An analysis of a mean-variance enhanced index tracking problem with weights constraints
-
Author(s)Wanderlei Lima de PauloLink to ORCID Index: https://orcid.org/0000-0001-5242-3230
,
Marta Ines Velazco FontovaLink to ORCID Index: https://orcid.org/0000-0002-7685-1229
,
Renato Canil de Souza
-
DOIhttp://dx.doi.org/10.21511/imfi.15(4).2018.15
-
Article InfoVolume 15 2018, Issue #4, pp. 183-192
- Cited by
- 1419 Views
-
124 Downloads
This work is licensed under a
Creative Commons Attribution 4.0 International License
In this paper, the authors deal with a mean-variance enhanced index tracking (EIT) problem with weights constraints. Using a shrinkage approach, they show that constructing the constrained EIT portfolio is equivalent to constructing the unconstrained EIT portfolio. This equivalence allows to study the effect of weights constraints on the covariance matrix and on the EIT portfolio. In general, the effects of weights constraints on the EIT portfolio are different from those observed in the case of global minimum variance portfolio. Finally, the authors present a numerical asset allocation example, where the S&P 500 index is used as the market index to be tracked using a portfolio composed of ten stocks, in which the constrained EIT portfolio shows a satisfactory performance when compared to the unconstrained case.
view full abstract
- Keywords
-
JEL Classification (Paper profile tab)G10, G11
-
References16
-
Tables4
-
Figures3
-
- Figure 1. Cumulative monthly portfolio values, obtained by the constrained EIT portfolio ω~ and by the unconstrained EIT portfolio , ω* considering an in-sample analysis
- Figure 2. Cumulative monthly portfolio values, obtained by the constrained EIT portfolio ω~ and by the unconstrained EIT portfolio , ω* considering an out-of-sample analysis
- Figure 3. Cumulative monthly portfolio values, obtained by rebalancing the weights ω~ and ω* during the out-of-sample period
-
- Table 1. Elements of the perturbation matrix, Δ i, j, related to the optimized weights ω~i and ω~j
- Table 2. Market parameters and optimal solution for the unconstrained EIT problem (ω*)
- Table 3. Results for the constrained EIT problem, with weights constraints 0.10 ≤ ωi ≤ 0.30
- Table 4. Solutions for the unconstrained EIT problem, ω*, for the constrained EIT problem with 0.1 ≤ ωi ≤0.3, ω~ and for the unconstrained EIT problem with ri = 0.02 and β i = 1.0, ω-
-
- Alexander, C. (2008). Market Risk Analysis: Quantitative Methods in Finance. New Jersey: Wiley.
- Alexander, G. J., & Baptista, A. M. (2010). Active portfolio management with benchmarking: A frontier based on alpha. Journal of Banking and Finance, 34, 2185- 2197.
- Benidis, K., Feng, Y., & Palomar, D. P. (2018). Sparse portfolios for high-dimensional financial index tracking. IEEE Transactions on signal processing, 66, 155-170.
- Canakgoz, N. A., & Beasley, J. E. (2008). Mixed-integer programming approaches for index tracking and enhanced indexation. European Journal of Operational Research, 196, 384-399.
- DeMiguel, V., Garlappi, L., Nogales, F. J., & Uppal, R. (2009). A generalized approach to portfolio optimization: Improving performance by constraining portfolio norms. Management Science, 55, 798-812.
- Fan, J., Zhang, J., & Yu, K. (2012). Vast portfolio selection with gross-exposure constraints. Journal of the American Statistical Association, 107, 592-606.
- Filippi, C., Guastaroba, G., & Speranza, M. G. (2016). A heuristic framework for the bi-objective enhanced index tracking problem. Omega, 65, 122-137.
- Goel, A., Sharma, A., & Mehra, A. (2018). Index tracking and enhanced indexing using mixed conditional value-at-risk. Journal of Computational and Applied Mathematics, 335, 361-380.
- Jagannathan, R., & Ma, T. (2003). Risk reduction in large portfolios: Why imposing the wrong constraints helps. The Journal of Finance, 58, 1651-1683.
- Kim, J. H., Kim, W. C., & Fabozzi, F. J. (2016). Portfolio selection with conservative short-selling. Finance Research Letters, 18, 363-369.
- Ledoit, O., & Wolf, M. (2004). A well-conditioned estimator for large-dimensional covariance matrices. Journal of Multivariate Analysis, 88, 365-411.
- Pantaleo, E., Tumminello, M., Lillo, F., & Mantegna, R. N. (2011). When do improved covariance matrix estimators enhance portfolio optimization? An empirical comparative study of nine estimators. Quantitative Finance, 11, 1067-1080.
- Paulo, W. L., Oliveira, E. M., & Costa, O. L. V. (2016). Enhanced index tracking optimal portfolio selection. Finance Research Letters, 16, 93-102.
- Roll, R. (1992). A mean/variance analysis of tracking error. The Journal of Portfolio Management, 18, 13-22.
- Roncalli, T. (2011). Understanding the Impact of Weights Constraints in Portfolio Theory.
- Sant’Anna, L. R., Filomena, T. P., & Caldeira, J. F. (2017). Index tracking and enhanced indexing using cointegration and correlation with endogenous portfolio selection. The Quarterly Review of Economics and Finance, 65, 146-157.
Close
Investment Management and Financial Innovations