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 provide an explanation for safety returns: Edwin Burmeister, Richard Roll, and Stephen Ross clarify the fundamentals of Arbitrage Pricing idea and speak about the macroeconomic forces which are the underlying assets of threat; Edwin J. Elton and Martin J. Gruber current multi-index types and supply tips on their reliability and value; and Richard C. Grinold and Ronald N. Kahn tackle multiple-factor types for portfolio hazard.
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If the Sharpe-Lintner version of the CAPM is correct, the right index to use An additional assumption that is frequently made is that the indexes are uncorrelated. This assumption does not create problems, because a set of correlated indexes can always be converted to a set of uncorrelated indexes. A Practitioner's Guide to Factor Models for explaining equilibrium returns is an index of the return on all risky assets in which the weight on each return is the relevant market proportion of that asset.
Table 3 presents the average (across four samples) squared canonical correlation for the first canonical variate out of the one-factor solution, the second canonical variate out of the two-factor solution, proceeding through the seventh canonical variate out of the seven-factor solution. The results indicate that the likely solution is either four or five factors. The canonical R2 of the fourth linear combination from a four-factor solution is almost 60 percent; for the fifth linear combination from a five-factor solution, it is slightly more than 20 percent; but for the sixth linear combination of the six-factor solution, it is less than 5 percent.
A fourth problem with factor analysis is the difficulty of factor analyzing returns for a large number of securities. The primary problem is computational. Analyzing a large number of securities is costly and impossible to do with most standard statistical packages. To get a meaningful factor analysis, however, requires a longer data series than the number of firms being analyzed. With 20 years of monthly data, one is restricted to fewer than 240 firms. Two procedures have been introduced to deal with difficulties in factor analyzing a large number of securities.
A Practitioner's Guide to Factor Models by Edwin Burmeister; Richard Roll; Stephen A. Ross; Edwin J. Elton; Martin J. Gruber; Richard Grinold and Ronald N. Kahn