ANALYZING THE FRACTAL STRUCTURE OF STOCK RETURNS: EVIDENCE FROM ISTANBUL STOCK EXCHANGE

Efficient Market Hypothesis States that alt new information is reflected in the market price fully and immediately. Security returns are essentially unpredictable since they follow a random walk. Therefore the impact of the new information is essentially unpredictable; it is as likely to be negative as positive. Financial asset returns are often modeled with a series of small, normally distributed changes. Brownian motion asserts the independence of the changes but there are patterns or trends in Capital market returns and they persist over time. Therefore security returns are not fully random. This paper applies Hurst’s R/S (Rescaled Range) analysis to XU030 and XU100 index within different time horizons. The analysis proceeded from two basic principles: dependence of each period in time series data and fractional Brownian motion of time series. The persistence behaviour of İstanbul Stock Exchange is investigated. The results show that each series taken into consideration exhibits a biased process characteristic of fractal Brownian motion.

Anahtar Kelimeler:

Brownian Motion, Fractal Brownian Motion, Hurst Exponent, Rescaled Range Analysis

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[1] Hurst, H.E. (1951). Long-Term Storage Capacity of Reservoirs. Transactions of the American Society of Civil Engineers, 116, 770-799.
[2] Peters, E.E. (1992). R/S Analysis Using Logarithmic Retums. Financial Analysts Journal, November/December, 81-82.
[3] Mandelbrot, B.B. (1972). Statistical Methodology for Nonperiodic Cycles from Covariance to R/S Analysis. Annals of Economic and Social Measurement, 1(3), 259- 290.
[4] Lo, A.W. (1991). Long-Term Memory in Stock Market Prices. Econometrica, 59(5), 1279-1313.
[5] Baxter, M. & Rennie, A. (2003). Financial'Calculus:An Introduction to Derivative Pricing. Cambridge: Cambridge University Pres.
[6] Peters, E.E. (1989). Fractal Structure in the Capital Markets. Financial Analysts Journal, 45(4), 32-37.
[7] Peters, E.E. (1991). Chaos and Order in the Capital Markets. New York: John Wiley&Sons.
[8] Peters, E.E. (1994). Fractal Market Analysis: Applying Chaos Theory to Investment and Economics, New York: John Wiley&Sons.
[9] Pallikari, F. & Boller, E. (1999). A Rescaled Range Analysis of Random Events. Journal of Scientifıc Exploration, 13(1), 25-44.
[10] Aysoy, C. & Balaban, E. (1996). The Term Structure of Volatility in the Turkish Foreign Exchange: Implications for Option Pricing and Hedging Decisions. Central Bank of the Republic of Turkey, Discussion Paper No: 9613.