Of course, you can remove one of those biases by using ATM IV instead of VIX (which is derived from the var swap) This *can* be useful cos it "knows" about future events, whereas your realized estimate/forecast won't unless you adjust it yourself.
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Wait - isn't it possible 1M returns aren't very predictable but 10Y returns are? That's the whole theory of long-term valuations: short-term is dominated by noise, long-term much more predictable.
That’s the cool thing about smoothing the regressor with a 10Y MA — it incorporates long horizon predictability but in a way which makes the statistical inference more reliable! The regr coefficients are identical, it is testing exactly the same thing but with better inference.
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Details of how the regression works and why it is testing the same thing are in the paper, but the core idea is that smoothing the regressors over N months and predicting 1 month is identical to forecasting price changes over N months with an unsmoothed regressor.
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Ahh... this method is in the paper I referenced, I guess you're saying. Ok, obv. I need to go back and read that paper again! It's been a long time.
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