Factor Analysis and Independent Component Analysis in Presence of High Idiosyncratic Risks

This paper addresses the case when stock market returns are assumed being generated through a factorial structure. High levels of idiosyncratic risk are shown to exist for most stocks on the US market, when CAPM or APT are used for the estimation of diversifiable risks. The presence of these high idiosyncratic risks may not allow a correct estimation of the generating factors when using a classic factor analysis method. The Independent Component Analysis is introduced as an adequate method for factor estimation; using neural networks, this method allows taking into account the information contained in higher moments. Through simulations of markets with various assumptions on the kind of processes followed by the generating factors, this method is shown to strongly improve the factors estimation, especially when high idiosyncratic risks are present. In the latter case, a traditional factor analysis, such as the Principal Component Analysis, may fail to estimate the generating factors.
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