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Below is a list of different research articles pertaining to the math behind style analysis and asset allocation with details about what they comprise. To view these articles simply click on the link for the desired article and in the dialog that pops up either open or save to disk. The format of the document is also listed. There are PDF files (which open with Adobe Acrobat), Microsoft Word and PowerPoint documents. For other interesting research please visit our Newsletters or Articles page.
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- This is the third and last article in a short series on the mathematics of returns-based style analysis. This article takes a different approach to looking at the mathematics of returns-based style analysis, namely, the Euclidean space of return series with the covariance as the scalar product.
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- One of the most frequently asked questions concerning the mathematics of StyleADVISOR is how exactly we calculate the style attribution coefficients which are displayed in the style map view, the asset allocation view, and the style table. The short answer to this question is very easy: We perform the returns-based style analysis that was invented by Stanford professor and Nobel laureate William F. Sharpe. In this article, I will explain the mathematics of Sharpe's algorithm. As it turns out, a fairly complete and mathematically rigorous description of the algorithm can be given without using a lot of mathematical formalism.
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- How do we calculate alpha? What does alpha mean? When is it useful? These are the questions posed in this presentation given at the 2002 Client Conference. The discussion includes an explanation of linear regression, the role of R-Squared in determining the usefulness of alpha and why the alpha in StyleADVISOR may be different from alpha as calculated by other software programs.
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- One of the most frequently asked questions concerning the mathematics of StyleADVISOR is how exactly we calculate the style attribution coefficients which are displayed in the style map view, the asset allocation view, and the style table. The short answer to this question is very easy: We perform the returns-based style analysis that was invented by Stanford professor and Nobel laureate William F. Sharpe. In this article, I will explain the mathematics of Sharpe's algorithm. As it turns out, a fairly complete and mathematically rigorous description of the algorithm can be given without using a lot of mathematical formalism.
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- This presentation explains the different definitions of annualized excess returns, the information ratio, significance level, and in-sample versus out-of-sample analysis.
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- The presentation explains the different definitions of standard deviation and of annualized excess returns.
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- This presentation explains (in English, not complicated mathematical formulas) how the single computation style benchmark is calculated.
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