**3. Empirical results**

In this section, we present our empirical results for the NYSE and the NASDAQ. We define the analyst recommendation revision date as day 0. We begin the empirical analysis by investigating the daily abnormal return (AR) over the event window surrounding the analyst recommendation revision. We use the market model to calculate AR*<sup>i</sup>* [16]:

$$R\_{i,t} = \alpha\_i + \beta\_i R\_{m,t} + \varepsilon\_{i,t},\tag{1}$$

where *Ri*,*<sup>t</sup>* is the daily return for stock *i* on date *t*, and *Rm*,*<sup>t</sup>* is the market return. *α<sup>i</sup>* and *β<sup>i</sup>* are the corresponding regression coefficients, and *ε<sup>i</sup>*,*<sup>t</sup>* is the error term. We use the NYSE composite index return and the NASDAQ composite index return as the market returns, respectively. We estimate Eq. (1) using an estimation window that covers day �251 to day �30. Following Savor [35], we calculate the abnormal return AR*i,t* as:

$$AR\_{i,t} = R\_{i,t} - \hat{\beta}\_i R\_{m,t},\tag{2}$$

where *β*^*<sup>i</sup>* is the estimated coefficient of market returns in Eq. (1).

**Table 2** reports the average daily stock ARs for upgrades and downgrades over the [�10,+10] event window.<sup>9</sup> Panel A and Panel B are for the NYSE and NASDAQ, respectively. For visualization, we take the NYSE for example to plot the average ARs for downgrades (Panel A) and upgrades (Panel B) over this event window. **Figure 1** shows the plots.

For both the NYSE and the NASDAQ, we observe that abnormal stock returns increase (decrease) considerably on the day of recommendation upwards (downwards), that is, day 0 (or event day), with some abnormal behavior on day �1. This tendency reflects analysts' perspectives on stocks' performance - upgraded (downgraded) stocks might be underestimated (overestimated) after experiencing a period of negative (positive) ARs [16].

<sup>9</sup> We also calculate ARs for the event window [�30,+10] and obtain qualitatively similar results, which are available upon request.


**Event window [**�**10,+10] Upgrades Downgrades Average AR (%)** *t***-statistics Average AR (%)** *t***-statistics** �6 �0.10 �3.51 0.14 4.82 �5 �0.16 �5.05 0.10 3.47 �4 �0.09 �3.31 0.11 3.77 �3 �0.05 �1.45 0.11 3.51 �2 -0.05 �1.68 0.18 4.63 �1 0.12 2.60 �0.12 �2.20 0 3.17 57.26 �3.47 �48.94 1 0.28 9.89 �0.22 �7.35 2 0.09 3.54 �0.10 �3.63 3 0.05 2.04 �0.08 �2.75 4 0.04 1.44 �0.05 �2.05 5 0.07 2.54 �0.01 �0.44 6 0.04 1.67 0.06 2.23

*Investors' Greed and Fear: An Event Study of Analyst Recommendations DOI: http://dx.doi.org/10.5772/intechopen.107187*

#### **Table 2.**

*The abnormal returns (ARs) around analyst recommendation revisions for the NYSE (Panel A) and the NASDAQ (Panel B).*

 �0.02 �0.64 0.03 1.16 0.03 1.05 �0.01 �0.36 0.02 0.75 �0.04 �1.51 0.00 �0.13 0.00 0.16

Furthermore, we find that the corresponding increase or decrease of abnormal returns around recommendation revisions is larger for the NASDAQ than for the NYSE. Specifically, on day 0, the average abnormal return of upgrades (downgrades) is 3.17% (�3.47%) for the NASDAQ and 1.77% (�2.02%) for the NYSE. This suggests the potential difference of stocks and investor perspectives on these stocks between the NYSE and the NASDAQ. The firms listed on the NASDAQ are generally small and young, and accordingly, their share prices are highly volatile. For example, the mean of the MarketCap for stocks listed on the NASDAQ is \$7296 million, much smaller than the mean of the MarketCap of \$13,582 million for stocks listed on the NYSE. The average standard deviation of historical returns for stocks listed on the NASDAQ (0.083%) is higher than that for stocks listed on the NYSE (0.056%).

#### **3.1 The effect of SKEW**

Similar to Kliger and Kudryavtsev [16], we document a significant relationship between abnormal returns around recommendation revisions and contemporaneous SKEW changes (ΔSKEW). To compare with Kliger and Kudryavtsev [16], we also present the results concerning VIX in the next subsection.
