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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 provides the paintings of 3 teams of specialists addressing using single-factor versions to provide an explanation for defense returns: Edwin Burmeister, Richard Roll, and Stephen Ross clarify the fundamentals of Arbitrage Pricing idea and talk about the macroeconomic forces which are the underlying assets of chance; Edwin J. Elton and Martin J. Gruber current multi-index versions and supply advice on their reliability and usability; and Richard C. Grinold and Ronald N. Kahn handle multiple-factor types for portfolio danger.

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Although alternative theory suggests certain broad influences that might affect equilibrium returns, these influences are not easily translated into empirically measurable influences. An alternative to prespecdymg indexes is to try to have the historical return series itself suggest what portfolios of securities would best serve as indexes. Equation (1) and its explanation suggest the characteristics these indexes should possess. In particular, they should separate the common influences in returns from the unique influences in returns.

PK such that It then follows immediately that the APT holds provided that for all j = 1, . . , K. Conversely, if the APT is true and the above K CAPM restrictions on the Pis hold, then the CAPM is also true. Given an LFM for asset returns, these are the CAPM restrictions that are rejected in favor of the APT in statistical tests. Appendix B We will show that K well-diversified portfolios can substitute for the factors in an APT model. To simplify the computations, we assume that K = 2; the general case is easily handled using matrix algebra.

Appendix A Several statistical techniques can be used to produce a set of indexes that explain the interrelationship among security returns. The most commonly used techniques for identifying the influences (factors) affecting security returns and sensitivities (factor loadings) simultaneously are principal component analysis and factor analysis. Principal Component Analysis Principal component analysis is perhaps easier to understand than factor analysis. For returns on a defined set of stocks over a predetermined time span, compute an index (weighted average of that set of returns) that explains the maximum amount of the variation in the variance-covariance matrix of security returns.

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