Financial Applications of Random Matrix Theory: Old Laces and New Pieces

By Marc Potters, Jean-Philippe Bouchaud, L. Laloux. 2005

157 citations recorded by the source corpus.

This contribution to the proceedings of the Cracow meeting on `Applications of Random Matrix Theory' summarizes a series of studies, some old and others more recent on financial applications of Random Matrix Theory (RMT). We first review some early results in that field, with particular emphasis on the applications of correlation cleaning to portfolio optimisation, and discuss the extension of the Marcenko-Pastur (MP) distribution to a non trivial `true' underlying correlation matrix. We then present new results concerning different problems that arise in a financial context: (a) the generalisation of the MP result to the case of an empirical correlation matrix (ECM) constructed using exponential moving averages, for which we give a new elegant derivation (b) the specific dynamics of the `market' eigenvalue and its associated eigenvector, which defines an interesting Ornstein-Uhlenbeck process on the unit sphere and (c) the problem of the dependence of ECM's on the observation frequency of the returns and its interpretation in terms of lagged cross-influences.

Subfields: Economics and Econometrics, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/51f67482f4a3488df25192e026828a7d901ebca3

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Citations in the corpus

Portfolio optimization for heavy-tailed assets: Extreme Risk Index vs. Markowitz (2015, background): “To some extent, these technical difficulties can be addressed by advanced estimation methods – see [22] and [14], just to call a few.”
High Dimensional Statistical Inference and Random Matrices (2006, methodology): “Bulk Graphical methods [92], [93] [finance [15], [77], communications [91]] Linear Statistics Hypothesis tests, distribution theory Extremes Hypothesis tests, distribution theory, role in proofs [21], [33] Spacings [[10], otherwise few so far] General Computational tools [65], role in proofs”
Random matrix theory analysis of cross-correlations in the US stock market: Evidence from Pearson’s correlation coefficient and detrended cross-correlation coefficient (2013, methodology): “[7,12,16,26] stated that the aforementioned interpretation can be explained more precisely in the context of the one factor model, i.”
Correlation, Hierarchies, and Networks in Financial Markets (2008, unknown): “We also consider filtering procedures based on the shrinkage technique (Ledoit and Wolf, 2003) and on the random matrix theory (RMT) (Laloux et al., 1999; Plerou et al., 1999; Rosenow et al., 2002; Potters et al., 2005).”