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A Model-Free Measure of Aggregate Idiosyncratic Volatility and the Prediction of Market Returns

In this paper, we formally show that the cross-sectional variance of stock returns is a consistent and asymptotically efficient estimator for aggregate idiosyncratic volatility. This measure has two key advantages: it is model-free and observable at any frequency. Previous approaches have used monthly model based measures constructed from time series of daily returns. The newly proposed cross-sectional volatility measure is a strong predictor for future returns on the aggregate stock market at the daily frequency. Using the cross-section of size and book-to-market portfolios, we show that the portfolios' exposures to the aggregate idiosyncratic volatility risk predict the cross-section of expected returns.
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