There are several approaches used for the evaluation of return premiums and risk characteristics to factors. In this section, we discuss the four most commonly used approaches: portfolio sorts, factor models, factor portfolios, and information coefficients. We examine the methodology of each approach and summarize its advantages and disadvantages.

In practice, to determine the right approach for a given situation there are several issues to consider. One determinant is the structure of the financial data. A second determinant is the economic intuition underlying the factor. For example, sometimes we are looking for a monotonic relationship between returns and factors while at other times we care only about extreme values. A third determinant is whether the underlying assumptions of each approach are valid for the data generating process at hand.

In the asset pricing literature, the use of portfolio sorts can be traced back to the earliest tests of the capital asset pricing model (CAPM). The goal of this particular test is to determine whether a factor earns a systematic premium. The portfolios are constructed by grouping together securities with similar characteristics (factors). For example, we can group stocks by market capitalization into 10 portfolios—from smallest to largest—such that each portfolio contains stocks with similar market capitalization. The next step is to calculate and evaluate the returns ...

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