Eigenvalue...........groooooooan!

[Keith Davis]

Greetings, Earthlings!

Www.innergroovemusic.com

> On May 20, 2017, at 11:28 PM, Charles Albert <cfalbert at gmail.com> wrote:
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> PCA involves transforming the original correlation matrix to derive factor loadings and eigenvalues. The loadings are in the form of a matrix with the same dimensions as the original correlation matrix. For example, if there were 30 rows and 30 columns in the original correlation matrix, the loadings matrix will also have 30 rows and 30 columns. Each column of the loadings matrix represents a latent factor that explains a portion of the movement of the underlying portfolio. Each row of the loadings matrix corresponds to an asset contained in the original investment universe. Where an asset intersects a column we observe the sensitivity – or “loading” – of that asset on a particular factor. By design, each factor is independent of the other factors, which means they have zero correlation with each other, and represent independent bets in the portfolio.
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> When PCA is applied to portfolio analysis, columns in the loadings matrix are referred to as ‘principal portfolios’ because they are composed of long or short positions in the constituent assets. In this way, the factor loadings can be interpreted as asset “weights” in that factor’s “principal portfolio.” The returns from these principal portfolios can be observed by applying the weight vector to the asset returns, and, because they are independent, the returns to each principal portfolio will have a correlation of exactly 0 to one another. We can “project” the returns for principal portfolios back through time just as we can for any other type of portfolio.
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> Each principal portfolio has a corresponding eigenvalue, which describes the proportion of total portfolio standardized variance attributable to that factor. When the correlation matrix is used in the analysis, the sum of standardized variances is equal to the number of variables or assets in the universe under analysis; when the covariance matrix is used, the eigenvalues sum to the total portfolio variance.
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> http://www.investresolve.com/blog/the-case-for-tactical-alpha-part-2-the-fundamental-flaw-of-grinolds-fundamental-law/
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> A LIfe,
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> A Life,
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> My Kingdom for a Life!
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> love
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> cfa
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