Non-linear Dynamics and Recurrent Patterns in Stock Markets: A Comparison Between BIST-100 and S&P500 Indices

Öz

The financial systems, and particularly stock markets are complex systems. In this study, we investigate the evidence of chaotic dynamics of both BIST-100 stock market index and S&P 500 index. We compute Lyapunov exponents of stock market indices daily return series over the period from 27 May 2018 to 26 May 2022. The time interval under examination is chosen to reflect the effects of Covid-19 pandemic crisis on global financial markets, where extraordinary economic and financial policies have been implemented.The results of the study demonstrate that both BIST-100 and S&P500 indices exhibit chaotic behavior and associated maximal Lyapunov exponents are calculated to be positive, respectively. Both BIST-100 and S&P500 indices have equilibria around positive return values, reflecting the extraordinary effects of expansionary monetary and fiscal policies. Moreover, the magnitude of equilibria positive returns in S&P500 index is greater than that of BIST-100 index, which implies that cumulative effect of expansionary monetary and fiscal policy in U.S. economy overwhelms. The findings of the study suggest that greater positive return availability in S&P500 lowers the demand for emerging market assets and hence the capital inflow in BIST-100 stock market. The chaotic behavior eventually leads to an increase in complexity and recurrently causes volatility in stock markets. Therefore, in perspective of policy making inflation targeting should be considered as a main financial stability strategy to increase demand for Turkish assets and to enable capital inflows. Given upcoming monetary policy of global Central banks, our findings have important implications for policy making as well as portfolio and risk management.

Anahtar Kelimeler

• Covid-19
• Chaos
• Lyapunov exponent
• Market efficiency
• BIST-100
• S&P 500

Hisse Senedi Piyasalarında Lineer-olmayan Dinamikler ve Düzensiz Örüntüler:BIST- 100 ve S&P500 Endeksleri Karşılaştırması

Öz

Finansal sistemler, özellikle de hisse senedi piyasaları karmaşık sistemlerdir. Bu çalışmamızda BIST-100 endeksi ve S&P500 endeksinde kaotik dinamikleri araştıracağız. 27 Mayıs 2018 ile 26 Mayıs 2022 tarihlerini kapsayan dönemde ABD Doları bazındaki günlük getiri oranları zaman serisi verisinde Lyapunov katsayılarını hesaplayacağız. İncelemeye konu olan zaman aralığı, Covid-19 pandemisi krizinin küresel finansal piyasalar üzerindeki etkilerini ve bu etkilerin uygulanan sıradışı para ve mali politkaların yansımalarını da içermektedir. Çalışmamızın sonuçlarına göre ilgili dönemde BIST-100 ve S&P 500 endeksleri kaotik davranış sergilemektedir ve eşlik eden en büyük Lyapunov katsayısı pozitif olarak hesaplanmaktadır. BIST-100 ve S&P500 endeksleri poizitif getiri değerleri etrafında denge kümesi oluşturmaktadırlar, bu durum da genişlemeci para ve maliye politikalarının etkilerini yansıtmaktadır. Ayrıca, S&P500 endeksinin pozitif getirisi BIST-100 endeksi pozitif getiri denge kümelenmesinden daha büyük değer almaktadır. ABD’de genişlemeci parasal ve mali önlemlerin birikimli miktar etkisinin çok daha büyük olması bu durumun önemli bir nedeni olarak değerlendirilebilir. S&P500 endeksinin daha fazla pozitif getiri sağlamış olması, gelişmekte olan piyasalara olan küresel yatırımcı ilgisini düşürürken, BIST-100 piyasasına olan yabancı sermaye akımını da zayıflatmaktadır. Endekslerdeki kaotik dinamikler er ya da geç piyasadaki karmaşıklık düzeyini artırırken hisse senedi piyasalarında sığ koşulda düzensiz volatilite döngülerine neden olacaktır. Bu yüzden, politika yapıcılar enflasyon hedeflemesi temelinde finansal stabiliteyi önceleyen stratejiler üretmek durumundalar. Türk ekonomis özelinde bu strateji hayata geçirilebilirse Türkiye finansal piyasalarındaki varlıklara talebin artması ve küresel sermaye akımlarının yoğunlaşması ihtimali yükselecektir. Küresel Merkez bankalarının para politikalarında sıkılaşmaya gittikleri veri kabul edilirse, bulgularımız para ve maliye politikaları ile portföy ve risk yönetimi açısından katkı sunmaktadır.

Anahtar Kelimeler

• Covid-19
• Kaos
• Lyapunov katsayısı
• Piyasa verimi
• BIST-100
• S&P500

Kaynakça

1. Abarbanel, H.D.I. (1995), Analysis of observed chaotic data. Springer.
2. Abhyankar A., Copeland, L.S., & Wong, W. (1997). Uncovering nonlinear structure in real time stock market indexes: The S&P 500, the DAX, the Nikkei 225, and the FTSE-100. Journal of Business & Economic Statistics, 15(1), 1-14
3. Atsalakis, G.S., and Valavanis, K.P. (2009). Surveying stock market forecasting techniques - Part II: Soft computing methods. Expert Systems with Applications. 36(3), 5932-5941.
4. Badshah, I.U., Frijns, B. and Tourani-Rad, A. (2013), Contemporaneous Spill-Over Among Equity, Gold, and Exchange Rate Implied Volatility Indices. Journal of Future Markets, 33, 555-572. https://doi.org/10.1002/fut.21600
5. Borges, M.R. (2010) Efficient market hypothesis in European stock markets, The European Journal of Finance, 16:7, 711-726, DOI: 10.1080/1351847X.2010.495477
6. Brock, W.A., Lakonishok, J., & LeBaron, B. (1992). Simple technical trading rules and the stochastic properties of stock returns. Journal of Finance, 47, 1731–1764.
7. Casdagli, M. (1989). Nonlinear Prediction of Chaotic Time Series. Physica D, 335–356.
8. Chan, K.F., & Gray, P. (2018).Volatility jumps and macroeconomic news announcements. Journal of Futures Markets. 38: 881– 897. https://doi.org/10.1002/fut.21922

9. Chopra, N., Lakonishok, J., & Ritter, J.R. (1992). Performance measurement methodology and the question of whether stocks overreact. Journal of Financial Economics, 31, 235–268.
10. Chu, H.H., Chen, T.L., Cheng, C.H., & Huang, C.C. (2009). Fuzzy dual-factor time-series for stock index forecasting. Expert Systems with Applications, 36(1),165-171.
11. Conrad, J., & Kaul, G. (1988). Time-variation in expected returns. Journal of Business, 61, 409–425.
12. Cutler, D.M., Poterba, J.M., & Summers, L.H. (1991). Speculative dynamics. Review of Economic Studies, 58, 529–546.
13. Cybenko, G., (1989). Approximation by superposition of a sigmoidal function. Mathematics of Control, Signals and Systems, 2, 303–314.
14. Dawson, P., & Staikouras, S.K. (2009). The impact of volatility derivatives on S&P500 volatility. Journal of Future Markets. 29: 1190-1213. https://doi.org/10.1002/fut.20424
15. De Bondt, W.F.M., & Thaler, R.H. (1985). Does the stock market over react. Journal of Finance, 40, 793–805.
16. Edgar, E. P. (1991). A Chaotic Attractor for the S&P 500. Financial Analysts Journal, 47(2), 55-62.
17. Ehrmann, M., Fratscher, M., & Rigobon, R. (2011). Stocks, bonds, money markets and exchange rates: Measuring international financial transmission. Journal of Applied Econometrics, 26, 948–974.
18. Fama, E.F., & French, K.R. (1986). Permanent and temporary components of stock prices. Journal of Political Economy, 98, 246–274.
19. Farmer, J. D., & Sidorowich, J. (1987). Predicting Chaotic Time Series. Physical Review Letters, 59, 845–848.
20. Farmer, J. D., & Sidorowich, J. (1988). “Predicting Chaotic Dynamics,” in Dynamic Patterns in Complex Systems. Kelso, J. A. S., Mandell, A. J., and Schlesinger, M. F., (eds.). Singapore: World Scientific.
21. Fernández-Rodríguez, F., Sosvilla-Rivero, S., & García-Artiles, M.D. (1999). Dancing with bulls and bears: Nearest-neighbour forecasts for the Nikkei index. Japan and the World Economy, 11(3), 395-413
22. French, K.R., & Roll, R. (1986). Stock return variances: The arrival of information and the reaction of traders. Journal of Financial Economics, 17, 5–26.
23. Gencay R., & Dechert, W.D. (1992). Algorithm for the n Lyapunov exponents of an n-dimensional unknown dynamical system. Physica D, 59,142-157.
24. Gencay, R. (1998). The predictability of security returns with simple technical trading rules. Journal of Empirical Finance. 5, 347–359
25. Hagtvedt, R. (2009). Stock return dynamics and the CAPM anomalies. Applied Economics Letters, 16(16),1593-1596.
26. Hasanov,M., & Omay, T. (2008). Nonlinearities in emerging stock markets: evidence from Europe’s two largest emerging markets. Applied Economics 40:20, 2645-2658.
27. Hegger, R., Kantz, H., & Schreiber, T. (1999). Practical implementation of nonlinear time series methods: The TISEAN package, Chaos, 9, 413.
28. Hendricks D., Kambhu, J. &Mosser, P. (2007). New Directions For Understanding Systemic Risk. Federal Reserve Economic Policy Review, 13, 2.
29. Jegadeesh, N. (1990). Evidence of predictable behavior of security returns. Journal of Finance, 45,881–898.
30. Kantz, H. (1994). A robust method to estimate the maximal Lyapunov exponent of a time series. Physics Letters A, 185, 77-87.
31. Lapedes, A. S., & Farber, R. (1987). Nonlinear Signal Processing Using Neural Networks: Prediction and System Modeling. Technical report LA-UR- 87-2662, Los Alamos National Laboratory.
32. Lehmann, B.N. (1990). Fads, martingales and market efficiency. Quarterly Journal of Economics, 105, 1–28.
33. Lo, A.W., & MacKinlay, A.C. (1988). Stock market prices do not follow random walks: Evidence from a simple specification test. Review of Financial Studies, 1, 41–66.
34. Lo, A.W., & MacKinlay, A.C. (1990). When are contrarian profits due to stock market overreaction? Review of Financial Studies, 3, 175–205.
35. Mayfield, E.S., & Mizrach, B. (1989) On Determining the Dimension of Real Time Stock Price Data. Working paper, Boston College, Dept. of Economics.
36. Oduncu, A., Akcelik,Y. & Ermisoglu, E. (2013). Reserve Options Mechanism and FX Volatility. Working Papers 1303, Research and Monetary Policy Department, Central Bank of the Republic of Turkey.
37. Ozdemir, Z.A. (2008). Efficient market hypothesis: evidence from a small open-economy. Applied Economics, 40:5, 633-641, DOI: 10.1080/00036840600722315
38. Poon, S.H., & Granger,C. (2005) Practical Issues in Forecasting Volatility, Financial Analysts Journal, 61:1, 45-56, DOI: 10.2469/faj.v61.n1.2683
39. Poterba, J.M., & Summers, L.H. (1988). Mean reversion in stock prices: Evidence and implications. Journal of Financial Economics, 22, 27–59.
40. Rigobon, R., & Sack, B., (2003). Spillovers across U.S. financial markets. NBER Working paper, Vol. 9640, Cambridge, MA.
41. Schaffer, W.M., & Tidd, C. W. (1991). NLF: Nonlinear Forecasting for Dynamical System. Dynamical Systems, Inc.
42. Scheinkman, J.A., & LeBaron, B. (1989). Nonlinear Dynamics and Stock Returns, Journal of Business, 62, 311-337.
43. Takens, F. (1981). Detecting Strange Attractors in Turbulence, in Dynamical Systems and Turbulence (Lecture Notes in Mathematics, 898), Berlin: Springer-Verlag, 366-381.
44. Vaidyanathan, R., & Krehbiel, T. (1992), Does the S&P 500 Futures Mispricing Series Exhibit Nonlinear Dynamics Dependence Across Time? Journal of the Future Market, 12, 659-677.
45. Vasilios P., Rangan G., Gil-Alana, L.A. & Wohar, M.E. (2019) Are BRICS exchange rates chaotic?, Applied Economics Letters, 26:13, 1104-1110, DOI: 10.1080/13504851.2018.1537473
46. Wolf, A., Swift, J.B., Swinney, H.L., & Vastano, J.A. (1985). Determining Lyapunov Exponents from a time series. Physica D,16(3)
47. Yoon, J., Ruan, X., & Zhang, J. E. (2022). VIX option-implied volatility slope and VIX futures returns. Journal of Futures Markets, 42, 1002– 1038. https://doi.org/10.1002/fut.22317
48. https://fred.stlouisfed.org/series/SP500