FACTOR UNIQUENESS IN THE S&P 500 UNIVERSE: CAN PROPRIETARY FACTORS EXIST?

In this paper, we analyze factor uniqueness in the S&P 500 universe. The current theory of approximate factor models applies to infinite markets. In the limit of infinite markets, factors are unique and can be represented with principal components. If this theory would apply to realistic markets such as the S&P 500 universe, the quest for proprietary factors would be futile. We find that this is not the case: in finite markets of the size of the S&P 500 universe different factor models can indeed coexist. We compare three dynamic factor models: a factor model based on principal component analysis, a classical factor model based on industry, and a factor model based on cluster analysis. Dynamic behavior is represented by fitting vector autoregressive models to factors and using them to make forecasts. We analyze the uniqueness of factors using Procrustes analysis and correlation analysis. Forecasting performance of the factor models is analyzed by forming active portfolio strategies based on the forecasts for each model using sample data from the S&P 500 index in the 21-year period 1989–2010. We find that one or two factors which we can identify with global factors are common to all models, while the other factors for the factor models we analyzed are truly different. Models exhibit significant differences in performance with principal component analysis-based factor models appearing to behave better than the sector-based factor models.