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1.Assuming a one period economy with two assets in which cash flows are assigned certain probabilities, using the CAPM, we can derive the P0 given the E(CF) at t1. Within this distribution, we have idiosyncratic and systematic risk (total volatility). Traditionally, it is assumed that this stochastic process is stationary.

2.However, if the stock return distribution itself changes unexpectedly (e.g., probabilities, correlations, expected cash flows), there should obviously be a repricing of the stock. Is this an example of non-stationarity? Moreover, the price movement resulting from this repricing itself, is it also idiosyncratic or systematic risk (depending on its nature) or is it some other type of risk? Is it a "risk of change in parameters"? This new distribution can have a lower risk as a whole but also a much lower E(CF), resulting in a lower price despite lower ex-ante risk!

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Stationarity as a phenomenon arises from the time dimension. In a single period economy, there is no time dimension, so we cannot talk about stationarity.

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  • $\begingroup$ I think that is what my second part of the question is about, when investors price assets using a multi-period model and a multi-period probability distribution. $\endgroup$ May 12, 2023 at 18:45
  • $\begingroup$ @LeonidKonoplev, hmm, but you mention stationarity under your first point. $\endgroup$ May 12, 2023 at 19:06

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