'Rational' or 'Intuitive': Are Behavioral Biases Correlated Across Stock Market Investors?

Human judgments are systematically affected by various biases and distortions. The main goal of our study is to analyze the effects of five well-documented behavioral biases — namely, the disposition effect, herd behavior, availability heuristic, gambler’s fallacy and hot hand fallacy — on the mechanisms of stock market decision making and, in particular, the correlations between the magnitudes of the biases in the cross-section of market investors. Employing an extensive online survey, we demonstrate that, on average, active capital market investors exhibit moderate degrees of behavioral biases. We then calculate the cross-sectional correlation coefficients between the biases and find that all of them are positive and highly significant for both professional and non-professional investors and for all categories of investors, as classified by their experience levels, genders, and ages. This finding suggests that an investor who is more inclined to employ a certain intuitive decision-making technique will most likely accept other techniques as well. Furthermore, we determine that the correlation coefficients between the biases are higher for more experienced investors and male investors, indicating that these categories of investors are likely to behave more consistently, or, in other words, are more likely to decide for themselves whether to rely on simplifying decision-making techniques in general or to reject all of them. Alternatively, this finding may suggest that these investors develop more sophisticated “adaptive toolboxes,” or collections of heuristics, and apply them more systematically.


Introduction
People are not rational utility-optimization machines. we calculate her personal "bias grades", each of which is higher the more her reported behavior, as discerned from her answers, is consistent with the respective behavioral effect. On average, our survey participants exhibit moderate degrees of behavioral biases.
The major focus of our research is calculating the cross-sectional correlation coefficients between the "bias grades". All of the correlations are positive (in fact, close to one) and highly significant for both professional and non-professional investors. Therefore, we infer that if an investor accepts a certain intuitive decision-making technique, she will likely accept other techniques as well.
Furthermore, we perform a subsample analysis of the correlations. We document that the correlation coefficients between the biases are higher for more experienced investors and male investors, indicating that these categories of investors likely behave more consistently, or, in other words, are more likely to decide for themselves whether to rely on simplifying decision-making techniques in general or to reject all of them. Alternatively, this finding may suggest that more experienced investors manage to develop (everyone for herself) a more sophisticated "adaptive toolbox" or collection of heuristics (Gigerenzer, & Selten, 2001) and apply it more systematically, possibly arriving at better investment results. We also find that the correlation coefficients for the most experienced non-professional investors are lower than those for the professional investors, likely suggesting that the latter group, though not necessarily more rational (as shown by Hon-Snir et al., 2012), at least behaves more consistently, or based on a more ample collection of decisionmaking rules. Conversely, the correlations appear to be independent from investors' ages. Importantly, all of the correlation coefficients we obtain for all of the subsamples and categories of participants are positive and highly significant, providing a strong robustness check for our major finding.
The rest of the paper is structured as follows. In Section 2, we review the literature on behavioral biases, featuring both psychological aspects and economic applications. In Section 3, we describe our survey design and research approach. Section 4 defines our hypotheses and provides the empirical tests and the results. Section 5 concludes and provides a brief discussion.  (2000) compare the durations of winning and losing round trips and document the disposition effect for all groups of accounts, finding that it is less pronounced for managed accounts than for independent ones. Kliger and Kudryavtsev (2008) discover that investors update their reference points on stocks based on the perception of stock exchange-listed firms' quarterly earnings announcements as "good" or "bad surprises" and subsequently exhibit the disposition effect with respect to these reference points.

Psychological biases in finance: Literature review
The third group of papers that sheds light on the disposition effect consists of papers employing experimental design. Weber and Camerer (1998) conduct a multi-stage experiment examining different characteristics and determinants of the disposition effect and find that subjects tend to sell fewer shares when the price falls than when it rises and also sell less when the price is below the purchase price than when it is above.
(2002) use the purchase price and the last period price as alternative reference points. The disposition effect is found to be stronger when the purchase price is taken as a reference point.

Herd behavior (herding)
In financial markets, herding is usually termed as the behavior of an investor imitating the observed actions of others or the movements of the market instead of following her own beliefs and information. Herd behavior is possibly among the most mentioned but least understood terms in the financial lexicon. Difficulties in measuring and quantifying the existence of the behavior form obstacles to extensive research. Even so, there are at least two points people tend to unanimously agree upon. First, as one of the founding pillars in the newly developed behavioral asset pricing area, herd behavior helps explain market-wide anomalies.
Because individual biases are not influential enough to move market prices and returns, they only have real anomalous effects if they create social contamination with a strong emotional content, leading to more widespread phenomena such as herd behavior. Second, it is generally accepted that the flood of herding may lead to a situation in which the market price fails to reflect all relevant information; therefore, the market becomes unstable and moves towards inefficiency. Empirical studies of herd behavior employ either laboratory or market data. In all the models, "herding" means making the same decision independently of the private information that one receives. The problem for the empiricist is that there are no data on the private information available to traders; therefore, it is difficult to understand whether traders make similar decisions because they disregard their own information and imitate (as opposed, for instance, to reacting to the same piece of public information). To overcome this prob- to those between two markets from different groups.
They also argue that herd behavior shows significant movements and persistence independently from market conditions.

Availability heuristic
The availability heuristic (Tversky, & Kahneman, 1973) refers to the phenomenon of determining the likelihood of an event according to the easiness of recalling similar instances. In other words, the availability heuristic may be described as a rule of thumb, which occurs when people estimate the probability of an outcome based on how easy that outcome is to imagine.
As such, vividly described, emotionally charged possibilities will be perceived as being more likely than those that are harder to picture or difficult to understand. Tversky and Kahneman (1974), provide examples of ways availability may provide practical clues for assessing frequencies and probabilities. They argue that "recent occurrences are likely to be relatively more available than earlier experiences" (p. 1127) and thus conclude that people assess probabilities by overweighting current information, as opposed to processing all relevant information.
A number of papers discuss the influence of the availability heuristic on market investors. Shiller  document weaker (stronger) reactions to recommendation upgrades (downgrades) on days of substantial stock market moves. They dub this finding the "risk availability effect" and explain it by higher availability of risky outcomes on such "highly volatile" days.

Gambler's fallacy
The gambler's fallacy is defined as an (incorrect) belief in the negative autocorrelation of a non-autocorrelated random sequence. For example, individuals who believe in the gambler's fallacy believe that after three red numbers appearing on the roulette wheel, a black number is "due", or, in other words, is more likely to appear than a red number.
The first published account of the gambler's fallacy is from Laplace (1951). Gambler's fallacy-type beliefs are first observed in the laboratory (under controlled conditions) in the literature on probability matching.
In these experiments, subjects are asked to guess which of two colored lights will next illuminate. After seeing a string of one outcome, subjects are significantly more likely to guess the other, an effect referred to in that literature as negative recency (see Estes, 1964; Lee, 1971, for reviews). Ayton and Fischer (2004) also demonstrate the existence of gambler's fallacy beliefs in the lab when subjects choose which of two colors will appear next on a simulated roulette wheel. Gal and Baron (1996) show that gambler's fallacy behavior is not simply caused by boredom. They ask participants in their experiments how they would best maximize their earnings and receive responses based on gambler's fallacy-type logic.
The gambler's fallacy is usually thought to be caused Overall, the gambler's fallacy is well-documented both in the laboratory and in the real world, including money-related behavior. However, there seems to be little evidence of this pattern in financing, including stock market decision making.

Hot hand fallacy
As people exhibit the gambler's fallacy, which is a tendency to predict the opposite of the last event (negative recency), they may also express beliefs that certain events will be repeated (positive recency). The latter tendency is known as the hot hand fallacy, and unlike the gambler's fallacy, it refers to people's belief that a particular person, rather than a particular outcome, is hot. For example, if an individual has won in the past, whatever numbers she chooses to bet on are likely to win in the future, not only the numbers she had won with previously.
Gilovich, Vallone and Tversky (1985) were the first to use the term "hot hand". They demonstrate that individuals believe in the hot hand in basketball shooting and that these beliefs are not correct (i.e., basketball shooters' probability of success is serially uncorrelated). They suggest that the hot hand also arises out of the representativeness heuristic just as the gambler's fallacy. They write, "A conception of chance based on representativeness produces two related biases. First, it induces a belief that the probability of heads is greater after a long sequence of tails than after a long sequence of heads -this is the notorious gambler's fallacy. Second, it leads people to reject the randomness of sequences that contain the expected number of runs because even the occurrence of, say, four heads in a row -which is quite likely in a sequence of 20 tosses -makes the sequence appear non-representa- and to inanimate chance mechanisms, whereas the latter refers to processes that seem to be non-random and related to human skilled performance.
Field evidence for the hot hand is weaker. Camerer (1989) compares odds in the betting market for basketball teams with their actual performance and finds that bettors do appear to believe in the "hot team".

Croson and Sundali (2005) and Sundali and Croson
(2006) document hot hand-consistent behavior in casinos. Clotfelter and Cook (1989) note the tendency of gamblers to redeem winning lottery tickets for more tickets rather than for cash. This behavior is also consistent with hot hand beliefs because the individuals who have recently won seem to believe they are more likely to win again.
Overall, similarly to the gambler's fallacy, the hot fallacy is widely discussed in different branches of literature but is not sufficiently documented in financial research, possibly because it is quite difficult to establish the hot hand feelings particular investors may have at certain moments of time.
In the present study, we first wish to shed additional light on the effects of the above-discussed psychological patterns on financial decision-making. This understanding may be especially valuable for the case of the gambler's fallacy and the hot hand fallacy, whose potential effects on the field of finance are not sufficiently studied in previous literature. However, the major goal of this study is to analyze the cross-sectional correlations between the magnitudes of different behavioral biases in stock market decision-making, a matter that is, to our best knowledge, not at all discussed in previous literature.

Survey design and research approach
We gathered the data for this study in the framework of a computerized survey, consisting of two stages: • First, we asked a group of professional portfolio managers (41 managers) at one of the major Israeli investment houses to fill out a short questionnaire.
This stage of the survey took place in January 2011. We asked all of the respondents to indicate their gender, age, and number of years of active experience in the capital market. Table 1 (in Appendix 1) reports the basic descriptive statistics of our sample.
The majority of our participants were males (78.05% and 74.10% in the professionals and non-professionals groups, respectively), 30 to 40 years old (53.66% and 55.08%, respectively), and had more than 10 years of experience in stock market investments (39.02% and 40.98%, respectively).
Our survey questionnaire consisted of 10 questions, which are presented in Appendix 2. In each question, participants were asked to rate the appropriateness of a statement on a Likert scale between 1 (strongly disagree) and 5 (strongly agree). To capture the effect of each of the behavioral biases on each of our participants, we calculate their personal "bias grades". To do so, we first control for the crosssectional correlations of grades given by the participants within the "pairs" of the questions we employed for each of the biases. The correlation coefficients between the grades within the pairs are reported in Table   2. The table clearly demonstrates that the correlations within all of the pairs are highly significant for both the professional and non-professional participants.
We also note that the sign of the correlation between the grades on questions 1 and 2 is negative, which is because investment behavior consistent with the disposition effect requires a high grade on question 1 and a low grade on question 2.
Strong correlations within the pairs of questions allow us to aggregate the bias grades for each participant i and for each of the biases in the following way: • Herd (behavior) grade ( i B G ): According to this approach, the resulting personal bias grades we attain for each participant i and for each question N range from 2, meaning that the respective bias has virtually no effect on the respective participant, or, in other words, that the participant's behavior is fully "rational", to 10, meaning that the respective participant tends to make decisions that are completely based on the respective simplifying decision-making rule (bias), or, in other words, that the participant's behavior is completely "intuitive".

Testable hypotheses and results
First, we look at the general picture of the bias grades in our sample. Table 3 concentrates the descriptive statistics in this respect, and shows some general results: All of the bias grades for both groups range from 2 (minimal possible grade) to 9-10 (maximal possible grade). In other words, in our sample, we have both participants who seem to be fully affected and those who seem to be completely unaffected by the respective behavioral patterns.
The mean bias grades range from 4.927 to 5.646, and the majority of the participants have bias grades lower than 6. Therefore, we may infer that our participants are, on average, moderately affected by behavioral biases.
However, the major goal of our paper is to analyze the cross-sectional correlations between the magni-tudes of different psychological biases in stock market behavior, a matter that is, to our best knowledge, not discussed at all in previous financial literature. We suggest that investors tend to rely either on purely rational considerations or on their feelings and intuition. That is, we expect "rational" investors to remain rational in all of the decisions they make and "intuitive" investors to employ not simply one or two, but various simplifying decision-making rules. Therefore, we hypothesize that: Hypothesis 1: The magnitudes of the behavioral effects are positively correlated in the cross-section. Table 4 presents cross-sectional correlation coefficients between the personal bias grades for the professional portfolio managers (Panel A) and for the nonprofessional investors (Panel B). The results strongly support Hypothesis 1. All of the correlations are positive (in fact, close to 1) and highly significant. That is, we may conclude that if an investor accepts a certain intuitive decision-making technique, she will most likely accept others as well. This result may be especially valuable because the matter of cross-sectional correlations between different behavioral biases is, to our best knowledge, not discussed in previous economic and financial literature. This finding implies that investors tend to behave in a consistently "rational" or "intuitive" way. Based on this, one may be able to better predict future decisions to be made by an investor, or even a group of investors, with relatively scarce information about their past decisions. We may also note that at first glance, the fact that the Gambler's grades and the Hot-hand grades are positively correlated in "Rational" or "Intuitive": Are Behavioral Biases Correlated Across Stock Market Investors? the cross-section might seem puzzling. However, as we have noted in Section 2, these two behavioral biases do not contradict each other and may well co-exist within one person because they refer to people's beliefs with respect to different types of processes. For example, Ayton and Fischer (2004) experimentally document both the gambler's fallacy and the hot hand fallacy and conclude that the former is attributed to "randomly looking" processes and to inanimate chance mechanisms, whereas the latter refers to processes that seem to be non-random and related to human skilled performances.

Cross-sectional correlations between the behavioral biases: Total sample
Finally, we may note that personal bias grades seem to be equally strongly correlated for both professional and non-professional investors, as demonstrated by the two panels of Table 4. 4

Subsample analysis
Having documented high correlations between the behavioral biases within both major groups of our participants, we now proceed to analyzing the nature of the correlations within different subsamples. We clas- an "adaptive toolbox" and mention that it is not universal but rather developed and amplified during each of our lives depending on the types of situations and problems we face. In this context, we may expect more experienced investors to possess more ample "adaptive toolboxes" and to employ the heuristics (or the rational criteria for investment decisions) in a more systematic way. In other words, we (again) expect that more experienced investors are more likely to decide whether to employ "rational" or "intuitive" decisionmaking techniques.
Thus, we hypothesize the following: Hypothesis 2: The correlations between the behavioral effects are higher for more experienced investors.
To test this hypothesis, we calculate correlation coefficients between the biases separately by the categories of investors' reported market experiences. Because the subsample of professional investors is relatively small, we employ only the subsample of website visitors for this analysis. Table 5  To test the hypothesis, we once again employ only the non-professional investors' responses. Table 6 comprises the correlation coefficients and their averages, separately for male and female investors. The results support Hypothesis 3. As reported in Panel B, 9 out of 10 coefficients are higher for male investors (or lower for female investors), 6 of them significantly at the 5% level, including 3 at the 1% level. These findings indicate that it is likely that male investors are more consistent in employing behavioral decision-making techniques or, alternatively, possess more ample "adaptive toolboxes".
Finally, we compare the correlations between the biases for different groups of ages. Again, the literature dealing with age differences in the magnitudes of behavioral biases is rather scarce. Kudryavtsev and Cohen (2010, 2011a, 2011b) report that younger people are slightly less affected by anchoring bias 7 and hindsight bias 8 when recalling financial information.
Therefore, we might expect them, in general, to use more ample collections of decision-making rules. That is, we hypothesize the following: Hypothesis 4: The correlations between the behavioral effects are higher for younger investors.
In Table 7, we divide the subsample of non-profes-sional investors into three categories of age-18-30 years old, 30-40 years old, and older than 40 9 -and calculate the correlations between the biases for each of the categories. The results do not support Hypothesis 4. The correlation coefficients are very similar for all of the age categories, and the differences between the correlations for the youngest and the oldest investors are of different signs, the majority of them being nonsignificant, as demonstrated by Panel C. Therefore, investors' ages most likely do not significantly affect the consistency of the decisions. However, the very high and strongly significant correlation coefficients we obtain for all of the age categories serve as important robustness checks for our general Hypothesis 1.

Conclusions and Discussion
Our paper explores the effects of behavioral biasesnamely, the disposition effect, herd behavior, availability heuristic, gambler's fallacy and hot hand fallacyon the mechanism of stock market decision-making and, in particular, the cross-sectional correlations between the magnitudes of the biases.
Employing an extensive online survey, we demonstrate that on average, active stock market investors exhibit moderate degrees of behavioral biases. We then calculate cross-sectional correlation coefficients between the biases, and as a major contribution of our study, confirm that all of them are positive and highly significant for both professional and non-professional investors. This finding shows that if an investor accepts certain intuitive decision-making technique, she will most likely accept others as well.
Furthermore, we perform a subsample analysis of the correlations and determine that the correlation coefficients between the biases are higher for more experienced investors and male investors, indicating that these categories likely behave more consistently, or, in other words, are more likely to decide for themselves whether to rely on simplifying decision-making techniques in general or reject all of them. Alternatively, this finding may suggest that the more experienced investors manage to develop (everyone for herself) more sophisticated "adaptive toolboxes", or collections of heuristics, and apply them more systematically, possibly arriving at better investment results. We also find that the correlation coefficients for the most experienced non-professional investors are lower than those for the professional in-"Rational" or "Intuitive": Are Behavioral Biases Correlated Across Stock Market Investors?
vestors, suggesting that it is likely that the latter group, though not necessarily more rational, at least makes more consistent decisions, or possesses more ample "adaptive toolboxes". However, the correlations appear to be independent from investors' ages. Importantly, all of the correlation coefficients we obtain for all of the subsamples and categories of participants are positive and highly significant, providing a strong robustness check for our major finding.
Our investor who appears to be affected by one of the biases to make a decision consistent with another bias or biases 10 or, on the contrary, to convince a "rational" investor to remain rational "all along the way". Both "sides of the game" might pay attention to this finding.
With regards to the higher correlations between the biases for more experienced investors and for male investors, this finding implies that the latter group, being in general less inclined to employ "intuitive" decisionmaking techniques, may also find it easier to "heal themselves" of all the behavioral biases knowing that one of them may result in inferior investment performances. They, and actually all the investors, simply have to be aware of as many known biases as possible to avoid them and choose appropriate investment strategies.  Table 2. Cross-sectional correlation coefficients of grades within the bias-related pairs of questions Table 3. Basic descriptive statistics of "bias grades The table reports, by groups of participants, basic statistics of the "bias grades" calculated as follows: is the grade (answer) given by participant i for question (statement) N.

Panel A: Portfolio managers (41 respondents)
Pair of questions Cross-sectional correlation coefficient between the question grades  Note Asterisks denote 1-tailed p-values: *p<0.10; **p<0.05; ***p<0.01 Table 5. Cross-sectional correlations between behavioral biases: Subsample analysis by categories of reported stock market experience. The table compares the correlation coefficients between the "bias grades" for different categories of investors according to their reported investment experience. In Panel D, the second row in each square reports the z-statistic according to the Fisher r-to-z transformation for the comparison of correlation coefficients between investors with more than 10 years of experience and those with less than 3 years of experience (in this order).

Panel A: Reported stock market investment experience of less than 3 years (107 participants)
Correlation coefficients between "bias grades"

Note
Asterisks denote 1-tailed p-values: *p<0.10; **p<0.05; ***p<0.01 Table 6. Cross-sectional correlations between behavioral biases: Male versus female investors The table compares the correlation coefficients between the "bias grades" for male and female investors. In Panel B, the second row in each square reports the z-statistic according to the Fisher r-to-z transformation for the comparison of correlation coefficients between women and men (in this order).