Orthogonalized factors and systematic risk decomposition

Time-varying systematic and idiosyncratic risk exposures of US bank holding companies

“…Second, the democratic technique ensures that the orthogonalized factors best resemble the original factors compared to a set of commonly applied orthogonalization approaches. Klein and Chow (2013) demonstrate that the correlations between each possible original/orthogonal factor pair is highest for the democratic procedure while Principal Component Analysis and the sequential approach often identify orthogonal factors that are significantly different from their original counterparts exacerbating their economic interpretation. Therefore, other orthogonalization techniques often produce factor series that may become rather unrelated to the information provided by the original factors.…”

“…The recently introduced democratic technique does not suffer from this difficulty because it treats all factors equally (Klein and Chow, 2013). The approach conducts a simultaneous orthogonal transformation of the factors to identify their uncorrelated components.…”

Hedge funds and optimal asset allocation: Bayesian expectations and spanning tests

“…To investigate the relative importance of the traditional and alternative asset classes for explaining hedge fund returns over time, we employ the novel variance decomposition procedure proposed by Klein and Chow (2010). Their approach addresses the potential multicollinearity between the factors by a democratic factor orthogonalization that identifies the underlying uncorrelated components of common factors.…”

“…Hence, it eliminates the impact of the choice of the starting vector and the orthogonalization sequence. Following Klein and Chow (2010), the matrix of mutually uncorrelated and variance-preserving…”

“…Third, we analyze time-variation in the relative importance of traditional and alternative asset classes for explaining hedge fund returns by employing a novel democratic variance decomposition procedure proposed by Klein and Chow (2010). In comparison to the traditional sequential approach (Fama and French 1993;Bessler and Opfer 2003;Bessler and Holler 2010), this democratic procedure is not sensitive to the choice of a particular starting vector and the order in which the factors are orthogonalized.…”