- 3. 9,649 additional multi-word expressions (MWE). To identify these, we first tag all words in the corpus using a part-of-speech tagger from the Stanford NLP group, and then tabulate tag patterns likely to correspond to meaningful sequences Justeson and Katz (1995). Our final set of MWE is the resulting trigrams that appear more than 150 times in the corpus, and bigrams that appear more than 500 times. This approach finds an additional 68 phrases also present in the dictionaries, and 265 phrases also present in named entities, and so are redundant. We then follow standard steps to complete pre-processing: • Lowercase all text (case-folding). • Tokenize text by breaking it into individual terms. Continuing from the above example, the tokenized representation of ‘We owe additional income tax’ would be the four-element list [‘we’, ‘owe’, ‘additional’, ‘income tax’].
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- A Sample and Feature Space Construction A.1 Sample of firms The following are the details on how we construct our analysis sample: • We link 3,154 firms (i) with at least one 10-K filing (with a non-empty Part 1a) from January 2010 to July 2016, and (ii) with equity return data for all business days between Feb 24, 2020 and March 27, 2020. • We remove 19 firms with no leverage information.
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- • Drop common words from a standard stopword list, e.g. ‘for’, ‘to’, etc. • Drop any terms that appear in the Risk Factors text of fewer than 25 firms from 2010 to 2016.
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- • In order to compute abnormal returns, we first need to get estimates of stocklevel betas. Hence, we keep stocks for which we have at least 125 daily return observations in 2019. We lose 28 firms in this step.
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- • We also drop small caps: either because they are in the first quartile of equity market value or because their share price is smaller than 5 dollars on February 21, 2020 (i.e. the last trading day before the stock market jump days we consider in this paper). Dropped small caps account for 2.5 percent of total equity market value in the sample. In this step, we remove 968 firms. • We discard 5 companies with no available NAICS2 code in our dataset. Finally, we keep only NAICS2 codes with at least 5 companies. We drop one firm in this last step. • We end up with an analysis sample of 2,155 stocks for 2,133 companies.
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- COVID-19 and Economic Fallout Monetary Policy Easing Fiscal Policy Stimulus Super Tuesday Aftermath Oil Price Crash Unclassified All trading days in 2019 Figure B.3: Value-Weighted Cross-Sectional IQR of U.S. Equity Returns, Daily for 2019 and for Large Daily Jumps in 2020 This Figure considers all 2,155 securities in our analysis sample. The daily cross-sectional IQR is value-weighted (i.e. by equity market value).
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- COVID-19 and Economic Fallout Monetary Policy Easing Fiscal Policy Stimulus Super Tuesday Aftermath Oil Price Crash Unclassified All trading days in 2019 Figure B.4: Value-Weighted Cross-Sectional SD of U.S. Equity Returns, Daily for 2019 and for Large Daily Jumps in 2020 This Figure considers all 2,155 securities in our analysis sample. The daily cross-sectional SD is value-weighted (i.e. by equity market value).
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- COVID-19 and Economic Fallout Monetary Policy Easing Fiscal Policy Stimulus Super Tuesday Aftermath Oil Price Crash Unclassified All trading days in 2019 ŷ = 1.1 + 0.37 max{0, x} + 0.39 max{0, −x} (0.03) (0.04) (0.05) Figure B.1: Value-Weighted Mean and Cross-Sectional SD of U.S. Equity Returns, Daily for 2019 and for Large Daily Jumps in 2020 We consider the value-weighted distribution of daily returns over 2,155 stocks for trading days in 2019 and jump days in 2020.
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- The heights on the vertical axis refer to normalized values for the histogram of 2019 returns. Mar 16 Mar 18 Mar 24 Mar 23 Mar 13 Mar 20 Mar 17 Mar 09 Mar 10 Mar 12 Mar 26 Mar 27 Mar 11 Mar 02 Mar 03 Feb 25 Feb 24 Feb 27 Mar 05 Mar 04 0 .05 .1 .15 .2 Fraction 1 2.5 4 5.5 7 Daily Cross-Security IQR of Equity Returns, %
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- The heights on the vertical axis refer to normalized values for the histogram of 2019 returns. Mar 18 Mar 16 Mar 24 Mar 09 Mar 17 Mar 23 Mar 20 Mar 13 Mar 12 Mar 26 Mar 27 Mar 10 Mar 11 Mar 02 Feb 27 Mar 05 Mar 03 Mar 04 Feb 24 Feb 25 0 .05 .1 .15 .2 Fraction 1 2.25 3.5 4.75 6 Daily Cross-Security SD of Equity Returns, %
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- The mean (s.d.) of the daily average return for trading days in 2019 is 0.12 (0.80) percent, and the mean (s.d.) of the daily SD is 1.34 (0.34). The regression has 271 observations and an R-squared of 0.61, with standard errors in parentheses. A test of the null hypothesis that the two rays have equal slopes with opposite signs yields a p-value of 0.66. Mar 24 Mar 13 Mar 26 Mar 17 Mar 10 Mar 02 Mar 04 Mar 23 Mar 03 Feb 25 Feb 24 Mar 05 Mar 27 Mar 20 Feb 27 Mar 11 Mar 18 Mar 09 Mar 12 Mar 16 0 .1 .2 .3 Fraction -12 -6.75 -1.5 3.75 9 Daily Average of Equity Returns, %
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- The mean (s.d.) of the daily average return for trading days in 2019 is 0.12 (0.80) percent.
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- The mean (s.d.) of the daily IQR for trading days in 2019 is 1.28 (0.36) percent.
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- We first find and replace meaningful phrases in the 10-K corpus with a single term in the feature space. For example, ‘We owe additional income tax’ becomes ‘We owe additional income tax’, where ‘income tax’ is treated as an individual term. This ensures that the meaning conveyed by key phrases is retained in our analysis. These phrases come from multiple sources: 1. 433 phrases from the baseline dictionaries in Baker et al. (2019). 2. 3,803 phrases that correspond to named entities that appear more than 25 times in the corpus. We identify these entities with the named entity recognizer (NER) from the Stanford NLP group. The NER finds an additional 63 entities that also appear in the dictionaries, and so are redundant.
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