dorsal/arxiv
View SchemaFinancial Applications of Random Matrix Theory: Old Laces and New Pieces
| Authors | M. Potters, J. P. Bouchaud, L. Laloux |
|---|---|
| Categories | |
| ArXiv ID | physics/0507111 |
| URL | https://arxiv.org/abs/physics/0507111 |
Abstract
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.
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"abstract": "This contribution to the proceedings of the Cracow meeting on `Applications\nof Random Matrix Theory\u0027 summarizes a series of studies, some old and others\nmore recent on financial applications of Random Matrix Theory (RMT). We first\nreview some early results in that field, with particular emphasis on the\napplications of correlation cleaning to portfolio optimisation, and discuss the\nextension of the Marcenko-Pastur (MP) distribution to a non trivial `true\u0027\nunderlying correlation matrix. We then present new results concerning different\nproblems that arise in a financial context: (a) the generalisation of the MP\nresult to the case of an empirical correlation matrix (ECM) constructed using\nexponential moving averages, for which we give a new elegant derivation (b) the\nspecific dynamics of the `market\u0027 eigenvalue and its associated eigenvector,\nwhich defines an interesting Ornstein-Uhlenbeck process on the unit sphere and\n(c) the problem of the dependence of ECM\u0027s on the observation frequency of the\nreturns and its interpretation in terms of lagged cross-influences.",
"arxiv_id": "physics/0507111",
"authors": [
"M. Potters",
"J. P. Bouchaud",
"L. Laloux"
],
"categories": [
"physics.data-an",
"cond-mat.dis-nn",
"q-fin.ST"
],
"title": "Financial Applications of Random Matrix Theory: Old Laces and New Pieces",
"url": "https://arxiv.org/abs/physics/0507111"
},
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