How are Exposure, Risk, and Sentiment defined?

All document level metrics are integer counts of sentences.

Definition of Exposure

The Exposure of a document is the number of sentences $𝑠$ containing at least one of the keywords from the query:

$Exposure =\sum_{s} \mathbb{1} (\text{at least one keyword in } s)$

where $\mathbb{1}(\cdot)$is the indicator function, in this case equal to one if one keyword is in sentence $s$ and zero otherwise.

Definition of Risk

The Risk of a document is the number of sentences $𝑠$ containing at least one of the keywords from the query and at least one synonym for risk, risky, uncertain, or uncertainty:

$Risk = \sum_{s} \mathbb{1} (\text{at least one keyword in } s)\times \mathbb{1} (\text{at least one risk synonym in } s)$

where again $\mathbb{1}(\cdot)$is the indicator function.

Definition of Sentiment

The Positive Sentiment of a document is the number of sentences $𝑠$ containing at least one of the keywords from the query and at least one positive sentiment word:

$\textit{Positive Sentiment} = \sum_{s} \mathbb{1}(\text{at least one keyword in } s) \times \mathbb{1}(\text{at least one positive word in } s)$

where again $\mathbb{1}(\cdot)$is the indicator function.

The Negative Sentiment of a document is the number of sentences $𝑠$ containing at least one of the keywords from the query and at least one negative sentiment word:

$\textit{Negative Sentiment} = \sum_{s} \mathbb{1}(\text{at least one keyword in } s) \times \mathbb{1}(\text{at least one negative word in } s)$

where once more $\mathbb{1}(\cdot)$is the indicator function.

The Sentiment of a document is simply the difference between Positive Sentiment and Negative Sentiment:

$\textit{Sentiment} = \textit{Positive Sentiment} - \textit{Negative Sentiment}$

Full list of positive and negative words

NL Analytics uses the following list of positive and negative sentiment words. These words are taken from the following paper:

Tim Loughran and Bill McDonald, 2011, When is a Liability not a Liability? Textual Analysis, Dictionaries, and 10-Ks, Journal of Finance, 66:1, 35-65.

The SSRN version of their paper is here.

NL Analytics excludes 'question', 'questions' from the list of negative sentiment words. This is consistent with Hassan et al. (2019), who found that these synonyms more often than not are not used to convey negative sentiment.

Full list of synonyms for risk, risky, uncertain, and uncertainty

The following list of single-word synonyms for risk, risky, uncertain, and uncertainty are used to indicate a "risk synonym" in the above definition for Risk. The words were transcribed from the Oxford Thesaurus in early 2016.

Please note that the list has one column of synonyms for each of the four words: risk, risky, uncertain, and uncertainty. While this makes plain which single-word synonym belongs to which of the four words, it results in some duplicate single-word synonyms across columns. Our final list is the deduplicated union of these four columns.

NL Analytics excludes 'question', 'questions' and 'venture' from the list. This is consistent with Hassan et al. (2019), who found that these synonyms more often than not are not used to convey risk.