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Robust mean-variance portfolio through the weighted \(L^p\) depth function. (English) Zbl 1455.91240

The main contribution of this paper is the extension of statistical data depth-based estimators to financial portfolio selection as it was already done with some other well-known robust techniques. To start with, the authors recall the classical mean-variance portfolio model. Then they offer some background on the notion of statistical depth functions along with their main properties and the estimation of the mean and covariance matrix through the weighted \(L^p\)-depth function. Such approach has the advantage to be independent of parametric assumptions, and less sensitive to changes in the asset return distribution than traditional techniques. The exposition is concluded with an out-of-sample evaluation through simulated data and an application to a real data set.

MSC:

91G10 Portfolio theory
62P05 Applications of statistics to actuarial sciences and financial mathematics

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FinTS
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[1] Ceria, S.; Stubbs, RA, Incorporating estimation errors into portfolio selection: Robust portfolio construction, Journal of Asset Management, 7, 2, 109-127 (2006)
[2] Chopra, VK; Ziemba, WT, The effect of errors in means, variances, and covariances on optimal portfolio choice, The Journal of Portfolio Management, 19, 2, 6-11 (1993)
[3] DeMiguel, V.; Nogales, FJ, Portfolio selection with robust estimation, Operations Research, 57, 3, 560-577 (2009) · Zbl 1233.91240
[4] Donoho, DL; Gasko, M., Breakdown properties of location estimates based on halfspace depth and projected outlyingness, The Annals of Statistics, 20, 1803-1827 (1992) · Zbl 0776.62031
[5] Efron, B.; Tibshirani, RJ, An introduction to the bootstrap (1994), Boca Raton: CRC Press, Boca Raton
[6] Gervini, D., Outlier detection and trimmed estimation for general functional data, Statistica Sinica, 22, 1639-1660 (2010) · Zbl 1253.62019
[7] Goldfarb, D.; Iyengar, G., Robust portfolio selection problems, Mathematics of operations research, 28, 1, 1-38 (2003) · Zbl 1082.90082
[8] Hampel, F., Contributions to the theory of robust estimation (1968), Berkeley: University of California, Berkeley
[9] Kaszuba, B., Empirical comparison of robust portfolios’ investment effects, The Review of Finance and Banking, 5, 2013, 47-61 (2012)
[10] Kim, JH; Kim, WC; Kwon, D-G; Fabozzi, FJ, Robust equity portfolio performance, Annals of Operations Research, 266, 1, 293-312 (2018) · Zbl 1400.90235
[11] Kosiorowski, D., & Zawadzki, Z. (2015). Locality, robustness and interactions in simple cooperative dynamic game. In Proceedings from 15th International Conference on Group Decissions and Negotiation (pp. 185-188).
[12] Liu, RY, On a notion of data depth based on random simplices, The Annals of Statistics, 18, 1, 405-414 (1990) · Zbl 0701.62063
[13] López-Pintado, S.; Romo, J., On the concept of depth for functional data, Journal of the American Statistical Association, 104, 486, 718-734 (2009) · Zbl 1388.62139
[14] Markowitz, H., Portfolio selection, The Journal of Finance, 7, 1, 77-91 (1952)
[15] Martin, RD; Clark, A.; Green, CG; Guerard, JB, Robust portfolio construction, Handbook of portfolio construction, 337-380 (2010), Boston: Springer, Boston
[16] Paç, AB; Pınar, MÇ, On robust portfolio and naïve diversification: Mixing ambiguous and unambiguous assets, Annals of Operations Research, 266, 1, 223-253 (2018) · Zbl 1417.91475
[17] Pandolfo, G.; Paindaveine, D.; Porzio, GC, Distance-based depths for directional data, Canadian Journal of Statistics, 46, 4, 593-609 (2018) · Zbl 1492.62095
[18] Perret-Gentil, C., & Victoria-Feser, M.-P. (2005). Robust mean-variance portfolio selection. Available at SSRN 721509.
[19] Rocke, DM, Robustness properties of S-estimators of multivariate location and shape in high dimension, The Annals of statistics, 24, 1327-1345 (1996) · Zbl 0862.62049
[20] Scutellà, MG; Recchia, R., Robust portfolio asset allocation and risk measures, Annals of Operations Research, 204, 1, 145-169 (2013) · Zbl 1269.91081
[21] Serfling, R., Depth functions in nonparametric multivariate inference, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 72, 1-16 (2006)
[22] Supandi, ED; Rosadi, D., An empirical comparison between robust estimation and robust optimization to mean-variance portfolio, Journal of Modern Applied Statistical Methods, 16, 1, 32 (2017)
[23] Toma, A.; Leoni-Aubin, S., Robust portfolio optimization using pseudodistances, PLoS ONE, 10, 10, 1-26 (2015)
[24] Tsay, RS, Analysis of financial time series (2005), Hoboken: Wiley, Hoboken · Zbl 1086.91054
[25] Tukey, J., Mathematics and the picturing of data, Proceedings of the International Congress of Mathematicians, 2, 523-531 (1975) · Zbl 0347.62002
[26] Van Aelst, S.; Rousseeuw, P., Minimum volume ellipsoid, Wiley Interdisciplinary Reviews: Computational Statistics, 1, 1, 71-82 (2009)
[27] Victoria-Feser, M.-P. (2000). Robust portfolio selection. Available at SSRN 1763322.
[28] Welsch, RE; Zhou, X., Application of robust statistics to asset allocation models, REVSTAT-Statistical Journal, 5, 1, 97-114 (2007) · Zbl 1513.62225
[29] Zuo, Y.; Cui, H., Depth weighted scatter estimators, The Annals of Statistics, 33, 1, 381-413 (2005) · Zbl 1065.62048
[30] Zuo, Y.; Cui, H.; He, X., On the Stahel-Donoho estimator and depth-weighted means of multivariate data, The Annals of Statistics, 32, 1, 167-188 (2004) · Zbl 1105.62349
[31] Zuo, Y.; Cui, H.; Young, D., Influence function and maximum bias of projection depth based estimators, The Annals of Statistics, 32, 189-218 (2004) · Zbl 1105.62350
[32] Zuo, Y.; Serfling, R., General notions of statistical depth function, The Annals of Statistics, 28, 2, 461-482 (2000) · Zbl 1106.62334
[33] Zuo, Y.; Serfling, R., Robustness of weighted \(L^p\)-depth and \(L^p\)-median, Allgemeines Statistisches Archiv, 88, 2, 215-234 (2004) · Zbl 1294.62116
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