**2. Data and descriptive statistics**

We focus on analyst recommendation revisions for the NYSE-listed and NASDAQlisted companies, from January 2002 to December 2019. We collect data from several data sources. Analyst recommendation data are from the Institutional Brokers' Estimate System (I/B/E/S) through the Wharton Research Data System (WRDS). I/B/E/S ranks recommendations from 1 (strong buy) to 5 (sell)<sup>6</sup> . For ease of interpretation, we

<sup>4</sup> The abnormal return is only negative and with a small magnitude on day �1 for <sup>Δ</sup>SKEW<0. Taking the NYSE for example, the magnitude of abnormal return for ΔSKEW>0 is 0.60%, but it is only 0.13% for ΔSKEW<0 (roughly one-fifth of that for ΔSKEW>0).

<sup>5</sup> Except for a smaller negative return on day �1 for <sup>Δ</sup>SKEW>0, the explanation for this is similar to that in footnote 3.

<sup>6</sup> Specifically, analyst recommendations in I/B/E/S are ranked as: 1 = Strong buy, 2 = Buy, 3 = Hold,

<sup>4 =</sup> Underperform, 5 = Sell.

follow Howe. et al. [29] and Loh and Stulz [30] and reverse the recommendation ratings so that the highest (lowest) rating represents the most (least) favorable recommendation. After reversing, we have 1 = Sell, 2 = Underperform, 3 = Hold, 4 = Buy and 5 = Strong buy.<sup>7</sup> We require any analyst recommendation to have a CUSIP number and a recommendation date.

We analyze revisions, rather than levels, in analyst recommendations. This is because Jegadeesh et al. [31] find that recommendation levels provide little incremental investment value relative to other investment signals, and Jegadeesh and Kim [14] show that recommendation changes are more informative than levels in predicting stock returns. We follow Loh and Stulz [30] and calculate the difference between current and prior ratings made by the same analyst. As recommendation levels range from 1 (sell) to 5 (strong buy), recommendation revisions range from �4 to +4. We define the recommendation revision with a positive (negative) value as an upgrade (downgrade). We omit zero recommendation revisions because zero changes suggest that the analysts possess no incremental new information. We also follow Barber et al. [32] and remove outdated observations whose prior recommendation exceeds 1 year. When multiple analysts issue recommendations for one stock within one trading day, we average all of the recommendation revisions. If the average value of recommendation revisions is positive (negative), we define it as an upgrade (downgrade) [33].

We collect stock prices from the Center for Research in Security Prices (CRSP) database. To be included in our sample, the stock must have a CUSIP number and have at least 251 trading days before, and 10 days after the corresponding recommendation revisions. The absolute daily historical stock return should not exceed 65% [16]. We identify stocks listed on the NYSE and the NASDAQ using the stock exchange code (EXCHCD). The NYSE-listed stock has an EXCHCD of 1 and the NASDAQ-listed stock has an EXCHCD of 3. The NYSE and the NASDAQ index prices are extracted from www.finance.yahoo.com. SKEW and VIX data are obtained from the CBOE website.<sup>8</sup>

**Table 1** reports the yearly descriptive summary for the stocks listed on the NYSE (Panel A) and the NASDAQ (Panel B). The market capitalization (MarketCap) is computed as the share price multiplied by the total shares outstanding on the event day. The stock's market model beta is estimated over an estimate window [�251, �31] prior to the recommendation revision. For the NYSE, the MarketCap ranges from \$1 to \$461,021 million with a standard deviation of \$31,130 million. The market model beta varies from �1.359 to 5.818 and the standard deviation is 0.486. The daily historical return ranges from �0.632% to 0.621%, with a standard deviation of 0.056%. We observe a very low mean and high standard deviation of stock returns in 2002 and around 2008 and 2009. It is very clear that the year 2008–2009 is related to the global financial crisis, but the year 2002 might be affected by the NASDAQ "bubble." [34] Accordingly, we observe a higher market model beta with a value of 1.21 in 2009 and 1.24 in 2016.

<sup>7</sup> "Underperform" is a type of stock trading recommendation between "Sell" and "Hold". Clearly, analysts recommend that a stock's performance is below the average market performance. In different databases or analyst ranking systems, different terms may be used. For example, "Strong sell" and "Sell" would be used rather than "Sell" and "Underperform".

<sup>8</sup> https://www.cboe.com/us/indices/dashboard/skew/

http://www.cboe.com/products/vix-index-volatility/vix-options-and-futures/vix-index/vix-historical-data.

