In the February 2010 version of their paper entitled “Long-run Idiosyncratic Volatilities and Cross-sectional Stock Returns”, Xuying Cao, and Yexiao Xu decompose idiosyncratic volatility into long-run (trend derived from monthly data) and short-run (residual noise derived from daily data) components to investigate why some studies find that idiosyncratic volatility and future stock return relate negatively and others find they relate positively. Using daily stock return data for a broad sample of U.S. stocks spanning January 1963 through June 2008, they conclude that:
- The empirical idiosyncratic risk-return relationship depends on both the volatility measurement and the measurement interval.
- Stocks with high long-run (short-run) idiosyncratic volatility tend to have relatively high (low) future returns.
- Volatility measurements that combine long-run and short-run components may find a negative, positive or null risk-return relationship depending on the degree to which the long-run or short-run component dominate. Each researcher may “look at the crystal ball from a different angle.”
- Conclusions are robust to subperiods and stock subsamples.
In summary, evidence indicates that stock return predictions based on past volatility are sensitive to the interval of measurement. Measurement over long intervals supports the conventional reward-for-risk belief, while measurement at short intervals turns this belief upside down.
