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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 offers the paintings of 3 teams of specialists addressing using single-factor versions to give an explanation for safeguard returns: Edwin Burmeister, Richard Roll, and Stephen Ross clarify the fundamentals of Arbitrage Pricing thought and speak about the macroeconomic forces which are the underlying assets of possibility; Edwin J. Elton and Martin J. Gruber current multi-index versions and supply suggestions on their reliability and value; and Richard C. Grinold and Ronald N. Kahn deal with multiple-factor types for portfolio probability.

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For example, assume that changes in oil prices affect equity returns. Using returns from a period with minimal changes in oil prices will probably mean that changes in oil prices had a very small influence on security returns in the period and that this factor will not be recovered by factor analysis. Similarly, if the researcher selected a sample of stocks that happened to have only a few stocks that are sensitive to changes in oil prices, the influence of oil prices would not show up as a factor.

If beta is a risk measure, this evidence strongly favors the purchase of small stocks. Alternatively, perhaps beta is not a sufficient metric for risk. The relationship between return and size is at least partially captured by the four-factor model. For example, the sensitivities shown to Factor 4 are ranked by size. A similar pattern, although less pronounced, is seen in Factors 2 and 3. Thus, part of what the four-factor model is picking up relative to the one-factor model is a size effect. Factor sensitivity stationarity.

The stability is even more pronounced for the other factors. In this section, we have shown that a four-factor model explains returns better than a one-factor model and exhibits stable sensitivities over time. Although some increase in explanatory power is guaranteed as we move from a one-factor to a four-factor model, the magnitude of the increase, particularly for low-capitalization portfolios was unusually large. A much more powerful test A Practitioner's Guide to Factor Models TABLE 7. Sensitivity to Factor 4 Portfolio April 1976March 1986 April 1981March 1986 April 1976March 1981 April 1971March 1976 'Insimcant at 5 percent level.

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