The ability of disagreement to predict market returns is robust to alternative econometric methods. Also, while the disagreement index represents one type of uncertainty (see, e.g., Anderson, Ghysels, Juergens, 2009, Atmaz, Basak, 2018), it is distinct from extant uncertainty measures, such as economic uncertainty (Bali et al., 2014), treasury implied volatility (Choi et al., 2017), financial uncertainty and macro uncertainty (Jurado et al., 2015), economic policy uncertainty (Baker et al., 2016), news implied volatility (Manela and Moreira, 2017), sample variance (Welch and Goyal, 2008), and the Chicago Board Options Exchange (CBOE) volatility index (VIX). It remains significant after controlling for the 14 economic predictors in Welch and Goyal (2008), output gap in Cooper and Priestley (2009), and aggregate short interest in Rapach et al. (2016). The forecasting power of the disagreement index is not subsumed by economic predictors and uncertainty measures.
Empirically, Kelly and Pruitt (2013), Lyle and Wang (2015), Huang et al. (2015), Giglio et al. (2016), Light et al. (2017), and Gu et al. (2020), among others, show that PLS is effective at extracting factors for predicting stock returns and economic activities in the time series and cross-section. The intuition is that, as a supervised learning technique, PLS incorporates the target information-market returns-in the factor extracting procedure and teases out any common component that is uncorrelated with future market returns. Theoretically, PLS outperforms principal component analysis (PCA) in extracting factors for prediction if individual predictors contain a common (noise) component that is unrelated to future market returns. Initially proposed by Wold (1966) and further developed by Kelly, Pruitt, 2013, Kelly, Pruitt, 2015, it extracts the disagreement index with a three-pass regression filter to reduce common noises in the individual disagreement measures. PLS is chosen for information aggregation due to its simplicity and efficacy. In contrast, there are only four individual disagreement measures that are significant at the one-month horizon and four others significant at the 12-month horizon for in-sample forecasting, but none of the 24 individual measures exhibits any out-of-sample forecasting power. The in- and out-of-sample R 2s are 2.52% and 1.56% at the one-month horizon and 13.88% and 13.26% at the 12-month horizon. Over the sample period of 1969:12–2018:12, a one-standard-deviation increase in the disagreement index is associated with a 0.83% decrease in the next one-month market return and a 7.04% decrease in the next 12-month market return, where the latter is comparable to 6.6% in Yu (2011), who measures investor disagreement with analyst forecast dispersion. Empirically, we show that the 24 individual measures do have a common factor and the disagreement index significantly predicts market returns up to 12 months. To aggregate information across 24 individual measures, we propose a disagreement index by using the partial least squares (PLS) method in Kelly, Pruitt, 2013, Kelly, Pruitt, 2015. If extant measures capture disagreement, they should display commonality and have a common factor. This paper examines whether extant disagreement measures can become agreeable. 1 To date, there is a lack of research that examines disagreement measures collectively and it is unclear whether they are able to predict market returns in real time. However, unlike Baker and Wurgler (2006) sentiment index that has been widely used to capture the first moment of investor expectations (see, e.g., Yu, Yuan, 2011, Stambaugh, Yu, Yuan, 2012), investor disagreement has only been approximated through various proxies in the literature. Due to its wide impacts, Hong and Stein (2007) conclude that disagreement represents “the best horse” for behavioral finance to obtain as many insights as classical asset pricing theories. Investor disagreement, usually measured by the second moment of investor expectations, plays an important role in explaining stock returns, volatility, and trading volume. Researchers in economics and finance have long been interested in studying the effects of expectations across investors.