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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 safety returns: Edwin Burmeister, Richard Roll, and Stephen Ross clarify the fundamentals of Arbitrage Pricing conception and speak about the macroeconomic forces which are the underlying resources of hazard; Edwin J. Elton and Martin J. Gruber current multi-index versions 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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And hence is generated by a LFM with Pmj = Wml X Plj + . + w m X~PNj for j = 1, . . , K. Using Footnote 1, the CAPM beta for the ith asset is The latter can be computed from the LFM generating the return for the ith asset: A Practitioneh Guide to Factor Models Because by Postulate 1cov[e,(t), fi(t)] = 0, it follows that cov[a,(t), rm(t)] = cov[ei(t), ~,(t)]. Thus, under the usual assumption that the market index is well diversified and am(t)is approximately zero, we may set the last covariance term in the above expression for pi equal to zero.

This approach has two disadvantages. F i s t , no matter how large the sample used to form portfolios, one cannot tell whether the factors are unique to that sample or common to all securities. Two papers, Cho, Elton, and Gruber (1984) and Brown and Weinstein (1983), discuss techniques for identifying the common factors across groups. A Practitioner's Guide to Factor Models Second, the results obtained by this methodology are very sensitive to the portfolio formatioli technique that was used. Applications of Multi-Index Models In this section, we will discuss one simple example to illustrate the principles discussed earlier, and then we will describe two applications: one to the Japanese equity market and the second to the U.

With size, which was not at all expected, because beta is usually considered a measure of risk. For U. S. data, the beta coefficient increases as size decreases, so smaller firms are viewed as having greater risk. For Japanese data, the reverse is true. This result must be interpreted with some caution, however. The firms in the sample are all fairly large. The 400 companies that compose the NRI 400 are selected from among the largest firms on the TSE, which lists 1,100 h s in its first section.

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