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 protection returns: Edwin Burmeister, Richard Roll, and Stephen Ross clarify the fundamentals of Arbitrage Pricing concept and speak about the macroeconomic forces which are the underlying assets of hazard; Edwin J. Elton and Martin J. Gruber current multi-index versions and supply information on their reliability and usability; and Richard C. Grinold and Ronald N. Kahn deal with multiple-factor versions for portfolio possibility.

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It rests on the choice of the test used to determine sigmficance. The answer would seem to be either four, ten, or more factors. This ambiguity illustrates how cautious one should be about placing too much reliance on statistical sigmficance in deciding on the number of factors. The next step is to use information from more than one group to decide on the number of factors. Mult$le-group tests. The intent of our analysis was to estimate a returngenerating process that describes the return on all stocks that are comparable to the stocks in the NRI 400 Index.

The second step is to examine the ability of these portfolios to match the index over a period of time subsequent to when they are formed. The index-matching test is a joint test of a number of hypotheses. One aspect affecting performance is whether the market has one or four factors. Even with four factors, the one-factor model could still perform better than the four-factor model if the historically estimated sensitivities for the four-factor model were poor forecasts of future sensitivities and the historical sensitivities for the single-index model were a good predictor of future sensitivities.

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. Under the CAPM, E[ri(t) - TB(t)] = Pi x E[rm(t) - TB(t)].

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