The Wiley Finance Series : Handbook of News Analytics in Finance

Definition 5.4.LetUbe the universe of companies andCbe a company such that
C2U. Letpbe a time period denoting a certain number of days. LetPNbe the records
of all stories published withinpdays before publication of news recordNup to and
includingNsuch that 8 Ni 2 PN. For 8 Nithere exist someCwith CRS90. In other
words, every story inPNis about some companyC2U. Finally, letn¼jPNj. The
trailingsentiment ratio RUðN;SÞforUis the quantity

RUðN;SÞ¼

Xn

i¼ 1

SCðNiÞ½SCðNiÞ¼ 1 Š

Xn

i¼ 1

jSCðNiÞ½SCðNiÞ¼ 1 Šj

: ð 5 : 5 Þ

In order to compare and rank industries according to sentiment, the sentiment ratio
needs to be normalized with the objective to ‘‘neutralize’’ any industry-specific biases or
characteristics of such measure. Therefore, I suggest performing some adjustment that
considers the standard deviation of the industry-specific sentiment ratio. Such normal-
ization could depend on a trailing volatility measure, or on the empirical distribution of
the sentiment ratio of the entire backtesting period. In order to center normalized values,
I map the mean of the empirical distribution into a sentiment index value of 50, and
apply stepwise linear mapping of the remaining values based on standard deviations.
LetBibe some mapping function that depends on, where the family ofBare the
number of standard deviations away from the mean. Furthermore, letYibe a function
ofBisuch that more extreme sentiment ratios, in terms of distance to the mean, will
receive sentiment index values closer to either 0 or 100 depending on whether the
sentiment ratio is below or above its mean value, respectively.

Definition 5.4.Letbe the standard deviation ofRUover the entire backtesting period.
FixBiðÞfori2f 0 ;...;kgto be the cut-off points for a mapping function, and let
YðBiÞbe the mapping score at the cut-offBiwithYðB 0 Þ¼0andYðBkÞ¼100, then the
sentiment index valueforUatNwill be the quantity

VUðRÞ¼

YðB 0 Þ; ifRUðN;SÞ<B 0 ðÞ;

ð 1 WðRÞÞYðBiÞþWðRÞYðBiþ 1 Þ; ifB 0 ðÞRUðN;SÞ<BkðÞ;

YðBkÞ; ifRUðN;SÞBkðÞ;

8

><

>:

ð 5 : 6 Þ

with

WðRÞ¼

RUðN;SÞBiðÞ

Biþ 1 ðÞBiðÞ

; ð 5 : 7 Þ

and whereBiðÞRUðN;SÞ<Biþ 1 ðÞandi2f 0 ;...;k 1 g:

Based on the normalized indexes, it is possible to rank industries, for instance, on a
monthly basis in order to construct long and short portfolios of the top- and bottom-
ranked industries. In the following section, I will present an empirical study focusing on
the constituents of the S&P 500 equity index.

138 Quantifying news: Alternative metrics