Measuring capital market efficiency: Global and local correlations structure

Abstract

We introduce a new measure for the capital market efficiency. The measure takes into consideration the correlation structure of the returns (long-term and short-term memory) and local herding behavior (fractal dimension). The efficiency measure is taken as a distance from an ideal efficient market situation. Methodology is applied to a portfolio of 41 stock indices. We find that the Japanese NIKKEI is the most efficient market. From geographical point of view, the more efficient markets are dominated by the European stock indices and the less efficient markets cover mainly Latin America, Asia and Oceania. The inefficiency is mainly driven by a local herding, i.e. a low fractal dimension.

Has the 2008 financial crisis affected stock market efficiency? The case of Eurozone

“…The Hurst exponent has been used in several studies in the past as a tool for detecting long-range deviations from the random walk hypothesis in financial returns (e.g., Refs. [9][10][11][12][13][14][15][16][17][18][19]). To this extent, an important aspect of the utilized methodology is that, to avoid potential finite sample biases, the statistical significance of the estimated Hurst exponents is assessed by means of Monte-Carlo sampling [8,20].…”

Market Efficiency, Roughness and Long Memory in PSI20 Index Returns: Wavelet and Entropy Analysis

“…it is verified that D + H = 2 (see, for instance, [1]). In these processes, the global long memory characteristic of the series is a reflection of its local roughness characteristic.…”

“…The fractal dimension is a measure of roughness, and in opposition to the Long memory characterization, it measures the local memory of the series (Kristoufek and Vorvsda [1]). When modeling the dynamic behavior of a variable, by the solution of deterministic equations, the set of all instantaneous states of the system is the phase space.…”

“…As Kristoufek and Vosvrda [1] state, entropy can be seen as measuring the complexity of the system, so that the greater the entropy, the greater the randomness. Approximate entropy was introduced by Pincus [26].…”

“…The first issue is market efficiency (see Kristoufek and Vorvsda [1,2]). A market is called efficient if prices are adjusted so that they reflect the new information (see Fama [3] and Samuelson [4]).…”