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I am trying to interpret a statement about volatility and stock returns made during an interview which I really do not understand. The original task was as follows:

Given a time series of the volatility of a single stock, and using it to predict the returns of the stock using linear regression, explain why this works well for in-sample data, not for out-of-sample data the accuracy.

The interviewer made a comment along the lines of:

Since volatility is calculated as a square root, therefore it is always positive. Furthermore, if you only have one variable, then if your beta is positive, the stock returns predicted will also be positive. However, in reality, this can be negative.

Could someone clarify this statement in relation to the original task?

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  • $\begingroup$ Not sure what the interviewer might have exactly meant but it appears like s/he has been referring to CAPM which is a statistical model. Statistical models are meant to estimate parameters or probabilities of parameters for populations. So I think the prices of some stocks, despite having positive betas, occasionally or eventually declining even if the market is up are to be expected and do not have anything to do with volatilities being indicated by positive numbers. $\endgroup$
    – Alper
    Dec 3 '21 at 8:39

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