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 give 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 assets of chance; Edwin J. Elton and Martin J. Gruber current multi-index versions and supply suggestions on their reliability and usability; and Richard C. Grinold and Ronald N. Kahn deal with multiple-factor types for portfolio threat.
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Extra resources for A Practitioner's Guide to Factor Models
If, in fact, one has estimated too many factors, then after removing the common factors, the remaining canonical variates should be uncorrelated. Table 3 presents the average (across four samples) squared canonical correlation for the first canonical variate out of the one-factor solution, the second canonical variate out of the two-factor solution, proceeding through the seventh canonical variate out of the seven-factor solution. The results indicate that the likely solution is either four or five factors.
The formal problem is to find portfolio weights, w,, w,, . , wN, for the N stocks in the selection universe such that the portfolio score is maximized but the risk exposure profile is similar to that of the S&P 500. More formally, the weights should result in the highest possible value for .. subject to the constraint that the portfolio betas, .. for j = 1, . , K, are close to the betas for the S&P 500. That is, the weights should make the risk exposure profile for the portfolio close to the risk exposure profile for the S&P 500 while maximizing the value of the portfolio's ranking score.
Furthermore, prespecifying the sensitivities as durations rather than estimating them from the data produced the poorest results. In this case, however, prespeclfylng the two indexes as returns on a widely diversified portfolio of short bonds and a widely diversified portfolio of long bonds outperformed the model for which the two indexes were estimated empirically by factor analysis. The factor structure was sufficiently unstable over time that it was better to select two portfolios widely separated l3 See Elton, Gruber, and Nabar (1988) for a more detailed description of the methodology and results described in this section.