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The Profitability in the FTSE 100 Index: A New Markov Chain Approach

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Abstract

In this paper, we propose a new method to predict stock market trends based on the multivariate Markov chain (MMC) methodology. Our approach consists of forecasting the one-period ahead FTSE 100 Index behavior, using the MTD-Probit model. The MTD-Probit model is a new approach for estimating MMC, based on multiple categorical data sequences that can be used to forecast financial markets. In this context, we propose a simple trading strategy and analyze its profitability using the White “Reality Check” and the Hansen SPA data snooping bias tests. Our empirical results suggest that the MTD-Probit model applied to the FTSE 100 Index cannot significantly out-perform the buy-and-hold benchmark after data-snooping is controlled.

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Notes

  1. As suggested by Nicolau (2014), we have used the constrained maximum likelihood module in GAUSS software (Aptech Systems, Chandler, Arizona, United States) that allows switching between several algorithms (BFGS, Broyden–Fletcher–Goldfarb–Shanno, DFP, Davidon–Fletcher–Powell, Newton, BHHH, Berndt–Hall–Hall–Hausman, scaled BFGS and scaled DFP) depending on either of three methods of progress: change in function value, number of iterations or change in line search step length.

  2. The co-movements in return and volatility among markets have been commonly termed as mean and volatility spillover, respectively.

  3. For an in-depth review of the literature in the area see Singh (2015).

  4. World Federation of Exchanges, 2015.

  5. In this study, we use the adjusted closing market prices to calculate the Index log returns (see, e.g. Hsu et al. 2005).

  6. In “Appendix 1”, we provide the explanatory variables (covariates), parameter definitions and values.

  7. We could equally account equal for the overnight cash rate, calculated on the basis, for example, of the “3-month Treasury Bill Yield”.

  8. White (2000) shows in the corollary 2.4 that under a suitable regularity condition, the distribution of \(\overline{V}_{n}\) and \(\overline{V}_{n}^{*}\) are asymptotically equivalent.

  9. In “Appendix 2” we provide an explanation of the SB method. For a more detailed explanation see, e.g. Romano and Wolf (2005).

  10. White (2000) obtains the null distribution based on irrelevant models, i.e. \(\varphi _{1}=\varphi _{2}=\cdots =\varphi _{M}=0\), artificially enhancing the p values of the RC test (see, e.g. Hsu et al. 2010).

  11. Hansen’s threshold is motivated by the law of the iterated logarithm. Nonetheless, as pointed out by Hansen (2005), other threshold values can also produce valid results with different p values in finite samples, for example, Hsu et al. (2005) used \(n^{\frac{1}{4}}/4\). The log is the natural logarithm.

  12. In this paper, we use the same \(\hat{\sigma }_{m}\) in \(\tilde{V_{n}}\) and \(\tilde{V_{n}}^{*}(b)\) (see e.g. Shynkevich 2012).

  13. The t-statistics for the buy-sell mean log returns difference are computed according to Brock et al. (1992).

References

  • Abou-zaid, A. S., et al. (2011). Volatility spillover effects in emerging MENA stock markets. Review of Applied Economics, 7, 107–127.

    Google Scholar 

  • Akca, K., & Ozturk, S. S. (2016). The effect of 2008 crisis on the volatility spillovers among six major markets. International Review of Finance, 16(1), 169–178.

    Article  Google Scholar 

  • Baele, L. (2005). Volatility spillover effects in European equity markets. Journal of Financial and Quantitative Analysis, 40(02), 373–401.

    Article  Google Scholar 

  • Bajgrowicz, P., & Scaillet, O. (2012). Technical trading revisited: False discoveries, persistence tests, and transaction costs. Journal of Financial Economics, 106(3), 473–491.

    Article  Google Scholar 

  • Berchtold, A. (2001). Estimation in the mixture transition distribution model. Journal of Time Series Analysis, 22(4), 379–397.

    Article  Google Scholar 

  • Berchtold, A., & Raftery, A. E. (2002). The mixture transition distribution model for high-order Markov chains and non-Gaussian time series. Statistical Science, 17, 328–356.

    Article  Google Scholar 

  • Bessembinder, H., & Chan, K. (1995). The profitability of technical trading rules in the Asian stock markets. Pacific-Basin Finance Journal, 3(2), 257–284.

    Article  Google Scholar 

  • Brock, W., Lakonishok, J., & Lebaron, B. (1992). Simple technical trading rules and the stochastic properties of stock returns. The Journal of Finance, 47(5), 1731–1764.

    Article  Google Scholar 

  • Chan, J. S. P., Jain, R., & Xia, Y. (2008). Market segmentation, liquidity spillover, and closed-end country fund discounts. Journal of Financial Markets, 11(4), 377–399.

    Article  Google Scholar 

  • Chen, C. W., Huang, C. S., & Lai, H. W. (2011). Data snooping on technical analysis: Evidence from the Taiwan stock market. Review of Pacific Basin Financial Markets and Policies, 14(02), 195–212.

    Article  Google Scholar 

  • Chen, D. G., & Lio, Y. L. (2009). A novel estimation approach for mixture transition distribution model in high-order Markov chains. Communications in Statistics-Simulation and Computation, 38(5), 990–1003.

    Article  Google Scholar 

  • Ching, W. K., Fung, E. S., & Ng, M. K. (2002). A multivariate Markov chain model for categorical data sequences and its applications in demand predictions. IMA Journal of Management Mathematics, 13(3), 187–199.

    Article  Google Scholar 

  • Ching, W. K., Fung, E. S., & Ng, M. K. (2004). Higher-order Markov chain models for categorical data sequences*. Naval Research Logistics (NRL), 51(4), 557–574.

    Article  Google Scholar 

  • Ching, W. K., Ng, M. K., & Fung, E. S. (2008). Higher-order multivariate Markov chains and their applications. Linear Algebra and its Applications, 428(2), 492–507.

    Article  Google Scholar 

  • Christiansen, C. (2007). Volatility-spillover effects in European bond markets. European Financial Management, 13(5), 923–948.

    Article  Google Scholar 

  • Dai, Y. S., & Lee, W. M. (2011). The profitability of technical analysis in the Taiwan-US forward foreign exchange market. Economics Bulletin, 31(2), 1606–1612.

    Google Scholar 

  • Doubleday, K. J., & Esunge, J. N. (2011). Application of Markov chains to stock trends. Journal of Mathematics and Statistics, 7(2), 103.

    Article  Google Scholar 

  • Fama, E. F. (1965). The behavior of stock-market prices. The Journal of Business, 38(1), 34–105.

    Article  Google Scholar 

  • Fama, E. F. (1970). Efficient capital markets: A review of theory and empirical work. The Journal of Finance, 25(2), 383–417.

    Article  Google Scholar 

  • Fielitz, B. D., & Bhargava, T. N. (1973). The behavior of stock-price relatives–a Markovian analysis. Operations Research, 21(6), 1183–1199.

    Article  Google Scholar 

  • Forbes, K. J., & Rigobon, R. (2002). No contagion, only interdependence: Measuring stock market comovements. The Journal of Finance, 57(5), 2223–2261.

    Article  Google Scholar 

  • Hamao, Y., Masulis, R. W., & NG, V. (1990). Correlations in price changes and volatility across international stock markets. Review of Financial studies, 3(2), 281–307.

    Article  Google Scholar 

  • Hansen, P. R. (2005). A test for superior predictive ability. Journal of Business & Economic Statistics, 23, 4.

    Article  Google Scholar 

  • Hsu, P. H., & Kuan, C. M. (2005). Re-examining the profitability of technical analysis with White’s reality check and Hansen’s spa test. Available at SSRN. https://ssrn.com/abstract=685361. Retrieve 15 June 2014.

  • Hsu, P. H., Hsu, Y. C., & Kuan, C. M. (2010). Testing the predictive ability of technical analysis using a new stepwise test without data snooping bias. Journal of Empirical Finance, 17(3), 471–484.

    Article  Google Scholar 

  • Hsu, P. H., Taylor, M. P., & Wang, Z. (2016). Technical trading: Is it still beating the foreign exchange market? Journal of International Economics, 102, 188–208.

  • Kanas, A. (1998). Volatility spillovers across equity markets: European evidence. Applied Financial Economics, 8(3), 245–256.

    Article  Google Scholar 

  • Kuang, P., Schröder, M., & Wang, Q. (2014). Illusory profitability of technical analysis in emerging foreign exchange markets. International Journal of Forecasting, 30(2), 192–205.

    Article  Google Scholar 

  • Lai, T. L., & Xing, H. (2008). Statistical models and methods for financial markets. New York: Springer.

    Book  Google Scholar 

  • Lèbre, S., & Bourguignon, P. Y. (2008). An EM algorithm for estimation in the mixture transition distribution model. Journal of Statistical Computation and Simulation, 78(8), 713–729.

    Article  Google Scholar 

  • Lo, A. W., & Mackinlay, A. C. (1990). data snooping biases in tests of financial asset pricing models. Review of Financial Studies, 3(3), 431–467.

    Article  Google Scholar 

  • Mcqueen, G., & Thorley, S. (1991). Are stock returns predictable? A test using Markov chains. The Journal of Finance, 46(1), 239–263.

    Article  Google Scholar 

  • Metghalchi, M., Marcucci, J., & Chang, Y. H. (2012). Are moving average trading rules profitable? Evidence from the European stock markets. Applied Economics, 44(12), 1539–1559.

    Article  Google Scholar 

  • Mills, T. C., & Jordanov, J. V. (2003). The size effect and the random walk hypothesis: Evidence from the London Stock Exchange using Markov chains. Applied Financial Economics, 13(11), 807–815.

    Article  Google Scholar 

  • Mitra, S. K. (2011). How rewarding is technical analysis in the Indian stock market? Quantitative Finance, 11(2), 287–297.

    Article  Google Scholar 

  • Natarajan, V. K., Singh, A. R. R., & Priya, N. C. (2014). Examining mean-volatility spillovers across national stock markets. Journal of Economics Finance and Administrative Science, 19(36), 55–62.

    Article  Google Scholar 

  • Neuhierl, A., & Schlusche, B. (2011). Data snooping and market-timing rule performance. Journal of Financial Econometrics, 9(3), 550–587.

    Article  Google Scholar 

  • Nicolau, J. (2014). A New Model for Multivariate Markov Chains. Scandinavian Journal of Statistics, 41(4), 1124–1135.

    Article  Google Scholar 

  • Niederhoffer, V., & Osborne, M. F. M. (1966). Market making and reversal on the stock exchange. Journal of the American Statistical Association, 61(316), 897–916.

    Article  Google Scholar 

  • Onwukwe, C. E., & Samson, T. K. (2014). On predicting the long run behaviour of nigerian bank stocks prices: A Markov chain approach. American Journal of Applied Mathematics and Statistics, 2(4), 212–215.

    Article  Google Scholar 

  • Park, C. H., & Irwin, S. H. (2010). A reality check on technical trading rule profits in the US futures markets. Journal of Futures Markets, 30(7), 633–659.

    Google Scholar 

  • Politis, D. N., & Romano, J. P. (1994). The stationary bootstrap. Journal of the American Statistical Association, 89(428), 1303–1313.

    Article  Google Scholar 

  • Raftery, A. E. (1985). A model for high-order Markov chains. Journal of the Royal Statistical Society. Series B (Methodological), 47(3), 528–539.

    Article  Google Scholar 

  • Romano, J. P., & Wolf, M. (2005). Stepwise multiple testing as formalized data snooping. Econometrica, 73(4), 1237–1282.

    Article  Google Scholar 

  • Shynkevich, A. (2012). Performance of technical analysis in growth and small cap segments of the US equity market. Journal of Banking & Finance, 36(1), 193–208.

    Article  Google Scholar 

  • Singh, P., et al. (2015). Volatility spillover across major equity markets: A critical review of literature. International Journal of Research in Commerce & Management, 6, 4.

    Google Scholar 

  • Sullivan, R., Timmermann, A., & White, H. (1999). Data-snooping, technical trading rule performance, and the bootstrap. The Journal of Finance, 54(5), 1647–1691.

    Article  Google Scholar 

  • Svoboda, M., & Lukas, L. (2012). Application of Markov chain analysis to trend prediction of stock indices. In Proceedings of 30th international conference mathematical methods in economics. Karviná: Silesian University, School of Business Administration (pp. 848–853).

  • Vasanthi, D. R. S., Subha, D. R. M. V., Nambi, M. R. S., & Thirupparkadal, (2011). An Empirical study on stock index trend prediction using Markov chain analysis. Journal of Banking Financial Services and Insurance Research, 1, 72–91.

    Google Scholar 

  • White, H. (2000). A reality check for data snooping. Econometrica, 68(5), 1097–1126.

    Article  Google Scholar 

  • Yu, H., et al. (2013). Predictive ability and profitability of simple technical trading rules: Recent evidence from Southeast Asian stock markets. International Review of Economics & Finance, 25, 356–371.

    Article  Google Scholar 

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Correspondence to Flavio Ivo Riedlinger.

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Appendices

Appendix 1: List of Independent Variables and Parameters

In this appendix we present the list of categorized explanatory variables and parameters used in the MTD-Probit noise estimation model (Table 4):

Table 4 Explanatory variables and parameters MTD-Probit model

Appendix 2: Stationary Block Bootstrap Method

The basic idea of the stationary bootstrap method is to construct random data blocks that are independent, yet preserve the time dependence inside each block. The unknown population distribution structure is approximated by block sampling distributions based on a statistical model. As such, the stationary bootstrap methodology provides a re-sampling method which is applicable for weakly-dependent time series, where the pseudo-time series are stationary time series.

The method is based on two basic steps that provide proper consistency and weak convergence properties. Firstly, the original series is re-sampled into a set of b random length overlapping blocks of observations, determined by the realization of a geometric distribution with parameter \(q{{\in }}(0,1)\) . In this case, the average block size is the inverse of q. Secondly, the stationary bootstrap method “wraps” the data around in a “circle” to avoid the block end effects (Politis and Romano 1994, p.1304). The idea is to choose a large enough block length, preferably based on the sample size, so that observations greater than 1 / q time units apart will be nearly independent.

However, the major difficulty of this method lies in choosing the size of q. Indeed, the size of the block is a controversial topic in the literature (e.g. Sullivan et al. 1999; Hsu et al. 2005, 2010; Metghalchi et al. 2012), as a small size will not reproduce the data dependence, and a large value will reduce the statistical efficiency. In this study we adopt what is usually presented in the previous research in this area, and set \(q=0.1\).

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Riedlinger, F.I., Nicolau, J. The Profitability in the FTSE 100 Index: A New Markov Chain Approach. Asia-Pac Financ Markets 27, 61–81 (2020). https://doi.org/10.1007/s10690-019-09282-4

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