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 types to give an explanation for protection returns: Edwin Burmeister, Richard Roll, and Stephen Ross clarify the fundamentals of Arbitrage Pricing concept and talk about the macroeconomic forces which are the underlying assets of probability; Edwin J. Elton and Martin J. Gruber current multi-index versions and supply advice 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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Extra resources for A Practitioner's Guide to Factor Models
To this point, we have intentionally defined our analysis in the terminology of multi-index models. Historically, starting with Sharpe's single-index model, this terminology was commonly used both in the literature and practice of financial analysts. With Ross's (1976) description of the arbitrage pricing theory (APT) and the initial tests of Roll and Ross (1980) of the APT methodology, a different terminology came into existence. Expressions like equation (2) became known as a multi-factor return-generating process.
03 We ran a principal components analysis on the variance-covariance matrix and obtained two explanatory factors. The return on one factor was given by where R = return, f = factor value, B = Belgium, C = Canada, U = United States, F = France, and t = time period. Note from equation (3) that the first index is very close to an equally weighted index of the four country indexes. Thus, we might label the first factor a "world factor. The second factor is This index is long in North America and short in Europe.
Nonuniqueness is a concern in certain applications and not in others. Any solution is correct in the sense that it explains (and predicts) returns as well as any other solution. Some solutions, however, are easier to interpret economically than others. Also, two researchers using slightly different solution algorithms or slightly different samples can come up with solutions that are simply transformations of each other but that appear to be very different. Computational Problems. A fourth problem with factor analysis is the difficulty of factor analyzing returns for a large number of securities.