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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 types to provide an explanation for safeguard 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 chance; Edwin J. Elton and Martin J. Gruber current multi-index types and supply suggestions on their reliability and usability; and Richard C. Grinold and Ronald N. Kahn tackle multiple-factor versions for portfolio threat.

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We can illustrate this problem with the case of the single-index model. Usually, when estimating a single-index model, the index is taken to be the return or excess return (over the riskless rate) on some widely diversified portfolio. The most commonly used portfolios are the S&P 500 Index or the CRSP Index. One of these is simply asserted as being the relevant factor. 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.

Obviously, the data cannot suggest a factor if that factor was not present during the time period chosen. 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.

As a second example of the estimation of a multi-index model from historical returns, we will discuss an application to bonds. In this case, we were attempting to find a returngenerating model that would be useful in protecting against shifts in the term structure of interest rates. Estimation of a multi-index model using bond returns has a basic problem. An assumption underlying most estimation techniques is that the structure of the multi-index model remains stable over time. For bond returns, however, this is unlikely to be true.

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