Relevance of Hurst's pattern in equity portfolio management

Authors

DOI:

https://doi.org/10.46661/revmetodoscuanteconempresa.4122

Keywords:

persistence, long term dependency, rescaled rank, portfolio optimization, Hurst estimation

Abstract

In this article, the behavior of the returns of some assets of MILA is analyzed, with the objective of looking for evidence of persistence and evaluating the impact of their presence in the decision making of investment portfolios. The methodology of the rescaled range is used in the estimation of the Hurst coefficient as a measure of persistence and the results are verified with the adjustment of Anis and Lloyd and the estimation of Higuchi. An inferential process is added to the Hurst coefficient for each of the assets analyzed. The performance of portfolio optimization including estimates of persistence and the results of its inference were compared with independently optimized portfolios. A better risk-return relationship is observed by including the pattern of persistence, only when the inference is supported by evidence.

Downloads

Download data is not yet available.

References

Acuña, C., & Álvarez, A. (2017). Dependencia serial de largo plazo en el índice bursátil chileno, a través del coeficiente de Hurst y Hurst ajustado. Journal of Economics, Finance and Administrative Science, 22(42), 37-50.

Anis, A.A., & Lloyd, E.H. (1976). The expected value of the adjusted rescaled Hurst range of independent normal summands. Biometrika, 63(1), 111-116.

Auer, B.R., & Hoffmann, A. (2016). Do carry trade returns show signs of long memory? The Quarterly Review of Economics and Finance, 61, 201-208. https://doi.org/10.1016/j.qref.2016.02.007

Benth, F. (2003). On arbitrage-free pricing of weather derivatives based on fractional brownian motion. Applied Mathematical Finance, 10(4), 303-324.

Biagini, F., Campanino, M., & Fuschini, S. (2008). Discrete approximation of stochastic integrals with respect to fractional Brownian motion of Hurst index H>1/2. Stochastics An International Journal of Probability and Stochastic Processes, 80(5), 407-426.

Caberra, A.I., López, S.S., & López, F. (2012). Dependencia de largo plazo en los rendimientos de acciones mexicanas selectas. Panorama Económico, 7(14), 59-78.

Cajueiro, D.O., & Tabak, B.M. (2007). Long-range dependence and multifractality in the term structure of LIBOR interest rates. Physica A: Statistical Mechanics and Its Applications, 373, 603-614. https://doi.org/10.1016/j.physa.2006.04.110

Cajueiro, D.O., & Tabak, B.M. (2008). Testing for long-range dependence in world stock markets. Chaos, Solitons & Fractals, 37(3), 918-927. https://doi.org/10.1016/j.chaos.2006.09.090

Cheridito, P. (2001). Mixed fractional Brownian motion. Bernoulli, 7(6), 913-934. https://projecteuclid.org/download/pdf_1/euclid.bj/1078951129

Domínguez, A. (2016). Análisis multifractal de correlaciones en series temporales de sistemas económicos. Memoria del Trabajo de Fin de Máster, Universitat de Les Illes Balears, Palma de Mallorca.

Duarte, J., Sierra, K., & Mascareñas, J.M. (2014). Evaluación de la Memoria de Largo Plazo del Mercado Bursátil Colombiano mediante el Coeficiente de Hurst (Evaluation of Long-Term Memory in Colombian Stock Market by Hurst Coefficient). Revista Internacional Administración & Finanzas, 7(4), 1-10.

Greene, M., & Fielitz, B. (1980). Long-term dependence and least squares regression in investment analysis. Management Science, 26(10), 1031-1038.

Grimm, C., & Schluechtermann, G. (2008). IP-traffic theory and performance. Heidelberg: Springer.

Guasoni, P., Nika, Z., & Rásonyi, M. (2019). Trading Fractional Brownian Motion. SIAM Journal on Financial Mathematics, 10(3), 769-789. https://doi.org/10.1137/17m113592x

Hu, Y., & Øksendal, B. (2003). Fractional white noise calculus and applications to finance. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 6(1), 1-32.

Kristoufek, L., & Vosvrda, M. (2013). Measuring capital market efficiency: Global and local correlations structure. Physica A: Statistical Mechanics and Its Applications, 392(1), 184-193. https://doi.org/10.1016/j.physa.2012.08.003

Leiton, K. (2011). Validez del supuesto de neutralidad del horizonte de tiempo en el CAPM y la metodología del rango reescalado: aplicación a Colombia. Borradores de Economía, 672, 1-42. https://doi.org/10.32468/be.672

León, C., & Reveiz, A. (2011). Portfolio Optimization and Long-Term Dependence. Banco de la Republica Working Paper, 602, 1-26. http://dx.doi.org/10.2139/ssrn.1686115

León, C., & Vivas, F. (2010). Dependencia de largo plazo y la regla de la raiz del tiempo para escalar la volatilidad en el mercado colombiano. Borradores de Economía, 603, 1-47. https://doi.org/10.32468/be.603

Lo, A. (1991). Long-term Memory in Stock Market Prices. Econometrica, 59 (5), 1279-1313.

López, F., Villagómez, J., & Venegas, F. (2011). Evidencias de memoria larga en el Índice de Precios y. En M. d. Martínez, C. Zubieta, & F. López, Administración del Riesgo (2 ed.). México: Azcapotzalco.

Luna, S., & Agudelo. D. (2019). ¿Agrega Valor el Modelo Black-Litterman en Portafolios del Mercado Integrado Latinoamericano (MILA)? Evaluación Empírica 2008-2016. Revista de Métodos Cuantitativos para la Economía y la Empresa, 27, 55-73.

Mandelbrot, B. (1972). Statistical methodology for nonperiodic cycles: from the covariance to r/s analysis. Annals of Economic and Social Measurement, 1(3), 259-290.

Mandelbrot, B., & Hudson, R. (2005). Fraktale und Finanzen: Märkte zwischen Risiko, Rendite und Ruin. München und Zürich: Piper.

Mandelbrot, B., & Vann Ness, J. (1968). Fractional Brownian Motions, Fractional Noises and Applications. SIAM Review, 10(4), 422-437.

Mandelbrot, B., & Wallis, J. (1969). Computer Experiments with Fractional Noises. Water Resources Research, 5, 228-267.

Montarani, A., Taqqu, M & Teverovsky, V. (1999). Estimating long-range dependence in the presence of periodicity: an empirical study. Mathematical Computer Modelling, 29(10-12), 2217-2228.

Nieto, H.D., Álvarez, J.E., & Rodríguez, E.L. (2016). Análisis de persistencia en acciones financieras en el mercado colombiano a través de la metodología de Rango Reescalado (R/S). Cuadernos Latinoamericanos de Administración, 12(22), 23-32.

Nualart, D. (2003). Stochastic integration with respect to fractional brownian motion and applications. Contemporary Mathematics, 3-40. https://www.researchgate.net/profile/David_Nualart2/publication/242388658_Stochastic_integration_with_respect_to_the_fractional_Brownian_motion/links/542588c40cf238c6ea7414f0/Stochastic-integration-with-respect-to-the-fractional-Brownian-motion.pdf

Pfaff, B. (2008). Analysis of integrated and cointegrated time series with R. New York: Springer Science & Business Media.

Quiroga, C., & Villalobos, A. (2016). Aplicación de dos técnicas del análisis multivariado en el mercado de valores mexicano. Revista de Métodos Cuantitativos para la Economía y la Empresa, 22, 104-119.

Samaniego, Á., & Rodríguez, L. (2018). Passive Portfolio Management by Indexing: A Performance Analysis of High, Medium and Low Capitalization Indices in Mexico. Revista de métodos cuantitativos para la economía y la empresa, 26, 269-293.

Sánchez, M.A., Trinidad, J.E., & García, J. (2008). Some comments on Hurst exponent and the long memory processes on capital markets. Physica A: Statistical Mechanics and Its Applications, 387(22), 5543-5551. https://doi.org/10.1016/j.physa.2008.05.053

Sensoy, A. (2013). Time-varying long range dependence in market returns of FEAS members. Chaos, Solitons & Fractals, 53, 39-45. https://doi.org/10.1016/j.chaos.2013.05.004

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

Srbek, P. (2018). Estimation of the Hurst Exponent in Time Series of Daily Returns of Stock Indices. Politicka Ekonomie, 66(4), 508-524.

Teverovsky, V., Taqqu, M.S., & Willinger, W. (1999). A critical look at Lo's modified R/S statistic. Journal of statistical Planning and Inference, 80(1-2), 211-227.

Urquhart, A. (2016). How predictable are precious metal returns? The European Journal of Finance, 23(14), 1390-1413. https://doi.org/10.1080/1351847x.2016.1204334

Weron, R. (2002) Estimating long-range dependence: finite sample properties and confidence intervals. Physica A, 312, 285-299.

Willinger, W., Taqqu, M., & Teverovsky, V. (1999). Stock market prices and long-range dependence. Finance and Stochastics, 3(1), 1-13.

Published

2021-12-01

How to Cite

Martinez Patiño, M. A., Ariza Garzón, M. J., & Cadena Lozano, J. B. (2021). Relevance of Hurst’s pattern in equity portfolio management. Journal of Quantitative Methods for Economics and Business Administration, 32, 66–82. https://doi.org/10.46661/revmetodoscuanteconempresa.4122

Issue

Section

Articles