R-Squared, Noise, and Stock Returns

Abstract

Return R2 is the statistic obtained by regressing individual stock returns on return factors. We find that stocks with lower R2 are more difficult to value, tend to be affected by investor sentiment, attract retail investors, and are avoided by institutional investors. We examine the relation between R2 and expected stock returns, and find that stocks with lower R2 earn higher future returns. From July 1966 through June 2008, the average return on low R2 stocks exceeds that on high R2 stocks by 0.39% per month, after adjusting for the market return as well as size, value, momentum, and liquidity factors. These results are consistent with the conjecture that stocks with lower R2 have poor information quality and are more likely to be subject to noise trading. According to DeLong, Shleifer, Summers and Waldmann (1990), such stocks assume higher noise trader risk and hence command higher expected returns. Based on R2, we form a noise trader risk factor by constructing a factor mimicking portfolio that goes long on stocks with low R2 and short on stocks with high R2. We find that the sensitivities of stocks to this factor could explain the cross-section of stock returns, even when their sensitivities to other conventional return factors are controlled. The results suggest that the trading activities of noise traders are correlated and affect stock returns in a systematic way.