Non-Stationarity, Repricing, and Risk in Asset Returns

Summary

The document asks how unexpected changes in an asset’s return distribution relate to non-stationarity and risk. It starts from a one-period, two-asset setting in which cash-flow probabilities determine prices through a CAPM framework, then considers changes in probabilities, correlations, or expected cash flows. Such changes can trigger repricing, including cases where a lower-risk distribution still produces a lower price because expected cash flows have fallen.

The answer draws a conceptual boundary: stationarity concerns behavior over time, so a single-period economy has no time dimension in which to assess stationarity. This clarifies why the stated one-period setup cannot itself demonstrate non-stationarity. The exchange does not develop a multi-period model or classify repricing shocks as systematic or idiosyncratic risk. Those questions therefore remain open and require a time-series framework that specifies how distributional parameters evolve and how shocks relate across assets.

Key ideas

• Stationarity is a property of a process over time, not of a single-period distribution by itself.
• Unexpected changes in expected cash flows or return-distribution parameters can lead to asset repricing.
• A lower ex-ante risk level does not guarantee a higher price if expected cash flows also decline.
• The response clarifies the limits of a one-period setup but does not classify parameter changes as systematic or idiosyncratic risk.

Tags

# Non-stationarity and repricing as a source of idiosyncratic and systematic "risk"?


# Non-stationarity and repricing as a source of idiosyncratic and systematic "risk"?












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!

## Answer by Richard Hardy (score 1)

https://quant.stackexchange.com/a/75526

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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