Spectral Properties of Financial Correlation Matrices
Random matrix theory (RMT) is applied to investigate the cross-correlation matrix of a financial time series in four different stock markets: Russian, American, German, and Chinese. The deviations of distribution of eigenvalues of market correlation matrix from RMT global regime are investigated. Specific properties of each market are observed and discussed.
The article describes proposed by the authors methodology of analysis of the Russian mutual funds. The aim of this methodology is to find out how attractive they are to investors and if they are able to provide the possibility of obtaining higher returns with less risk than the market in general. The study determines what type of fund management (active or passive) is more optimal. It also explains the effectiveness of focusing on past performance of the funds for making future investments. In addition, the ability of the management companies to repeat their past results is analyzed. Moreover, it is shown if it makes sense to focus on management companies that achieved the best results in the past while making decisions about future investments. These and other results achieved in this article reveal the features of the Russian market of collective investments and allow investors to form more competent policy of mutual funds’ investments. The methodology proposed by the authors is universal. Its application for the analysis of the other markets of collective investments will allow revealing their features.
The present article is devoted to consideration of investment strategy in stock market. The questions connected with designing of such strategy are systemically considered in it. The emphasis is thus placed on adaptation of the general (managerial) theory of engineering to engineering of investment strategy. Engineering of investment strategy is considered in indissoluble interrelation with the analysis of their typology. The most actual types and directions of engineering of investment strategy are characterized in the conclusion of article.
A class of distribution free multiple decision statistical procedures is proposed for threshold graph identification in correlation networks. The decision procedures are based on simultaneous application of sign statistics. It is proved that single step, step down Holm and step up Hochberg statistical procedures for threshold graph identification are distribution free in sign similarity network in the class of elliptically contoured distributions. Moreover it is shown that these procedures can be adapted for distribution free threshold graph identification in Pearson correlation network.
Market graph is known to be a useful tool for market network analysis. Cliques and independent sets of the market graph give an information about con- centrated dependent sets of stocks and distributed independent sets of stocks on the market. In the present paper the connections between market graph and classical Markowitz portfolio theory are studied. In particular, efﬁcient frontiers of cliques and independent sets of the market graph are compared with the efﬁcient frontier of the market. The main result is: efﬁcient frontier of the market can be well ap- proximated by the efﬁcient frontier of the maximum independent set of the market graph constructed on the sets of stocks with the highest Sharp ratio. This allows to reduce the number of stocks for portfolio optimization without the loss of quality of obtained portfolios. In addition it is shown that cliques of the market graphs are not suitable for portfolio optimization.
To a $N \times N$ real symmetric matrix Kerov assigns a piecewise linear function whose local minima are the eigenvalues of this matrix and whose local maxima are the eigenvalues of its $(N-1) \times (N-1)$ submatrix. We study the scaling limit of Kerov's piecewise linear functions for Wigner and Wishart matrices. For Wigner matrices the scaling limit is given by the Verhik-Kerov-Logan-Shepp curve which is known from asymptotic representation theory. For Wishart matrices the scaling limit is also explicitly found, and we explain its relation to the Marchenko-Pastur limit spectral law.
We show that beta ensembles in Random Matrix Theory with generic real analytic potential have the asymptotic equipartition property. In addition, we prove a Central Limit Theorem for the density of the eigenvalues of these ensembles.