However this is far less restrictive than might first seem. There are no restrictions on correlations among the enumerated factors, so it perfectly possible to include some that are correlated with others or are transforms of others. In general, we will not do so. This allows the expected return of e i to be positive, negative, or zero for any asset. Terminology Factor models are used in many domains in the field of investments, so it should not be surprising that different factors are used and different terms employed to describe the key components.
Different problems require different factors and emphasize different economic relationships.
The job of the Analyst is to either construct and apply an appropriate factor model for the task at hand or to at least understand the underlying structures and economic meanings of models constructed by others. A factor model is especially useful when analyzing historic asset returns, since such a model allows the Analyst to separate components of the overall return of the asset. In the former case, there are S scenarios. In the latter, there are T time periods. This is innocuous in the latter case, since every scenario involves the same future period.