There are many approaches to estimating fundamental factor equity models. I would like to focus on two traditional methods:
- The time-series regression approach of Fama and French. Factors are defined ex ante. Betas to the factors are estimated in the time-series.
- The Barra cross-sectional regression approach described in Menchero, Orr, and Wang (2011), Grinold and Kahn (2000) and Sheikh (1995). Factor realizations are derived ex post. Factors are estimated independently in each time period in the cross-section.
I'll sketch the methodology of each and the high-level pros/cons. I'm curious if anyone has experience or links to research regarding which approach is better for the purposes of hedging, optimal portfolio construction, and alpha generation.
Fama-French time-series regression approach:
Build a design matrix where each column is a time-series of economic factor returns. These factors could be traditional economic factors but also may include "spread" returns such as Fama-French factors SMB, HML, MKT generated from portfolio sorts.
Perform N time-series regressions (one per security). In particular, for each security regress the security returns on the economic factor returns and estimate the beta.
In this approach, the betas are constant and the factors are time-varying depending on the regression window. The advantage here is that estimation of beta is diversified away across securities, so it seems to be this approach would be superior for portfolio construction. The disadvantage is that betas are slower to respond to changes that change the risk profile of a firm (for example, in a sudden shift in Debt-to-Equity ratio).
Barra cross-sectional regression approach:
Assume that fundamental factor characteristics are Betas. For example, create z-scores of the fundamental factor characteristics thereby generating Betas for each time slice for each security.
Perform T cross-sectional regressions (one per factor). In particular, at each time slice regress the panel of security returns on the normalized Betas to estimate the un-observable factor realizations.
The advantage here is that the betas respond instantaneously to changes in firm characteristics. The disadvantage is that there is a potential errors-in-variable bias -- in fact, the errors from model mis-specification do not diversify away. Intuition suggests this approach may be better suited for alpha signal generation.
Is there research comparing the out-of-sample performance of these two methods for various applications (i.e. risk decomposition, portfolio construction, hedging, alpha signal generation)?