The Wiley Finance Series : Handbook of News Analytics in Finance

that the price of a stock tracked the S&P 500 index. Then, also assuming the number of
shares outstanding remains constant, its market cap back at a certain timetwill be
exactly the present market cap deflated by the percentage change of the S&P 500 since
timet.
Whenever returns for a universe of stocks are computed, something must be done to
control for outliers. This is a particularly sensitive issue when the returns are long-term,
seeing as longer holding periods tend to emphasize theright-skewednature of return
distributions (stocks can return much higher than 100%; however, they never return
below100%). Therefore in each universe of stocks we require returns to bewinsorized
(see Definition 4). For more on statistical methods of outlier-trimming, see Hempel et al.
(2005). Our approach in the definition below is fairly intuitive: if a return causes the
arithmetic average over the entire universe to move by more than 5%, replace it with the
next smallest return in the universe that does not cause such a movement. The 5%
stipulation is a reasonable limit for long-term returns derived from universes of around
200–400 events, as is the case for most of the sentiment reversal universes to be
considered.

Remark 3.When the ‘‘return’’ of an individual stock within a universe is mentioned it is
understood to be a holding period return without dividends from the closing price on
the event date to the closing price on the day when the holding period has expired. To
be precise, if a stock has closing pricep 1 on its event date and closing pricep 2 on the
holding period expiration date (assuming it was still trading), its return is computed as
ðp 2 p 1 Þ=p 1.

Definition 4.LetR¼fr 1 ;:::;rmgbe the holding period returns for a universe of stocks
Uover the time periodP. Assuming the universe is sufficiently large and such a return
exists, letridenote the largest member ofRsuch that

Xm

j¼ 1

rj=m

X

j6¼i

rj=ðm 1 Þ<5%:

In other words,riis the largest return whose absence within the universe does not cause
the arithmetic average return to drop by more than 5%. Letfrk 1 ;:::;rklgRbe such
that for eachp¼ 1 ;:::;lwe have

Xm

j¼ 1

rj=m

X

j6¼kp

rj=ðm 1 Þ5%:

In other words,rk 1 ;:::;rklare the returns whose individual absence within the universe
causes the arithmetic average return to drop by more than 5%, otherwise known as
outliers. LetR^0 be the set obtained by replacingrkpwithrifor eachp¼ 1 ;:::;l. Finally,
define thewinsorized P-return of Uto be the equally weighted average
X

r2R^0

r=m:

In computing performance for the 24 universes of sentiment reversals, it is important
to considerexcessreturns. This is especially true when the distribution of events is over a
long period of history. For example, events might cluster around bull markets, and such
universes could have good absolute returns but bad excess returns. We therefore focus

Sentiment reversals as buy signals 237