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A Practitioner's Guide to Factor Models by Edwin Burmeister; Richard Roll; Stephen A. Ross; Edwin J.

By Edwin Burmeister; Richard Roll; Stephen A. Ross; Edwin J. Elton; Martin J. Gruber; Richard Grinold and Ronald N. Kahn

This monograph offers the paintings of 3 teams of specialists addressing using single-factor types to give an explanation for safeguard returns: Edwin Burmeister, Richard Roll, and Stephen Ross clarify the fundamentals of Arbitrage Pricing conception and talk about the macroeconomic forces which are the underlying assets of chance; Edwin J. Elton and Martin J. Gruber current multi-index types and supply assistance on their reliability and value; and Richard C. Grinold and Ronald N. Kahn deal with multiple-factor versions for portfolio danger.

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That is, for each sample, a maximum likelihood solution involving first one factor, then two factors, then three factors, and continuing through ten factors was calculated. Three techniques in the literature on factor analysis are commonly used to decide on the correct number of factors needed to explain the covariance matrix. These are chi square (Lawley & Maxwell 1971), information This section is based on an article by Elton and Gruber (1990). Other authors have documented the success of alternative forms of multi-index models in Japan.

Finally, having the indexes represent separate influences would be desirable. Two statistical techniques accomplish these goals: factor analysis and The most common technique is factor analysis. ~ Factor analysis was devised to define a set of indexes mathematically so that the covariance between security returns is minimized after the indexes have been removed. This assures that cov(e,ej) is as close to zero as it can be. More precisely, once the user sets the number of indexes desired, factor analysis wik Define the optimal composition of each index (the weight on each security in each index), See the appendix to this chapter for a more detailed discussion of factor analysis and principal components analysis, as well as the differences between them.

For example, when factor analyzing a time series of returns, generally the first index is a portfolio of most of the assets whose returns are being factor analyzed and the sensitivity of all assets to the index is positive. This is not true with subsequent indexes, however. Additional indexes generally measure nonmarket influences. For example, it is not uncommon when factor analyzing equity returns that the second index is highly correlated with firm capitalization (captures the small-stock phenomenon) with the effect of the market removed.

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