Computing portfolio risk using Gaussian mixtures and independent component analysis

Addressing the problem of non-normal portfolio returns, we introduce a novel approach for estimating the distribution of portfolio returns considering higher order mutual information. It allows us to extend the standard variance-covariance framework and efficiently re-compute measures of market risk such as the standard Value-at-Risk or any other probability density based measure. The approach combines two clean and transparent methodologies-independent component analysis and finite Gaussian mixture distributions-and is formulated algorithmically in three steps.

[1]  Stanley J. Kon.  Models of Stock Returns—A Comparison , 1984 .

[2]  J. Cardoso,et al.  Blind beamforming for non-gaussian signals , 1993 .

[3]  Patrick Wegmann,et al.  Lower Partial Moments und Value-at-Risk: Eine Synthese , 1998 .

[4]  Vijay S. Bawa,et al.  Abstract: Capital Market Equilibrium in a Mean-Lower Partial Moment Framework , 1977, Journal of Financial and Quantitative Analysis.

[5]  Christian Jutten,et al.  Blind separation of sources, part I: An adaptive algorithm based on neuromimetic architecture , 1991, Signal Process..

[6]  Andrew D. Back,et al.  A First Application of Independent Component Analysis to Extracting Structure from Stock Returns , 1997, Int. J. Neural Syst..

[7]  Barak A. Pearlmutter,et al.  A Context-Sensitive Generalization of ICA , 1996 .

[8]  Jean-Francois Cardoso,et al.  Source separation using higher order moments , 1989, International Conference on Acoustics, Speech, and Signal Processing,.

[9]  Ali Mansour,et al.  Blind Separation of Sources , 1999 .

[10]  Pierre Comon,et al.  Blind separation of sources, part II: Problems statement , 1991, Signal Process..

[11]  Walter L. Smith.  Probability and Statistics , 1959, Nature.

[12]  A. Sveshnikov,et al.  Problems in Probability Theory, Mathematical Statistics and Theory of Random Functions , 1979 .

[13]  P. Fishburn.  Mean-Risk Analysis with Risk Associated with Below-Target Returns , 1977 .

[14]  Henry C. Tuckwell.  Elementary applications of probability theory - with an introduction to stochastic differential equations (2. ed.) , 1995, Texts in statistical science series.

[15]  Peter C. Cheeseman,et al.  Bayesian Classification (AutoClass): Theory and Results , 1996, Advances in Knowledge Discovery and Data Mining.

[16]  E. Elton.  Modern portfolio theory and investment analysis , 1981 .

[17]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[18]  D. Duffie,et al.  An Overview of Value at Risk , 1997 .

[19]  Anthony S. Tay,et al.  Evaluating Density Forecasts of Inflation: The Survey of Professional Forecasters , 1997 .

[20]  J. Stutz,et al.  Autoclass — A Bayesian Approach to Classification , 1996 .

[21]  Anthony S. Tay,et al.  Evaluating Density Forecasts , 1997 .

[22]  C. L. Nikias,et al.  Higher-order spectra analysis : a nonlinear signal processing framework , 1993 .

[23]  Terrence J. Sejnowski,et al.  An Information-Maximization Approach to Blind Separation and Blind Deconvolution , 1995, Neural Computation.