South Asian Journal of Management

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Stock Market Portfolio Construction:A Four-stage Model Based on Fractal Analysis


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1 Calcutta Business School, Diamond Harbour Road, Bishnupur 743503, 24 Paraganas (South), West Bengal, India
     

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The paper exploits fractal characteristics of time series of stock returns of Indian companies and uses them for portfolio construction. To model the dynamics of return series of the respective stocks, we use single Fractal model based on Hurst Exponent and Multi Fractal Detrended Fluctuation Analysis. For simulations, daily stock returns of fifty three Indian companies belonging to nine different industrial sectors during January, 2009 to October, 2016 have been considered. The paper considers a four stage framework for portfolio construction. The first stage is achieved by selection stocks through fractal modeling from different sectors. In the second stage, the stocks are arranged in descending order based on Hurst exponent. In third stage, pair correlation is applied for final selection of stocks in the portfolio. In the fourth stage, Evolutionary Algorithm is used for calculation of the weights of each stock in the portfolio. Our results indicate that the portfolio so chosen, outperforms the market in each year of the study.

Keywords

Evolutionary Algorithm, Fractal Analysis, Hurst Exponent, Markowitz Model, Multi Fractal Detrended Fluctuation Analysis, Portfolio.
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  • Abhyankar, A. H., Copeland, L. S., & Wong, W. (1995). Nonlinear dynamics in real-time equity market indices: evidence from the United Kingdom. Economic Journal, 105(431), 864-880.

  • Barkoulas, J., & Travlos, N. (1998). Chaos in an emerging capital market? The case of the Athens Stock Exchange. Applied Financial Economics, 8(3), 231-243.

  • Batten, J., & Ellis, C., (1996). Fractal structures and naive trading systems: Evidence from the spot US dollar/Japanese yen. Japan and the World Economy, 8(4), 411-421.

  • Cao, J., & Gu, R, (2011). Multi-fractal analysis on gold market with MF-DFA method. Gold, 9(3), 5-7.

  • Cajueiro, D. O., & Tabak, B. M. (2004). Evidence of long-range dependence in Asian equity markets: The role of liquidity and market restrictions. Physica A: Statistical Mechanics and its Applications, 342(3-4), 656–664.

  • Cajueiro D. O., & Tabak B. M. (2004). Ranking efficiency for emerging markets. Chaos, Solitons and Fractals, 22(2), 349-352.

  • Cajueiro, D. O. &Tabak, B.M. (2005). Ranking efficiency for emerging equity markets II. Chaos, Solitons and Fractals, 23(2), 671-675.

  • Choudhury, M. K., & Rajib, P. (2017). Informational Efficiency of National Stock Exchange (NSE), India: A Comparison with Seven Selected Markets. South Asian Journal of Management, 24(1), 56-80.

  • Cura, T. (2012). A particle swarm optimization approach to clustering. Expert Systems with Applications, 39(1), 1582-1588.

  • Datta Chaudhuri, T., Ghosh, I., & Eram, S. (2016). Application of Unsupervised Feature Selection, Machine Learning and Evolutionary Algorithm in Predicting Stock Returns – A Study of Indian Firms. IUP Journal of Financial Risk Management, 13(3), 20-47.

  • Deb, K. (2001). Multi-objective optimization using evolutionary algorithms (1sted.). New York, NY: John Wiley & Sons.

  • Deng, G. F., & Lin, W. T. (2010). Ant colony optimization for markowitz meanvariance portfolio model. In B. K. Panigrahi, S. Das S., P. N. Suganthan., & S. S. Dash. (Eds.) Swarm, evolutionary, and memetic computing (pp. 238-245). Lecture Notes in Computer Science, Heidelberg, Germany: Springer Berlin.

  • Fallahpour, S., Zadeh, M. H., & Lakvan, E. N. (2014). Use of Clustering Approach For Portfolio Management. International SAMANM Journal of Finance and Accounting, 2(1), 115-136.

  • Grech, D., & Pamula, G. (2008). The local Hurst exponent of the financial time series in the vicinity of crashes on the Polish stock exchange market. Physica A: Statistical Mechanics and its Applications, 387(16-17), 4299-4308.

  • Greene, M. T., & Fielitz, B. D. (1977). Long-term dependence in common stock returns. Journal of Financial Economics, 4(3), 339-349.

  • Guhathakurtha, K., Bhattacharya, B., & Roy Chowdhury, A. (2010). Using recurrence plot analysis to distinguish between endogenous and exogenous stock market crashes, Physica A: Statistical Mechanics and its Applications, 389(9), 1874-1882.

  • Guhathakurtha, K. (2015). Investigating the Nonlinear Dynamics of Emerging and Developed Stock Markets. Journal of Engineering Science and Technology Review, 8(1), 65-71.

  • Ho, D. S., Lee, C. K., Wang, C. C., & Chuang, M. (2004). Scaling characteristics in the Taiwan stock market. Physica A: Statistical Mechanics and its Applications, 332(1), 448-460.

  • Hsieh, D. A. (1989). Testing for non-linearity in daily foreign exchange rate changes. Journal of Business, 62(3), 339-368.

  • Hurst, H. E. (1951). Long-term storage capacity of reservoirs. Transactions of the American Society of Civil Engineers, 116(1), 770-808.

  • Jiang, Z. Q., & Zhou, W. X. (2008). Multifractal analysis of Chinese stock volatilities based on partition function approach. Physica A: Statistical Mechanics and its Applications, 387(19-20), 4881-4888.

  • Jiang, K., Li, D., Gao J., & Yu, J. X. (2014, August). Factor model based clustering approach for cardinality constrained portfolio selection. Proceedings of the 19th World Congress of the International Federation of Automatic Control Cape Town, South Africa, 47(3), 10713-10718.

  • Kazemi, M. A. A., Roodposthi, F. R., & Kheyrkhyah, A. (2014). Clustering Tehran Stocks Exchange for Portfolio Management. International Journal of Basic Sciences & Applied Research, 3(Sp.), 168-175.

  • Kim, K., & Yoon, S. (2004). Multifractal features of financial markets. Physica A: Statistical Mechanics and its Applications, 344(1-2), 272-278.

  • Kumar, D., & Maheswaran, S. (2013). Evidence of long memory in the Indian stock market. Asia-Pacific Journal of Management Research and Innovation, 9(1), 9-21.

  • Lemieux, V., Rahmdel, P. S., Walker, R., Wong, B. L. W., & Flood, M. (2014). Clustering techniques and their effect on portfolio formation and risk analysis. Proceedings of the International Workshop on Data Science for Macro-Modeling (pp. 1-6).

  • Li, E., Mu, X., Zhao, G., & Gao, P. (2015). Multifractal Detrended Fluctuation Analysis of Streamflow in the Yellow River Basin, China. Water, 7(4), 1670-1686.

  • Mandelbrot, B., & Wallis, J. (1968). Noah, Joseph and operational hydrology. Water Resources Research, 4(5), 909-918.

  • Mandelbrot, B. (1972). Statistical methodology for non-periodic cycles from the co-variances of R/S Analysis. Annals of Economics and Social Measurement, 1(3), 189-196.

  • Mandelbrot, B., & Taqqu, M. (1979). Robust R/S analysis of long run serial correlation. Bulletin of the International Statistical Institute, 48(2), 59-104.

  • Markovitz, H. (1952). Portfolio selection. Journal of Finance, 7(1), 77-99.

  • Mulligan, R. F. (2004). Fractal analysis of highly volatile markets: an application to technology equities. The Quarterly Review of Economics and Finance, 44(1), 155-179.

  • Mukhopadhyay, S., & Chaudhuri, T. D. (2018). Different length genetic algorithm-based clustering of indian stocks for portfolio optimization. In J. Mandal, P. Dutta, and S. Mukhopadhyay (Eds.) Advances in Intelligent Computing (pp. 45-59). Studies in Computational Intelligence. Singapore: Springer: doi: 10.1007/978-981-10-8974-9_3

  • Nanda, S. R., Mahanty, B., & Tiwary, M. K. (2010). Clustering Indian stock market data for portfolio management. Expert Systems with Applications, 37(12), 8793-8798.

  • Oh, K. J., Kim, T. Y. & Min, S. (2005). Using genetic algorithm to support portfolio optimization for index fund management. Expert Systems with Applications, 28(2), 371-379.

  • Onali, E., & Goddard, J. (2011). Are European equity markets efficient? New evidence from fractal analysis. International Review of Financial Analysis, 20(2), 59-67.

  • Opong, K. K., Mulholland, G., Fox, A. F., & Farahmand, K. (1999). The behavior of some UK equity indices: an application of Hurst and BDS tests. Journal of Empirical Finance, 6(3), 267-282.

  • Peters, E. E. (1991). Chaos and order in the capital markets: A new view of cycle, prices and market volatility. New York, NY: John Wiley & Sons.

  • Portes, A., & Sensenbrenner, J. (1993). Embeddedness and immigration: Notes on the social determinants of economic action. American Journal of Sociology, 98(6), 1320-1350.

  • Priyadarshini, E., & Chandra Babu, A. (2012). Fractal analysis of Indian financial markets: An empirical approach. Asia-Pacific Journal of Management Research and Innovation, 8(3), 271-281.

  • Sen, J., & Datta, Chaudhuri, T. (2015). A framework for predictive analysis of stock market analysis of stock market indices – A study of the Indian auto sector. CBS Journal of Management Practices, 2(2), 1-20.

  • Sen, J., & Datta, Chaudhuri, T. (2016a). An Investigation of the Structural Characteristics of the Indian IT Sector and the Capital Goods Sector – An Application of the R Programming in Time Series Decomposition and Forecasting. Journal of Insurance and Financial Management, 1 (4), 68-130.

  • Sen, J., & Datta Chaudhuri, T. (2016b). An alternative framework for time series decomposition and forecasting and its relevance for portfolio choice – A comparative study of the Indian consumer durable and small cap sectors. Journal of Economics Library, 3(2), 303-326.

  • Sen, J., & Datta, Chaudhuri, T. (2018). Understanding the sectors of Indian economy for portfolio choice. International Journal of Business Forecasting and Marketing Intelligence, 4(2), 178-222.

  • Sun, X., Chen, H. P., Yuan, Y. Z., & Wu, Z. Q. (2001). Predictability of multifractal analysis of Hang Seng stock index in Hong Kong. Physica A: Statistical Mechanics and its Applications, 301(1-4), 473-482.

  • Tola, V., Lillo, F., Gallegati, M., & Mantegna, R. N. (2008). Cluster analysis for portfolio optimization. Journal of Economic Dynamics and Control, 32(1), 235-258.

  • Tripathi, V., & Seth, R. (2016). Market Efficiency, Inter-linkages and Volatility Transmission in Stock Markets of Selected SAARC Countries. South Asian Journal of Management, 23(4), 149-174.

  • Wang, J., & Ma, J. (2011). Gold markets price analysis and application studies based on complexity theories. Complex Systems and Complexity Science, 5(3), 54-59.

  • Wanous, J. P., Reichers, A. E., &Hudy, M. J. (1997). Overall job satisfaction: how good are single-item measures?. Journal of applied Psychology, 82(2), 247.

  • Yin, K., Zhang, H., Zhang, W., & Wei, Q. (2013). Fractal analysis of gold market in China. Romanian Journal of Economic Forecasting, 16(3), 144-163.

  • Zhang, J., & Maringer, D. (2010). A Clustering Application in Portfolio Management. Lecture Notes in Electrical Engineering, 60, 309-321.

  • Zhow, W. X. (2008). Multifractal detrended cross-correlation analysis for two nonstationary signals. Physical Review E, 77(6), 066211(1-4).


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  • Stock Market Portfolio Construction:A Four-stage Model Based on Fractal Analysis

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Authors

Indranil Ghosh
Calcutta Business School, Diamond Harbour Road, Bishnupur 743503, 24 Paraganas (South), West Bengal, India
Tamal Datta Chaudhuri
Calcutta Business School, Diamond Harbour Road, Bishnupur 743503, 24 Paraganas (South), West Bengal, India

Abstract


The paper exploits fractal characteristics of time series of stock returns of Indian companies and uses them for portfolio construction. To model the dynamics of return series of the respective stocks, we use single Fractal model based on Hurst Exponent and Multi Fractal Detrended Fluctuation Analysis. For simulations, daily stock returns of fifty three Indian companies belonging to nine different industrial sectors during January, 2009 to October, 2016 have been considered. The paper considers a four stage framework for portfolio construction. The first stage is achieved by selection stocks through fractal modeling from different sectors. In the second stage, the stocks are arranged in descending order based on Hurst exponent. In third stage, pair correlation is applied for final selection of stocks in the portfolio. In the fourth stage, Evolutionary Algorithm is used for calculation of the weights of each stock in the portfolio. Our results indicate that the portfolio so chosen, outperforms the market in each year of the study.

Keywords


Evolutionary Algorithm, Fractal Analysis, Hurst Exponent, Markowitz Model, Multi Fractal Detrended Fluctuation Analysis, Portfolio.

References