1. Investor Sentiment

2. BW(2006): Empirical Approach
Because mispricing is hard to identify directly, the approach in this paper is to look for systematic patterns of mispricing correction.
Specifically, to identify sentiment-driven changes in cross-sectional predictability patterns, two more basic effects are needed to be controlled. One is the generic impact of investor sentiment on all stocks and the other is the generic impact of characteristics across all time periods.

3. BW(2006): Empirical Approach
In eq. (1), T is a proxy for sentiment and a1 picks up the generic effect of sentiment; x is a vector of characteristics and b1 is the generic effect of characteristics. The interest centers on b2 . The null is that b2 equals zero, and the alternative is that b2 is nonzero and reveals cross- sectional patterns in sentiment-driven mispricing.
The characteristics considered include size (ME, June of year t), age (the number of years since the firm’s first appearance on CRSP) and sigma (the standard deviation of monthly returns over the 12 months ending in June of year t), etc. Table I illustrates the summary statistics.

4. BW(2006): Empirical Approach
Investor Sentiment (p.1655)
This paper form a composite index of sentiment that is based on the common variation in six underlying proxies for sentiment. The sentiment proxies are measured annually from 1962 to 2001.
Closed-end fund discount (CEFD,封閉型基金的折 價程度): the average difference between the net asset value (NAV) of closed-end stock fund shares and their market prices. (-)
NYSE share turnover (TURN, 周轉率) (+)

5. BW(2006): Empirical Approach
The number and average first-day returns on IPOs (NIPO, RIPO) (+)
The equity share in new issues(S): The share of equity issues in total equity and debt issues (+)
Dividend premium(P): The log difference of the average market-to-book value ratios for payers and nonpayers (-)
1. The authors use principal components analysis to form a composite index that captures the common component in the six proxies and incorporate the fact that some variables take longer to reveal the same sentiment. The resulting composite index is shown in

6. BW(2006): Empirical Approach
eq. (2) (p.1657).
2. Moreover, the authors construct a second index that explicitly removes business cycle variation from each of the six proxies prior to the principal components analysis. The resulting index is shown in eq. (3) (p.1658).
3. Table II summaries and correlates the sentiment measures, and Figure 1 plots them.

7. BW(2006): Empirical Tests The empirical tests include two parts:
Sorts: Place each monthly return observation into a bin according to the decile rank that a (firm) characteristic takes at the beginning of that month, and according to the level of SENTIMENT at the previous calendar year. Then compute the equal- weighted average monthly return for each bin and look for pattern.
Predictive regressions for long-short portfolios: Use sentiment to forecast equal-weighted portfolios that are long on stocks with high values of a characteristic

8. BW(2006): Empirical Tests and short on stocks with low values.
1. Sorts: Table III and Figure 2 show the conditional effect of firms’ characteristics (the effect of characteristics conditional on sentiment).
The value effect (small firms have higher future returns) appears in low sentiment periods only. The average returns illustrate that subsequent returns tend to be higher when sentiment is low (sentiment has broad effects).

9. BW(2006): Empirical Tests
The effects of age and sigma: Investors appear to demand young and high sigma stocks when sentiment is high (resulting in lower subsequent returns), while prefer older and low sigma stocks when sentiment is low. Highly volatile and young stocks are relatively hard to value and relatively hard to arbitrage .
The effects of profitability: When sentiment is high, profitable and dividend-paying firms have higher future returns than unprofitable and nonpaying firms (0.61% and 0.75 higher). However, these firms have lower future returns (0.95% and 0.89% less) than unprofitable and

10. BW(2006): Empirical Tests
nonpaying firms when sentiment is low. Unprofitable, nonpaying firms are harder to value and to arbitrage .
The effects of growth and distress:
Unconditional effect: future returns are generally higher for high BE/ME stocks, low EF/A stocks, and low GS decile stocks.
Conditional effect: There is a inverted U-shaped pattern in the conditional difference. Firms with extreme values react more to sentiment than firms with middle values.

11. BW(2006): Empirical Tests
2. Regressions
The regression model is shown in eq. (4) (p.1667). The dependent variable is the monthly return on a long- short portfolio, and the monthly returns from January through December of year t are regressed on the sentiment index that prevailed at the end of the prior year. The results are shown in Table V.
Panel A: Returns on small, young, and high volatility firms are relatively low over the coming year when sentiment is high.

12. BW(2006): Empirical Tests
Panel B: Higher sentiment forecasts relatively higher returns on payers and profitable firms.
Panel D, E, and F: D reveals that sentiment does not predict simple high minus low portfolios formed on BE/ME, EF/A, or GS. E and F show that when sentiment is high, subsequent returns on both low and high values (of GS and EF/A) firms are low relative to more typical firms (the effects of BE/ME are insignificant).

13. Baker et al., (2012): Sentiment Indices
This paper investigates the effect of global and local components of investor sentiment on six major stock markets, at the level of the country average and the time-series of the cross-section.
Three types of sentiment indices
1. Four underlying proxies are used to form the three types of composite sentiment indices.
Volatility premium (PVOL): the yearend log of the ratio of the value-weighted average M/B of high volatility stocks to that of low volatility stocks.

14. Baker et al., (2012): Sentiment Indices
IPO volume(NIPO) and IPO first-day returns (RIPO)
Market Turnover (TURN)
2. Total sentiment index for each country
Table 2 reveals the total sentiment index coefficients for each country (loadings column). The index coefficients are estimated using the first principal component of each of the macro-orthogonalized sentiment proxies. The equations are eq. (1) ~ eq.(6).
3. Global and local sentiment indices

15. Baker et al., (2012): Sentiment Indices
The total sentiment indices are separated into one global and six local components. The global index is the first principal component of the six total indices. The loadings are reported in Table 3 (eq. (7)).
The local sentiment is the residual from regressing the total sentiment indices on the global index.

16. Baker et al., (2012): Market Returns
Hypotheses: The sentiment indices are contrarian predictors of international index-level returns. The regression models are eq. (10) and eq.(11).
Pool monthly returns from 1981 to 2006 for six countries and regress the monthly market returns for country c in year t on its beginning-of-year sentiment index value.
Total sentiment index serves as a significant contrarian predictor of market returns across these six markets. A one standard deviation increase in a country’s

17. Baker et al., (2012): Market Returns
total sentiment index is associated with 3.5 percent points per year lower value-weighted market returns.
The country-level results are mainly driven by global sentiment. A one standard deviation increase in the global sentiment index is associated with 5.4 percent points per year lower value-weighted market returns. The impact of local sentiment index is insignificant.

18. Baker et al., (2012): Cross-section of Returns
Brown and Cliff (2004), Lemmon and Portniaguina (2006), and Baker and Wurgler (2006) investigate the ability of sentiment to explain the time series of the cross section. The basic empirical prediction is that sentiment may serve as a contrarian predictor of “high sentiment beta” portfolios.
Two-way sorts
Form cross-sectional portfolios based on four firm or stock characteristics: firm size, total risk, B/M, and sales growth. Returns are equal-weighted within each

19. Baker et al., (2012): Cross-section of Returns
decile portfolio. The results are presented in Table 6.
The effect of sentiment is much smaller on low volatility stocks (-0.01 vs ) or large stocks ( vs ).
A inverted U-shaped effect of sentiment on B/M and sales growth stocks are observed, especially in the sales growth portfolios.
Time-series regression
Pool monthly long-short portfolios returns from to 2006 for six countries and regress the monthly returns

20. Baker et al., (2012): Cross-section of Returns
on the beginning-of- year sentiment index value.
The total sentiment column in Table 7 is highly consistent with the results from the sorts. In five out of six hypothesis tests, the effect of total sentiment is statistically significant with the expected sign.
The influence of local sentiment is more prominent in the cross-section (than in the market returns).