Variety and Volatility in Financial Markets

Abstract

We study the price dynamics of stocks traded in a financial market by considering the statistical properties both of a single time series and of an ensemble of stocks traded simultaneously. We use the $n$ stocks traded in the New York Stock Exchange to form a statistical ensemble of daily stock returns. For each trading day of our database, we study the ensemble return distribution. We find that a typical ensemble return distribution exists in most of the trading days with the exception of crash and rally days and of the days subsequent to these extreme events. We analyze each ensemble return distribution by extracting its first two central moments. We observe that these moments are fluctuating in time and are stochastic processes themselves. We characterize the statistical properties of ensemble return distribution central moments by investigating their probability density functions and temporal correlation properties. In general, time-averaged and portfolio-averaged price returns have different statistical properties. We infer from these differences information about the relative strength of correlation between stocks and between different trading days. Lastly, we compare our empirical results with those predicted by the single-index model and we conclude that this simple model is unable to explain the statistical properties of the second moment of the ensemble return distribution.

10 pages, 11 figures

References in corpus (5)

• Noise Dressing of Financial Correlation Matrices
• Universal and non-universal properties of cross-correlations in financial time series
• The statistical properties of the volatility of price fluctuations
• Scaling of the distribution of price fluctuations of individual companies
• Symmetry alteration of ensemble return distribution in crash and rally days of financial markets

Cited by in corpus (30)

• A Random Matrix Approach to Cross-Correlations in Financial Data
• Fluctuation scaling in complex systems: Taylor's law and beyond
• 1/f Noise and Extreme Value Statistics
• Scaling and memory of intraday volatility return intervals in stock market
• Role of Noise in a Market Model with Stochastic Volatility
• Size matters: some stylized facts of the stock market revisited
• Correlations, Risk and Crisis: From Physiology to Finance
• Levels of complexity in financial markets
• PCA meets RG
• Roughness distributions for 1/f^alpha signals
• Maximal height statistics for 1/f^alpha signals
• Symmetry alteration of ensemble return distribution in crash and rally days of financial markets
• Individual and collective stock dynamics: intra-day seasonalities
• Volatility return intervals analysis of the Japanese market
• Analysis of Data Clusters Obtained by Self-Organizing Methods
• Statistical properties of daily ensemble variables in the Chinese stock markets
• Analysis of cyclical behavior in time series of stock market returns
• From code to market: Network of developers and correlated returns of cryptocurrencies
• Ensemble properties of securities traded in the NASDAQ market
• The dynamics of traded value revisited
• Alternation of different fluctuation regimes in the stock market dynamics
• Power law for ensembles of stock prices
• Time-reversal asymmetry in Cont-Bouchaud stock market model
• Physics of Econophysics
• Introducing Variety in Risk Management
• Edwards-Wilkinson surface over a spherical substrate: $1/f$ noise in the height fluctuations
• Economic Amplifier - A New Econophysics Model
• An Econophysics Model for the Migration Phenomena
• Macrostate Parameter, an Econophysics Approach for the Risk Analysis of the Stock Exchange Market Transactions
• An Econophysics Model for the Currency Exchange with Commission