State of Investor Sentiment and Aggregate Stock Market Returns Muhammad A. Cheema, Yimei Man, and Kenneth R. Szulczyk
Abstract
The research literature shows that investor sentiment is a contrarian predictor of aggregate stock market returns; however, we contend that investor sentiment only predicts aggregate stock market returns during high sentiment states where overpricing is more prevalent than underpricing since short-sale restrictions limit the ability of rational investors to exploit overpricing but not underpricing. Using a two-state predictive regression model, we find that investor sentiment indexes of both Baker and Wurgler (2006) and Huang et al. (2014) are contrarian predictor of aggregate stock market returns at all horizons but only during high sentiment states that agrees with our suggestion.
I. Introduction
Investor sentiment portrays investor’s beliefs about future cash flows that the prevailing fundamentals cannot explain (e.g. Baker and Wurgler, 2006), which leads to mispricing. Eventually, the mispricing is corrected when the fundamentals are revealed, which makes investor sentiment a contrarian predictor of aggregate stock market returns.
However, the contrarian predictability of investor sentiment is more extensive for long-term stock market returns (e.g., Baker and Stein, 2004; Brown and Cliff, 2005) than short-term stock market returns. For example, Brown and Cliff (2004) find that investor sentiment has a negligible impact on subsequent monthly market returns. However, Huang et al. (2014) show that investor sentiment is a reliable contrarian predictor of subsequent monthly market returns at all horizons with their aligned sentiment index.
In a related strand of literature, Stambaugh et al. (2012) combine investor sentiment with Miller’s (1977) argument that short-sale restrictions limit the ability of rational investors
to exploit overpricing. Stambaugh et al. (2012) further argue that overpricing prevails more during high sentiment states where investors tend to be overoptimistic, resulting in
overpricing as a primary form of mispricing. Consistent with their argument, they find that stock market anomalies are stronger following high levels of investor sentiment suggesting that overpricing causes the mispricing of anomalies.
Following Stambaugh et al.’s (2012) argument that mispricing should prevail more during high sentiment states, we suggest that investor sentiment is a reliable contrarian predictor of aggregate stock market returns only during high sentiment states where stock prices rise above their fundamental values since short-sale restrictions limit the ability of rational investors to exploit overpricing. Consequently, investor sentiment cannot predict aggregate stock market returns during low sentiment states where stock prices lie close to fundamental values since underpricing does not restrict rational investors to buy undervalued securities.
To empirically examine the relationship between investor sentiment and subsequent aggregate stock market returns, we employ a two-state predictive regression model where high (low) sentiment state is defined as above (below) the aligned sentiment or the BW sentiment index’s median value. Our results show that the ordinary least squares (OLS) slope of aligned sentiment index of Huang et al. (2014) during high sentiment states is -0.90% (t- stat = -4.89) over subsequent month market returns; whereas it is insignificant during low sentiment states.Furthermore, we find that the OLS slope of the investor sentiment index of Baker and Wurgler (2006) (BW index) during high sentiment states is -0.83% (t-stat = -3.07) over subsequent month market returns, while it is insignificant in low sentiment states. This is a crucial finding since BW index is perceived to be a reliable contrarian predictor of returns in the cross-section such as hard to value stocks (e.g., high volatility, small size, etc.) but it shows modest statistical evidence for the aggregate market returns (e.g., Baker and Wurgler,
2007). We also find that both aligned sentiment and BW sentiment indexes are reliable predictors of subsequent 6- and 12-month market returns but again only during high sentiment states.
Our study adds a crucial contribution to the literature by showing that regardless whether investor sentiment arises from either the aligned sentiment or the BW sentiment index, investor sentiment is a contrarian predictor of aggregate stock market returns only during high sentiment states. Therefore, it is imperative to employ a two-state predictive regression model in a situation where a market wide variable (e.g., investor sentiment, market states, economic variables) can lead to either an overpriced or underpriced stock market. The rest of the paper is organized as follows, Section II describes data and methodology, Section III provides empirical findings, and the last section concludes the paper.
II. Data and Methods
We compute the market return as the log return on S&P 500 index (including dividends) minus the risk-free rate, available from Robert Shiller’s website1. We collect the orthogonalized BW index data from Jeffrey Wurgler’s website2 and orthogonalized aligned sentiment index data from Mendley3. The data sample ranges from July 1965 to October 2015.4
We run following two-state predictive regression5:
1 http://www.econ.yale.edu/~shiller/data.htm
2 http://people.stern.nyu.edu/jwurgler/
3 https://data.mendeley.com/datasets/nndf9yy426/2
4 The aligned sentiment index is available until December 2014.
5 Our two state predictive regression model resembles the two-state predictive regression model employed by Cooper et al. (2004), Boyd et al. (2005) and Huang et al. (2017). Cooper et al. (2004) use the two-state
predictive regression model to define UP and DOWN market states based on lagged market returns. Boyd et al.
𝑅𝑚,𝑡+𝑘 = 𝛼 + 𝛽ℎ𝑖𝑔ℎ.𝐷ℎ𝑖𝑔ℎ,𝑡.𝑆𝑇𝑀𝑡+ 𝛽𝑙𝑜𝑤.𝐷𝑙𝑜𝑤,𝑡. 𝑆𝑇𝑀𝑡+ 𝜇𝑡+𝑘 (1) where 𝑅𝑚,𝑡+𝑘 is the excess average monthly market returns in t+k (k=1, 6, 12) month; 𝑆𝑇𝑀 is either the BW or aligned sentiment index in month t. Dhigh (Dlow) is the high (low) sentiment state dummy that equals one when the sentiment is above (below) the sample’s median, and zero otherwise.6 We use the OLS estimation and also multivariate augmented regression method (mARM). The mARM uses the procedures of Amihud et al. (2009) to calculate the Stambaugh (1999) bias-adjusted regression coefficients.
For the out-of-sample prediction, we generate the next period’s expected market return recursively from
𝑅̂𝑚,𝑡+𝑘 = 𝛼̂𝑡+ 𝛽̂ℎ𝑖𝑔ℎ,𝑡𝐷ℎ𝑖𝑔ℎ,𝑡.𝑆𝑇𝑀𝑡+ 𝛽̂𝑙𝑜𝑤,𝑡.𝐷𝑙𝑜𝑤,𝑡𝑆𝑇𝑀𝑡 (2) Where 𝛼̂𝑡, 𝛽̂ℎ𝑖𝑔ℎ,𝑡, and 𝛽̂𝑙𝑜𝑤,𝑡are parameter estimates for the in-sample between 1965 and time t.
To evaluate the out-of-sample forecasting performance, we use the Campbell and Thompson’s (2008) out-of-sample R2 statistic that is defined as:
𝑅𝑂𝑆2 = 1 −∑𝑇𝑡=1(𝑟𝑡−𝑟̂𝑡)2
∑𝑇𝑡=1(𝑟𝑡−𝑟̄𝑡)2 (3)
Where T represents the number of out-of-sample observations, r̂ denotes the excess return forecast from equation (2) while r̄ is the historical in-sample mean. Both r̂ and r̄ are estimated recursively up to t-1 month. The out-of-sample 𝑅𝑂𝑆2 lies between (−∞, 1] and resembles the in-sample OLS R2. For a 𝑅𝑂𝑆2 > 0, the predictive regression outperforms the historical in-sample mean since the predictive regression attains a lower mean-squared forecast error (MSFE) than the MSFE of the in-sample mean. Finally, to test the statistical
(2005) use economic expansion and contraction to define the two states while Huang et al. (2017) utilize good and bad times to portray states.
6 Our results remain robust when we define high (low) sentiment state based on positive (negative) sentiment values.
significance of the ROS2 , we estimate the MSFE-adjusted statistic (C-W test) of Clark and West (2007) by regressing 𝑓𝑡+1 on a constant, defined as:
𝑓𝑡+1= (𝑟𝑡+1− 𝑟̅𝑡+1)2− [(𝑟𝑡+1− 𝑟̂𝑡+1)2 − (𝑟̅𝑡+1− 𝑟̂𝑡+1)2] (4)
III. Empirical Findings
Table 1 reports the regression slope, t-statistic, in-sample R2, and out-of-sample 𝑅𝑂𝑆2 of the two-state predictive regression. The statistical significance of regression slopes is based on the empirical p-values using a wild bootstrap procedure as in Huang et al. (2014).
For the out-of-sample performance, we use the data from July 1965 to December 1984 as an in-sample training period and from January 1985 until end of the sample as the out-of-sample period.
Panel A summarizes the results for the aligned sentiment index. Consistent with our suggestion, we find that sentiment index predicts aggregate stock market returns only during high sentiment states. For example, in high sentiment states, the OLS predictive regression slope is -0.90%, -0.76%, -0.53% per month over 1-, 6-, and 12-month market returns, respectively. All the OLS high sentiment slopes are statistically significant at 1% level. The in-sample R2swith two-state OLS predictive regression are 2.30%, 8.67% and 8.30% over the 1-, 6- and 12-month market returns, respectively, which exceeds the in-sample R2 of 1.70%, 5.99%, 6.11% with one-state OLS predictive regressionreported in Huang et al. (2014).7 The out-of-sample 𝑅𝑂𝑆2 with two-state OLS predictive regression are 1.26, 6.59, and 9.69 over 1-, 6-, and 12-month market returns, respectively, and statistically significant based on C-W test.
The out-of-sample 𝑅𝑂𝑆2 indicates a significant predictive ability of investor sentiment since an out-of-sample 𝑅𝑂𝑆2 of at least 0.50% can generate significant economic value (Campbell and
7 Huang et al. (2014) uses a sample period from July 1965 to December 2010 to calculate R2. The R2 with one- state predictive regression for our sample are similar to R2 reported in Huang et al. (2014).
Thompson, 2008). Our regression slopes based on the mARM method are similar to the OLS method.
Panel B provides the results for BW sentiment index. Consistent with our results in Panel A, we find that the sentiment index predicts aggregate stock market returns only during high sentiment states. The OLS predictive regression slope is -0.82%, -0.72%, -0.57% per month over 1-, 6- and 12- month market returns, respectively, with all high sentiment slopes statistically significant at 1% level except OLS slope for 12-month market returns at the 5%
level. The in-sample R2swith two-state OLS predictive regression are 1.13%, 4.60% and 5.74% over 1-, 6- and 12-month market returns, respectively, substantially larger than the in- sample R2s of 0.30%, 1.13%, 1.11% with the one-state OLS predictive regressionfor the BW index reported in Huang et al. (2014). The out-of-sample 𝑅𝑂𝑆2 with two-state OLS predictive regression are large and statistically significant based on C-W test except for the 1-month market returns. The mARM regression slopes are similar to the OLS method. In sum, both the aligned and BW sentiment indexes predict aggregate stock market returns only during high sentiment states but not during low sentiment states.
IV. Concluding Remarks
Using a two-state predictive regression model, we show that both the aligned and BW sentiment indexes are reliable contrarian predictors of aggregate stock market returns during high sentiment states. These results agree with a setting such as high sentiment states where overpricing prevails more than underpricing since short-sale restrictions limit the ability of rational investors to exploit overpricing but not underpricing.
Table 1: Predictive Regressions
The table summarizes the OLS and mARM parameter estimates for the two-state predictive regression 𝑅𝑚,𝑡+𝑘= 𝛼 + 𝛽ℎ𝑖𝑔ℎ.𝐷ℎ𝑖𝑔ℎ,𝑡.𝑆𝑇𝑀𝑡+ 𝛽𝑙𝑜𝑤.𝐷𝑙𝑜𝑤,𝑡. 𝑆𝑇𝑀𝑡+ 𝜇𝑡+1
Where 𝑅𝑚,𝑡+𝑘 is the excess monthly market return with k=1, 6, 12 months, STM is the level of sentiment index, and Dhigh (Dlow) is the high (low) sentiment state dummy that equals one for sentiment above (below) the sample’s median, and zero otherwise. R2 is the in-sample R-square whereas R2OS is the Campbell and Thompson (2008) out-of-sample R2OS. The t-statistics are the Newey-West adjusted t-statistics with 12 lags. The Clark and West (2007) MSFE adjusted statistic evaluates the statistical significance of 𝑅𝑂𝑆2 . The ∗∗∗, ∗∗, and ∗ denote significance at the 1%, 5%, and 10% levels, respectively.
Panel A: Aligned investor sentiment index
Method Βhigh t-stat Βlow t-stat R2 R2OS
One-month excess market returns
OLS -0.900*** -4.89 0.016 0.031 2.30 1.26**
mARM -0.918*** -4.56 0.027 0.052 3.36 0.67*
Six-month excess market returns
OLS -0.763*** -4.55 0.025 0.066 8.67 6.59***
mARM -0.775*** -4.72 0.025 0.067 11.10 7.07***
12-month excess market returns
OLS -0.532*** -2.82 0.018 0.056 8.30 9.69***
mARM -0.543*** -3.07 0.015 0.047 12.03 10.21***
Panel B: BW investor sentiment index
Method Βhigh t-stat Βlow t-stat R2 R2OS
One-month excess market returns
OLS -0.824*** -3.07 0.436 1.22 1.13 -0.37
mARM -0.861*** -3.16 0.478 1.36 3.75 -0.59
Six-month excess market returns
OLS -0.720*** -3.25 0.388 1.35 4.60 4.66***
mARM -0.731*** -3.43 0.405 1.40 6.36 2.20***
12-month excess market returns
OLS -0.568** -2.54 0.352 1.60 5.74 8.76***
mARM -0.570*** -2.73 0.356 1.60 7.56 6.85***
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