#### Investor Sentiment Aligned: A Powerful Predictor of Stock Returns

**Abstract: **

**1. Introduction**

At least as early as Keynes (1936), researchers have analyzed whether investor sentiment can affect asset prices due to the well-known psychological fact that people with high (low) sentiment tend to make overly optimistic (pessimistic) judgments and choices. Empirically, a major chal-lenge for testing the importance of investor sentiment is that it is not directly observable. In their influential study, Baker and Wurgler (2006) construct a novel investor sentiment index (BW index hereafter) that aggregates the information from six proxies, and find that high investor sentiment strongly predicts low returns in the cross-section, such as stocks that are speculative and hard to arbitrage. Stambaugh, Yu, and Yuan (2012) show that investor sentiment is a significant negative predictor for the short legs of long-short investment strategies. Baker, Wurgler, and Yuan (2012) provide further international evidence for the forecasting power of investor sentiment.^{1} Howev-er, whether investor sentiment can predict the aggregate stock market is still an open question. For example, Baker and Wurgler (2007) note that the predictability on the market is statistically insignificant.

In this paper, we exploit the information of Baker and Wurgler’s (2006) six sentiment proxies in a more efficient manner to obtain a new index for the purpose of explaining the expected return on the aggregate stock market.^{2} In their pioneering study, Baker and Wurgler use the first prin-cipal component of the proxies as their measure of investor sentiment. Econometrically, the first principal component is the best combination of the six proxies that maximally represents the total variations of the six proxies. Since all the proxies may have approximation errors to the true but unobservable investor sentiment, and these errors are parts of their variations, the first principal component can potentially contain a substantial amount of common approximation errors that are not relevant for forecasting returns. Our idea is to align the investment sentiment measure with the purpose of explaining the returns by extracting the most relevant common component from the proxies. In other words, economically, we separate out information in the proxies that is relevant to the expected stock returns from the error or noise. Statistically, the partial least squares (PLS) method pioneered by Wold (1966, 1975) and extended by Kelly and Pruitt (2012, 2013) does ex-actly this job. We call the new index extracted this way the aligned investor sentiment index, which does incorporate efficiently all the relevant forecasting information from the proxies as shown by forecast encompassing tests in our applications.

^{1}There are a number of other applications and related studies. The latest number of Google citations of Baker and Wurgler (2006) reaches 1266.

^{2}The same method may apply to explaining the expected return on any other asset.

Empirically, we find that the aligned sentiment index can predict the aggregate stock market remarkably well. The monthly in- and out-of-sample R^{2}s are 1:70% and 1.23%, more than five and eight times larger than 0.30% and 0.15%, the counterparts of BW index. Since a monthly out-of-sample R^{2} of 0.5% can signal substantial economic value (Campbell and Thompson, 2008), our aligned investor sentiment index is not only statistically significant, but also economically significant in providing sizable utility gains or certainty equivalent returns for a mean-variance investor.

Our finding of strong market predictability of investor sentiment compliments in a unique way to early studies by Baker and Wurgler (2007) and many others who find investor sentiment plays an important role in explaining returns on the cross-section of stock returns. Since forecasting and understanding how the market risk premium varies over time is one of the central issues in financial research that has implications in both corporate finance and asset pricing (see, e.g., Spiegel, 2008 and Cochrane, 2011), our study suggests that investor sentiment is related to central problems in finance beyond its impact on certain segments of the market. De Long, Shleifer, Summers, and Waldmann (1990), among others, provide theoretical explanations why sentiment can cause asset price to deviate from its fundamental in the presence of limits of arbitrage even when informed traders recognize the opportunity. But almost all such theories deal with one risky asset in their analysis, that is, they effectively study the role of investor sentiment on the aggregate market. Hence, the empirical results of our paper can also be interpreted as perhaps the first strong empirical evidence supporting those theoretical models on investor sentiment.

It is of interest to compare how well the aligned investor sentiment index performs relative to al-ternative predictors, such as the short-term interest rate (Fama and Schwert, 1977; Breen, Glosten, and Jagannathan, 1989; Ang and Bekaert, 2007), the dividend yield (Fama and French, 1988; Campbell and Yogo, 2006; Ang and Bekaert, 2007), the earnings-price ratio (Campbell and Shiller, 1988), term spreads (Campbell, 1987; Fama and French, 1988), the book-to-market ratio (Kothari and Shanken, 1997; Pontiff and Schall, 1998), inflation (Fama and Schwert, 1977; Campbell and Vuolteenaho, 2004), corporate issuing activity (Baker and Wurgler, 2000), the consumption-wealth ratio (Lettau and Ludvigson, 2001), stock volatility (French, Schwert, and Stambaugh, 1987; Guo, 2006), asset accrual (Hirshleifer, Hou, and Teoh, 2009), and economic policy uncertainty (Baker, Bloom, and Davis, 2013). In our study here, we consider the same 14 most prominent predictors examined earlier by Goyal and Welch (2008). The in-sample R^{2}s of these well known macroe-conomic variables vary from 0.01% to 1.23% (only two of them exceeding 1%), all of which are

below 1.70% of the aligned investor sentiment. In terms of the out-of-sample R^{2}, none of macroe-conomic variables has a positive R^{2}, while the the aligned investor sentiment has an R^{2} of 1.23%. When each of these macroeconomic predictors is augmented in the predictive regression, the pre-dictive ability of the aligned investor sentiment is still significant and the in-sample R^{2} ranges from 1.71% to 2.72%.

Cross-sectionally, we compare how the aligned investor sentiment index performs relative to BW index. When stocks are sorted by industry, BW index has an impressive in-sample R^{2} of 1.10% in explaining the time-varying returns on Technology, but the aligned investor sentiment index raises it to 1.92%. When stocks are sorted by size, value, and momentum, the aligned investor sentiment index always increases the predictive power, and doubles the R^{2}s on average. Hence, the aligned investor sentiment index is useful cross-sectionally as well.

We also explore the economic driving force of the predictive power of the aligned investor sentiment. We ask whether the predictability comes from time variations in cash flows or discount rates. We find that the aligned investor sentiment index forecasts significantly future aggregate dividend growth (a standard cash flow proxy), but does not forecast future dividend price ratio (a proxy of discount rate), supporting that the cash flow channel is the source for predictability. In addition, the ability of investor sentiment to forecast the cross-section of stock returns is strongly correlated with its ability to forecast the cross-section of future cash flows as well. Hence, our findings are consistent with Baker and Wurgler (2007) that the low aggregate stock return following high investor sentiment seems to represent investors’ overly optimistic belief about future cash flows that cannot be justified by subsequent economic fundamentals.

The rest of the paper is organized as follows. Section 2 discusses the construction of the aligned investor sentiment index. Sections 3 and 4 provide the summary statistics of the data and the empirical results, respectively. Section 5 explores the sources of predictability, and Section 6 concludes.

Via Huang, Dashan and Jiang, Fuwei and Tu, Jun and Zhou, Guofu, Investor Sentiment Aligned: A Powerful Predictor