38269

Paulo Ferreira Naibert
João Frois Caldeira

Revista Brasileira de Finanças

In this paper we study the problem of minimum variance portfolio selection based on a recent methodology for portfolio optimization restricting the allocation vector proposed by Fan et al. (2012). To achieve this, we consider different conditional and unconditional covariance matrix estimators. The main contribuition of this paper is one of empirical nature for the brazilian stock market. We evaluate out of sample performance indexes of the portfolios constructed for a set of 61 different stocks traded in the São Paulo stock exchange (BM&FBovespa). The results show that the restrictions on the norms of the allocation vector generate substantial gains in relation to the no short-sale portfolio, increasing the average risk-adjusted return (larger Sharpe Ratio) and lowering the portfolio turnover

mean-variance, norm constrained allocation vector, Performance Assessment, portfolio optimization

NAIBERT, P. F.; CALDEIRA, J. F. Seleção de carteiras ótimas sob restrições nas normas dos vetores de alocação: uma avaliação empírica com dados da BM&FBovespa. Revista Brasileira de Finanças, v. 13, n. 3, p. 504-543, 2015.

Naibert, P. F., & Caldeira, J. F. (2015). Seleção de carteiras ótimas sob restrições nas normas dos vetores de alocação: uma avaliação empírica com dados da BM&FBovespa. Revista Brasileira de Finanças, 13(3), 504-543.

https://www.spell.org.br/documentos/ver/38269/selection-of-optimal-portfolios-under-norm-constraints-in-the-allocation-vectors--an-empirical-evaluation-with-data-from-bm-f-bovespa/i/en

Artigo

Português

Ang, Andrew, Hodrick, Robert J.; Xing, Yuhang; Zhang, Xiaoyan. (2006). The Cross-Section of Volatility and Expected Returns. The Journal of Finance, 61(1), 259-299.

Baker, Malcolm, Bradley, Brendan; Wurgler, Jeffrey. (2011). Benchmarks as Limits to Arbitrage: Understanding the Low-Volatility Anomaly. Financial Analysts Journal, 67(1), 40-54.

Best, Michael J.; Grauer, Robert R. (1990). The efficient set mathematics when mean-variance problems are subject to general linear constraints. Journal of Economics and Business, 42(2), 105-120.

Best, Michael J; Grauer, Robert R. (1991). On the Sensitivity of Mean Variance-Efficient Portfolios to Changes in Asset Means: Some Analytical and Computational Results. Review of Financial Studies, 4(2), 315-42.

Best, Michael J.; Grauer, Robert R. (1991). Sensitivity Analysis for Mean-Variance Portfolio Problems. Management Science, 37(8), 980-989.

Black, Fischer; Litterman, Robert. 1992. Global Portfolio Optimization. Financial Analysts Journal, 48(5), 28-43.

Blitz, David C; van Vliet, Pim. (2007). The Volatility Effect. Journal of Portfolio Management, 34(1), 102-113.

Blitz, David, Falkenstein, Eric; Vliet, Pim van. 2014. Explanations for the Volatility Effect: An Overview Based on the CAPM Assumptions. The Journal of Portfolio Management, 40(3), 61-76.

Broadie, Mark. 1993. Computing efficient frontiers using estimated parameters. Annals of Operations Research, 45(1), 21-58.

Brodie, Joshua, Daubechies, Ingrid, De Mol, Christine, Giannone, Domenico; Loris, Ignace. (2009). Sparse and stable Markowitz portfolios. Proceedings of the National Academy of Sciences, 106(30), 12267-12272.

Caldeira, João, Moura, Guilherme; Santos, André. (2013). Seleção de carteiras utilizando o modelo Fama-French-Carhart. Revista Brasileira de Economia, 67(1), 45-65.

Ceria, S.; Stubbs, R.A. 2006. Incorporating estimation errors into portfolio selection: Robust portfolio construction. Journal of Asset Management, 7(2), 109-127.

Chan, L.K.C.; Karceski, J.; Lakonishok, J. (1999). On portfolio optimization: forecasting covariances and choosing the risk model. Review of Financial Studies, 12(5), 937-974.

Chopra, Vijay K.; Ziemba, William T. (1993). The Effect of Errors in Means, Variances, and Covariances on Optimal Portfolio Choice. Journal of Portfolio Management, 19(2), 6-11.

DeMiguel, Victor, Garlappi, Lorenzo, Nogales, Francisco J.; Uppal, Raman. (2009). A Generalized Approach to Portfolio Optimization: Improving Performance by Constraining Portfolio Norms. Management Science, 55(5), 798-812.

DeMiguel, Victor, Garlappi, Lorenzo; Uppal, Raman. (2009). Optimal Versus Naive Diversification: How Inefficient is the 1-N Portfolio Strategy? Review of Financial Studies, 22(5), 1915-1953.

DeMiguel, Victor; Nogales, Francisco J. (2009). Portfolio Selection with Robust Estimation. Operations Research, 57(3), 560-577.

De Pooter, Michiel, Martens, Martin; van Dijk, Dick. (2008). Predicting the Daily Covariance Matrix for S&P 100 Stocks Using Intraday Data- But Which Frequency to Use? Econometric Reviews, 27(1-3), 199-229.

Engle, Robert; Sheppard, Kevin. Evaluating the specification of covariance models for large portfolios. Working Paper. New York University, working paper. 2008.

Fan, Jianqing, Fan, Yingying; Lv, Jinchi. High dimensional covariance matrix estimation using a factor model. Journal of Econometrics, 147(1), 186-197. 2008.

Fan, Jianqing, Zhang, Jingjin; Yu, Ke. Vast Portfolio Selection With Gross-Exposure Constraints. Journal of the American Statistical Association, 107(498), 592-606. 2012.

Fleming, Jeff, Kirby, Chris; Ostdiek, Barbara. The Economic Value of Volatility Timing. Journal of Finance, 56(1), 329-352. (2001).

Fleming, Jeff, Kirby, Chris; Ostdiek, Barbara. The economic value of volatility timing using "realized" volatility. Journal of Financial Economics, 67(3), 473-509. 2003.

Francq, Christian, Horvath, Lajos; Zakoïan, Jean-Michel. Merits and drawbacks of variance targeting in GARCH models. Journal of Financial Econometrics, 9(4), 619-656. 2011.

Garlappi, Lorenzo, Uppal, Raman; Wang, Tan. Portfolio Selection with Parameter and Model Uncertainty: A Multi-Prior Approach. Review of Financial Studies, 20(1), 41-81. 2007.

Gastineau, Gary L. The Short Side of 130/30 Investing. The Journal of Portfolio Management, 34(2), 39-52. 2008.

Goldfarb, D.; Iyengar, G. Robust portfolio selection problems. Math. Oper. Res.; 28(1), 1-38. 2003.

Grant, Michael, & Boyd, Stephen. 2014 (Mar.). CVX: Matlab Software for DisciplinedConvexProgramming,version2.1. http://cvxr.com/cvx.

Green, Richard C; Hollifield, Burton. When Will Mean-Variance Efficient Portfolios Be Well Diversified? Journal of Finance, 47(5), 1785-809.

Jacobs, Bruce I; Levy, Kenneth N. Enhanced Active Equity Strategies. The Journal of Portfolio Management, 32(3), 45-55. 2006. 1992.

Jagannathan, Ravi; Ma, Tongshu. Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps. Journal of Finance, 58(4), 1651-1684. 2003.

Klein, Roger W.; Bawa, Vijay S. The effect of estimation risk on optimal portfolio choice. Journal of Financial Economics, 3(3), 215-231. 1976.

Klein, Roger W.; Bawa, Vijay S. The effect of limited information and estimation risk on optimal portfolio diversification. Journal of Financial Economics, 5(1), 89- 111. 1977.

Kolm, Petter N.; Tütüncü, Reha; Fabozzi, Frank J. 60 Years of portfolio optimization: Practical challenges and current trends. European Journal of Operational Research, 234(2), 356- 371. 2014.

Kritzman, Mark. Invited Editorial Comment. The Journal of Portfolio Management, 37(2), 3-5. 2011.

Ledoit, Oliver; Wolf, Michael. Robust performance hypothesis testing with the Sharpe ratio. Journal of Empirical Finance, 15(5), 850-859. 2008.

Ledoit, Olivier; Wolf, Michael. A well-conditioned estimator for large-dimensional covariance matrices. Journal of Multivariate Analysis, 88(2), 365-411. 2004.

Ledoit, Olivier; Wolf, Michael. Honey, I Shrunk the Sample Covariance Matrix. The Journal of Portfolio Management, 30(4), 110-119. 2004

Ledoit, Olivier; Wolf, Michael. Improved estimation of the covariance matrix of stock returns with an application to portfolio selection. Journal of Empirical Finance, 10(5), 603-621. 2003.

Liu, Qianqiu. On portfolio optimization: How and when do we benefit from high-frequency data? Journal of Applied Econometrics, 24(4), 560-582. 2009.

Lo, Andrew W.; Patel, Pankaj. N. 130/30: The New Long-Only. The Journal of Portfolio Management, 34(2), 12-38. 2008.

Markowitz, Harry. Portfolio Selection. Journal of Finance, 7(1), 77-91. 1952.

Markowitz, H. M. Portfolio Selection: Efficient Diversification of Investments. Cowles Commission for Research in Economics: Monographs. Yale University Press. 1959.

Mendes, B. V.; Leal, R. P. C. Robust multivariate modeling in finance. International Journal of Managerial Finance, 1(2), 95-106. 2005.

Merton, Robert C. On estimating the expected return on the market: An exploratory investigation. Journal of Financial Economics, 8(4), 323-361. 1980.

Michaud, Richard O. The Markowitz Optimization Enigma: Is ’Optimized’ Optimal? Financial Analysts Journal, 45(1), 31-42. 1989.

Neto, César Thomé, Leal; Ricardo Pereira Câmara, Almeida; Vinício de Souza, E. Um índice de mínima variância de ações brasileiras. Economia Aplicada, 15, 535-557. 2011.

Pesaran, M. H.; Zaffaroni, P. Optimal Asset Allocation with Factor Models for Large Portfolios. Cambridge Working Papers in Economics 0813. Faculty of Economics, University of Cambridge. 2008 (Mar.).

Politis, Dimitris N.; Romano, Joseph P. 1994. The Stationary Bootstrap. Journal of the American Statistical Association, 89(428), 1303-1313.

Rubesam, Alexandre; Beltrame, André Lomonaco. Carteiras de Variância Mínima no Brasil. Revista Brasileira de Finanças, 11(1), 81-118. 2013.

Santos, André Alves Portela; Tessari, Cristina. Técnicas Quantittativas de Otimização de Carteiras Aplicadas ao Mercado de Ações Brasileiro. Revista Brasileira de Finanças, 10(3), 369-394. 2012.

Sharpe, William F. A Simplified Model for Portfolio Analysis. Management Science, 9(2), 277-293. 1963.

Stein, Charles. Inadmissibility of the Usual Estimator for the Mean of a Multivariate Normal Distribution. Tech. Rept.: Berkeley, CA. 1956.

Thornton, Daniel L.; Valente, Giorgio. Out-of-Sample Predictions of Bond Excess Returns and Forward Rates: An Asset Allocation Perspective. Review of Financial Studies, 25(10), 3141-3168. 2012.

Tsay, Ruey S. Analysis of Financial Time Series. 3 ed. Cambridge, Mass: Wiley. 2010.