Description
In this paper, we will offer some evidence indicating that investor sentiment plays a central role in
explaining trading intensity and market trend changes. Based on both econometric and fuzzy logic
approaches, the empirical findings show that pessimistic sentiment has a particularly significant impact on
the French financial market trend. Moreover, the results suggest that the impact of pessimism on asset
returns exceeds that of optimism as a direct indicator of investor’s beliefs. Indirect indicators of agent
sentiment present more smoothed effects on these two market components. Our results indicate that
incorporating psychological factors in macro-financial models leads to better supervision and control of
the main drivers of the markets.
2214-4625/$ – see front matter © 2014 Holy Spirit University of Kaslik. Hosting by Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.aebj.2014.05.008
ARAB ECONOMICS AND BUSINESS JOURNAL 9 (2014) 115–132
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j our nal homepage: www. el sevi er. com/ l ocat e/ aebj
* Corresponding author. Tel.: +216-73-301-808; fax: +216-73-301-888.
E-mail address: [email protected]
Peer review under responsibility of Holy Spirit University of Kaslik.
Conference Title
Sensitivity of trading intensity to optimistic and pessimistic beliefs:
Evidence from the French stock market
Abderrazak Dhaoui
a
*, Naceur Khraief
b
a
University of Sousse, Erriadh City 4023, Tunisia
b
University of Sousse, Erriadh City 4023, Tunisia
A R T I C L E I N F O
Article history:
Received 20 December 13
Received in revised form 16 March 14
Accepted 09 May 14
Keywords:
Trading intensity
Market trend
Animal spirits
Fuzzy logic
A B S T R A C T
In this paper, we will offer some evidence indicating that investor sentiment plays a central role in
explaining trading intensity and market trend changes. Based on both econometric and fuzzy logic
approaches, the empirical findings show that pessimistic sentiment has a particularly significant impact on
the French financial market trend. Moreover, the results suggest that the impact of pessimism on asset
returns exceeds that of optimism as a direct indicator of investor’s beliefs. Indirect indicators of agent
sentiment present more smoothed effects on these two market components. Our results indicate that
incorporating psychological factors in macro-financial models leads to better supervision and control of
the main drivers of the markets.
© 2013 Holy Spirit University of Kaslik. Hosting by Elsevier B.V. All rights reserved.
1. Introduction
Although there are many studies supporting the Rational Expectations
Hypothesis in financial markets, the incorporation of psychology to
financial theory stills relatively a new area of research. Baker and
Nofsinger (2002) note “proponents of behavioral finance contend that
people may not always be ‘rational’, but they are always ‘human’. Thus,
behavioral finance exposes the irrationality of investors in general and
shows human fallibility in competitive markets”. Recently however,
psychological components have come to the forefront of academic
research, and this probably because of the financial crises and recessions
that emerged and for which the hypothesis of rationality failed to find
convincing evidence. The evidence in fact suggests that behavioral factors
always play a central role in financial markets. Over the last two decades
many recent studies such as Haruvy et al., (1999), Barberis et al., (1998),
© 2014 Holy Spirit University of Kaslik. Hosting by Elsevier B.V. All rights reserved.
116 ARAB ECONOMICS AND BUSINESS JOURNAL 9 (2014) 115–132
Akerlof (2009), Guldberg and Shiller (2010), emphasize psychological
factors in explaining financial crisis.
Not all the investors are rational and their demand for risky
assets is influenced by their beliefs or sentiments. Optimism, pessimism
and overconfidence help determine how in-depth the decision-making
process can be changed over the time. Baker and Wurgler (2006) show
that when agent sentiment is high (low) for stocks that are hard to value or
arbitrage; they tend to earn relatively low (high) subsequent returns. The
aim of this paper is to examine the relationship between investor
sentiment on one hand, and the trend of trade and its intensity on the other
hand. One of the most important issues investigated is the sensitivity of
investors’ behavior to their feelings and beliefs. In other words: How do
investors’ sentiments and beliefs influence their investment strategies?
We aim to analyze how the investors’ belief impacts the trading behavior
in financial markets and in what degree the market trade and the trading
intensity are sensitive to investors’ beliefs and sentiments.
We use econometric and fuzzy logic approaches to investigate
the sensitivity of both market trend and trading intensity on the investors’
beliefs. The use of the fuzzy logic approach is motivated by the need for
supervising of the investors’ sentiments and beliefs evolution. The
optimism as a positive sentiment can be built over the time, but can be
broken after a single shock. Since sentiments are not explicitly supervised
due to their fuzzy nature, classical econometric models are not suitable for
a good prevision. Fuzzy logic approach is oppositely more appropriate to
predict the relationship type between unobservable variables. This
technique was been used in Hachicha et al. (2011) to control the fuzzy
complementarity between the fundamentalists and the behaviourists in the
explanation of financial market dynamics. The authors attribute the use of
this approach to the difficulty of prediction due to the complexity and the
behavior of traders. In the same way, Bekiros (2009) used a fuzzy
approach to investigate the decision making of rational investors in
speculative stock markets and the trading strategies with behavioral
approach. Dhaoui et al. (2013) used the same approach to investigates
how human psychology drive economies and markets. They document
that the fuzzy logic controller constitutes one of the most effective
methodology that allows controlling the sensitivity financial market
component (trading volume and stock returns) to behavioral variables
such the investors’ feelings and sentiments.
Earlier studies have predicted the sentiments and beliefs
impacts only theoretically. We believe our work is an important first step
to an empirical validation of the behavioral macroeconomic model with
non-observable investors’ characteristics.
This paper contributes to the behavioral financial literature on
how investor sentiments (optimism, pessimism, overconfidence) impact
stock price movements, and it does so using French data and fuzzy logic
techniques. Our results seem to confirm a fuzzy relationship between
these variables. The remainder of this paper is organized as follows:
Section 2 presents a literature overview on investors’ sentiments and
beliefs. Section 3 deals with the description of data and the new fuzzy
methodology implemented. In section 4 we present and discuss the major
results, while section 5 concludes.
2. Literature Review
The Efficient Market Hypothesis assumes that there is perfect information
in the stock market and that the investors are rational decision makers.
However, by the start of the twenty-first century a new stream of financial
literature emerged advocating that stock prices depend on psychological
and behavioral factors. In that, the behavioral finance approach has
quickly become the dominant model for understanding the variation of
stock prices.
Behavioral finance incorporates psychological components to
counteract the widely advocated rationality in conventional finance.
Investor sentiment was introduced as a relevant factor that significantly
influences the financial market behavior. The basic idea behind this
approach is that human nature includes both rationality and animality and
the latter has more significant effect on investor behavior than the former.
Keynes was the first to suggest that emotions can influence human
behavior instead of rational processes. In his book “The General Theory
of Employment, Interest, and Money”, Keynes introduced the term
"animal spirits" as “a spontaneous urge to action rather than inaction” to
explain the economic realities. He states specifically that “most, probably,
of our decisions to do something positive, the full consequences of which
will be drawn out over many days to come, can only be taken as the
results of animal spirits […] and not at the outcome of a weighted
average of quantitative benefits multiplied by quantitative probabilities”.
In the same way as Keynes (1936), Akerlof and Shiller (2009)
suggested the incorporation of “animal spirits” to macroeconomic models.
They argue that “it is necessary to incorporate animal spirits into
macroeconomic theory in order to know how the economy really works. In
this respect the macroeconomics of the past thirty years has gone in the
wrong direction. In their attempts to clean up macroeconomics and make
it more scientific, the standard macroeconomists have imposed research
structure and discipline by focusing on how the economy would behave if
people had only economic motives and if they were also fully rational.”
Akerlof and Shiller (2009) describe different aspects of "animal
spirits" such as corruption, money illusion, stories, exuberance and
overconfidence (Akerlof and Shiller (2009), Guldberg (2010). Moreover,
other authors suggest that there exist additional factors in order to better
explain the behavioral and psychological bias on the decision-making
process in financial markets. In particular, optimism (Haruvy et al.,
(1999), Weinstein (1989), Otten (1989), pessimism (De Bondt and Thaler
(1987), Barberis et al., (1998), or overconfidence (Daniel, (1998),
Hirshleifer and Subrahmanyam (1998) have been shown to affect the
financial investment decisions.
Undoubtedly, differences in preferences and beliefs lead to
differences in investors’ behaviors. Optimistic as well as pessimistic
ARAB ECONOMICS AND BUSINESS JOURNAL 9 (2014) 115–132 117
investors adapt their behavioral trading strategy to their expectations of
future risk and return. More optimistic investors suppose that an increase
of returns will be followed by another new increase. On the other side,
more pessimistic investors suppose that the decrease on return will be
followed by a new series of down-trending behavior. Therefore, optimistic
investors are more sensitive to returns increase than to returns decrease. In
contrast, the pessimistic investors are more sensitive to the returns
decrease.
According to theoretical predictions (Hayes (1998), Jackson (2005),
Beyer and Guttman (2011), trade demand is asymmetrically responsive to
optimistic versus pessimistic analyst earnings forecasts. In expense to
these forecasts we suppose that both optimistic and pessimistic investors
react differently to an increase or a decrease in price. The more the
investor is optimistic the more her trading volume increases. In fact, the
optimistic investor expects an increase on prices because she predicts that
this increase will be followed by a new price increase, which allows her to
realize future gains. On the other side, when prices decrease the investor
continues to trade normally since she is less sensitive to negative results.
In a similar way, the more pessimistic investors expect that a decrease of
prices will be followed by a new series of decreases; as a result, they
reduce their trading volume to avoid potential losses. However, since they
are less sensitive to positive results, the pessimistic investors will trade
normally when they expect an increase in future prices.
In the same vein, the empirical evidence supports a significant and
positive relationship between price changes and trading volume. Using
daily data for both market indices and individual stocks Crouch (1970,
1998) found a positive correlation between the absolute price changes and
trading volume. Clark (1973) found also a positive relationship between
the square of the price change and aggregated trading volume using daily
data. Specifically, optimistic investors’ underestimate their exposure to
risk and exaggerate their reaction since they expect only positive results
and neglect the failure. In the same vein, Shu (2010) being aware of the
characteristics assigned to each type of sentiment, argues that optimistic
investors are less patient than those who are more pessimistic and react
aggressively by underestimating their exposure to risk. Instead, the more
pessimistic investors display a high-level of risk aversion. They become
more and more receding when they make a decision to invest in risky
assets which leads to a decrease in trading volume. Chuang, Ouyang and
Lo (2010) use a weekly data during the period January 1990 - December
2004 to supervise the change in investor sentiments in Taiwan Stock
Market. They find that the change in trading volume can be used as a
proxy for investor sentiments. They argue that a positive deviation of
trading volume implies that investor sentiment jumps to become more
optimistic and vice-versa.
For the French stock market, Rousseau, Germain and Vanhems
(2008) argue that pessimistic investors decrease their trading volume and
avoid risky assets to prevent a loss. Psychological literature assimilates
the pessimism to a statement of impotence or to an absurdity of human
existence. Alongside, the authors find that optimistic investors increase
their trading volume and invest more in risky assets waiting for a higher
yield in the future.
Carver, Scheier and Segerstrom (2010) suggest that optimism and
pessimism sentiments focus on expectancies for the future and the way
that the investors confront problems. The authors find that optimistic
investors face adversity differently than pessimistic ones. They presume
that optimistic investors use more adaptive ways and "commit" to cope
with the worst scenarios. In contrast to optimism, pessimism refers to fear,
doubt and stress, in that pessimistic investors tend to be hesitant and
doubtful in the face of different challenges. All these empirical findings
lead to the conclusion that investor sentiment constitutes an important
factor that determines the trading volume and investment strategies.
3. Data and behavioral indices
A recent study showed that the French were among the most pessimistic
people in the world; hence the French Stock Market was a suitable choice
for our study. French data are more ideal since for controlling the
influences of investor sentiments and beliefs. The French population is
prone to be the most pessimistic all over the world
*
. The optimism, as a
positive sentiment, can be built over the time, but can be broken after a
single shock; investors will be more sensitive to pessimistic aspects than
to optimistic aspects. Based on this argument the most appropriate data to
supervise the investors’ sentiments remained that reflecting the dominant
characteristic which is the pessimism in investor sentiment. The data
sample includes individual daily stock prices and trading volumes on the
CAC40 Stock Index between January 2005 and December 2011. The
analysis also required the construction of aggregate data. The output
variables include returns and trading volume of the CAC40 index. In order
to determine the input variables we need to use individual prices and
returns to calculate their average and conditional measures.
According to the behavioral finance literature “animal spirits” create
waves of optimism and pessimism. The Optimism about a given asset is
occurring when expected prices increase abnormally. However,
pessimism takes place when investors estimate a dramatic decrease in
prices. There are two direct analytical methods for measuring investor
sentiment. An optimistic investor expects an above average stock price
level at any given time. She becomes pessimist when the price falls below
the average level. Then, the average of individual stocks is used to
calculate optimism and pessimism variables of CAC40 Stock index. We
report a strong evidence of optimistic behavior when individual stock
price increases abnormally. Considering the aggregate market, the average
of conditional absolute price forms the best measure of optimism
sentiment. The investor reacts as an optimist if she realizes that the price
increase over the medium level. Then, giving the conditional expectations,
optimism about the stock price will be calculated as follows:
0pt
t
=
1
N
(P
it
|P
it
>E|P
i
])
i=1
(1)
where, Pit represents the price of the stock i at the time t and E[Pi]
the mathematical expectation of price series of the stock i at the time t.
*
According to the interview realized by the « Gallup International Association » for
the journal “Le Parisien” for the years 2011 and 2012, the French population
constitutes the most pessimistic population all over the world. For more details see:http://www.lexpress.fr/actualites/2/les-francais-champions-du-monde-du-
pessimisme-en-2011-selon-bva_949381.html ;http://www.lefigaro.fr/international/2011/01/03/01003-
20110103ARTFIG00628-les-francais-champions-du-monde-du-
pessimisme.php ;http://www.lexpress.fr/actualites/1/societe/55-des-
francais-pessimistes-pour-2012_1067011.html
118 ARAB ECONOMICS AND BUSINESS JOURNAL 9 (2014) 115–132
E|p
ì
] =
1
I
p
ìt
1
t=1
(2)
N is the number of individual stock in the French CAC 40
stock market index. We use the inverse of the absolute value since more
the stock prices are lower more likely the investors are pessimistic. A
positive correlation observed between the standard price and the trading
volume suggests a negative effect of pessimistic investor on the trading
volume. To avoid certain opposite effects we propose using the inverse of
the pessimism measurement. Therefore, giving the conditional
expectations, this index is calculated as follows:
Pcs
t
= _
1
N
(P
ìt
|P
ìt
< E|P
ì
])
N
ì=1
_
-1
× 1uu
(3)
Investor sentiment about stock prices can also be controlled by using
the following factors:
Scnt
1
= IÐ
t
=
APSI
t
ÐPSI
t
(4)
where Sent1t is defined as the Increase vs. Decrease in stock price at
the time t, APSVt represents the number of securities that experience a
price increase at the time t, and DPSVt the number of securities that know
a price decrease at the time t. Similarly,
Scnt
2
= NINÐ
t
=
NAPSI
t
NÐPSI
t
(5)
where Sent2t represents new increases vs. new decreases in stock
prices at the time t, NAPSVt defines the number of new securities that
experience a price increase at the time t, and NDPSVt denotes the number
of new securities that show a price decrease at the time t.
Market Trend (MT) gives a signal for investors’ decision: “BUY”,
“SELL” or “Hold”. The MT can be defined as the ratio of the difference
between the closing price and the lowest one observed over the latter x-
days to the difference between the highest and the lowest prices noticed
over the latter x-days. Considering weekly analysis time unit we set x
equal to the number of trading day per week, that is x equal to 5.
Therefore, using the aggregate prices of CAC40, the MT can be written as
follows:
HI =
Closing Pricc
t
-Iowcst Pricc
(t,t-5)
Eigbcst Pricc
(t,t-5)
-Iowcst Pricc
(t,t-5)
(6)
We use the trading volume as a proxy for trading intensity (TI).
Investors increase their trading when they expect an increase of prices
(optimistic sentiment). However, the trading volume decreases, if they
expect the prices to go down. Using aggregate data, this variable is
computed as follows:
II = In(IroJing Iolumc) (7)
4. Investor beliefs and sentiments: Econometric and Fuzzy
analysis
In the first step we try to control the sensitivity of MT and TI against the
investors’ beliefs and sentiments (Optimism, Pessimism, Sent1, Sent2)
using econometric modeling based on a SUR estimation.
_
TI
t
= u
û
+u
1
Opt
t
+u
2
Pex
t
+u
3
Sent
1t
+ u
4
Sent
2t
+
MT
t
= ß
û
+ß
1
Opt
t
+ß
2
Pex
t
+ß
3
Sent
1t
+ß
4
Sent
2t
+
(Model 1)
TIt : represents the Trading Intensity at time t;
MTt : represents the Market trend at time t;
OPTt : represents the investor Optimism indicator at time t;
PESt : represents the investor Pessimism indicator at time t;
Sent1t : represents the first indicator for the investor sentiment at time t;
Sent2t : represents the second indicator for the investor sentiment at time t.
The results in Table 1 show on average that the number of stocks
that experiences an increase in prices is quite higher than that of stocks
that experiences a decrease. The number of new stocks realizing an
increase reaches about more than three times the number of new stocks in
which a decrease is observed. The number of new stocks having an
increase exceeds by about 1.8 times the number of new stocks having a
decrease. Furthermore, MT is very centralized nearly to its average level.
The number of stocks having less MT is very important compared to the
number of stocks having a high MT. However the TI is centralized on
average nearly its maximal level. The differences between the average and
both the maximal and the minimal level reach respectively about 1.31681
and 2.43039. The optimism and pessimism of investors are quite weak.
They are centralized on average around their minimal levels. By
construction, the market trend is a transformation of the stock returns.
Moreover, the evolution of the trading intensity depends substantially on
the evolution of stock returns. For these reasons, the MT and TI seem to
be apparently unrelated however; they are related across their residual
terms. Thus a seemingly unrelated regression is appropriate to estimate
the multi-equation model presented above (Model 1). The estimation of a
simultaneous multi-equation model requires that this model is
overidentified. One model can be overidentified if each of his equations is
at least just-identified. To examine the overidentification of our multi-
equation model we denote W as the number of endogenous variables
included in the model; W’ is the number of endogenous variables included
in the equation; K the number of exogenous variables included in the
model; W’ the number of exogenous variables included in the equation. If
there is any restriction in each of the model equations, an equation is
qualified to be overidentified if W-1 W – W’ + K – K’. In our case, since
W-1 = W – W’ + K – K’ for each equation, the model is mainly
overidentified. Thus, a two-stage-least square estimation is more
appropriate in particular a SUR estimation is recommended. Table 2
presents the results for SUR estimation of the regression of TI and MT on
beliefs and sentiment indicators using two least square methods.
The results in Table 2 show that both MT and TI are significantly
sensitive to optimism. However, while the effect is positive on the MT it
is oppositely negative on the TI. This indicates that optimistic investors
react by decreasing their trading when the MT shows favorable evolution
of returns waiting for better results in the future. Also, the pessimism is
positively related to both MT and TI. When stock index experience
favorable tendencies, pessimistic investors express worries on future
unfavorable evolution of returns and thus liquidate their positions in
ARAB ECONOMICS AND BUSINESS JOURNAL 9 (2014) 115–132 119
increasing their sell-trading. Sent1 and Sent2 exert only significant effect
on the Market Trend. The trading intensity is not significantly sensitive to
these sentiment indicators. Investors react following their beliefs and
withdraw the individual stock characteristics as indirect sentiment proxies.
Even though the results show statistical significance, the sensitivity
of TI and MT on optimism and pessimism indicators as well as the
indicator of the last evolution that stocks experience, remains
questionable. In fact, when results indicate positive (negative) reaction of
TI to the pessimism (optimism), we cannot judge if this increase
(decrease) is due to a sell or another strategy. To find an answer to this
problem, a fuzzy control system is introduced. It allows investigating with
more preciseness the evolution of TI and MT following the variations of
the investors’ beliefs and sentiments. To explore the relationship between
MT and TI on one hand and the indicators of beliefs and sentiments (Opt,
Pes, Sent1 and Sent2) on the other hand, we present in the remainder of
this section a fuzzy model in an attempt to support and/or challenge the
econometrical results presented in Table 2.
Fuzzy logic as a branch of artificial intelligence was introduced for
the first time in 1965 by Zadeh (1965). It deals with reasoning algorithms
used to emulate human thinking and decision making. These algorithms
are used when process data cannot be represented by classical logic. For
example, when investigating the level of information that an investor
withholds, in classical logic there is a double sided result. An investor can
be either informed or uninformed. There is no an intermediate position.
However, the fuzzy logic analysis includes all intermediate positions. Not
only extreme values are considered, but also the whole range between the
two extreme values will be included. The investors can be uninformed or
quite informed or informed. In this paper we introduce a Fuzzy control
model that includes four input variables. For each input we attribute three
belief intervals: High, Medium, and Low. After defuzzification, two
output variables are controlled. Following the fuzzy logic process (IF-
THEN), the model takes the form depicted in Figure 1.
120 ARAB ECONOMICS AND BUSINESS JOURNAL 9 (2014) 115–132
Table 1- Summary statistics for dependent and independent variables.
Statistics Endogenous variables Exogenous variables
TI MT Opt Pes Sent1 Sent2
Mean 14.95998 0.738998 2.601749 2.92743 1.005945 3.279962
Min 12.52959 0.016847 0 0 0.464206 1.792425
Max 16.27679 4.104432 35 34 2.945429 5.847581
Sd 0.357970 0.424101 5.121306 5.47156 0.378252 0.859178
Skewness -0.81657 2.045383 4.296946 2.91583 1.765905 0.682185
Kurtosis 7.260038 11.58979 24.79376 11.9142 7.719614 2.680998
Table 2- Results for the SUR model estimation.
Cons. Opt Pes Sent1 Sent2 R-Squared Chi-2
TI 14.88178
(164.01)***
-0.1247673
(3.62)***
0.0617291
(-3.22)***
-0.0019077
(-0.98)
0.0021196
(1.16)
0.0711 120.10
(0.0000)
a
MT 0.0732104
(0.70)
0.4099946
(9.18)***
0.0874386
(4.45)***
0.0115987
(5.15)***
-0.0217364
(-10.32)***
0.1193 212.38
(0.0000)
b
Table 2 summarizes the results for the SUR estimation of the regression of TI and MT on beliefs and sentiment indicators. Z-statistics are given into
Brackets. *** indicate the significance level of 1%. a and b indicate the p-values of the Chi-2 test. TI denotes the trading intensity computed based on the
natural logarithm of trading volume. MT measures the Market trend which indicates the investors’ strategy (buy, sell, or hold). Explanatory variables give
information about the investors’ sentiments. Opt. and Pes. variables represent direct indicators of optimistic and pessimistic sentiments and feelings of the
investors based on their perceptions of the evolution of the stock returns. Sent1 and Sent2 give indirect information on investors’ sentiments.
Fig. 1- Fuzzy logic control system.
Fuzzy input
Fuzzy Logic process
Fuzzy output
Input data
Output data
Process
ARAB ECONOMICS AND BUSINESS JOURNAL 9 (2014) 115–132 121
TIt : Trading Intensity at time t;
MTt : Market trend at time t;
OPTt : investor Optimism indicator at time t;
PESt : investor Pessimism indicator at time t;
Sent1t : first indicator for the investor sentiment at time t;
Sent2t : second indicator for the investor sentiment at time t.
Fig. 2- The fuzzy logic model.
THEN
TI I
S
Increase
Hold
Decrease
I
S
Buy
Hold
Sell
MT
IF
OPT
PES
Sent1
Sent2
I
S
High
Medium
Low
122 ARAB ECONOMICS AND BUSINESS JOURNAL 9 (2014) 115–132
Traditional control theory poses that we must at least (i) know the
model of the controlled system, (ii) know the objective function
formulated in precise term, and (iii) be able to solve the corresponding
mathematical problem. If one of these conditions is not satisfied, the
traditional methodology will not be applicable. In our case, the model is
known, yet the objective function is unknown and cannot be formulated in
precise terms since the model includes factors that are related to human
nature and behavior which are difficult to be controlled with certainty.
Indeed, considering human psychology, an expert cannot usually express
his knowledge (beliefs and sentiments) in precise numerical terms but in
linguistic terms. Bekiros (2009, 2010) has recently utilized fuzzy logic in
economic and financial applications with highly promising results. For
our specific model, the knowledge that we extract from an expert can be
formulated in terms of rage of optimism, pessimism, overconfidence, and
the rationality varying from a low sentiment to a medium and high
sentiment. Given these specifications, the fuzzy control methodology
presents an important differentiation. The fuzzy logic control system is
presented in Figure 2. In this set-up we (i) know the expert’s control rules
formulated by words from natural language, and (ii) we produce a precise
control strategy. This methodology indeed transforms the informal expert
control rules into a precise control strategy. The fuzzy modeling system is
the process of formulating the mapping from a given input to an output
using fuzzy functions. The mapping then provides a basis from which
decisions can be made, or patterns discerned. The fuzzy logic process
concerns different steps. Figure 3 summarizes these steps.
Identification of belief
functions
&
Fuzzy sets definition affecting
investor Behavior
?? ??
Fuzzy rules construction
?? ??
Fuzzification
?? ??
Fuzzy inference module
generation
?? ??
Defuzzification
Fig. 3- Steps of the fuzzy logic process.
2.1. Identification of critical factors and belief functions
The specification of the fuzzy logic model requires to define the so-called
“belief functions”. We suppose that the investor sentiment can be
considered as Low, Medium or High, depending on what the prices are
less than a level “a”, belong to the interval [a, b], or are higher than the
level “b”, respectively. Based on the continuous uniform distribution and
considering “c” as the median of the interval [a, b], the belief function for
the fuzzy controller system can be presented as follows:
?x ( High) =
1 If P > b
x -o
b -o
If a < P < b
0 If P < a
?x (Medium) =
0 If P < a
x -o
c -o
If a < P < c
b -x
b -c
If c b
?x (Low) =
1 If P < a
b -x
b -o
If a < P < b
0 If P > b
As indicated in equations 1 and 2 our model includes 2 equations
with 4 input variables (OPT, PES, Sent1, Sent2) and 2 output variables (TI,
MT). For the optimism and pessimism input variables, we assume that
investors’ beliefs change dramatically following the evolution of stock
prices. Considering the change of prices spanning the inter-quartile
intervals optimism is considered as Higher when prices exceed the third
quartile. If prices are under the value corresponding to the first quartile the
variable “Optimism” takes the statue “Low”. Medium Optimism occurs
when prices are included into the interval [Q1, Q3]. Accordingly, the belief
function for this variable, and after considering the value Q2 to control the
Medium Optimism, can be computed as follows:
?x (High) =
1 If x > 44.41
x -S.8
S8.61
If 5.8 < x < 44.41
0 If x < 5.8
?x (Low) =
1 If x < 5.8
44.41 -x
S8.61
If 5.8 < x < 44.41
0 If x > 44.41
ARAB ECONOMICS AND BUSINESS JOURNAL 9 (2014) 115–132 123
?x (Medium) =
0 If x < 5.8
x -S.8
29.u8
If 5.8 < x < 34.88
44.41 -x
9.SS
If 34.88 < x < 44.41
0 If x > 44.41
Moreover, the belief function for the “Pessimism” input variable -
considering the same evolution of prices into these limits discussed above
- can be calculated as follows:
?x (High) =
1 If x < 4.87
SS.64 -x
28.77
If 4.87 < x < 33.64
0 If x > 33.64
?x (Medium) =
0 If x < 4.87
x -4.87
9.u7
If 4.87 < x < 13.94
SS.64 -x
19.7
If 16.94 < x < 33.64
0 If x > 33.64
?x (Low) =
1 If x > 33.64
x -4.87
28.77
If 4.87 < x < 33.64
0 If x < 4.87
In the same way we compute the modalities for the variable Sent1:
?x (Low) =
1
If x < 0.18
S -x
2.82
If Q 1 < x < 3
0 If x > 3
?x (High) =
1 If x > 3
x -u.18
2.82
If 0.18 < x < 3
0 If x < 0.18
For the variable and Sent2, the sentiment function is set as follows:
?x (Low) =
1
If x < 0.05
S -x
2.9S
If 0.05 < x < 3
0 If x > 3
?x (High) =
1 If x > 3
x -u.uS
2.9S
If 0.05 < x < 3
0 If x < 0.05
?x (Medium) =
0
If x < 0.05
x -u.uS
u.S7
If 0.05 < x < 0.42
S -x
2.8S
If 0.42 < x < 3
0 If x > 3
For the TI output variable respectively:
?x (Decrease) =
1
If x < 18.63
18.98 -x
u.SS
If 18.63 < x < 18.98
0 If x > 18.98
?x (Increase) =
1
If x > 18.98
x -18.6S
u.SS
If 18.63 < x < 18.98
0 If x < 18.63
?x (Hold) =
0
If x < 18.63
x -18.6S
u.1S
If 18.63 < x < 18.78
18.98 -x
u.2
If 18.78 < x < 18.98
0 If x > 18.98
For the MT output variable:
?x (Sell) =
1
If x < 0.29
u.68 -x
u.S9
If 0.29 < x < 0.68
0 If x > 0.68
?x (Medium) =
0
If x < 0.18
x -u.18
u.SS
If 0.18 < x < 0.71
S -x
2.29
If 0.71 < x < 3
0 If x > 3
124 ARAB ECONOMICS AND BUSINESS JOURNAL 9 (2014) 115–132
?x (Buy) =
1
If x > 0.68
x -u.29
u.S9
If 0.29 < x < 0.68
0 If x < 0.29
?x (Hold) =
0
If x < 0.29
x -u.29
u.21
If 0.29 < x < 0.5
u.68 -x
u.18
If 0.5 < x < 0.68
0 If x > 0.68
Based on the above specifications the input vs. output interface for the
“Optimism”, the “Pessimism”, “Sent1” and “Sent2” input variables is
presented below (Figures 4 to 7):
Fig. 4- Optimism input variable in the fuzzy expert system for
French stock Market.
Fig. 5- Pessimism input variable in the fuzzy expert system for
French stock Market.
Fig. 6- Sent1 input variable in the fuzzy expert system for French
stock Market.
Fig. 7- Sent2 input variable in the fuzzy expert system for
French stock Market.
Similarly, the output data interaction corresponding to the “Market
trend” and the “Trading intensity” belief functions are presented in
Figures 8 and 9:
Fig. 8- Market Trend output variable in fuzzy expert system for
French stock Market.
Fig. 9- Trading Intensity output variable in fuzzy expert system
for French stock Market.
ARAB ECONOMICS AND BUSINESS JOURNAL 9 (2014) 115–132 125
2.2. Fuzzy rules construction
In the proposed model with 4 inputs and 2 outputs the IF-THEN rules are
formulated as shown in Figure 12. The range of each input and output
variables is given in parenthesis. The range for each variable changes
between the min and the max value of data. The Rules for the fuzzy logic
process are analyzed in detail in Table 3. In addition, the fuzzy rule base
view of the fuzzy expert system is presented in Figure 13.
126 ARAB ECONOMICS AND BUSINESS JOURNAL 9 (2014) 115–132
Figure 10: Detailed structure of the fuzzy system
Fig. 10- Detailed structure of the fuzzy system.
Input 1
Opt (0 51.33)
Input 2
Pes (0 39.77)
Input 3
Sent1 (0 39)
Input 4
Sent2 (0 35)
Rule 1 : OPT is High and PES is Low and Sent1
is High and Sent2 is High, then MT is Buy and TI
Rule 2 : OPT is Low and PES is High and Sent1
is Low and Sent2 is Low , then MT is Sell and TI
Rule 3 : OPT is Med and PES is Low and Sent1 is
Low and Sent2 is Med, then MT is Hold and TI is
Rule 4 : OPT is Low and PES is High and Sent1
is Low and Sent2 is High, then MT is Decrease
.
.
.
Rule 81 : OPT is High and PES is Low and Sent1
is Med and Sent2 is Low, then MT is Increase
?
Output 1
TI
(17.5 19.78)
Output 2
MT
(0.04 0.95)
The inputs are crisp (non-
fuzzy) numbers limited to
a specific range
Parallel evaluation using Fuzzy
reasoning of all rules
Combination and
defuzzification of the
rules
The result is a crisp
(non -fuzzy) number
ARAB ECONOMICS AND BUSINESS JOURNAL 9 (2014) 115–132 127
Table 3- Fuzzy system Rules.
If Then If Then If Then
N° Opt Sent1 Sent2 Pes TI MT N° Opt Sent1 Sent2 Pes TI MT N° Opt Sent1 Sent2 Pes TI MT
1 High High High High Increase Buy 28 Med High High High Increase Buy 55 Low High High High Hold Hold
2 High High High Med Increase Buy 29 Med High High Med Increase Buy 56 Low High High Med Increase Buy
3 High High High LOW Increase Buy 30 Med High High LOW Increase Buy 57 Low High High LOW Increase Buy
4 High High Med High Increase Buy 31 Med High Med High Hold Hold 58 Low High Med High Decrease Sell
5 High High Med Med Increase Buy 32 Med High Med Med Increase Buy 59 Low High Med Med Hold Hold
6 High High Med LOW Increase Buy 33 Med High Med LOW Increase Buy 60 Low High Med LOW Increase Buy
7 High High Low High Hold Hold 34 Med High Low High Decrease Sell 61 Low High Low High Decrease Sell
8 High High Low Med Increase Buy 35 Med High Low Med Hold Hold 62 Low High Low Med Decrease Sell
9 High High Low LOW Increase Buy 36 Med High Low LOW Increase Buy 63 Low High Low LOW Hold Hold
10 High Med High High Increase Buy 37 Med Med High High Hold Hold 64 Low Med High High Decrease Sell
11 High Med High Med Increase Buy 38 Med Med High Med Increase Buy 65 Low Med High Med Hold Hold
12 High Med High LOW Increase Buy 39 Med Med High LOW Increase Buy 66 Low Med High LOW Increase Buy
13 High Med Med High Hold Hold 40 Med Med Med High Decrease Sell 67 Low Med Med High Decrease Sell
14 High Med Med Med Increase Buy 41 Med Med Med Med Hold Hold 68 Low Med Med Med Decrease Sell
15 High Med Med LOW Increase Buy 42 Med Med Med LOW Increase Buy 69 Low Med Med LOW Hold Hold
16 High Med Low High Decrease Sell 43 Med Med Low High Decrease Sell 70 Low Med Low High Decrease Sell
17 High Med Low Med Hold Hold 44 Med Med Low Med Decrease Sell 71 Low Med Low Med Decrease Sell
18 High Med Low LOW Increase Buy 45 Med Med Low LOW Hold Hold 72 Low Med Low LOW Decrease Sell
19 High Low High High Hold Hold 46 Med Low High High Decrease Sell 73 Low Low High High Decrease Sell
20 High Low High Med Increase Buy 47 Med Low High Med Hold Hold 74 Low Low High Med Decrease Sell
21 High Low High LOW Increase Buy 48 Med Low High LOW Increase Buy 75 Low Low High LOW Hold Hold
22 High Low Med High Decrease Sell 49 Med Low Med High Decrease Sell 76 Low Low Med High Decrease Sell
23 High Low Med Med Hold Hold 50 Med Low Med Med Decrease Sell 77 Low Low Med Med Decrease Sell
24 High Low Med LOW Increase Buy 51 Med Low Med LOW Hold Hold 78 Low Low Med LOW Decrease Sell
25 High Low Low High Decrease Sell 52 Med Low Low High Decrease Sell 79 Low Low Low High Decrease Sell
26 High Low Low Med Decrease Sell 53 Med Low Low Med Decrease Sell 80 Low Low Low Med Decrease Sell
27 High Low Low LOW Hold Hold 54 Med Low Low LOW Decrease Sell 81 Low Low Low LOW Decrease Sell
128 ARAB ECONOMICS AND BUSINESS JOURNAL 9 (2014) 115–132
Fig. 11- Rules base view of the fuzzy expert system.
ARAB ECONOMICS AND BUSINESS JOURNAL 9 (2014) 115–132 129
2.3. Results and sensitivity analysis
Figures 12 to 23 present the sensitivity analysis of the fuzzy
system to trading intensity and market trend. In particular, Figures 12
and 13 show that the market trend is more sensitive than the trading
intensity to the change in the rage of optimism and pessimism inputs.
Considering the sensitivity for the optimism and the pessimism,
investors decrease slowly their trading activity even if the market
trend is “Sell”, i.e., corresponding to high pessimism and low
optimism. However, they increase aggressively their trading activity
when the market trend becomes “Buy”, which corresponds to high
optimism and low pessimism. The sensitivity to medium optimism
and medium pessimism is higher for the case of the market trend
output variable than for the case of trading intensity. Despite this
difference in sensitivity, we see that the weight of the two inputs
(optimism and pessimism) is almost identical in terms of impact on
each individual output. The effect is almost symmetric.
Fig. 12- Optimism-Pessimism sensitivity analysis of fuzzy system
for trading intensity.
Fig. 13- Optimism-Pessimism sensitivity analysis of fuzzy system
for market trend.
Figures 14 and 15 show that the sensitivity of both trading intensity and
market trend to the change in rage of optimism and Sent1 remains about the
same with a non-significant difference in sensitivity when the input
variables take the level High for Sent1 and Low of Optimism. The
sensitivity of both to the input Optimism is much higher than to the input
Sent1. We see clearly that the change in range for the optimism affects
significantly the trading intensity and the market trend. Instead, only
extreme value of Sent1 influence the two output variables. In fact,
regardless of the change in Optimism input variable, trading intensity is
“Decrease” and market trend is “Sell” when Sent1 is “Low”. However
when Sent1 is “Medium” or “High” trading intensity and market trend
become respectively “Increase” and “Buy”. Overall, the change in range
for the Optimism input variable induces significant a change in trading
intensity and the market trend.
Fig. 14- Optimism - Sent1 sensitivity analysis of fuzzy system
for Trading Intensity.
Fig. 15- Optimism - Sent1 sensitivity analysis of fuzzy system
for Market Trend.
In the same way, figures 16 and 17 show similar sensitivity for both
trading intensity and market trend to Optimism and Sent2 input variables.
However, the sensitivity to the Optimism input variable is higher than that
to Sent2 input variable. A Medium range of Sent2 has no significant effect
on the change in trading intensity or the market trend. Only extreme levels
(High or Low) have significant influences. However, the two output
variables are significantly sensitive to the change in range of the Optimism
input variable.
130 ARAB ECONOMICS AND BUSINESS JOURNAL 9 (2014) 115–132
Fig. 16- Optimism - Sent2 sensitivity analysis of fuzzy system for
Trading Intensity.
Fig. 17- Optimism - Sent2 sensitivity analysis of fuzzy system for
Market Trend.
Next, Figures 18 and 19 show clear differences in sensitivity for
Trading Intensity and Market Trend to Pessimism and Sent1 input
variables. Whereas the sensitivity of the TI to the pessimism input variable
is fairly smooth, the sensitivity of the MT is more observable especially
when the input variable takes medium values. Moreover, the change in
range for the Sent1 input variable is insignificant on both TI and MT output
variables once this input variable takes a medium value. The sensitivity of
output variable becomes significant when the Sent1 input variable is
“High” or “Low”.
Fig. 18- Pessimism - Sent1 sensitivity analysis of fuzzy system for
Trading Intensity.
Fig. 19- Pessimism - Sent1 sensitivity analysis of fuzzy system for
Market Trend.
The sensitivity of both TI and MT to the two input variables “Sent2”
and “Pessimism” is about the same to that observed for the “Sent1” and the
“Pessimism” as shown in Figures 20 and 21. In fact, while TI is less
sensitive to the medium pessimism, the MT is highly sensitive to this same
range of change in pessimism. Medium value in “Sent2” has however
insignificant impact on the two output variables.
Fig. 20- Pessimism - Sent2 sensitivity analysis of fuzzy system for
Trading Intensity.
Fig. 21- Pessimism - Sent2 sensitivity analysis of fuzzy system
for Market Trend.
Finally, Figures 22 and 23 present that there is no significant difference in
sensitivity to the change in rage of the two indicators of investors’
sentiment Sent1 and Sent2 for both the Trading Intensity and the Market
Trend. The investors tend to increase their trading and to choose the
strategy Buy when both Sent1 and Sent2 are “High”. Once the two investor
sentiment indicators are “Low” Investors tend to decrease their trading.
However they prefer to Hold or choose to keep a “normal” level of trading
when one single indicator of sentiment tends to be closer to the “High”
level and the other indicator remains “Low”.
ARAB ECONOMICS AND BUSINESS JOURNAL 9 (2014) 115–132 131
Fig. 22- Sent1 - Sent2 sensitivity analysis of fuzzy system for
Trading Intensity.
Fig. 23- Sent1 - Sent2 sensitivity analysis of fuzzy system for
Market Trend.
These findings indicate that human psychology matters significantly when
decision-making is performed in financial markets. The strategy the market
agents choose (sell or buy) is significantly sensitive to the change in their
anticipations and to their optimistic and pessimistic beliefs. This confirms
the theoretical predictions and accords with the conclusions of Keynes
(1936) that all of our decisions are taken as the result of the influence of
psychological factors or “animal spirits”. Our results also follow the
theoretical implications of Akerlof and Shiller (2009) who conclude that
human psychology drives economies and markets and suggest to always
incorporate psychological factors into macro-financial theory in order to
understand “how the economy really works” (Kahneman, 2003).
3. Conclusion
This paper attempts to investigate the sensitivity of various investment
strategies to the investor sentiment. We focus on French stock market
because we wish to control for the level of financial sector development in
this country. We revealed through an exhaustive analysis that trading
intensity and market trend are both highly sensitive to investor sentiments
and beliefs. Mainly, these two variables are more sensitive to a pessimistic
investor sentiment than to optimistic one. This result is attributed to the
fact that the optimistic sentiment can be built over the long time, but can be
broken after a single shock, and hence pessimism dominates optimism.
Indirect indicators of agent beliefs present more smoothed effects on these
two market components. These results verify that the incorporation of
psychological factors in financial modeling may lead efficiently to
enhanced control of market trading behavior.
Considering the results of the fuzzy logic, investors are required to give
more attention to their feelings and sentiments. The pessimistic sentiment
presents a heavy impact on their decision making. Optimism can be built
over a long time but can be broken suddenly and a pessimistic sentiment
rises dramatically. When making decision, investors must take into account
the feeling and the sentiments of others decision makers and incorporate
their perceptions as a fundamental factor having impact on the market
behavior (evolution of trading and returns).
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doc_472630261.pdf
In this paper, we will offer some evidence indicating that investor sentiment plays a central role in
explaining trading intensity and market trend changes. Based on both econometric and fuzzy logic
approaches, the empirical findings show that pessimistic sentiment has a particularly significant impact on
the French financial market trend. Moreover, the results suggest that the impact of pessimism on asset
returns exceeds that of optimism as a direct indicator of investor’s beliefs. Indirect indicators of agent
sentiment present more smoothed effects on these two market components. Our results indicate that
incorporating psychological factors in macro-financial models leads to better supervision and control of
the main drivers of the markets.
2214-4625/$ – see front matter © 2014 Holy Spirit University of Kaslik. Hosting by Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.aebj.2014.05.008
ARAB ECONOMICS AND BUSINESS JOURNAL 9 (2014) 115–132
Contents lists available at ScienceDirect
ScienceDirect
j our nal homepage: www. el sevi er. com/ l ocat e/ aebj
* Corresponding author. Tel.: +216-73-301-808; fax: +216-73-301-888.
E-mail address: [email protected]
Peer review under responsibility of Holy Spirit University of Kaslik.
Conference Title
Sensitivity of trading intensity to optimistic and pessimistic beliefs:
Evidence from the French stock market
Abderrazak Dhaoui
a
*, Naceur Khraief
b
a
University of Sousse, Erriadh City 4023, Tunisia
b
University of Sousse, Erriadh City 4023, Tunisia
A R T I C L E I N F O
Article history:
Received 20 December 13
Received in revised form 16 March 14
Accepted 09 May 14
Keywords:
Trading intensity
Market trend
Animal spirits
Fuzzy logic
A B S T R A C T
In this paper, we will offer some evidence indicating that investor sentiment plays a central role in
explaining trading intensity and market trend changes. Based on both econometric and fuzzy logic
approaches, the empirical findings show that pessimistic sentiment has a particularly significant impact on
the French financial market trend. Moreover, the results suggest that the impact of pessimism on asset
returns exceeds that of optimism as a direct indicator of investor’s beliefs. Indirect indicators of agent
sentiment present more smoothed effects on these two market components. Our results indicate that
incorporating psychological factors in macro-financial models leads to better supervision and control of
the main drivers of the markets.
© 2013 Holy Spirit University of Kaslik. Hosting by Elsevier B.V. All rights reserved.
1. Introduction
Although there are many studies supporting the Rational Expectations
Hypothesis in financial markets, the incorporation of psychology to
financial theory stills relatively a new area of research. Baker and
Nofsinger (2002) note “proponents of behavioral finance contend that
people may not always be ‘rational’, but they are always ‘human’. Thus,
behavioral finance exposes the irrationality of investors in general and
shows human fallibility in competitive markets”. Recently however,
psychological components have come to the forefront of academic
research, and this probably because of the financial crises and recessions
that emerged and for which the hypothesis of rationality failed to find
convincing evidence. The evidence in fact suggests that behavioral factors
always play a central role in financial markets. Over the last two decades
many recent studies such as Haruvy et al., (1999), Barberis et al., (1998),
© 2014 Holy Spirit University of Kaslik. Hosting by Elsevier B.V. All rights reserved.
116 ARAB ECONOMICS AND BUSINESS JOURNAL 9 (2014) 115–132
Akerlof (2009), Guldberg and Shiller (2010), emphasize psychological
factors in explaining financial crisis.
Not all the investors are rational and their demand for risky
assets is influenced by their beliefs or sentiments. Optimism, pessimism
and overconfidence help determine how in-depth the decision-making
process can be changed over the time. Baker and Wurgler (2006) show
that when agent sentiment is high (low) for stocks that are hard to value or
arbitrage; they tend to earn relatively low (high) subsequent returns. The
aim of this paper is to examine the relationship between investor
sentiment on one hand, and the trend of trade and its intensity on the other
hand. One of the most important issues investigated is the sensitivity of
investors’ behavior to their feelings and beliefs. In other words: How do
investors’ sentiments and beliefs influence their investment strategies?
We aim to analyze how the investors’ belief impacts the trading behavior
in financial markets and in what degree the market trade and the trading
intensity are sensitive to investors’ beliefs and sentiments.
We use econometric and fuzzy logic approaches to investigate
the sensitivity of both market trend and trading intensity on the investors’
beliefs. The use of the fuzzy logic approach is motivated by the need for
supervising of the investors’ sentiments and beliefs evolution. The
optimism as a positive sentiment can be built over the time, but can be
broken after a single shock. Since sentiments are not explicitly supervised
due to their fuzzy nature, classical econometric models are not suitable for
a good prevision. Fuzzy logic approach is oppositely more appropriate to
predict the relationship type between unobservable variables. This
technique was been used in Hachicha et al. (2011) to control the fuzzy
complementarity between the fundamentalists and the behaviourists in the
explanation of financial market dynamics. The authors attribute the use of
this approach to the difficulty of prediction due to the complexity and the
behavior of traders. In the same way, Bekiros (2009) used a fuzzy
approach to investigate the decision making of rational investors in
speculative stock markets and the trading strategies with behavioral
approach. Dhaoui et al. (2013) used the same approach to investigates
how human psychology drive economies and markets. They document
that the fuzzy logic controller constitutes one of the most effective
methodology that allows controlling the sensitivity financial market
component (trading volume and stock returns) to behavioral variables
such the investors’ feelings and sentiments.
Earlier studies have predicted the sentiments and beliefs
impacts only theoretically. We believe our work is an important first step
to an empirical validation of the behavioral macroeconomic model with
non-observable investors’ characteristics.
This paper contributes to the behavioral financial literature on
how investor sentiments (optimism, pessimism, overconfidence) impact
stock price movements, and it does so using French data and fuzzy logic
techniques. Our results seem to confirm a fuzzy relationship between
these variables. The remainder of this paper is organized as follows:
Section 2 presents a literature overview on investors’ sentiments and
beliefs. Section 3 deals with the description of data and the new fuzzy
methodology implemented. In section 4 we present and discuss the major
results, while section 5 concludes.
2. Literature Review
The Efficient Market Hypothesis assumes that there is perfect information
in the stock market and that the investors are rational decision makers.
However, by the start of the twenty-first century a new stream of financial
literature emerged advocating that stock prices depend on psychological
and behavioral factors. In that, the behavioral finance approach has
quickly become the dominant model for understanding the variation of
stock prices.
Behavioral finance incorporates psychological components to
counteract the widely advocated rationality in conventional finance.
Investor sentiment was introduced as a relevant factor that significantly
influences the financial market behavior. The basic idea behind this
approach is that human nature includes both rationality and animality and
the latter has more significant effect on investor behavior than the former.
Keynes was the first to suggest that emotions can influence human
behavior instead of rational processes. In his book “The General Theory
of Employment, Interest, and Money”, Keynes introduced the term
"animal spirits" as “a spontaneous urge to action rather than inaction” to
explain the economic realities. He states specifically that “most, probably,
of our decisions to do something positive, the full consequences of which
will be drawn out over many days to come, can only be taken as the
results of animal spirits […] and not at the outcome of a weighted
average of quantitative benefits multiplied by quantitative probabilities”.
In the same way as Keynes (1936), Akerlof and Shiller (2009)
suggested the incorporation of “animal spirits” to macroeconomic models.
They argue that “it is necessary to incorporate animal spirits into
macroeconomic theory in order to know how the economy really works. In
this respect the macroeconomics of the past thirty years has gone in the
wrong direction. In their attempts to clean up macroeconomics and make
it more scientific, the standard macroeconomists have imposed research
structure and discipline by focusing on how the economy would behave if
people had only economic motives and if they were also fully rational.”
Akerlof and Shiller (2009) describe different aspects of "animal
spirits" such as corruption, money illusion, stories, exuberance and
overconfidence (Akerlof and Shiller (2009), Guldberg (2010). Moreover,
other authors suggest that there exist additional factors in order to better
explain the behavioral and psychological bias on the decision-making
process in financial markets. In particular, optimism (Haruvy et al.,
(1999), Weinstein (1989), Otten (1989), pessimism (De Bondt and Thaler
(1987), Barberis et al., (1998), or overconfidence (Daniel, (1998),
Hirshleifer and Subrahmanyam (1998) have been shown to affect the
financial investment decisions.
Undoubtedly, differences in preferences and beliefs lead to
differences in investors’ behaviors. Optimistic as well as pessimistic
ARAB ECONOMICS AND BUSINESS JOURNAL 9 (2014) 115–132 117
investors adapt their behavioral trading strategy to their expectations of
future risk and return. More optimistic investors suppose that an increase
of returns will be followed by another new increase. On the other side,
more pessimistic investors suppose that the decrease on return will be
followed by a new series of down-trending behavior. Therefore, optimistic
investors are more sensitive to returns increase than to returns decrease. In
contrast, the pessimistic investors are more sensitive to the returns
decrease.
According to theoretical predictions (Hayes (1998), Jackson (2005),
Beyer and Guttman (2011), trade demand is asymmetrically responsive to
optimistic versus pessimistic analyst earnings forecasts. In expense to
these forecasts we suppose that both optimistic and pessimistic investors
react differently to an increase or a decrease in price. The more the
investor is optimistic the more her trading volume increases. In fact, the
optimistic investor expects an increase on prices because she predicts that
this increase will be followed by a new price increase, which allows her to
realize future gains. On the other side, when prices decrease the investor
continues to trade normally since she is less sensitive to negative results.
In a similar way, the more pessimistic investors expect that a decrease of
prices will be followed by a new series of decreases; as a result, they
reduce their trading volume to avoid potential losses. However, since they
are less sensitive to positive results, the pessimistic investors will trade
normally when they expect an increase in future prices.
In the same vein, the empirical evidence supports a significant and
positive relationship between price changes and trading volume. Using
daily data for both market indices and individual stocks Crouch (1970,
1998) found a positive correlation between the absolute price changes and
trading volume. Clark (1973) found also a positive relationship between
the square of the price change and aggregated trading volume using daily
data. Specifically, optimistic investors’ underestimate their exposure to
risk and exaggerate their reaction since they expect only positive results
and neglect the failure. In the same vein, Shu (2010) being aware of the
characteristics assigned to each type of sentiment, argues that optimistic
investors are less patient than those who are more pessimistic and react
aggressively by underestimating their exposure to risk. Instead, the more
pessimistic investors display a high-level of risk aversion. They become
more and more receding when they make a decision to invest in risky
assets which leads to a decrease in trading volume. Chuang, Ouyang and
Lo (2010) use a weekly data during the period January 1990 - December
2004 to supervise the change in investor sentiments in Taiwan Stock
Market. They find that the change in trading volume can be used as a
proxy for investor sentiments. They argue that a positive deviation of
trading volume implies that investor sentiment jumps to become more
optimistic and vice-versa.
For the French stock market, Rousseau, Germain and Vanhems
(2008) argue that pessimistic investors decrease their trading volume and
avoid risky assets to prevent a loss. Psychological literature assimilates
the pessimism to a statement of impotence or to an absurdity of human
existence. Alongside, the authors find that optimistic investors increase
their trading volume and invest more in risky assets waiting for a higher
yield in the future.
Carver, Scheier and Segerstrom (2010) suggest that optimism and
pessimism sentiments focus on expectancies for the future and the way
that the investors confront problems. The authors find that optimistic
investors face adversity differently than pessimistic ones. They presume
that optimistic investors use more adaptive ways and "commit" to cope
with the worst scenarios. In contrast to optimism, pessimism refers to fear,
doubt and stress, in that pessimistic investors tend to be hesitant and
doubtful in the face of different challenges. All these empirical findings
lead to the conclusion that investor sentiment constitutes an important
factor that determines the trading volume and investment strategies.
3. Data and behavioral indices
A recent study showed that the French were among the most pessimistic
people in the world; hence the French Stock Market was a suitable choice
for our study. French data are more ideal since for controlling the
influences of investor sentiments and beliefs. The French population is
prone to be the most pessimistic all over the world
*
. The optimism, as a
positive sentiment, can be built over the time, but can be broken after a
single shock; investors will be more sensitive to pessimistic aspects than
to optimistic aspects. Based on this argument the most appropriate data to
supervise the investors’ sentiments remained that reflecting the dominant
characteristic which is the pessimism in investor sentiment. The data
sample includes individual daily stock prices and trading volumes on the
CAC40 Stock Index between January 2005 and December 2011. The
analysis also required the construction of aggregate data. The output
variables include returns and trading volume of the CAC40 index. In order
to determine the input variables we need to use individual prices and
returns to calculate their average and conditional measures.
According to the behavioral finance literature “animal spirits” create
waves of optimism and pessimism. The Optimism about a given asset is
occurring when expected prices increase abnormally. However,
pessimism takes place when investors estimate a dramatic decrease in
prices. There are two direct analytical methods for measuring investor
sentiment. An optimistic investor expects an above average stock price
level at any given time. She becomes pessimist when the price falls below
the average level. Then, the average of individual stocks is used to
calculate optimism and pessimism variables of CAC40 Stock index. We
report a strong evidence of optimistic behavior when individual stock
price increases abnormally. Considering the aggregate market, the average
of conditional absolute price forms the best measure of optimism
sentiment. The investor reacts as an optimist if she realizes that the price
increase over the medium level. Then, giving the conditional expectations,
optimism about the stock price will be calculated as follows:
0pt
t
=
1
N
(P
it
|P
it
>E|P
i
])
i=1
(1)
where, Pit represents the price of the stock i at the time t and E[Pi]
the mathematical expectation of price series of the stock i at the time t.
*
According to the interview realized by the « Gallup International Association » for
the journal “Le Parisien” for the years 2011 and 2012, the French population
constitutes the most pessimistic population all over the world. For more details see:http://www.lexpress.fr/actualites/2/les-francais-champions-du-monde-du-
pessimisme-en-2011-selon-bva_949381.html ;http://www.lefigaro.fr/international/2011/01/03/01003-
20110103ARTFIG00628-les-francais-champions-du-monde-du-
pessimisme.php ;http://www.lexpress.fr/actualites/1/societe/55-des-
francais-pessimistes-pour-2012_1067011.html
118 ARAB ECONOMICS AND BUSINESS JOURNAL 9 (2014) 115–132
E|p
ì
] =
1
I
p
ìt
1
t=1
(2)
N is the number of individual stock in the French CAC 40
stock market index. We use the inverse of the absolute value since more
the stock prices are lower more likely the investors are pessimistic. A
positive correlation observed between the standard price and the trading
volume suggests a negative effect of pessimistic investor on the trading
volume. To avoid certain opposite effects we propose using the inverse of
the pessimism measurement. Therefore, giving the conditional
expectations, this index is calculated as follows:
Pcs
t
= _
1
N
(P
ìt
|P
ìt
< E|P
ì
])
N
ì=1
_
-1
× 1uu
(3)
Investor sentiment about stock prices can also be controlled by using
the following factors:
Scnt
1
= IÐ
t
=
APSI
t
ÐPSI
t
(4)
where Sent1t is defined as the Increase vs. Decrease in stock price at
the time t, APSVt represents the number of securities that experience a
price increase at the time t, and DPSVt the number of securities that know
a price decrease at the time t. Similarly,
Scnt
2
= NINÐ
t
=
NAPSI
t
NÐPSI
t
(5)
where Sent2t represents new increases vs. new decreases in stock
prices at the time t, NAPSVt defines the number of new securities that
experience a price increase at the time t, and NDPSVt denotes the number
of new securities that show a price decrease at the time t.
Market Trend (MT) gives a signal for investors’ decision: “BUY”,
“SELL” or “Hold”. The MT can be defined as the ratio of the difference
between the closing price and the lowest one observed over the latter x-
days to the difference between the highest and the lowest prices noticed
over the latter x-days. Considering weekly analysis time unit we set x
equal to the number of trading day per week, that is x equal to 5.
Therefore, using the aggregate prices of CAC40, the MT can be written as
follows:
HI =
Closing Pricc
t
-Iowcst Pricc
(t,t-5)
Eigbcst Pricc
(t,t-5)
-Iowcst Pricc
(t,t-5)
(6)
We use the trading volume as a proxy for trading intensity (TI).
Investors increase their trading when they expect an increase of prices
(optimistic sentiment). However, the trading volume decreases, if they
expect the prices to go down. Using aggregate data, this variable is
computed as follows:
II = In(IroJing Iolumc) (7)
4. Investor beliefs and sentiments: Econometric and Fuzzy
analysis
In the first step we try to control the sensitivity of MT and TI against the
investors’ beliefs and sentiments (Optimism, Pessimism, Sent1, Sent2)
using econometric modeling based on a SUR estimation.
_
TI
t
= u
û
+u
1
Opt
t
+u
2
Pex
t
+u
3
Sent
1t
+ u
4
Sent
2t
+
MT
t
= ß
û
+ß
1
Opt
t
+ß
2
Pex
t
+ß
3
Sent
1t
+ß
4
Sent
2t
+
(Model 1)
TIt : represents the Trading Intensity at time t;
MTt : represents the Market trend at time t;
OPTt : represents the investor Optimism indicator at time t;
PESt : represents the investor Pessimism indicator at time t;
Sent1t : represents the first indicator for the investor sentiment at time t;
Sent2t : represents the second indicator for the investor sentiment at time t.
The results in Table 1 show on average that the number of stocks
that experiences an increase in prices is quite higher than that of stocks
that experiences a decrease. The number of new stocks realizing an
increase reaches about more than three times the number of new stocks in
which a decrease is observed. The number of new stocks having an
increase exceeds by about 1.8 times the number of new stocks having a
decrease. Furthermore, MT is very centralized nearly to its average level.
The number of stocks having less MT is very important compared to the
number of stocks having a high MT. However the TI is centralized on
average nearly its maximal level. The differences between the average and
both the maximal and the minimal level reach respectively about 1.31681
and 2.43039. The optimism and pessimism of investors are quite weak.
They are centralized on average around their minimal levels. By
construction, the market trend is a transformation of the stock returns.
Moreover, the evolution of the trading intensity depends substantially on
the evolution of stock returns. For these reasons, the MT and TI seem to
be apparently unrelated however; they are related across their residual
terms. Thus a seemingly unrelated regression is appropriate to estimate
the multi-equation model presented above (Model 1). The estimation of a
simultaneous multi-equation model requires that this model is
overidentified. One model can be overidentified if each of his equations is
at least just-identified. To examine the overidentification of our multi-
equation model we denote W as the number of endogenous variables
included in the model; W’ is the number of endogenous variables included
in the equation; K the number of exogenous variables included in the
model; W’ the number of exogenous variables included in the equation. If
there is any restriction in each of the model equations, an equation is
qualified to be overidentified if W-1 W – W’ + K – K’. In our case, since
W-1 = W – W’ + K – K’ for each equation, the model is mainly
overidentified. Thus, a two-stage-least square estimation is more
appropriate in particular a SUR estimation is recommended. Table 2
presents the results for SUR estimation of the regression of TI and MT on
beliefs and sentiment indicators using two least square methods.
The results in Table 2 show that both MT and TI are significantly
sensitive to optimism. However, while the effect is positive on the MT it
is oppositely negative on the TI. This indicates that optimistic investors
react by decreasing their trading when the MT shows favorable evolution
of returns waiting for better results in the future. Also, the pessimism is
positively related to both MT and TI. When stock index experience
favorable tendencies, pessimistic investors express worries on future
unfavorable evolution of returns and thus liquidate their positions in
ARAB ECONOMICS AND BUSINESS JOURNAL 9 (2014) 115–132 119
increasing their sell-trading. Sent1 and Sent2 exert only significant effect
on the Market Trend. The trading intensity is not significantly sensitive to
these sentiment indicators. Investors react following their beliefs and
withdraw the individual stock characteristics as indirect sentiment proxies.
Even though the results show statistical significance, the sensitivity
of TI and MT on optimism and pessimism indicators as well as the
indicator of the last evolution that stocks experience, remains
questionable. In fact, when results indicate positive (negative) reaction of
TI to the pessimism (optimism), we cannot judge if this increase
(decrease) is due to a sell or another strategy. To find an answer to this
problem, a fuzzy control system is introduced. It allows investigating with
more preciseness the evolution of TI and MT following the variations of
the investors’ beliefs and sentiments. To explore the relationship between
MT and TI on one hand and the indicators of beliefs and sentiments (Opt,
Pes, Sent1 and Sent2) on the other hand, we present in the remainder of
this section a fuzzy model in an attempt to support and/or challenge the
econometrical results presented in Table 2.
Fuzzy logic as a branch of artificial intelligence was introduced for
the first time in 1965 by Zadeh (1965). It deals with reasoning algorithms
used to emulate human thinking and decision making. These algorithms
are used when process data cannot be represented by classical logic. For
example, when investigating the level of information that an investor
withholds, in classical logic there is a double sided result. An investor can
be either informed or uninformed. There is no an intermediate position.
However, the fuzzy logic analysis includes all intermediate positions. Not
only extreme values are considered, but also the whole range between the
two extreme values will be included. The investors can be uninformed or
quite informed or informed. In this paper we introduce a Fuzzy control
model that includes four input variables. For each input we attribute three
belief intervals: High, Medium, and Low. After defuzzification, two
output variables are controlled. Following the fuzzy logic process (IF-
THEN), the model takes the form depicted in Figure 1.
120 ARAB ECONOMICS AND BUSINESS JOURNAL 9 (2014) 115–132
Table 1- Summary statistics for dependent and independent variables.
Statistics Endogenous variables Exogenous variables
TI MT Opt Pes Sent1 Sent2
Mean 14.95998 0.738998 2.601749 2.92743 1.005945 3.279962
Min 12.52959 0.016847 0 0 0.464206 1.792425
Max 16.27679 4.104432 35 34 2.945429 5.847581
Sd 0.357970 0.424101 5.121306 5.47156 0.378252 0.859178
Skewness -0.81657 2.045383 4.296946 2.91583 1.765905 0.682185
Kurtosis 7.260038 11.58979 24.79376 11.9142 7.719614 2.680998
Table 2- Results for the SUR model estimation.
Cons. Opt Pes Sent1 Sent2 R-Squared Chi-2
TI 14.88178
(164.01)***
-0.1247673
(3.62)***
0.0617291
(-3.22)***
-0.0019077
(-0.98)
0.0021196
(1.16)
0.0711 120.10
(0.0000)
a
MT 0.0732104
(0.70)
0.4099946
(9.18)***
0.0874386
(4.45)***
0.0115987
(5.15)***
-0.0217364
(-10.32)***
0.1193 212.38
(0.0000)
b
Table 2 summarizes the results for the SUR estimation of the regression of TI and MT on beliefs and sentiment indicators. Z-statistics are given into
Brackets. *** indicate the significance level of 1%. a and b indicate the p-values of the Chi-2 test. TI denotes the trading intensity computed based on the
natural logarithm of trading volume. MT measures the Market trend which indicates the investors’ strategy (buy, sell, or hold). Explanatory variables give
information about the investors’ sentiments. Opt. and Pes. variables represent direct indicators of optimistic and pessimistic sentiments and feelings of the
investors based on their perceptions of the evolution of the stock returns. Sent1 and Sent2 give indirect information on investors’ sentiments.
Fig. 1- Fuzzy logic control system.
Fuzzy input
Fuzzy Logic process
Fuzzy output
Input data
Output data
Process
ARAB ECONOMICS AND BUSINESS JOURNAL 9 (2014) 115–132 121
TIt : Trading Intensity at time t;
MTt : Market trend at time t;
OPTt : investor Optimism indicator at time t;
PESt : investor Pessimism indicator at time t;
Sent1t : first indicator for the investor sentiment at time t;
Sent2t : second indicator for the investor sentiment at time t.
Fig. 2- The fuzzy logic model.
THEN
TI I
S
Increase
Hold
Decrease
I
S
Buy
Hold
Sell
MT
IF
OPT
PES
Sent1
Sent2
I
S
High
Medium
Low
122 ARAB ECONOMICS AND BUSINESS JOURNAL 9 (2014) 115–132
Traditional control theory poses that we must at least (i) know the
model of the controlled system, (ii) know the objective function
formulated in precise term, and (iii) be able to solve the corresponding
mathematical problem. If one of these conditions is not satisfied, the
traditional methodology will not be applicable. In our case, the model is
known, yet the objective function is unknown and cannot be formulated in
precise terms since the model includes factors that are related to human
nature and behavior which are difficult to be controlled with certainty.
Indeed, considering human psychology, an expert cannot usually express
his knowledge (beliefs and sentiments) in precise numerical terms but in
linguistic terms. Bekiros (2009, 2010) has recently utilized fuzzy logic in
economic and financial applications with highly promising results. For
our specific model, the knowledge that we extract from an expert can be
formulated in terms of rage of optimism, pessimism, overconfidence, and
the rationality varying from a low sentiment to a medium and high
sentiment. Given these specifications, the fuzzy control methodology
presents an important differentiation. The fuzzy logic control system is
presented in Figure 2. In this set-up we (i) know the expert’s control rules
formulated by words from natural language, and (ii) we produce a precise
control strategy. This methodology indeed transforms the informal expert
control rules into a precise control strategy. The fuzzy modeling system is
the process of formulating the mapping from a given input to an output
using fuzzy functions. The mapping then provides a basis from which
decisions can be made, or patterns discerned. The fuzzy logic process
concerns different steps. Figure 3 summarizes these steps.
Identification of belief
functions
&
Fuzzy sets definition affecting
investor Behavior
?? ??
Fuzzy rules construction
?? ??
Fuzzification
?? ??
Fuzzy inference module
generation
?? ??
Defuzzification
Fig. 3- Steps of the fuzzy logic process.
2.1. Identification of critical factors and belief functions
The specification of the fuzzy logic model requires to define the so-called
“belief functions”. We suppose that the investor sentiment can be
considered as Low, Medium or High, depending on what the prices are
less than a level “a”, belong to the interval [a, b], or are higher than the
level “b”, respectively. Based on the continuous uniform distribution and
considering “c” as the median of the interval [a, b], the belief function for
the fuzzy controller system can be presented as follows:
?x ( High) =
1 If P > b
x -o
b -o
If a < P < b
0 If P < a
?x (Medium) =
0 If P < a
x -o
c -o
If a < P < c
b -x
b -c
If c b
?x (Low) =
1 If P < a
b -x
b -o
If a < P < b
0 If P > b
As indicated in equations 1 and 2 our model includes 2 equations
with 4 input variables (OPT, PES, Sent1, Sent2) and 2 output variables (TI,
MT). For the optimism and pessimism input variables, we assume that
investors’ beliefs change dramatically following the evolution of stock
prices. Considering the change of prices spanning the inter-quartile
intervals optimism is considered as Higher when prices exceed the third
quartile. If prices are under the value corresponding to the first quartile the
variable “Optimism” takes the statue “Low”. Medium Optimism occurs
when prices are included into the interval [Q1, Q3]. Accordingly, the belief
function for this variable, and after considering the value Q2 to control the
Medium Optimism, can be computed as follows:
?x (High) =
1 If x > 44.41
x -S.8
S8.61
If 5.8 < x < 44.41
0 If x < 5.8
?x (Low) =
1 If x < 5.8
44.41 -x
S8.61
If 5.8 < x < 44.41
0 If x > 44.41
ARAB ECONOMICS AND BUSINESS JOURNAL 9 (2014) 115–132 123
?x (Medium) =
0 If x < 5.8
x -S.8
29.u8
If 5.8 < x < 34.88
44.41 -x
9.SS
If 34.88 < x < 44.41
0 If x > 44.41
Moreover, the belief function for the “Pessimism” input variable -
considering the same evolution of prices into these limits discussed above
- can be calculated as follows:
?x (High) =
1 If x < 4.87
SS.64 -x
28.77
If 4.87 < x < 33.64
0 If x > 33.64
?x (Medium) =
0 If x < 4.87
x -4.87
9.u7
If 4.87 < x < 13.94
SS.64 -x
19.7
If 16.94 < x < 33.64
0 If x > 33.64
?x (Low) =
1 If x > 33.64
x -4.87
28.77
If 4.87 < x < 33.64
0 If x < 4.87
In the same way we compute the modalities for the variable Sent1:
?x (Low) =
1
If x < 0.18
S -x
2.82
If Q 1 < x < 3
0 If x > 3
?x (High) =
1 If x > 3
x -u.18
2.82
If 0.18 < x < 3
0 If x < 0.18
For the variable and Sent2, the sentiment function is set as follows:
?x (Low) =
1
If x < 0.05
S -x
2.9S
If 0.05 < x < 3
0 If x > 3
?x (High) =
1 If x > 3
x -u.uS
2.9S
If 0.05 < x < 3
0 If x < 0.05
?x (Medium) =
0
If x < 0.05
x -u.uS
u.S7
If 0.05 < x < 0.42
S -x
2.8S
If 0.42 < x < 3
0 If x > 3
For the TI output variable respectively:
?x (Decrease) =
1
If x < 18.63
18.98 -x
u.SS
If 18.63 < x < 18.98
0 If x > 18.98
?x (Increase) =
1
If x > 18.98
x -18.6S
u.SS
If 18.63 < x < 18.98
0 If x < 18.63
?x (Hold) =
0
If x < 18.63
x -18.6S
u.1S
If 18.63 < x < 18.78
18.98 -x
u.2
If 18.78 < x < 18.98
0 If x > 18.98
For the MT output variable:
?x (Sell) =
1
If x < 0.29
u.68 -x
u.S9
If 0.29 < x < 0.68
0 If x > 0.68
?x (Medium) =
0
If x < 0.18
x -u.18
u.SS
If 0.18 < x < 0.71
S -x
2.29
If 0.71 < x < 3
0 If x > 3
124 ARAB ECONOMICS AND BUSINESS JOURNAL 9 (2014) 115–132
?x (Buy) =
1
If x > 0.68
x -u.29
u.S9
If 0.29 < x < 0.68
0 If x < 0.29
?x (Hold) =
0
If x < 0.29
x -u.29
u.21
If 0.29 < x < 0.5
u.68 -x
u.18
If 0.5 < x < 0.68
0 If x > 0.68
Based on the above specifications the input vs. output interface for the
“Optimism”, the “Pessimism”, “Sent1” and “Sent2” input variables is
presented below (Figures 4 to 7):
Fig. 4- Optimism input variable in the fuzzy expert system for
French stock Market.
Fig. 5- Pessimism input variable in the fuzzy expert system for
French stock Market.
Fig. 6- Sent1 input variable in the fuzzy expert system for French
stock Market.
Fig. 7- Sent2 input variable in the fuzzy expert system for
French stock Market.
Similarly, the output data interaction corresponding to the “Market
trend” and the “Trading intensity” belief functions are presented in
Figures 8 and 9:
Fig. 8- Market Trend output variable in fuzzy expert system for
French stock Market.
Fig. 9- Trading Intensity output variable in fuzzy expert system
for French stock Market.
ARAB ECONOMICS AND BUSINESS JOURNAL 9 (2014) 115–132 125
2.2. Fuzzy rules construction
In the proposed model with 4 inputs and 2 outputs the IF-THEN rules are
formulated as shown in Figure 12. The range of each input and output
variables is given in parenthesis. The range for each variable changes
between the min and the max value of data. The Rules for the fuzzy logic
process are analyzed in detail in Table 3. In addition, the fuzzy rule base
view of the fuzzy expert system is presented in Figure 13.
126 ARAB ECONOMICS AND BUSINESS JOURNAL 9 (2014) 115–132
Figure 10: Detailed structure of the fuzzy system
Fig. 10- Detailed structure of the fuzzy system.
Input 1
Opt (0 51.33)
Input 2
Pes (0 39.77)
Input 3
Sent1 (0 39)
Input 4
Sent2 (0 35)
Rule 1 : OPT is High and PES is Low and Sent1
is High and Sent2 is High, then MT is Buy and TI
Rule 2 : OPT is Low and PES is High and Sent1
is Low and Sent2 is Low , then MT is Sell and TI
Rule 3 : OPT is Med and PES is Low and Sent1 is
Low and Sent2 is Med, then MT is Hold and TI is
Rule 4 : OPT is Low and PES is High and Sent1
is Low and Sent2 is High, then MT is Decrease
.
.
.
Rule 81 : OPT is High and PES is Low and Sent1
is Med and Sent2 is Low, then MT is Increase
?
Output 1
TI
(17.5 19.78)
Output 2
MT
(0.04 0.95)
The inputs are crisp (non-
fuzzy) numbers limited to
a specific range
Parallel evaluation using Fuzzy
reasoning of all rules
Combination and
defuzzification of the
rules
The result is a crisp
(non -fuzzy) number
ARAB ECONOMICS AND BUSINESS JOURNAL 9 (2014) 115–132 127
Table 3- Fuzzy system Rules.
If Then If Then If Then
N° Opt Sent1 Sent2 Pes TI MT N° Opt Sent1 Sent2 Pes TI MT N° Opt Sent1 Sent2 Pes TI MT
1 High High High High Increase Buy 28 Med High High High Increase Buy 55 Low High High High Hold Hold
2 High High High Med Increase Buy 29 Med High High Med Increase Buy 56 Low High High Med Increase Buy
3 High High High LOW Increase Buy 30 Med High High LOW Increase Buy 57 Low High High LOW Increase Buy
4 High High Med High Increase Buy 31 Med High Med High Hold Hold 58 Low High Med High Decrease Sell
5 High High Med Med Increase Buy 32 Med High Med Med Increase Buy 59 Low High Med Med Hold Hold
6 High High Med LOW Increase Buy 33 Med High Med LOW Increase Buy 60 Low High Med LOW Increase Buy
7 High High Low High Hold Hold 34 Med High Low High Decrease Sell 61 Low High Low High Decrease Sell
8 High High Low Med Increase Buy 35 Med High Low Med Hold Hold 62 Low High Low Med Decrease Sell
9 High High Low LOW Increase Buy 36 Med High Low LOW Increase Buy 63 Low High Low LOW Hold Hold
10 High Med High High Increase Buy 37 Med Med High High Hold Hold 64 Low Med High High Decrease Sell
11 High Med High Med Increase Buy 38 Med Med High Med Increase Buy 65 Low Med High Med Hold Hold
12 High Med High LOW Increase Buy 39 Med Med High LOW Increase Buy 66 Low Med High LOW Increase Buy
13 High Med Med High Hold Hold 40 Med Med Med High Decrease Sell 67 Low Med Med High Decrease Sell
14 High Med Med Med Increase Buy 41 Med Med Med Med Hold Hold 68 Low Med Med Med Decrease Sell
15 High Med Med LOW Increase Buy 42 Med Med Med LOW Increase Buy 69 Low Med Med LOW Hold Hold
16 High Med Low High Decrease Sell 43 Med Med Low High Decrease Sell 70 Low Med Low High Decrease Sell
17 High Med Low Med Hold Hold 44 Med Med Low Med Decrease Sell 71 Low Med Low Med Decrease Sell
18 High Med Low LOW Increase Buy 45 Med Med Low LOW Hold Hold 72 Low Med Low LOW Decrease Sell
19 High Low High High Hold Hold 46 Med Low High High Decrease Sell 73 Low Low High High Decrease Sell
20 High Low High Med Increase Buy 47 Med Low High Med Hold Hold 74 Low Low High Med Decrease Sell
21 High Low High LOW Increase Buy 48 Med Low High LOW Increase Buy 75 Low Low High LOW Hold Hold
22 High Low Med High Decrease Sell 49 Med Low Med High Decrease Sell 76 Low Low Med High Decrease Sell
23 High Low Med Med Hold Hold 50 Med Low Med Med Decrease Sell 77 Low Low Med Med Decrease Sell
24 High Low Med LOW Increase Buy 51 Med Low Med LOW Hold Hold 78 Low Low Med LOW Decrease Sell
25 High Low Low High Decrease Sell 52 Med Low Low High Decrease Sell 79 Low Low Low High Decrease Sell
26 High Low Low Med Decrease Sell 53 Med Low Low Med Decrease Sell 80 Low Low Low Med Decrease Sell
27 High Low Low LOW Hold Hold 54 Med Low Low LOW Decrease Sell 81 Low Low Low LOW Decrease Sell
128 ARAB ECONOMICS AND BUSINESS JOURNAL 9 (2014) 115–132
Fig. 11- Rules base view of the fuzzy expert system.
ARAB ECONOMICS AND BUSINESS JOURNAL 9 (2014) 115–132 129
2.3. Results and sensitivity analysis
Figures 12 to 23 present the sensitivity analysis of the fuzzy
system to trading intensity and market trend. In particular, Figures 12
and 13 show that the market trend is more sensitive than the trading
intensity to the change in the rage of optimism and pessimism inputs.
Considering the sensitivity for the optimism and the pessimism,
investors decrease slowly their trading activity even if the market
trend is “Sell”, i.e., corresponding to high pessimism and low
optimism. However, they increase aggressively their trading activity
when the market trend becomes “Buy”, which corresponds to high
optimism and low pessimism. The sensitivity to medium optimism
and medium pessimism is higher for the case of the market trend
output variable than for the case of trading intensity. Despite this
difference in sensitivity, we see that the weight of the two inputs
(optimism and pessimism) is almost identical in terms of impact on
each individual output. The effect is almost symmetric.
Fig. 12- Optimism-Pessimism sensitivity analysis of fuzzy system
for trading intensity.
Fig. 13- Optimism-Pessimism sensitivity analysis of fuzzy system
for market trend.
Figures 14 and 15 show that the sensitivity of both trading intensity and
market trend to the change in rage of optimism and Sent1 remains about the
same with a non-significant difference in sensitivity when the input
variables take the level High for Sent1 and Low of Optimism. The
sensitivity of both to the input Optimism is much higher than to the input
Sent1. We see clearly that the change in range for the optimism affects
significantly the trading intensity and the market trend. Instead, only
extreme value of Sent1 influence the two output variables. In fact,
regardless of the change in Optimism input variable, trading intensity is
“Decrease” and market trend is “Sell” when Sent1 is “Low”. However
when Sent1 is “Medium” or “High” trading intensity and market trend
become respectively “Increase” and “Buy”. Overall, the change in range
for the Optimism input variable induces significant a change in trading
intensity and the market trend.
Fig. 14- Optimism - Sent1 sensitivity analysis of fuzzy system
for Trading Intensity.
Fig. 15- Optimism - Sent1 sensitivity analysis of fuzzy system
for Market Trend.
In the same way, figures 16 and 17 show similar sensitivity for both
trading intensity and market trend to Optimism and Sent2 input variables.
However, the sensitivity to the Optimism input variable is higher than that
to Sent2 input variable. A Medium range of Sent2 has no significant effect
on the change in trading intensity or the market trend. Only extreme levels
(High or Low) have significant influences. However, the two output
variables are significantly sensitive to the change in range of the Optimism
input variable.
130 ARAB ECONOMICS AND BUSINESS JOURNAL 9 (2014) 115–132
Fig. 16- Optimism - Sent2 sensitivity analysis of fuzzy system for
Trading Intensity.
Fig. 17- Optimism - Sent2 sensitivity analysis of fuzzy system for
Market Trend.
Next, Figures 18 and 19 show clear differences in sensitivity for
Trading Intensity and Market Trend to Pessimism and Sent1 input
variables. Whereas the sensitivity of the TI to the pessimism input variable
is fairly smooth, the sensitivity of the MT is more observable especially
when the input variable takes medium values. Moreover, the change in
range for the Sent1 input variable is insignificant on both TI and MT output
variables once this input variable takes a medium value. The sensitivity of
output variable becomes significant when the Sent1 input variable is
“High” or “Low”.
Fig. 18- Pessimism - Sent1 sensitivity analysis of fuzzy system for
Trading Intensity.
Fig. 19- Pessimism - Sent1 sensitivity analysis of fuzzy system for
Market Trend.
The sensitivity of both TI and MT to the two input variables “Sent2”
and “Pessimism” is about the same to that observed for the “Sent1” and the
“Pessimism” as shown in Figures 20 and 21. In fact, while TI is less
sensitive to the medium pessimism, the MT is highly sensitive to this same
range of change in pessimism. Medium value in “Sent2” has however
insignificant impact on the two output variables.
Fig. 20- Pessimism - Sent2 sensitivity analysis of fuzzy system for
Trading Intensity.
Fig. 21- Pessimism - Sent2 sensitivity analysis of fuzzy system
for Market Trend.
Finally, Figures 22 and 23 present that there is no significant difference in
sensitivity to the change in rage of the two indicators of investors’
sentiment Sent1 and Sent2 for both the Trading Intensity and the Market
Trend. The investors tend to increase their trading and to choose the
strategy Buy when both Sent1 and Sent2 are “High”. Once the two investor
sentiment indicators are “Low” Investors tend to decrease their trading.
However they prefer to Hold or choose to keep a “normal” level of trading
when one single indicator of sentiment tends to be closer to the “High”
level and the other indicator remains “Low”.
ARAB ECONOMICS AND BUSINESS JOURNAL 9 (2014) 115–132 131
Fig. 22- Sent1 - Sent2 sensitivity analysis of fuzzy system for
Trading Intensity.
Fig. 23- Sent1 - Sent2 sensitivity analysis of fuzzy system for
Market Trend.
These findings indicate that human psychology matters significantly when
decision-making is performed in financial markets. The strategy the market
agents choose (sell or buy) is significantly sensitive to the change in their
anticipations and to their optimistic and pessimistic beliefs. This confirms
the theoretical predictions and accords with the conclusions of Keynes
(1936) that all of our decisions are taken as the result of the influence of
psychological factors or “animal spirits”. Our results also follow the
theoretical implications of Akerlof and Shiller (2009) who conclude that
human psychology drives economies and markets and suggest to always
incorporate psychological factors into macro-financial theory in order to
understand “how the economy really works” (Kahneman, 2003).
3. Conclusion
This paper attempts to investigate the sensitivity of various investment
strategies to the investor sentiment. We focus on French stock market
because we wish to control for the level of financial sector development in
this country. We revealed through an exhaustive analysis that trading
intensity and market trend are both highly sensitive to investor sentiments
and beliefs. Mainly, these two variables are more sensitive to a pessimistic
investor sentiment than to optimistic one. This result is attributed to the
fact that the optimistic sentiment can be built over the long time, but can be
broken after a single shock, and hence pessimism dominates optimism.
Indirect indicators of agent beliefs present more smoothed effects on these
two market components. These results verify that the incorporation of
psychological factors in financial modeling may lead efficiently to
enhanced control of market trading behavior.
Considering the results of the fuzzy logic, investors are required to give
more attention to their feelings and sentiments. The pessimistic sentiment
presents a heavy impact on their decision making. Optimism can be built
over a long time but can be broken suddenly and a pessimistic sentiment
rises dramatically. When making decision, investors must take into account
the feeling and the sentiments of others decision makers and incorporate
their perceptions as a fundamental factor having impact on the market
behavior (evolution of trading and returns).
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