.
References
Alexander, C. Market Risk Analysis. Volume I-IV. John Wiley & Sons, Ltd., 2008
Alexander, G. J.–Sharpe, W. F.–Bailey, J. V. Fundamentals of Investments. Prentice Hall, 1993
Dowd, K.. Adjusting for risk: An improved Sharpe ratio. In: International Review of Economics and Finance 9 (2000), 209–222
Ehrhardt, M. C. – Brigham, E. F. Financial Management: Theory and Practice. South – Western Cengage Learning, 2011
Embrechts, P. – Lindskog, F.– McNeil, A. J. Modelling Dependence with Copulas and Applications to Risk Management. Zürich, http://www.math.ethz.ch/finance, 2001
Focardi, S. M. – Fabozzi F. J. The mathematics of Financial Modeling and Investment Management. John Wiley & Sons, Ltd., 2004
Hubbert, S. Essential mathematics for market risk management. John Wiley & Sons, Ltd., 2012
Cherubini, U. – Luciano, E. – Vecchiato, W. Copula Methods in Finance. John Wiley&Sons, Ltd., 2004
Jorion, P. Value at risk: the new benchmark for controlling market risk. Irwin, Chicago. 1997
McNeil A.J., Frey, R. and Embrechts, P.. Quantitative Risk Management: Concepts, Techniques and Tools. Princeton University Press, Princeton, NJ, 2005
Sharpe, W. F. The Sharpe Ratio. Journal of Portfolio Management (Fall), 49–58., 1994
Sklar, A., 1959. Fonctions de répartition à n dimensions et leurs marges, Publications de l’Institut de Statistique de l’Université de Paris, 8, 229-231.
Sklar, A., 1996. Random variables, distribution functions, and copulas – a personal look backward and forward, in Distributions with Fixed Marginals and Related Topics, ed. By L.Rüschendorff, B. Schweizer and M. Taylor, pp. 1-14. Institute of Mathematical Statistics, Hayward, CA.
Tasche, D. – Tibiletti, L. Are independent risks substitutes according to the Generalized Sharpe Ratio? http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.63.2189&rep
=rep1&type=pdf
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