*3.3. Empirical Results*

#### 3.3.1. The U.S. Market

The dependent variable is the excess market return, continuously compounded log return on the S&P 500 index (including dividends), minus the risk-free rate. The risk free rate is represented by the three-month U.S. Treasury bill.

Figure 1 shows four of the sentiment indices used for the U.S. market. Both the BW index and the SPLS have a similar pattern, since they are constructed starting from the same six variables, even though using di fferent methods (PC and PLS, respectively). For this reason, the sentiment indices cannot be applied all together, but regress in separate equations.

**Figure 1.** Plot of the sentiment indices group for the entire range of 1990–2014.

Figure 2 reports two sentiment indices, SPLS, and BWORT, and stock market returns. The figure documents that the latter variable is much more volatile than the sentiment, with grea<sup>t</sup> positive and negative peaks in short periods. As discussed in (Baker and Wurgler 2006, 2007), first, orthogonalisation applied to sentiment indices reduces the systematic risk. Second, the sentiment changes are more difficult to be detected, and its volatility expressed only in periods of high speculation.

**Figure 2.** Plot of the sentiment indices, SPLS and BWORT, and the stock market returns, SEMRUS, for the entire range of 1990–2014.

Table 1 reports the results of the U.S. regression. The first four variables refer to indirect sentiment indices; the last two to (direct) consumer or market indices. All coefficients have negative posterior means, almost all the posterior mass has negative mass as the Bayesian *t*-statistics confirms and the posterior distribution assigns probability to positive numbers lower than 1%. The coefficient and the forecasts evaluation are consistent with the literature, proving that there exists a negative relationship between stock market returns and investor sentiment, supported by (Baker and Wurgler 2006, 2007; Huang et al. 2014). Economically, one-percentage change in the independent variable is associated with an average decrease of −2.20 (for the BW) in the excess market return.


**Table 1.** Set of regressions run on the U.S. market.

Note: This table reports the posterior mean of the sentiment indices used in the various regressions with US data; the Bayesian *t*-statistics, computed as the ratio of the posterior mean and the posterior standard deviation of the parameter; the probability of the positive posterior distribution. The last column gives the out-of-sample mean square error (MSPE) relative to the MSPE of the random walk benchmark. A MSPE ratio lower than 1 means that the alternative model based on the sentiment index outperforms the random walk benchmark. We measure statistical significance relative to the benchmark model using the (Diebold and Mariano 1995) *t*-tests for equality of the average loss. Asterisks indicate significance at \* 10% and \*\* 5% levels. All results are based on the whole forecast evaluation period January 2008–December 2014.

As next step, we produce one-month forecasts from January 2008 to December 2014 using an expanding window approach. We compute mean square prediction errors (MSPE) by comparing each (point) forecast to the realization. We also compute forecasts using the standard benchmark model used for studying return predictability, the random walk in mean. We report MSPE ratios by dividing the MSPE of each of our models based on one of the sentiment indices by the MSPE of the benchmark. A MSPE ratio lower than 1 means that the alternative model based on the sentiment index outperforms the random walk benchmark. A MSPE ratio larger than 1 means that the benchmark is more accurate. We also test the difference of the MSPE based on the alternative model and the one based on the benchmark model using the (Diebold and Mariano 1995) test; see (West 1996) for theoretical foundations.

Among the sentiment indices, we find that BW provides the most accurate predictions of stock market returns with a reduction on MSPE relative to the benchmark of almost 7.5%. The difference is statistically significant. This result contrasts with (Huang et al. 2014), who found the SPLS being more accurate in the out-of-sample analysis. The SPLS is still statistically superior to the benchmark, but adding the control variables in (Welch and Goyal 2008) reduces marginally its economic gains. When testing the difference in MSPE of the models based on BW and SPLS indices, the null of equal predictability is not rejected.

When comparing to the other indices, we find that all models statistically outperform the benchmark model and the VIX variable gives the lower gains. Interesting, an index like the CB\_CONS, which is made up of opinions and should be more inclined to errors, seems to be more appropriate (economically, but not statistically) to represent the investor sentiment, providing a larger predictability power than a financial variable as the VIX. We notice that the VIX and the stock variance in (Welch and Goyal 2008) dataset are highly correlated and this can create some imprecision on estimation. Finally we run two further set of regression models. The first one is a model based only on the (Welch and Goyal 2008) regressors and exclude the sentiment indices. The model gives a 3% reduction on MSPE relative to the benchmark, confirming the predictability power of the sentiment indices which all results on lower ratios. The second set of models removes control variables and apply the six sentiment indices individually in each regression. MSPE gains reduces, but BW and CB\_CONS still provide a statistical significant reduction up to 5%, providing further evidence of their predictability power.

#### 3.3.2. The European Market

In this section, we deal with the analysis and interpretation of the EU example. The excess stock market returns of the Euro Stoxx 50 is predicted through different European sentiment indices and a set of control variables.

Figure 3 plots the sentiment group on the entire sample, formed by the two Economic Sentiment Indicators, one for all Europe and one for the Eurozone, and the Consumer and Industrial Confidence Index. For making visible the trend of the series, the mean value is subtracted to the variables ESI\_EU and ESI\_EUZONE, levelling them to the other two indices. The two sentiment indices cannot be used all together because of multicollinearity issue since INDUCONF and CONSCONF are two of the five component sectors of the ESI.

**Figure 3.** Plot of the sentiment indices group for the entire range 2001–2017.

Figure 4 show the volatile pattern of Euro Stoxx 50 compared to Consumer and Industrial Indices. At the end of the 2008 the negative peak in sentiment indices due to the financial crises is evident. On the contrary, on the same period, in particular the following months, stock returns recorded an increasing evolution with positive peaks.

**Figure 4.** Plot of the economic indices, CONSCONF and INDUCONF, and the stock market returns, SEMREU, for the entire range 2001–2017.

Table 2 shows regression results. In this example, the Economic Sentiment Indicator and two specific components of it substitute the BW and SPLS indices. The economic indicators we choose are German industrial confidence index, ZEW\_DEU and IFO indicators. The choice of these two German indices comes from different reasons. First, Germany is considered as a leading country in Europe, with a stronger economic and political stability. Second, Germany is an industrial and financial centre, with contacts to many European regions. Finally, the surveys reflect optimistic and pessimistic share for the future expected economic development not only in Germany, but also in France, Italy, and other relevant countries.


**Table 2.** Set of regressions on the EU market.

*Note*: This table reports the posterior mean of the sentiment indices used in the various regressions with European data; the Bayesian *t*-statistics, computed as the ratio of the posterior mean and the posterior standard deviation of the parameter; the probability of the positive posterior distribution. The last column gives the out-of-sample mean square error (MSPE) relative to the MSPE of the random walk benchmark. A MSPE ratio lower than 1 means that the alternative model based on the sentiment index outperforms the random walk benchmark. We measure statistical significance relative to the benchmark model using the (Diebold and Mariano 1995) *t*-tests for equality of the average loss. Asterisks indicate significance at \* 10% and \*\* 5% levels. All results are based on the whole forecast evaluation period January 2008–April 2017.

Except for the Consumer Confidence Index, posterior probabilities of other variables assign large probabilities to positive numbers. Therefore, apart from CONSCONF, there is no strong evidence on the role of sentiment indices to drive the EU stock market. From the economic point of view, this can be justified by the fact that Europe has not a strong financial impact comparable to the volumes of the U.S., which has been historically the leader of the worldwide markets. Fernandes, Gonçalves, and

Vieira (Fernandes et al. 2013) concluded that the Portuguese market has tendency to be affected by the sentiment, because of the high level of collectivism in the country. The herding is counterbalanced by the presence of institutional investors, which are considered as rational. This statement could lead to think that it is likely to notice a majority of rational investors in the EU market, because of institutional level, than noise traders. The forecasting exercise over the sample 2008–2017 confirms evidence and all models perform similarly in terms of MSPE. None models statically outperform the random walk benchmark.
