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 provide an explanation for defense returns: Edwin Burmeister, Richard Roll, and Stephen Ross clarify the fundamentals of Arbitrage Pricing conception and talk 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 usability; and Richard C. Grinold and Ronald N. Kahn deal with multiple-factor types for portfolio possibility.
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Extra resources for A Practitioner's Guide to Factor Models
The index-matching test involves forecasting the model and parameters. Thus, the difference in number of factors during the fit period does not bias the results. The ability of the four-factor model to allow the construction of a portfolio that tracks a second portfolio more closely is powerful evidence that the four-factor model describes reality better than the single-factor model. l2 A Multi-Index Model of Bond Returns. As a second example of the estimation of a multi-index model from historical returns, we will discuss an application to bonds.
TABLE 1. 03 We ran a principal components analysis on the variance-covariance matrix and obtained two explanatory factors. The return on one factor was given by where R = return, f = factor value, B = Belgium, C = Canada, U = United States, F = France, and t = time period. Note from equation (3) that the first index is very close to an equally weighted index of the four country indexes. Thus, we might label the first factor a "world factor. The second factor is This index is long in North America and short in Europe.
Single- vs. Multi-Index Models Most of our analysis will be in the context of a generic multi-index model and a generic single-index model. The single-index model is included because it is familiar and because it serves as a useful benchmark against which to judge multi-index models. In addition, many of the problems with the multi-index model, and the economic intuitions behind the solution to those problems, can be illustrated for the case of a single-index model. The single-index model is simply a way of decomposing return on an asset into two parts.
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