*3.1.2 The effect on the cumulative days (*�*1,0)*

Now we look at the effect of the changes in SKEW on the cumulative abnormal returns (i.e., CARs) over days �1 and 0. **Table 4** reports the results for both the NYSE (Panel A) and the NASDAQ (Panel B). Cumulative ΔSKEW represents the contemporaneous cumulative changes in SKEW over days �1 and 0. We present further evidence that SKEW has a statistical and economic effect on stock returns around analyst recommendations. That is, we find similar return patterns for Cumulative ΔSKEW to those on separated single days (i.e., day �1 and day 0). Taking the NYSE for example, for upgrades, the significantly *positive* difference (i.e., Diff = 0.83% with *t*-statistic = 8.93) indicates that the CAR (with a value of 2.53%) is stronger when the cumulative change in SKEW is *positive* (i.e., Cumulative ΔSKEW>0) than that (with a value of 1.70%) when the cumulative change in SKEW is *negative* (i.e., Cumulative ΔSKEW<0). For downgrades, the significantly *positive* difference (i.e., Diff = 0.57% with *t*-statistic = 4.89) also indicates that the CAR (with a value of �1.87%) is stronger when the cumulative change in SKEW is *positive* (i.e., Cumulative ΔSKEW> 0) than that (with a value of �2.45%) when the cumulative change in SKEW is *negative* (i.e., Cumulative ΔSKEW<0).

Next, we find that the corresponding magnitudes of the CARs are larger for the NASDAQ than the NYSE. In summary, these results provide further evidence supporting the hypothesis that abnormal returns around analyst recommendation revisions are closely correlated with contemporaneous changes in SKEW.

### *3.1.3 Additional tests*

To further validate the event results obtained in Section 3.1, we apply a simple regression model (i.e., univariate model) to test whether SKEW could act as one measure of investors' greed or fear. We write the regression model as [7]:

$$AR\_{i,t} = a + \beta \Delta \text{SKEW}\_t + \varepsilon\_{i,t},\tag{3}$$

In the regression analysis, we take day 0 for example and present the results in **Table 5**. From Panel A, we observe that the regression coefficient on the changes in SKEW (i.e., ΔSKEW) is positive and significant, with a value of 0.11 (*t*-statistic = 9.81) for upgrades and 0.09 (*t*-statistic = 5.85) for downgrades. These results suggest that an


#### **Table 4**.

*The effect of changes in SKEW on the cumulative abnormal returns (CARs) for the NYSE (Panel A) and the NASDAQ (Panel B).*


#### **Table 5.**

*Regression results for the abnormal returns (ARs) and the changes in SKEW (ΔSKEW) on recommendation revision days.*

increase in SKEW is associated with an increase in abnormal returns regardless of recommendation upgrades or downgrades. Consistent with the event results presented in Sections 3.1.1 and 3.1.2, we argue that SKEW should be a proper measure of investors' greed.

We also examine the effect of positive and negative changes in SKEW on stock abnormal returns by separatingΔSKEW into the positive part (i.e., ΔSKEWþ) and the negative part (i.e., ΔSKEW�). We estimate the following regression:

$$AR\_{i,t} = a + \beta\_1 \Delta \text{SKEW}\_t^+ + \beta\_2 \Delta \text{SKEW}\_t^- + \varepsilon\_t,\tag{4}$$

where ΔSKEW<sup>þ</sup> and ΔSKEW<sup>þ</sup> are defined as:

ΔSKEW<sup>þ</sup> *<sup>t</sup>* = ΔSKEW*t*, if ΔSKEW*<sup>t</sup>* > 0; otherwise ΔSKEW<sup>þ</sup> *<sup>t</sup>* = 0, and

ΔSKEW� *<sup>t</sup>* = ΔSKEW*t*, if ΔSKEW*<sup>t</sup>* < 0; otherwise ΔSKEW� *<sup>t</sup>* = 0.

Panel B in **Table 5** reports the results. Again, regardless of upgrades or downgrades, we observe positive and significant estimated coefficients on both ΔSKEW<sup>þ</sup> and ΔSKEW�. We also use Eqs. (3) and (4) to test the effect of changes in SKEW on the day prior to recommendation revisions (i.e., day �1), and obtain qualitatively similar results.<sup>10</sup> In summary, these results provide further evidence that SKEW could be considered as an investors' greed indicator.
