The impact of economic agents perceptions on stock price
volatility
Bc. Jaroslav Bukovina, Faculty of Business and Economics, Mendel
University in Brno, [email protected]
Abstract
This paper studies perceptions of economic agents as one of factors connected with stock
price volatility. These perceptions are measured by stock price indexes and “mood
applications” on Facebook (likes, talking about it). The paper argues this information can help
us to explain deviations and volatility in stock prices during the short run. The contribution of
the paper is an empirical study accomplished on the unique database of Facebook activity.
The study presents the existence of relationship between price deviations in stock profits and
perceptions of crowds unified by stock indexes and Facebook activity.
Key Words
Facebook activity, stock indexes, stock prices deviations, perceptions of economic agents
Introduction and motivation
The volatility of stock prices is famous and still current topic in finance and economics. The
very beginning can be connected with name Charles Henry Dow who studied volatility and
created the first two stock indexes (Evensen 2013). Since then was financial market volatility
and its sources studied by thousands of economists. However, this subject attracts lots of
interest even nowadays. It was approved by the Nobel committee, when a few days ago
announced the winners of the Nobel Prize in economics for the year 2013. Eugen Fama
(1970), Lars Peter Hansen (1992) and Robert J. Shiller (1988) won Nobel Prize thanks their
great contribution to the topic of volatility at financial markets
Eugen Fama believes in effective financial markets, on the other side Robert J. Shiller thinks
opposite. He argues that psychological factors (expectations, preferences) can cause
deviations from fundamentals even a price bubbles, especially in a short run. The last example
of such behaviour was a home price bubble in the housing market in the USA where
psychological factors and positive expectations about future conditions in the economy caused
a distinct deviation from equilibrium price. (Shiller 2004)
This paper focuses on a short run profitability of stock prices and it is close to ideas of Robert
J. Shiller that financial markets and stock prices are in the short run biased by different
factors. It argues that one of influential factors is perceptions of economic agents. This
approach was studied by King (1966), Meyers (1973) or Hanousek and Kočenda (2010).
These economists generally claim that current market behaviour measured by stock indexes
has great influence on other markets and single stock prices. This idea is partially extended in
this paper together with a similar approach as was used by Bollen, Mao and Zeng (2011).
They applied really new methodology, where they argued that social media Twitter can help
predict the situation in financial markets. Presented literature studies perceptions of economic
agents generally at macroeconomic level. This paper uses microeconomic approach by
studying influence on specific stock prices. Analysis is possible thanks a unique database
(created for project IGA) which is fulfilled by Facebook activity for the 25 biggest companies
according the market capitalization. I analysed unique data recorded by Facebook together
with influence of major USA stock indexes and accomplished simple ARIMA model where is
identified current market behaviour and Facebook activity as a source of stock price volatility.
It is worth to note that this paper belongs to the first where is Facebook studied in the context
of finance and economics.
Methodology
This paper studies general market behaviour and perception of economic agents and its
influence on selected stock prices, more specifically deviations in equilibrium of stock
profitability. Profitability equilibrium was calculated by Capital asset pricing model (CAPM)
(Markowitz 1959). Market behaviour and economic perceptions were tracked by major USA
stock indexes and Facebook activity. Relationship between variables is analysed by simple
multivariate ARMA model or in other words Box-Jenkins methodology (Box, Jenkins,
Reinsel 2008) extended with independent explanatory variables. This approach allows us to
see if stock price evolution depends on past values of dependent one and/or independent
variables.
Data
The time period for all variables starts at 25. February 2013 and ends on 28. August 2013. All
variables are transformed as percentage changes of original daily returns or “talking about it”.
All financial data were recorded by Yahoo1 and mood applications were recorded by
Facebook2. No observation is missing.
Dependent variable is deviation in close stock price profitability of three companies with the
most followers on Facebook in the amount of “Likes” and “Talking about it”. Companies are
the following: Facebook, Coca Cola and McDonald.
Independent variables are major USA indexes and mood application “talking about it” for
three above mentioned companies. This study uses data of following USA indexes: Dow
Jones Composite Average (DJA), New Your Stock Exchange (NYSE), NASDAQ and S&P
500. Mood application “talking about it” is a selection of data for Facebook, Coca Cola and
McDonald from Project IGA database. Talking about it values were measured every day as a
sum of total day comments in week changes.
Model Formation
The first important step is calculation of stock profitability equilibrium. This step was
accomplished according the simple capital asset pricing model, expressed as follows:
(
)
(1)
Where
is equilibrium profitability,
is profitability of single stock price (close price) ,
is
riskless asset profitability - in this situation the token for this asset is profitability of three
months USA bonds. During the creation of this model was riskless profitability 0,02 %. Beta
is indicator of systemic risk for measured stock prices. The result of this equation is SLM
Curve and presents equilibrium profitability. The deviation in stock profitability was
calculated as
1
2
.
http://finance.yahoo.com/
https://www.facebook.com/
The relationship between variables is estimated in a second step. This paper work with a
simple multivariate model ARMA (p,q)3 extended with independent variables. Every variable
is stationary as requested by ARMA model. Model was accomplished in Gretl software.
(2)
Where
is deviation in stock profitability (
is MA process and
),
is model constant,
is white noise stochastic error term and
is AR process,
represents other
independent variables (stock indexes and talking about it).
Box Jenkins methodology is in the literature described more as an art than a science (Gujarati,
Porter 2009). I accomplished more models with different AR, MA time lags and below
presented results are models with the lowest information criteria and residuals of every model
meet the assumptions of white noise.
Results
The presentation of results needs to be connected with the understanding that above described
methodology is really simple. An original incentive of this study is question: Is there a
relationship between the behaviour of economic agents presented on Facebook and deviations
in stock price profitability? The empirical findings of above model approved positive answer,
but this paper is just the first step in this subject and latter is going to be extended with an aim
to create a more robust model. In general, the model presents reality where is deviation in
stock price profitability caused by three factors: by the past evolution of specific stock price,
by evolution of international markets and Facebook activity, i. e. talking about it.
In detail described results for each stock price can be seen in below tables. See tables I. – III.
All variables mentioned in the tables are statistically significant at least 5 % level. According
to the model, deviations in profitability for all three stock prices are caused by one or more
3
Box Jenkins methodology used to be applied when current values in time serie are explanated by past values.
Software Gretl has a specific option to use also other independent variables which can help to explain current
values of dependent one.
stock indexes in both directions (depends on the positive or negative mark of coefficient).
Coca Cola and McDonald are positively influenced by Facebook activity and stock prices of
Facebook and McDonald can be explained by past values described by AR process (Phi) or
MA process (Theta). AR, MA process and Facebook activity influence the deviations in
profitability with specific time lags. Deviation in profitability of Coca Cola stock price is not
explained by AR or MA process, in other words we can talk about simple ordinary least
square model.
From the first sight, results show great influence of stock price indexes and minimal influence
of Facebook activity. This results need to be discussed in detail. Stock indexes are expressed
in basis points where 100 basis points change is equal to 1 % change. The one percent change
in the stock index is not often a one day issue. This means that everyday deviations in
profitability are in absolute amount lower. For example in case of Coca Cola stock price,
positive 137 % change in deviation of profitability caused by 1 % change in S&P index can be
per day lower because average index day change during studied period was 28 basis points or
0,28 %. On the other side, it needs to be explained that the influence of Facebook activity can
be much higher. The one percent change in company profile comments (talking about it)
influences the profitability of McDonald stock by 8 % and Coca Cola stock by 13 %. We can
observe periods where a change in “talking about it” per day varies from 1 % to 30% or more
in both directions. This means increased volatility in stock price deviations in absolute
numbers.
Facebook
I. MA (4), observations (T = 130) Dependent variable FB_profits
Coefficient
Error
p-value
Phi_4
0,22
0,09
0,02
**
S&P
1,22
0,56
NASDAQ
-1,79
0,52
0,03
**
<0,01
***
Source: Gretl estimation
Coca Cola
II. OLS, observations (T = 126) Dependent variable: CC_profits
Coefficient
Error
p-value
NASDAQ
-0,75
0,20
<0,01
***
S&P
1,37
0,22
<0,01
***
Talkabout_CC_3
0,13
0,01
<0,01
***
Source: Gretl estimation
McDonald
III. ARMA (3,3), observations (T = 129) Dependent variable: McD_ profits
Coefficient
Error
p-value
Constant
-0,04
0,02
0,01
**
Phi_3
0,88
0,06
<0,01
***
Theta_3
-1,00
0,05
<0,01
***
DJA
0,42
0,59
<0,01
***
Talkabout_McD_1
0,08
0,03
<0,01
***
Source: Gretl estimation
Discussion
The above mentioned results are similar with another working papers or studies. Ambrosio
and Kinniry (2009) identified co-movements among stock indexes, Égert and Kočenda (2012)
documented short term movements in different markets connected with macroeconomic news
and perceptions of financial contagion. In other words current economic conditions influence
markets, indexes and specific stock prices.
In case of social media, Facebook activity and its influence is difficult to compare or discuss
the results with other studies, because actual research is aimed only at Twitter where Bollen,
Mao, Zeng (2011) described relationship between Twitter activity and Dow Jones stock index
or Mathiesen, Anghelura, Ahlgren and Jensen (2013) indicated the common features in the
complex process of decision making among users on Twitter and investors in financial
markets. According this analysis, information from social media can help us to explain stock
price volatility and this hypothesis is approved by former chapter.
As I mentioned above, this study is the first step in broader research of perceptions in
economy with influence on financial markets and concentration on new sources of economic
perceptions – social media. Positive signal of this paper is the existence of a relationship
between variables accomplished with simple methodology. Incentives and objectives of
further research lead to use more sophisticated methods and models with potential to see more
interesting information. Next studies will work with all data (25 companies) in Project IGA
database.
The field of social media is according my opinion under-researched. Modern technologies
spontaneously help to create great databases of information with potential benefits in the field
of economics, finance, marketing or psychology and researchers can help to explain
complicated economic reality by research in this field.
Conclusion
The deviations in volatility of stock prices is current topic even nowadays. Investors in
financial markets perceive this volatility as an opportunity to earn profits. However,
consequences for real economy can be in specific situations really negative. Prediction or
understanding of financial markets evolution is still complicated and identification of other
and new factors is a positive step in this subject. Previous chapters approved social media, in
particular Facebook activity as a potential new factor.
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