The statistical factor models are described as limited in the same way macroeconomic models are limited. that is, they depend on time-series regression to estimate a security’s factor beta, the accuracy of which depends heavily on "a long and stable history of returns for a security" (Connor). Fundamental factor models rely on empirical attributes of a company’s market elements, such as the size of the firm, its yield and book-to-market ratio, as well as its industry.

Though the fundamental model slightly outperforms the statistical model, and both outperform the macroeconomic model, Connor concludes that the macroeconomic is "probably the strongestof the three approaches" judged by such criteria as intuitive appeal and theoretical consistency. However, he also points out that the different model types are not inconsistent, and that, in fact, "in the absence of estimation error and with no limits on data availability, the three models are simply restatementsof one another" (Connor). He refers to the Fama and French article (discussed below) for their work on finding an approach to explain "how to rotate the fundamental risk attributes to equate some combination of them to the macroeconomic factor betas" (Connor).

"On Portfolio Optimization: Fo…

They acknowledge the prolific amount of historical research that has been conducted in seeking out ways to model expected returns, but also reiterate what is now common knowledge, that "numerous studies indicate that on average professional investment managers do not outperform passive benchmarks" (Chan, Karceski, and Lakonishok, 1999). The increasing popularity of indexing, "especially when full replication of the benchmark is not desired or not practical" coupled with "recent interest in asset allocation models" has spurred research in the area of portfolio optimization, fueled as well by the incredible amount computation power available to even the amateur investor.

The authors also point out the subtle difference between the investor’s perspective and that of the professional money manager:

"While the theory of optimal portfolio choice suggests that investors should be concerned with the variance of a portfolio’s return, in practice investment decisions are delegated to professional money managers [who are] evaluated relative to some benchmark, [therefore] it has become standard practice for [professional money managers] to optimize with respect tothe standard deviation of the difference between the portfolio’s return and the benchmark return" (Chan, et al).

As a result of their assertion that the benefits of portfolio optimization depend upon "how accurately the moments of the distribution of returns can be predicted," the article goes into some detail regarding their work comparing risk models beginning with the second moments of distribution rather than the first in light of the fact that "expected returns are notoriously difficult to predict, and that the optimization process is very

Factor Models of Asset Returns