An astute reader suggested reproducing the results from a recent article on regime analysis by Kritzman et al., Regime Shifts: Implications for Dynamic Strategies in FAJ (May / June 2012). Beyond identifying regimes, we also want to know the probability of being in a given regime at any given point in time.

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A variety of folks gave thoughtful replies: Josh Brown, Flex Salmon, David Merkel, Scott Bell, the Macro Men, and bunch of anonymous professional traders.

Yet, perhaps there is a common root cause at work, not yet stated: implicit momentum bias.

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Index Return Decomposition prompted several readers to inquire about forecasting the signs of returns, as implied by the decomposition variable. This literature tends to be a bit obtuse, due to commonly unstated stylistic assumptions regarding conditional return dynamics.

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Physics, Biology, or Peltzman? Although they have varying trading strategies, there is a common theme which unifies them: top-down systematic focus on the sociology of market participants.

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A variety of techniques exist for estimating parameters of the return decomposition model, previously introduced in Index Return Decomposition.

This assumption permits focus on estimating , providing insight into the mixing behavior of the return being decomposed: if a stock return behaves like its index, then mixing is low with small (in the limit, when a stock behaves identical to its index, as no mixing is required); in contrast, the stock return behaves independent from its index on a regular basis, then mixing is high with a large .

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This technique finds surprisingly often use in quant models.

To explain this model, let’s build it up from intuition.

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