Abstract
Style analysis, as originally proposed by Sharpe, is an asset class factor model aimed at obtaining information on the internal allocation of a financial portfolio and at comparing portfolios with similar investment strategies. The classical approach is based on a constrained linear regression model and the coefficients are usually estimated exploiting a least squares procedure. This solution clearly suffers from the presence of outlying observations. The aim of the paper is to investigate the use of a robust estimator for style coefficients based on constrained quantile regression. The performance of the novel procedure is evaluated by means of a Monte Carlo study where different sets of outliers (both in the constituent returns and in the portfolio returns) have been considered.
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References
Andrews, D.W.K.: Estimation when the parameter are on the boundary. Econometrica 67, 1341–1383 (1999)
Attardi, L., Vistocco, D.: Comparing financial portfolio style through quantile regression. Stat. Appl. 18, 6–16 (2006)
Attardi, L., Vistocco, D.: On estimating portfolio conditional returns distribution through style analysis models. In: Perna, C., Sibillo, M. (eds) Quantitative Methods for Finance and Insurance, pp. 11–17. Springer-Verlag, Milan (2007)
Attardi, L., Vistocco, D.: An index for ranking financial portfolios according to internal turnover. In: Greenacre, M., Lauro, N.C., Palumbo, F. (eds.) Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin-Heidelberg (in press)
Basset, G.W., Chen, H.L.: Portfolio style: return-based attribution using quantile regression. In: Fitzenberger, B., Koenker, R., Machado, J.A.F. (eds.) Economic Applications of Quantile Regression (Studies in Empirical Economics), pp. 293–305. Physica-Verlag, Heidelberg (2001)
Christodoulakis, G.A.: Sharpe style analysis in the msci sector portfolios: a Monte Carlo integration approach. Oper. Res. Int. J. 2, 123–137 (2003)
Christodoulakis, G.A.: Sharpe style analysis in the msci sector portfolios: a Monte Carlo integration approach. In: Knight, J., Satchell, S. (eds.) Linear Factor Models in Finance, pp. 83–94. Elsevier (2005)
Conversano, C., Vistocco, D.: Model based visualization of portfolio style analysis. In: Antock, J. (eds.) Proceedings of the International Conference “COMPSTAT 2004”, pp. 815–822. Physica-Verlag (2004)
Conversano, C., Vistocco, D.: Analysis of mutual fund management styles: a modeling, ranking and visualizing approach. J. Appl. Stat. (accepted)
Davis, W.W.: Bayesian analysis of the linear model subject to linear inequality constraints. J. Am. Stat. Assoc. 78, 573–579 (1978)
Geweke, J.: Exact inference in the inequality constrained normal linear regression model. J. Appl. Econometrics 1, 127–141 (1986)
Horst, J.R., Nijman, T.E., de Roon, F.A.: Evaluating style analysis. J. Empirical Finan. 11, 29–51 (2004)
Judge, G.G., Takayama, T.: Inequality restrictions in regression analysis. J. Am. Stat. Assoc. 61, 166–181 (1966)
Kim, T.H., White, H., Stone, D.: Asymptotic and bayesian confidence intervals for sharpe-style weights. J. Finan. Econometrics 3, 315–343 (2005)
Koenker R.: A note on L-estimator for linear models. Stat. Prob. Lett. 2, 323–325 (1984)
Koenker, R.: Quantile regression. Econometric Soc. Monographs (2005)
Koenker, R.: Quantreg: quantile regression. R package version 4.10 (2007) http://www.r-project.org.
Koenker R., Basset, G.W.: Regression quantiles. Econometrica 46, 33–50 (1978)
Koenker R., Basset, G.W.: L-estimation for linear models. J. Am. Stat. Assoc. 82, 851–857 (1987) 20
Koenker R., Ng, P.: Inequality constrained quantile regression. Sankhya Ind. J. Stat. 67, 418–440 (2005) 21
Lobosco, A., Di Bartolomeo, D.: Approximating the confidence intervals for sharpe style weights. Finan. Anal. J. 80–85 (1997)
Politis, D.N., Romano, J.P.: Large sample confidence regions based on subsamples under minimal assumptions. Ann. Stat. 22, 2031–2050 (1994)
Politis, D.N., Romano, J.P., Wolf, M.: Subsampling. Springer-Verlag, New York (1999)
R Development Core Team.: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna. http://www.R-project.org.
Sharpe, W.: Asset allocation: management styles and performance measurement. J. Portfolio Man. 7–19 (1992)
Sharpe, W.: Determining a fund’s effective asset mix. Invest. Man. Rev. 2, 59–69 (1998)
Wickham, H.: ggplot2: An implementation of the Grammar of Graphics. R package version 0.5.7, (2008) http://had.co.nz/ggplot2/.
Wood, S.N.: Generalized Additive Models: An Introduction with R. Chapman and Hall, CRC (2006)
Wuertz, D., Chalabi, Y., Miklovic, M. et al.: fGarch: Rmetrics — Autoregressive Conditional Heteroschedastic Modelling. R package version 260.72 (2007) http://www.rmetrics.org
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La Rocca, M., Vistocco, D. (2010). Robust estimation of style analysis coefficients. In: Corazza, M., Pizzi, C. (eds) Mathematical and Statistical Methods for Actuarial Sciences and Finance. Springer, Milano. https://doi.org/10.1007/978-88-470-1481-7_17
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DOI: https://doi.org/10.1007/978-88-470-1481-7_17
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