Evidence of Increment of Efficiency of the Mexican Stock Market Through the Analysis of its Variations

随机矩阵理论与墨西哥市场的嵌套聚类投资组合

Random matrix theory and nested clustered portfolios on Mexican markets

本文提出结合随机矩阵理论协方差估计与改进的嵌套聚类优化算法，解决了高维下Markowitz投资组合的不稳定性问题，并在墨西哥市场中实现了无需显式约束的稳定正权重配置，从而避免了高风险的做空策略。

Market Mill Dependence Pattern in the Stock Market: Asymmetry Structure, Nonlinear Correlations and Predictability

An empirical study of joint bivariate probability distribution of two consecutive price increments for a set of stocks at time scales ranging from one minute to thirty minutes reveals asymmetric structures with respect to the axes y=0, y=x, x=0 and y=-x. All four asymmetry patterns remarkably resemble a four-blade mill called market mill pattern. The four market mill patterns characterize different aspects of interdependence between past (push) and future (response) price increments. When analyzed in appropriate coordinates, each pattern corresponds to a particular nonlinear dependence between…

Market Mill Dependence Pattern in the Stock Market: Modeling of Predictability and Asymmetry via Multi-Component Conditional Distribution

Recent studies have revealed a number of striking dependence patterns in high frequency stock price dynamics characterizing probabilistic interrelation between two consequent price increments x (push) and y (response) as described by the bivariate probability distribution P(x,y) [1,2,3,4]. There are two properties, the market mill asymmetries of P(x,y) and predictability due to nonzero z-shaped mean conditional response, that are of special importance. Main goal of the present paper is to put together a model reproducing both the z-shaped mean conditional response and the market mill asymmetry…

Market Mill Dependence Pattern in the Stock Market: Individual Portraits

This paper continues a series of studies of dependence patterns following from properties of the bivariate probability distribution P(x,y) of two consecutive price increments x (push) and y (response). The paper focuses on individual differences of the P(x,y) for 2000 stocks using a methodology of identification of asymmetric market mill patterns developed in [1,2]. We show that individual asymmetry patterns (portraits) are remarkably stable over time and can be classified into three major groups - correlation, anticorrelation and market mill. We analyze the conditional dynamics resulting from…

The emergence of critical stocks in market crash

In complex systems like financial market, risk tolerance of individuals is crucial for system resilience.The single-security price limit, designed as risk tolerance to protect investors by avoiding sharp price fluctuation, is blamed for feeding market panic in times of crash.The relationship between the critical market confidence which stabilizes the whole system and the price limit is therefore an important aspect of system resilience. Using a simplified dynamic model on networks of investors and stocks, an unexpected linear association between price limit and critical market confidence is th…

Market Mill Dependence Pattern in the Stock Market: Distribution Geometry, Moments and Gaussization

This paper continues a series of studies devoted to analysis of the bivariate probability distribution P(x,y) of two consecutive price increments x (push) and y (response) at intraday timescales for a group of stocks. Besides the asymmetry properties of P(x,y) such as Market Mill dependence patterns described in preceding paper [1], there are quite a few other interesting geometrical properties of this distribution discussed in the present paper, e.g. transformation of the shape of equiprobability lines upon growing distance from the origin of xy plane and approximate invariance of P(x,y) with…