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Fractal dimensions for various time-lags are determined in order to reflect stability of the price return.  The Hurst exponent is determined from the FD.
Between-asset covariance and correlation (Pearson and Spearman) of log-returns are provided for portfolio construction.  Eigendecomposition is performed on each matrix along with determination of noise threshold for eigenvectors.  Component subtraction is performed to remove effects of the greatest eigenvector, noise eigenvectors, or both.  Shrinkage techniques are also applied to matrices.
Log-return distributions are fitted using various continuous probability distributions.
Percentile distributions are determined for each asset, along with the density fit results for log-returns, and Hurst exponent for the price return time series.
Linear regression is performed for the log-percentiles of left and right tail of the return distribution.  Statistical significance of the intercept term for the right-tail, i.e., abs(log-return)*I(right-tail) is identified.   If the intercept term is positive and significant, the the right tail has significantly greater log-return values.   

Price returns plots are also shown for each asset used for constructing a portfolio.
Wealth charts are presented for unbalanced (tangency) and rebalanced (MinVar) portfolios.   Asset weights are also adjusted for the Hurst exponent and tail probabilities for the right-tail linear regression fits to weight for stability and/or greater positive returns.  

Cumulative returns for each portfolio are presented for the 3-month, 6-month, 1-year, 2-year, 5-year, and 10-year timeframes.
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This webpage is provided for general information only, and nothing contained within the material constitutes a recommendation for the purchase or sale of any security. Although the data used for portfolio construction are considered reliable, we do not guarantee their accuracy, and any such information may be incomplete or condensed. Also, risk information and portfolios expressed on these pages, are based on research materials available from sources considered reliable. Views are subject to change on the basis of additional or new research, new facts or developments. The investment risks described herein are not purported to be exhaustive, any person considering an investment should seek independent advice on the suitability or otherwise of the particular investment. Investment products are not bank deposits or obligations or guaranteed by RMP unless specifically stated. Investment products are not insured by government or governmental agencies. Investment and Treasury products are subject to Investment risk, including possible loss of principal amount invested. Past performance is not indicative of future results: prices can go up or down. Investors investing in investments and/or treasury products denominated in foreign (non-local) currency should be aware of the risk of exchange rate fluctuations that may cause loss of principal when foreign currency is converted into the investor's home currency. All use of information is subject to Terms and Conditions of the individual investment and Treasury products. Users understand that it is their responsibility to seek legal and/or tax advice regarding the legal and tax consequences of his or her investment transactions. If a customer changes residence, citizenship, nationality, or place of work, it is his or her responsibility to understand how his or her investment transactions are affected by such change and comply with all applicable laws and regulations as and when such becomes applicable. Customer understands that RMP does not provide legal and/or tax advice and is not responsible for advising him/her on the laws pertaining to his/her potential investment transactions.

Last quarterly rebalance: May 1, 2013
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Random Matrix Portfolios
Exploiting Noise, Fractals, and Instability


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