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Some assets are know(or at-least assumed)to trend more than others. Is the probability of an asset trending equal to the probability of that same asset ranging(i.e 50-50)?

Is there a mathematical formula or theory to describe or calculate the probability of an asset to trend or range?

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  • $\begingroup$ Could you please make the terms 'trending' and 'ranging' more specific, optimally in mathematical notation? That would help the discussion, IMHO. $\endgroup$ Nov 3, 2023 at 8:31

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By trending I assume you mean $drift$ and by ranging I assume you mean $volatility$. I don't know if you can calculate the probability of an asset to trend or range, but there are measures such as the expected return, implied volatility and the Sharpe ratio that help to quantify what could be the future drift, volatility or the combination of the two.

You could run a regression on your model using historical data and test for the adjusted $R^2$ to see how well your model fits, essentially getting a "probability", but then you'd have to test for the significance of your coefficients on your regressors as well.

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