Enhanced indexing using weighted conditional value at risk
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We propose an enhanced indexing portfolio optimization model that not only seeks to maximize the excess returns over and above the benchmark index but simultaneously control the risk by introducing a constraint on the weighted conditional value at risk (WCVaR) of the portfolio. The constraint in the proposed model can be seen as hedging the risk described by WCVaR of the portfolio. To carry out a comparative analysis of the proposed model, we also suggest an enhanced indexing CVaR model. We analyze the performance of the proposed model at various risk levels on eight publicly available financial data sets from Beasley OR library, and S&P 500, S&P BSE 500, NASDAQ composite, FTSE 100 index, and their constituents, for average returns, Sharpe ratio, and upside potential ratio. Empirical analysis exhibits superior performance of the portfolios from the proposed WCVaR model over the respective benchmark indices and additionally the optimal portfolios obtained from various other enhanced indexing models that exist in the literature. Furthermore, we present evidence of better performance of WCVaR model over the CVaR model for long-term investment horizons.
KeywordsEnhanced indexing Conditional value at risk Weighted conditional value at risk Gini mean difference Sharpe ratio Upside potential ratio
The authors are profoundly thankful to the Editor-in-Chief and the esteemed referees for their valuable comments and suggestions.
- DiBartolomeo, D. (2000). The enhanced index fund as an alternative to indexed equity management. Boston: Northfield information services. http://www.northinfo.com/documents/70.pdf. Accessed 16 Jan 2019.
- Gilli, M., & Këllezi, E. (2002). The threshold accepting heuristic for index tracking. In P. Pardalos & V. K. Tsitsiringos (Eds.), Applied optimization series: Financial engineering, e-commerce and supply chain (pp. 1–18). Boston: Kluwer Academic.Google Scholar
- Guastaroba, G., Mansini, R., Speranza, M. G., Ogryczak, W. (2016b). Enhanced index tracking with cvar-based measures. https://www.academia.edu/32399307/Enhanced_Index_Tracking_with_CVaR-Based_Measures. Accessed 16 Jan 2019.
- Jeurissen, R., & Van den Berg, J. (2005). Index tracking using a hybrid genetic algorithm. In Proceedings of 2005 ICSC congress on computational intelligence methods and applications, Istanbul. https://doi.org/10.1109/CIMA. 2005.1662364.
- Keating, C., & Shadwick, W. F. (2002). A universal performance measure. Journal of Performance Measurement, 6(3), 59–84.Google Scholar
- Koshizuka, T., Konno, H., & Yamamoto, R. (2009). Index-plus-alpha tracking subject to correlation constraint. International Journal of Optimization: Theory, Methods and Applications, 1(2), 215–224.Google Scholar
- Linsmeier, T. J., Pearson, N. D., et al. (1996). Risk measurement: An introduction to value at risk. In Technical report 96-04. OFOR, University of Illinois, Urbana-Champaign.Google Scholar
- Mansini, R., Ogryczak, W., & Speranza, M. G. (2007a). Conditional value at risk and related linear programming models for portfolio optimization. Annals of Operations Research, 152(1), 227–256.Google Scholar
- Mansini, R., Ogryczak, W., & Speranza, M. G. (2007b). Tail Gini’s risk measures and related linear programming models for portfolio optimization. In HERCMA conference proceedings, CD, LEA Publishers, Athens.Google Scholar
- Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1), 77–91.Google Scholar
- Scowcroft, A., & Sefton, J. (2003). Enhanced indexation. In S. Satchell & A. Scowcroft (Eds.), Advances in portfolio construction and implementation (pp. 95–124). Butterworth-Heinemann Finance.Google Scholar
- Yitzhaki, S. (1982). Stochastic dominance, mean variance, and Gini’s mean difference. The American Economic Review, 72(1), 178–185.Google Scholar