What makes a Chart Risky? An analysis on characteristics of financial charts and perceived risk perception using survey data

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What makes a Chart Risky?

An analysis on characteristics of financial charts and perceived risk perception using survey data

Radboud University Nijmegen

Author: P.H.A. Postma (s4209583) Supervisor: Dr. S.M. Zeisberger Date: 14-07-2017

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1. Introduction

“Bei gleicher Umgebung lebt jeder in einer andern Welt”

Arthur Schopenhauer; Die Kunst, glücklich zu sein (1855/2005, p. 98).

Given the same environment, people disagree on how they perceive the world. Similar external conditions do not influence people in the same way. Instead, the perception of internal and external stimuli are to some extent unique for each individual. Nonetheless, the social sciences that studies mankind aims to discover reoccurring patterns based on scientific methods in order to penetrate the human psyche. One of these fields in which a myriad of outcomes occur is the perception of risk. Similar risk environments produces a variety of outcomes and responses, occurring in fields ranging from medicine and natural disasters, to investing and policy making (Slovic, 2000).

The study of risk perception literature goes back a long time in history for both the social and natural sciences (Covello et al., 1983; Kahneman & Tversky, 1979; Rhodes & Pivik, 2011; Slovic, 2000; Wachinger et al., 2013). In all these different fields, those in charge of presenting options to others have to think about how to adequately present, or hide these risks. Especially in the field of finance, there is an incentive to masks (financial) risk in order to attract customers. From the 18th_{century South-Sea bubble (Brunnermeier & Schnabel, 2015) to the Dutch}

“woekerpolissen” of the nineties (Kooman, 2010) and more recently, the sub-prime mortgage crisis of 2008 (Financial Crisis Inquiry Commission, 2011), time and time again retail investors fail to recognize the (financial) risks. As a result, regulation is developed aimed at protecting these retail investors. An example of such a measure is the European wide implementation of the Key Investor Information Document (KIID) in 2001 (European Commission, 2014). The goal of this document is to present a simplified prospectus that is: “giving key facts to investors

in a clear and understandable manner” (ibid.). However, what remains puzzling is which

elements play a role in recognizes these risks.

By looking at the price chart characteristics, this study aims to contributes in the protection of retail investors. Within the field of finance, a relatively new branch focuses on the graphical perception of risk by agents. This field believes that the different graphical representation formats influence the risk perception of its readers. Literature ranging from medicine to food security to finance confirms that representational formats matter (Diacon and Hasseldine, 2007; Keller & Siegrist, 2009; Lathrop, 1967; Van Kleef et al., 2008; Weber et al.,

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5 2005). The foundation of this study is built on literature of graphical representational formats in order to find out which elements of a chart make it perceive risky. The main question is therefore:

“What elements of a chart make it being perceived as risky?“

Studying the risk perception of retail investors is done by presenting 10 out of 45 artificially created charts to participants recruited via Amazon Mechanical Turk (MTurk). The respondents were asked to rate the riskiness of a graph on a scale from zero to ten. In total 301 responses were gathered. On the basis of the respondent’s results, this paper finds that the end point, range and standard deviation of a price line matters most for determining the riskiness of a chart, while the presence of extreme values also play a significant role. The salience of the range and the endpoint confirms earlier findings from the peak-and-end rule and increase its applicability to financial risk perception literature. Next, charts that have a decreasing sequence are significantly rate more risky than similar charts with end with an increasing trend. There was found no difference between charts with only salient peaks or salient troughs. In addition, females did not score the presented charts differently than males, although reporting higher levels of risk-aversion.

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2. Theoretical Framework

Scholars of finance have developed a myriad of risk theories, models and techniques in order to comprehend risk (McNeil et al., 2015). The most famous and accepted definition of financial risk was formulated by Markowitz in 1952, stating that risk is represented by volatility, which later on became the foundation of standard finance theory (Bodie et al., 2014). While Markowitz provided the foundation of modern portfolio management, Sharpe, Lintner and Mossin individually published articles that led to the creation of CAPM (Lintner, 1965; Mossin, 1966; Sharpe, 1964). CAPM is a mean-variance model framework, which uses the mean and the variance of individual asset to construct the optimal portfolio. It is assumed that investors like high means and dislike high variance (Bodie et al., 2014). However, contemporary literature mitigate the salience of volatility. Pincus and Kalman (2004) argue that the current measure of volatility -standard deviation- does not fully grasp the volatility of risk. They argue that: “(…) the extent of variation is generally not feared; rather, unpredictability is the

concern” (p. 13709). Other studies confirm that variance is not the only, or most important risk

factor for investors (Olsen, 1997; Saschse et al., 2012; Veld & Veld-Merkouvala, 2008). Hence, it is likely that other factors besides the mean and variance are important for retail investors deciding if they want to invest.

What then, is risk perception exactly? Wachinger et al. (2013) define it as: “(…) the

process of collecting, selection and interpreting signals about uncertain impacts of events, activities, or technologies” (p. 1049). According to standard financial theory, a rational agent

will maximize their utility with their: “unbounded, costless and calculating ability to analyze

any situation” (Van Damme, p. 184). Hence, the agent should be able to correctly collect,

selection and interpret signals about risk in price paths in order to maximize its utility. However, findings from the field of behavioral finance challenges the idea of rational agents and argues that agents are boundedly rational (Simon, 1982; Kahneman, 2003). Bounded rationality implies that, given that time is limited and information is characterized by uncertainty, agents are not utility maximizing but satisficing. A decision is not necessarily the most optimizing one, but the most satisficing one given the constraints of time and uncertainty. As a results, the agent is subject to systematic biases that “trick” our brain in making the rightful decision. An example is the cognitive dissonance bias: The tendency to adjust beliefs to justify past actions (Festinger, 1957). This systematic bias reduces the feeling that a past action was not optimal, often in order to give the individual a positive self-image. This is for instance applied to consumer and investment behavior (Ehrlich et al., 1957; Goetzmann & Peles, 1997).

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7 Given the constraints of time and information, it is not unlikely to assume that agents use mental heuristics in order to evaluate the riskiness of a graph. The next paragraphs discusses findings from (behavioral) finance and translates these findings to hypotheses about the risk perception

of charts.

2.1 Improving sequences

Say that your parents demand that in the upcoming two weeks, you have to spend one weekend with your aunt which you dislike. In the other weekend, you can organize the time as you like. In which of the upcoming two weekends would you most likely visit your disliked aunt? A study by Loewenstein and Prelec (1993) presented this dilemma to their respondents and found that 90% favored visiting the aunt in the first weekend over visiting the aunt in the second weekend. Loewenstein and Prelec (1993) explain this choice by the preference for individuals for improving sequences. An earlier study looks into this phenomena with respect to wage profiles (Loewenstein & Sicherman, 1991). The respondents were presented to types of wage structures: A) a decreasing wage profile and B) an increasing wage profile. The total of all payments was constructed such that the present value of the decreasing wage profile was higher than the increasing wage profile. Results demonstrated that the majority of the respondents favored the increasing wage profile, arguing that it is more satisfying to get a bigger payment each year, plus the disability in self-restraint yourself to save the money in the first years to have more later on by earning interest.

Literature seems to suggests that agents favor improving sequences over decreasing sequences. In risk-perception literature, this phenomena is explored by Grosshans and Zeisberger (2016), which found that respondents prefer price paths that first decrease and afterwards recover, over price paths that first increase and afterwards fall, independently of whether the final return is positive or negative. Hence, the following hypothesis is formulated:

H1a: People will perceive a graph which first increases and afterwards decreases as more risky than vice versa.

The idea of favoring improving sequences can be extrapolated to charts that become less volatile over time. Assuming that in general people are risk-averse, one would conclude that a stock that becomes less volatile over time is an improvement over a stock that becomes more volatile over time. So, the reduction in volatility over time would be regarded as an improving sequence. This brings us to the following hypothesis:

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H1b: People will perceive price paths that are volatile at the start of the period as less risky than price paths that are volatile at the end of a period.

2.2 Peaks and Troughs

The peak-and-end rule is a psychological bias first described by Fredrickson and Kahneman (1993). By this rule, an event is not judged by its entire experience, but only by certain aspects of the particular event. According to this study, these salient aspects of the experience are those most intense – peaks/troughs – and at the end of the event – end –, while paying limited attention to the duration of the experience. The insights from this study are applied to a variety of fields, ranging from political science to medicine (Burt et al., 2003; Chajut et al., 2014; Healy & Lenz, 2014). This is further examined in risk perception literature by studies that look at endings (Ross & Simonson, 1991) and at peaks (Duxbury and Summers, 2017; Mussweiler & Schneller, 2003). However, a combination of these aspects is to the knowledge of this author scarcely studied in finance risk perception literature. On the other hand, contrasting studies suggest that individuals in fact neglect rare peaks, and instead focus on the most frequent observations (Erev & Barron, 2005; Hertwig et al., 2004; Ungemach et al., 2009). Henceforth, the effect of salient peaks, troughs and different end points are to a large extent undocumented, especially when combining these characteristics. This brings us to the following hypotheses:

H2a: The peak-and-end rule can predict the perceived riskiness of price line charts.

Next, the paper will look if the order of how the peaks appear matters. In other words, if the price path first has their peak followed by a trough, or vice versa. Taking into account the preference of improving sequences of individuals, one could argue individuals will favor price paths that recover from the trough after experiencing a peak. However, other arguments could also be into play. Therefore, the following hypothesis is formulated:

H2b: People perceive charts that first have a upward peak followed by a trough as less risky, than charts that first have a trough, followed by a upward peak.

According to the peak-and-end rule, people pay most attention at two salient details of a graph: the peaks and the end point . However, it is unclear which of these is the most salient to the person. The study will therefore examine to which extent the peak is more salient than the end point or vice versa, which brings us to the following two explorative hypotheses:

H2c: The end point of a chart is more salient for a person than the range of the peaks in judging its riskiness.

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H2d: The range of the peaks is more salient for a person than the end point of a chart in judging its riskiness.

2.3 Prospect Theory

Prospect Theory states that the value function is concave in the gain domain and convex in the loss domain (Kahneman and Tversky, 1979). In addition, the function is steeper in the loss domain than in the gain domain, implying that losses affect utility more than a similar increase in wealth. If one assumes that respondents take the starting point as their reference point, price line charts performing below its starting point generate disutility by being in the negative domain. From this line of thought, the following hypothesis is formulated:

H3a: Price paths that are most of their time under their starting point are perceived as more risky.

This thought could be further extrapolated by comparing the presence of salient peaks with salient troughs. Assuming that a retail investors takes the starting point as reference point one would expect that charts that have salient troughs are disliked more than charts that have salient peaks. On the other hand, a retail investors could see the recovery from trough as less risky than the loss after a positive peak has occurred. The following hypothesis relies on the first thought:

H3b: Charts that only have salient troughs are perceived as more risky than charts that only have salient peaks.

2.4 Demographical influences

Gender differences between female and male behavior are part of a long-lasting discussed subject in literature. In finance-economic related literature, females are found to be less risk-seeking (Charness & Gneezy, 2012; Jianakoplos & Bernasek, 1998) than their males counterparts. Explanations for these differences are found in biological components (Freeman & Herron, 2007; Knight, 2002) or behavioral aspects like higher overconfidence of males (Lundeberg et al., 1994; Huang & Kisgen, 2013). Based on literature that females are indeed less risk-seeking, the following hypothesis is formulated:

H4a: Females will perceive charts as more risky than males.

2.5 Presentational influences

While beyond the scope of this research, it is worth addressing that the use of different graphical formats can influence the perception of risk by individuals (Weber et al., 2005). The designer

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10 of the chart can manipulate the data through various ways: graph type, color, scale, size and more (Penrose, 2008). An extensive study conducted by Beattie and Jones (2000) demonstrated that on a large world-wide scale, management use the corporate annual report to present a favorable view of the company’s performance. For example by highlighting (leaving out) favorable (unfavorable) information, or by using measurement distortion, e.g. using incorrect drawn axis to influence the trend lines in the particular graph.

While these factors play a significant role in the perception of risk of a graph, this study will only focus on characteristics of the stock itself without aiming to influence to individual via presentational deception. It does so by using a standardized presentation format for every chart shown.

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3. Experimental Design and Data

In this chapter, the experimental design of the paper is explained. The chapter starts with explaining the method of how the data is collected, before moving on to the presentation of the independent variables. Hereafter, the construction of the different charts is discussed, together with the function of each category.

3.1 Survey

This study made use of a survey constructed via Qualtrics. The participants were recruited from MTurk, an online platform on which so-called “workers” are hired to perform small tasks for a fee. The behavior of these workers are be found to be similar to behavior found in lab settings (Goodman et al., 2013). In addition, they provide a more representative sample of society than college samples (Paolacci & Chandler, 2014), which is in line with the target group of this study, namely retail investors.

Participants of the survey were asked in the opening text to rate the riskiness of a stock investment based on its past performance (see figure 4, Appendix A). They could use a slider bar to answer on a scale from 0 (not risky at all) to 10 (extremely risky) how they perceived the riskiness of a graph (see figure 5, Appendix A). Next, the participants were presented 10 different price charts out of 45 in total. The charts were grouped in ten different sections and were presented in a randomized way to the participants. Each section contains four or five charts, in order to generate equal views per graph. The chart within a section were also presented in a randomized manner. In appendix A, table 13, it can be found which charts were contained in which sections.

The ten sections were constructed in such a way that the majority of the participants will see all seven categories: Initially Up, Initially Down, Peak, Trough, High-Low, Low-High and Volatility. In addition, 75% of the respondents saw two charts ending at 90, five charts ending at 105 and three charts ending at 120. The remaining 25% of the respondents saw three charts ending at 90, four charts ending at 105 and 3 charts ending at 120. Furthermore, the order in which the charts were presented within a section were randomized for every respondent, as well as the order in which the sections appeared to the respondents.

At last, respondents several demographical questions were gathered like age, gender, experience with investments and statistical proficiency. The respondents were asked to rate their knowledge on investments and statistics, and the degree of the risk-aversion on a 7-point Likert scale. This scale is chosen because it produces similar relative means to a 5-point Likert scale, but gives more room for choice (Dawes, 2008).

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12 In total, 319 responses were gathered. However, several participants did not complete the survey in total. To ensure equal treatment of all participants, those who did not rate at all charts were removed from the data, bringing the total to 301. The author decided not to filter extreme entries to prevent subjectivism in using data1.

3.2 Charts characteristics

All charts were created via Excel 2016 and are similar in their design. This includes the measurement on the axes, the starting point, color, size, and returns format. The charts have three possible end points: 90, 105 and 120. The maximum value a graph could reach was 135, and the minimum value was 80. All charts had 252 days to make up for the number of days in a trading year and have an integer number for calculating monthly returns. Because literature about variables that capture risk (besides standard deviation) is scarce, most variables are constructed by the author itself based on (behavioral) finance literature and correspondence with experts from the field. For example, the variable FromMean_10 and FromMean_15 is based on Duxbury and Summers’ (2017) study, but the variables Endpoint and Range are deduced from the peak-and-end rule. As such, the study expects that certain variables will have some degree of correlation, which will be accounted for.

Variation in standard deviation and the mean is unintentional, because controlling for these two factors would leave little room to construct the seven different categories, which will be explained later. For testing the hypotheses and running regressions, eleven explanatory variables are constructed that are presented in table 1. Charts will be not be rated on the characteristics “maximum” or “minimum”, but on its range, calculated by subtracting the minimum point from the maximum point. It is expected that a higher value for Endpoint and/or L42Days will have a negative effect on the perceived riskiness of a chart, while the remaining variables have a positive effect. Values of standard deviation in the first period and the second period and can be found in appendix C, table 142.

1_{Examples of such “extreme entries” are participants which, often in a time-span of less than 100 seconds, rated}

charts only in the 1-3 range or 8-10 range. These entries could be classified as outliers, however a shortcoming of removing these outliers would be than entries averaging two or nine would in turn become extreme. In turn, a participant rating a chart with a mean of three with an eight rating could also be considered extreme and so forth, or every entry completed in less than 60 seconds etcetera. Henceforth, this study decided not to filter data based on extreme mean ratings, short completion times or any other characteristic.

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Table 1. Chart characteristics of the 45 charts.

Chart Mean Max Min Endpoint StDev_Year L42Days U_Start U_End

From Mean_10 From Mean_15 1 103.85 120 90 90 0.15145 -2.66 90 0 73 3 2 109.64 135 90 90 0.17829 -6.27 62 0 121 71 3 111.48 125 90 90 0.17603 -17.63 26 0 50 15 4 101.1 115 90 90 0.15571 -4.86 130 0 51 0 5 113.02 125 100 105 0.12069 -4.47 0 8 13 0 6 109.71 120 100 105 0.09488 -5.58 0 49 1 0 7 114.92 135 100 105 0.11895 -11.09 0 37 65 14 8 115.65 135 100 105 0.16162 -1.83 0 23 81 28 10 102.84 115 95 105 0.12482 3.36 88 170 13 0 11 110.52 120 100 120 0.06451 2.51 0 251 3 0 12 117.97 135 100 120 0.11467 -2.62 0 140 52 11 13 113.8 125 100 120 0.12186 2.7 0 224 16 0 14 91.45 100 85 90 0.13146 -0.58 251 106 0 0 15 96.18 110 85 90 0.18784 -1.91 166 40 22 0 16 96.74 105 90 105 0.11087 3.61 182 251 0 0 17 92.74 105 80 105 0.13996 5.2 214 251 18 0 18 104.56 115 90 105 0.11579 -7.3 79 106 24 0 19 100.9 120 85 120 0.17191 5.01 130 251 109 30 20 95.65 120 80 120 0.15710 8.95 188 251 59 29 21 100.04 120 90 90 0.22924 -3.63 146 0 23 6 22 101.1 120 90 90 0.24221 -19.39 132 0 16 3 23 103.17 120 95 105 0.16116 0.6 69 179 11 2 24 109.29 135 95 105 0.31974 -8.42 15 68 35 12 25 107.59 125 100 105 0.15247 -7.32 0 82 10 1 26 109.66 125 95 120 0.21125 4.2 16 239 28 1 27 116.96 135 100 120 0.21092 -1.92 0 164 30 7 28 97.22 110 85 90 0.1782 -2.04 154 32 13 0 29 106.88 115 95 105 0.21407 1.8 17 71 4 0 30 102.29 110 85 105 0.27585 -1.34 73 152 11 2 31 105.65 125 90 120 0.25035 14.37 35 247 26 5 32 115 130 95 120 0.22681 -0.21 7 185 31 9 33 155.11 125 95 120 0.26731 -0.87 8 198 20 9 34 100.78 120 85 90 0.12643 -2.15 100 16 39 8 35 103.37 120 90 105 0.19335 5.27 69 178 27 5 36 109.6 135 90 105 0.25171 1.08 28 76 56 24 37 103.59 125 80 120 0.28613 11.04 95 242 74 30 38 110.09 125 90 120 0.25476 0.33 22 234 39 8 39 105.91 130 90 90 0.26458 -17.01 67 0 68 28 40 106.18 125 90 105 0.19839 -11.46 43 125 46 12 41 101 120 85 105 0.15888 1.35 107 194 39 5 42 112.36 135 85 120 0.26456 -4.29 59 143 140 62 43 106.1 135 85 105 0.4232 -0.32 41 105 41 23 44 107.49 135 85 105 0.35082 -5.37 22 95 41 22 45 105.64 135 85 105 0.42261 12.25 51 130 36 16 46 110.24 125 85 120 0.16759 1.19 26 227 52 14

Notes: Chart: Number of the chart (see Appendix B). Mean: Mean value of the chart. Max: Maximum point which the chart reached. Min: Minimum point which the chart reached. Endpoint: value of the chart on day 252. StDev_Year: Standard deviation calculated for all 252 days, based on monthly returns. L42days: The value of the chart on day 252 minus the value of the chart on day 210. U_Start: Number of days the chart is below its starting point of 100. U_End: Number of days the chart is below its end point value, i.e. its value on day 252. FromMean_10: Number of days the chart has a value which lies 10 points from its mean. FromMean_15: Number of days the chart has a value which lies 15 points from its mean.

3.3 Categories

The 45 constructed charts all belong to one of the constructed seven categories. Charts 1 through 13 belong to the Initially Upwards category (see appendix B.1). These charts all start with a gradually moving upward trend, without the presence of salient peaks and/or troughs.

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14 Eventually after either 84, 126 or 168 days, these price chart gradually moves downwards upon reaching their end point of 90, 105 or 120 (except chart 11, 12 and 13 which end upwards). The second category is named Initially Downwards and includes the charts 14 up to and including 20 (see appendix B.2). These price charts first move downwards and eventually move upwards after either 84, 126 or 168 days (except 15 and 18, which end downwards). Alike the first category, these price charts have no salient peaks and/or troughs. Comparing price charts with similar characteristics from these two categories will give us indications if respondents prefer initially upwards (i.e. ending downwards) or initially downwards (i.e. ending upwards) price charts.

The third category is called Peak and concerns charts 21 through 27 (see appendix B.3). These charts all have in common that they exhibit the presence of at least one salient peak. They do not have salient troughs and/or a distinctive increasing/decreasing trend. Charts in this category vary in the height of the peaks and the number of the peaks, next to variations in their end point An example of a chart with salient peaks can be found in figure 1.

The next category is called Trough and includes charts 28 up to and including 33 (see appendix B.4). As an antipode of the Peak category, these charts have in common that they exhibit at least one salient troughs. In addition, these charts do not have salient peaks, nor have a clear upwards/downwards moving trend. A comparison will be made between charts from the Peak and Trough categories to see if these elements of charts have a significant impact on the perceived riskiness of chart.

The fifth category consists of charts which all first have a salient peak upwards, followed by a salient trough. This High-Low category includes the charts 34 through 38 (see

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15 appendix B.5). The occurrence of both the peak and the troughs varies across the several charts, and a peak is not necessarily immediately followed by a trough. The underlying idea behind this category is to see if the period in which the salient peak or trough occurs has an influence on the perceived riskiness of charts by investors. Next, the sixth category is named Low-High and includes charts 39 through 42 (see appendix B.6.). Chart in this category all have a salient trough, followed by a salient peak upwards. Alike the previous category, the occurrence of these two elements do not necessarily have to follow each other directly Charts including in this category are Comparing the High-Low and the Low-High category, this study will examine if the order of peaks and troughs have a significant impact on the perceived riskiness by investors. An example of a chart from the Low-High category is seen in figure 2.

Last but not least, the seventh category is named Volatile and consists of chart 43 through 46. These charts all have in common that they have one period, either at start (0-84 days), middle(85-168 days) or end (169-252 days), in which the price charts heavily fluctuates and can move from their absolute maximum point to their absolute minimum point in a short time notice. These charts can be found in appendix B.7.

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4. Results

The previous chapter described the methodology for obtaining the results. In this chapter, first the demographical results are presented. Hereafter, a separate regression on all explanatory variables is conducted followed by separate regression per end point category. Then, the study proceeds to the multiple regression which is followed by adaptations based on correlation and significance scores, and multiple regressions per end point are performed. Hereafter, the constructed hypotheses from chapter two are examined and at last, there is a brief paragraph contributed to demographical differences in the rating of the charts. In-depth interpretation and discussion of results will take place in chapter 5.

4.1 Demographics of the respondents

In total, the survey was completed by 319 respondents recruited via MTurk. Respondents which did not completed the survey completed were eliminated from the results, coming to a total respondents number of 301. Slightly more males (59.47%) than females (40.53%) responded the survey, and at least 70% of all respondents had at least a bachelor’s degree. The most common age category of the respondents was 25-34 years (44.85%), followed by 35-44 years (26.25%) and 55-64 years (9.97%). The majority of the respondents was employed (81.06%) at the time of the survey, and of those 73,76% reported average or higher knowledge of investments. Around 50% reported some degree of risk-averseness with respect to investments, compared to almost 30% that stated they were to risk-neutral. The remaining 20% all reported some degree of risk-seeking behavior when it comes to investments. Further demographical information can be found in table 15 in Appendix C. To examine if the characteristics of age, educational level, risk attitude, investment knowledge and statistical knowledge were evenly spread among females and males, several Mann-Whitney U tests were conducted on both the mean and median level to examine if there were any statistically significant differences, presented in table 23. The results showed that there was a statistically significant difference in the self-reported risk attitude, investment and statistical knowledge between males and females on the 1% level. Males self-reported both more investment and statistical knowledge, and describe themselves as more risk-seeking than their female counterparts. The educational level did not significantly differ for females and males. All questions can be found in Appendix A.2.

3_{The variables were tested for the assumptions of normality and equal variances with the use of respectively}

Shapiro Francia W test and Levene’s test to see if a one-way ANOVA analysis was possible. None of the variables passed both tests, hence a Mann Whitney U test was used.

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Table 2. Mann-Whitney U test on the dependent variable Gender for mean and median value, conducted on five independent variables.

Variable Mean females Mean males p value, mean | median

Age 2.8852 2.5363 0.015* | 0.026*

Education 3.6393 3.8156 0.222 | 0.637

Investment Knowledge 3.7213 4.2458 0.000*** | 0.000***

Statistical Knowledge 4.0492 4.5922 0.000***| 0.001***

Risk Attitude towards Investments 3.2213 3.8156 0.001*** | 0.015**

Notes: Age is defined on a ordinal scale ranging from 0-17 years to 75 years. The value of 2.88 and 2.54 is roughly equal to respectively 33 and 30 years. Education is defined on a ordinal scale ranging from secondary education to doctorate. The values of 3.64 and 3.81 lay between the trade/technical/vocational and bachelor level. * = p ≤ 0.05, ** = p ≤ 0.01, *** = p ≤ 0.001.

4.2 What makes a chart risky?

Table 3 depicts the mean ratings, standard deviation and number of observations of all charts. The weighted average of all averages is 5.45, hence the charts were on average rated slightly more risky than the numerical average of five4. Charts had on average 69 views, with a minimum of 59 views and a maximum of 77. With the exception of chart 27 and 34, all charts have a range of nine or higher (see appendix C, figure 51-53 for boxplots of all charts). Using Bulmer’s (1979) rule of thumb concerning skewness, eleven charts are marked as moderately skewed5. The remaining charts are normally distributed.

Table 3. Average rating per chart.

Chart Mean Std. Dev. Observations Chart Mean Std. Dev. Observations

1⁋ 7.21 2.88 61 25 4.23 2.26 75 2⁋ 7.56 2.37 62 26 4.35 2.23 62 3⁋ 6.87 2.41 58 27 4.05 2.30 61 4 6.34 2.42 59 28 6.02 2.09 59 5 5.35 2.21 60 29 4.66 2.05 74 6 4.43 2.32 60 30 5.41 2.25 76 7⁋ 6.08 2.55 61 31 5.23 2.40 60 8⁋ 6.5 2.01 62 32 4.72 2.44 60 10 4.23 2.01 74 33 4.97 2.29 61 11⁋ 2.98 2.57 60 34 6.60 1.88 60 12 4.19 2.16 59 35 5.53 2.20 75 13 4.20 2.07 59 36 5.72 2.16 76 14 4.77 2.68 60 37 5.93 2.50 75 15 5.20 2.28 59 38 4.96 2.35 74 16⁋ 3.05 2.18 76 39⁋ 7.10 2.41 61 17 4.44 2.19 73 40 5.21 2.09 75 18 3.90 2.19 77 41 4.13 1.91 75 19⁋ 3.83 2.32 60 42 4.70 2.47 77 20 4.43 2.37 60 43 5.43 2.08 74 21⁋ 6.15 2.39 60 44 6.12 2.21 76 22 6.56 2.41 61 45 6.43 2.17 77 23 4.85 2.28 75 46⁋ 5.53 2.48 75 24 6.11 2.22 76

Notes: Mean: The average of all ratings given by the respondents per chart. Std. Dev.: Standard deviation of the mean. Observations: Number of times the chart is rated. ⁋: Chart is moderately skewed.

4_{The weighted averages of all averages corrects for the number of observations per chart.}

5_{Bulmer (1979) proposes three categories to classify variables with respect to skewness. Normal distributed}

variables have a skewness value between -1/2 and 1/2. Moderately skewed variables have a skewness value between -1 and -1/2 or between 1/2 and 1 highly skewed variables have a skewness value that is lower than -1 or higher than 1.

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4.2.1 Separate regression

In order to see if the independent variables hold any explanatory power, separate regression models are performed, which can be found in table 4. Running separate regressions demonstrate that eight out of eleven independent variables have a significant effect. A higher standard deviation, range and the presence of more extreme values (FromMean_10/15) all have positive effect on the perceived riskiness of a chart. A greater endpoint and a greater decreasing trend in the last 42 days both have a negative effect on the perceived riskiness of a chart. Surprisingly, a chart which performs relatively long below its endpoint have lower ratings than charts that do not, while charts that perform relatively long below its starting point seem to be of no influence for the perceived riskiness of chart. An explanation, among further discussion of these results, can be found in chapter 5.

Table 4. Separate regression of all 11 independent variables on mean rating of the charts.

Independent variables (Adj. R2) Coefficient Std. Err. t value p value 95% Conf. Interval

Mean (-2.32%) -0.0010 0.0171 -0.06 0.956 -0.0355 0.0336 Endpoint (35.90%) -0.0593 0.0117 -5.06 0.000*** -0.0829 -0.0357 StDev_Year (12.32%) 5.173112 1.930204 2.68 0.010** 1.280486 9.065739 StDev_FirstHalf (0.23%) 2.537875 2.416473 1.05 0.299 -2.335408 7.411159 StDev_SecondHalf (6.78%) 4.316207 2.105565 2.05 0.047* .0699295 8.562484 L42Days (13.20%) -0.0599 0.0216 -2.77 0.008** -0.1035 -0.0164 U_Start (-2.29%) -0.0003 0.0025 -0.12 0.907 -0.0054 0.0048 U_End (47.74%) -0.0084 0.0013 -6.42 0.000*** -0.0110 -0.0058 FromMean_10 (12.89%) 0.0134 0.0049 2.74 0.009** 0.0035 0.0233 FromMean_15 (10.48%) 0.0250 0.0101 2.48 0.017* 0.0047 0.0453 Range (18.84%) 0.0533 0.0159 3.35 0.002** 0.0212 0.0853

Notes: Bold independent variables have coefficients signs as predicted. Mean: Mean value of the chart. Endpoint: value of the chart on day 252. StDev_Year: Standard deviation calculated over all 252 day based on monthly returns. StDev_FirstHalf: Standard deviation calculation over 0-126 days, based on monthly returns. StDev_SecondHalf: Standard deviation calculated over 127-252 days, based on monthly returns. L42days: The value of the chart on day 252 minus the value of the chart on day 210. U_Start: Number of days the chart is below its starting point of 100. U_End: Number of days the chart is below its end point value, i.e. its value on day 252. FromMean_10: Number of days the chart has a value which lies 10 points from its mean. FromMean_15: Number of days the chart has a value which lies 15 points from its mean. Range: maximum point minus the minimum point of the chart. * = p ≤ 0.05, ** = p ≤ 0.01, *** = p ≤ 0.001.

Next, the study examines the explanatory power of the individual variables when grouped per end point of a chart, to get a deeper understanding of the salience of several explanatory variables (see table 5 below and table 16 and 17 in Appendix C). The first observation is that the explanatory variables have higher significance levels and coefficients for charts ending at 105. In addition, charts ending at 90 and 105 share the same significant variables, with the exception of the standard deviation, which seems not to play a role for charts ending at 90. The charts ending at 120 only have three significant variables, range, yearly standard deviation and standard deviation calculated over the first half of the trading year. Having a relatively large number of days in which the price line chart has extreme values does not influence the perceived riskiness for charts ending at 120, compared to a increasing effect for charts ending at 90 and 105. At last, the variable Mean is highly significant, although with

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19 the non-predicted coefficient sign. An explanation and further discussion of the results are presented in chapter 5.

Table 5. Separate regression of the 10 independent variables on the mean rating of the charts ending at 105. N=20.

Independent variables (Adj. R2₎ _Coefficient _{Std. Err.} _{t value} _{p value} _{95% Conf. Interval}

Mean (34.96%) .1044384 .0311871 3.35 0.004** .0389168 .1699601 StDev_Year (31.69%) 5.454686 1.741061 3.13 0.006** 1.796853 9.11252 StDev_FirstHalf (3.88%) 3.142549 2.364427 1.33 0.200 -1.824927 8.110025 StDev_SecondHalf (26.50%) 5.55216 1.981819 2.80 0.012* 1.388512 9.715807 L42Days (-4.91%) -.0120142 .0362314 -0.33 0.744 -.0881337 .0641052 U_Start (29.40%) -.0091333 .0030592 -2.99 0.008** -.0155604 -.0027061 U_End (24.81%) -.0071938 .0026682 -2.70 0.015* -.0127994 -.0015882 FromMean_10 (45.01%) .0292773 .007196 4.07 0.001*** .014159 0443956 FromMean_15 (54.12%) .072833 .0150521 4.84 0.000*** .0412097 .1044563 Range (51.73%) .0636519 .0137718 4.62 0.000*** .0347184 .0925854

Notes: Bold independent variables have coefficients signs as predicted. Mean: Mean value of the chart. Endpoint: value of the chart on day 252. StDev_Year: Standard deviation calculated over all 252 day based on monthly returns. StDev_FirstHalf: Standard deviation calculation over 0-126 days, based on monthly returns. StDev_SecondHalf: Standard deviation calculated over 127-252 days, based on monthly returns. L42days: The value of the chart on day 252 minus the value of the chart on day 210. U_Start: Number of days the chart is below its starting point of 100. U_End: Number of days the chart is below its end point value, i.e. its value on day 252. FromMean_10: Number of days the chart has a value which lies 10 points from its mean. FromMean_15: Number of days the chart has a value which lies 15 points from its mean. Range: maximum point minus the minimum point of the chart. * = p ≤ 0.05, ** = p ≤ 0.01, *** = p ≤ 0.001.

4.2.2 Multiple regression

The study now moves on to the general model to examine if the variables have predictive power in a multiple regression. These findings are presented in table 6. The general model explains up to 73.27% of the variation in the riskiness perception of individuals. Of all the variables in the general model, three are found to be significant: one on the 1% confidence level and two on the 10% confidence level. With respect to the separate regression models, these results are rather poor. The reason for these poor results is the relatively large degree of collinearity present between the variables, as measured by the Variance Inflation Factors (VIF)6. These can be found respectively in Appendix C, table 18. The Pearson correlation test can be found in table 7 and 8.

Table 6. Multiple regression of all 11 independent variables on mean rating of the charts.

Independent variables Coefficient Std. Err. t value p value 95% Conf. Interval

Mean 0.0209187 .0135298 1.55 0.132 -.0066079 .0484453 Endpoint -.0831851 .0242837 -3.43 0.002*** -.1325907 -.0337796 StDev_Year 2.362287 5.991251 0.39 0.696 -9.827004 14.55158 StDev_FirstHalf -1.053985 4.322984 -0.24 0.809 -9.849163 7.741193 StDev_SecondHalf .0923533 3.760909 0.02 0.981 -7.559273 7.74398 L42Days .0271591 .0179567 1.51 0.140 -.009374 .0636922 U_Start -.002529 .0024763 -1.02 0.315 -.007567 .0025091 U_End -.0010622 .00268 0.40 0.694 -.0065147 .0043904 FromMean_10 .0130012 .0067578 1.92 0.063* -.0007477 .02675 FromMean_15 -.0163089 .0131927 -1.24 0.225 -.0431498 .0105319 Range .0416924 .0242515 1.72 0.095* -.0076476 .0910325

Notes: Bold independent variables have coefficients signs as predicted.. * = p ≤ 0.1, ** = p ≤ 0.05, *** = p ≤ 0.01.

6_{Discussion has been taking place over a long time about the acceptable VIF factor ranges. While the majority}

of scholars (see Dormann et al., 2013), follow the threshold of 10, this study takes the more conservative threshold of 5 as proposed by Hair et al. (1995).

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20

Table 7. Pearson correlation coefficient matrix between the individual variables (N=45). #1.

Mean Endpoint StDev_Year StDev_FirstHalf StDev_SecondHalf

Mean 1 Endpoint 0.4290** 1 StDev_Year 0.1321 0.0587 1 StDev_FirstHalf 0.0608 0.1252 0.7533*** 1 StDev_SecondHalf 0.1522 0.0132 0.7164*** 0.1485 1 L42Days -0.1322 0.5244*** 0.0877 0.1076 0.0385 U_Start -0.7041*** -0.4317** -0.1514 -0.0364 -0.2136 U_End 0.0466 0.8093*** -0.0178 0.0839 -0.0547 FromMean_10 0.1037 0.0846 0.1952 0.1952 -0.0889 FromMean_15 0.1391 0.0912 0.2943* 0.2943* 0.0057 Range 0.1885 0.1882 0.4680** 0.4680** 0.4252* Notes: * = p ≤ 0.05, ** = p ≤ 0.01, *** = p ≤ 0.001.

Table 8. Pearson correlation coefficient matrix between the individual variables (N=45). #2.

L42Days U_Start U_End FromMean_10 FromMean_15 Range

L42Days 1 U_Start 0.1552 1 U_End 0.7001*** 0.0344 1 FromMean_10 -0.0916 -0.0693 -0.1132 1 FromMean_15 -0.0665 -0.0873 -0.0837 0.8784*** 1 Range 0.0125 -0.2755 -0.0346 0.6907*** 0.7392*** 1 Notes: * = p ≤ 0.05, ** = p ≤ 0.01, *** = p ≤ 0.001.

Considering the multicollinearity issues of the general model, all possible combinations of uncorrelated multiple regressions are examined7. In addition, the standard deviation variables are never included in the same model. This gives us around 100 combinations in total, of which 29 are significant. The model which captures the majority of these significant variables, and are also uncorrelated when split up per end point, are presented in table 9.

Table 9. Multiple regression of uncorrelated variables.

Independent variables Coefficient Std. Err. t value p value 95% Conf. Interval

Mean .0311334 .0117989 2.64 0.012* .007268 .0549989

Endpoint -.0802031 .0118477 -6.77 0.000*** -.1041672 -.0562389

StDev_Year 4.304932 1.172661 3.67 0.001*** 1.933001 6.676863

L42Days .0135195 .0172883 0.78 0.439 -.0214494 .0484884

FromMean_10 .0131581 .0029746 4.42 0.000*** .0071413 .0191749

Notes: Bold independent variables have coefficients signs as predicted.. Mean value of the chart. Endpoint: value of the chart on day 252. Endpoint: value of the chart on day 252. StDev_Year: Standard deviation calculated over all 252 day based on monthly returns. L42days: The value of the chart on day 252 minus the value of the chart on day 210. FromMean_10: Number of days the chart has a value which lies 10 points from its mean. . Adjusted R2of 57.37%. * = p ≤ 0.05, ** = p ≤ 0.01, *** = p ≤ 0.001.

The multiple regression model from table 9 has a goodness of fit of 57.37% and its significant variables greatly improve with respect to the correlated multiple regression. Standard deviation and FromMean_10 now have high significant values. Another interesting finding is that almost every model which contains endpoint is extremely significant8 (all with p

≤ 0.001) with corresponding high goodness of fit values. If one excludes the Mean variable,

L42Days also become significant. As a robustness check for table 9, the yearly standard

7_{Combinations of variables which are Pearson correlation coefficient is > 0.6 are excluded.} 8_{These results not presented here, but available upon request.}

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21 deviation variable is replaced by standard deviation measuring the first half of the trading year and by standard deviation measuring the second half of the trading year (see table 19 in Appendix C). The results are similar with respect StDev_SecondHalf concerning adjusted R2 values and significance scores. Standard deviation capturing the first half over the year has no significant effect in this multiple regression, possibly suggesting that respondents are more influenced by recent volatility than by volatility at the start. Further elaboration on this and the non-presented significant multiple regression are given in chapter 5.

As end point shows to be a good predictor of the perceived riskiness of a chart, the multiple regression models are performed again grouped per end point, which can be found in table 10. Based on the correlation matrix for all independent variable per end point, similar explanatory variables are used alike table 9 except for the charts ending at 90. Correlation matrices can be found in Appendix C, table 20-25.

Table 10. Multiple regression of uncorrelated variables for charts ending at 90, 105 and 120.

Independent variables Coefficient Std. Err. t value p value 95% Conf. Interval Endpoint = 90 (N=11) StDev_Year 4.137548 3.445902 1.20 0.264 -3.808716 12.08381 FromMean_10 .0199016 .004439 4.48 0.002** .0096653 .030138 Endpoint = 105 (N=20) Mean .0816901 .0270735 3.02 0.009** .0239843 .1393959 StDev_Year 3.973309 1.197394 3.32 0.005** 1.421123 6.525494 L42Days .0223934 .0226656 0.99 0.339 -.0259173 .070704 FromMean_10 .0148512 .0061379 2.42 0.029* .0017687 .0279337 Endpoint = 120 (N=14) Mean .0016022 .0179968 0.09 0.931 -.0391094 .0423138 StDev_Year 7.778455 3.035117 2.56 0.031* .9125437 14.64437 L42Days .0318096 .0413381 0.77 0.461 -.0617035 .1253228 FromMean_10 .0002339 .0056571 0.04 0.968 -.0125633 .0130312

Notes: Bold independent variables have coefficients signs as predicted.. Mean value of the chart. StDev_Year: Standard deviation calculated over all 252 day based on monthly returns. L42days: The value of the chart on day 252 minus the value of the chart on day 210. FromMean_10: Number of days the chart has a value which lies 10 points from its mean.. * = p ≤ 0.05, ** = p ≤ 0.01, *** = p ≤ 0.001.

The model for charts ending at 90, 105 and 120 have goodness of fit values of respectively 66.50%, 73.27% and 39.72%. Taking into account the results of the separate regression, it is not surprising that the models for charts ending at 90 and 120 have few significant variables. With respect to the ending point 90, the extreme values (FromMean_10 and FromMean_15) seems to be the best predictors, while other variables fail. For the ending point 120, StDev_Year, FromMean_10 and Range (not presented due to collinearity) are one of the few significant variables. Most likely, the presence of their end point causes otherwise significant explanatory variables to become insignificant, which again stresses the salience of the end point of a chart. This reasoning would also explain the similarity of the results from charts ending at 105 and the general multiple regression model. The “neutral” end point leaves room for other factors to influence the perceived riskiness of charts. Running robustness checks

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22 by replacing StDev_Year with StDev_FirstHalf and StDev_SecondHalf, mainly reduces the explanatory power of the variables for all categories (table 27 in Appendix C). Worth mentioning is that StDev_SecondHalf gives better results than StDev_FirstHalf, again stressing the finding that the respondents place more value on recent volatility.

4.3 Hypotheses

This paragraph will present the results with respect to the constructed hypotheses. It will do so in the order of construction. In-depth interpretation and discussion of results will take place in chapter 5.

4.3.1 Hypotheses 1a-b

Hypothesis 1a predicted that on average, charts in the Initially Upwards (decreasing ending sequence) category are perceived as more risky than those in the Initially Downwards category (increasing ending sequence). On average, the perceived riskiness for charts in the Initially Upwards and Initially Downwards category is respectively 5.495 and 4.23, which differ significantly at the 5% level using Student’s t-test9. However, not all charts from the Initially Upwards (Downwards) have an decreasing (increasing) ending. Another Student’s t-test is conducted after dropping these charts10. The t-test show a difference on the 1% level for respective means of 6.06 and 4.109_{. Hence, the study concludes that hypothesis 1a is true at the}

99% confidence level, indicating that improving ending sequences are perceived as less risky than decreasing ending sequences. Hereafter, charts are compared within and across their end point category using pairwise comparisons11_{(see table 11). Based on their end point, again the}

two categories differ significantly, supporting hypothesis 1a.

Hypothesis 1b predicted that the period in which the chart is conceivably more volatile than in other periods matter in perceiving a chart as risky. Especially charts that are volatile in the end will be rated more risky. In doing so, charts 43, 44 and 45 from the Volatile category are studied. These charts have in common that they have one period12 in which the price path show large fluctuations with a standard deviation between 0.3 and 0.4.Charts from the Volatile

9_{Both categories did had equal variances according to Bartlett’s test for equal variances.} 10_{Chart 11, 12, 13, 15 & 18.}

11_{This study does not make use of pairwise adjustments when using pairwise comparisons. According to}

influential scholars like Rothman (1990) and Cohen (1994), it makes logically no sense to adjust a statistical measure depending on the number of tests in a specific study. The consequences of this adjustments mainly increase type II errors, instead of reducing type I errors. Running multiple pairwise comparisons in Stata 13 with various sample sizes provide very low differences in p values. Besides, there is no formal consensus of when to use Bonferroni adjustments (Perneger, 1998), which is why the Bonferroni adjustment is used in arbitrary ways (see Nakagawa, 2004).

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23 category also roughly have the same mean, yearly standard deviation and an equal range and end point. Using pairwise comparisons, chart 45, with a volatile period at the end, is indeed rated significantly more risky than chart 43 with a volatile period at the start, respectively with mean ratings of 6.43 and 5.43. Chart 44 with a volatile period in the middle falls between these two values with a mean rating of 6.12, giving some support for hypothesis 1b. In addition, the separate regression model from table 4 demonstrated that the standard deviation for the second half of a chart is a better predictor (greater coefficient and significance score) than the standard deviation for the first half of a chart. This gives again support for hypothesis 1b. The findings are in line with previous results, in the sense that participants place more value on recent phenomena in constructing their perceived riskiness.

Table 11. Pairwise comparison of the means from charts of the Initially Upwards and Initially Downwards category. Presented are their respective p-values.

Initially Downwards Initially Upwards Endpoint 90: 14 (4.77) Endpoint 105: 16 (3.05) 17 (4.44) Endpoint 120: 19 (3.38) 20 (4.43) Endpoint 90: 1 (7.21) 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 2 (7.56) 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 3 (6.87) 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 4 (6.34) 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** Endpoint 105: 5 (5.35) 0.241 0.000*** 0.020* 0.000*** 0.031* 6 (4.43) 0.323 0.001*** 0.945 0.014* 1.000 7 (6.08) 0.004** 0.000*** 0.000*** 0.000*** 0.000*** 8 (6.50) 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** Endpoint 120: 12 (4.19) 0.144 0.003** 0.671 0.046* 0.638

Bold entries are charts that share the same endpoint from the two categories. Charts from the Initially Downwards category

are presented horizontally, and from Initially Upwards vertically. In brackets behind the chart’s number is its respective riskiness rating. All charts can be found in Appendix B. * = p ≤ 0.05, ** = p ≤ 0.01, *** = p ≤ 0.001.

4.3.2 Hypotheses 2a-b-c-d

According to the peak-and-end rule, the most salient aspects of an experience are those most intense – peaks/troughs – and at the end of the event We test this hypothesis by using Range as proxy for the most intense events, and Endpoint for the ending of the event. Running a multiple regression model, that indeed that an increasing end point has a negative effect on the perceived riskiness, while an increasing range as a positive effect on the perceived riskiness (both p ≤ 0.001). These two variables explain up to 69.64% of the variance found in rating the charts which is substantial. Robustness checks for multicollinearity give VIF value within the acceptable range. This study therefore rejects the null hypothesis and concludes that hypothesis 2a is true at the 99.9% confidence level.

Next, this study examines how well the peak-and-end rule is a good predictor in explaining the individual seven categories, which can be found in table 12. The categories

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High-24 Low, Low-High and Volatile all have insignificant independent variables, suggesting that the peak-and-end rule does not apply to these categories. On the other hand, the remaining categories show a clear increase of the goodness of fit. Dropping observations from category 5, 6 and 7 lead to an increase in the model’s overall goodness of fit to 79.68%, giving further support for the peak-and-end rule.

Table 12. Linear regression results of testing the peak-and-end rule on the mean rating of all charts.

Category Endpoint coefficient (Std. Err.) t value Range coefficient (Std. Err.) t value Adjusted R2_(VIF)

All -0.0701*** (0.0082) -8.54 0.0691*** (0.0099) 6.99 69.64 (1.04) 1, 2, 3 & 4 -0.0769*** (0.0081) -9.44 0.0971*** (0.0130) 7.44 79.68 (1.03) 1. Initially Upwards -0.0866*** (0.0147) -7.30 0.0826*** (0.0178) 4.64 91.22 (1.16) 2. Initially Downwards -0.0837** (0.0147) -5.69 0.0946** (0.0193) 4.90 83.62 (2.42) 3. Peaks -0.0796** (0.0132) -6.02 0.0933* (0.0303) 3.08 86.41 (1.04) 4. Troughs -0.0536* (0.0169) -3.17 0.0677 (0.0342) 1.98 62.55 (2.22) 5. High-Low -0.0412 (0.0194) -2.12 0.0386 (0.0362) 1.07 40.24 (1.11) 6. Low-High -0.1210 (0.0441) -2.74 0.123 (0.0764) 1.61 64.84 (1.50) 7. Volatile -0.0309 (0.0394) -0.78 Omitted /// -14.75 (///)

Notes:. All coefficient signs are according as predicted. Range is omitted in category 7 due to collinearity. * = p ≤ 0.05, ** = p ≤ 0.01, *** = p ≤ 0.001.

Hereafter, in order to test hypotheses 2c and 2d about which characteristic of the peak-and-end rule is more important, we look back at the results from the separate regression in table 4. The size of the coefficients are almost equal, for the variable range 0.053 (p = 0.002) and for the variable endpoint -0.0593 (p = 0.000). The adjusted R2 of range and end point are respectively 18.84% and 35.90%, of which only the latter has a passable goodness of fit value. Furthermore, the separate and multiple regression already hinted on the salience of a changing endpoint. To explore these findings more in depth, a pairwise comparison of the mean analysis is conducted on charts with different end points and ranges. First, in order to prevent comparing too small groups, charts with ranges of 15 and 20 (N=6), 25 and 30 (N=16), 35 and 40 (n=16), and 45 and 50 (N=7) are grouped together. These groups have means of respectively 4.02, 5.29, 5.35 and 5.98, and only the first group differing significantly from the other groups using pairwise comparison (p ≤ 0.01). Next, charts with different end points are compared. Those ending at 105 and 120 have respectively means of 5.09 and 4.58 and differ on the 10% level of each other. Both groups differ on the 1% level with charts ending at 90, which has a mean of 6.40. So, while the differences between charts with different end points are more pronounced, Range also does a fairly good job in explaining the perceived riskiness. Evidence therefore slightly favors the salience of the end above the peaks, but only marginally. Therefore, the study concludes that there is not enough evidence to favor either the presence of peaks over the end point or vice versa.

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25 At last, hypothesis 2b is studied by comparing charts from the High-Low and Low-High category. Because both categories are relatively small in size, these charts are compared one-to-one based on their end points. Using pairwise comparison of the means, the ratings of charts from the category are compared, but fail to give consistent results across different end point (see figure 3). Within end point 105 and 120, charts from the High-Low category are rated as more risky than the Low-High category, although not always significantly. Given the relative low number of charts across these categories and mixed findings, doing generalizing comments would be inconsiderate. The study therefore fails to reject null hypothesis with respect to hypothesis 2b.

Figure 3. Presentation of the ratings given for charts of the High-Low (yellow) and Low-High (blue) category, grouped on their end point.

4.3.3 Hypotheses 3a-b

According to the separate regression of table 4, a chart performing a high number of days below its starting point does not lead to a higher riskiness rating, which hypothesis 3a predicted. The variable U_Start is highly insignificant and has the wrong coefficient. Running a separate regression split up per endpoint and per category also produces mixed results (see table 26 in Appendix C). A separate regression on charts ending at 90 and 105 does provide significant results, however the effect is negative. Reasons for this anomaly are given in chapter 5. On a side note, running separate regressions per category give mostly positive coefficients, although most regressions are insignificant, with the exception of the Peak and Trough category. Strengthened by the previous results of the separate and multiple regression, the study

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26 concludes that it fails to reject the null hypothesis regarding hypothesis 3a. Charts that perform relatively long below it starting point are not rated more risky as charts that do not.

Hypothesis 3b predicted that charts with only salient troughs will be on average rated more risky than charts with only salient peaks. A Student’s t-test was conducted to see if the means of both categories differed, which provided insignificant results13. Hereafter, charts with equal end points from both categories were compared on the individual level with the use of pairwise comparisons of means and by ordering them based on their rating, which provides mixed results (see appendix C, table 28 and figure 54). Interestingly, both the bottom and top three charts are from the peak category, with charts from the trough category falling in between. Possible explanations are given in chapter 5. Given these mixed results, the study fails to reject the null hypothesis with respect to hypothesis H3b.

4.3.4 Hypothesis 4a & demographical differences

To compare if females rated charts significantly higher than males, we first examine if females on average reported higher risk averseness than males with use of Welch’s unequal variances t-test. Females indeed did report higher levels of risk-averseness (p ≤ 0.001) with an average score of 3.22 versus 3.82 for males14. Hence when it comes to investments, females in this study report higher levels of risk-averseness. Hereafter, another Welch’s unequal variances t-test was conducted to examine if females rated charts significantly higher than males. The average mean rating for females and males are respectively 5.199 and 5.239 which did not differ significantly from each other. So, this study fails to reject the null hypothesis with respect to hypothesis 4a. However, because not all females and males encountered the same charts, it could be that the mean riskiness ratings are biased. Inspecting the data, charts differ in views at maximum 12 percent points, and differ on average 3.61 percent points in views. This amount is too small to have a significant impact, so this study concludes that both sexes encountered on average the same variation of charts. At last, this study compares the ratings of females and males for the five top and bottom rated charts. Except for Chart 11, Welch’s unequal variances t-test provided insignificant outcomes on the 5% level. Result can be found in Appendix C, table 29.

With use of a Kruskal-Wallis H test, other differences in rating of charts were explored based on demographical characteristics. Sorted on a respondents’ age, educational level, gender, working status, statistical knowledge, no significant statistical difference was found in the rating of charts. On the 10% level, however, there is a statistical difference if one compares

13_{The two categories met the assumption of equal variance using Bartlett’s test for equal variances.}

14_{Respondents could report their risk appetite when it comes to investments on a scale from one to seven, where}

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27 based on investment knowledge (p = 0.0645) and risk attitude (p = 0.0890). In order to see in which direction and which categories do significantly differ, a pairwise comparison of the means test is conducted, which can be found in Appendix C, table 30. Both groups show an increasing trend from their lowest group to their highest (risk-averse to risk-seeking and far below average to far above average knowledge) Those who self-identified as moderately and highly risk seeking significantly rated charts higher, than those who self-identified as slightly, moderately and very risk averse (p ≤ 0.05). However, the moderately and highly risk-seeking category are relatively small categories, (respectively N=34 and N=4), indicating that these differences are mainly attributable to several outlier values. This is similar for investment knowledge, where every category differs with the top category (far above average knowledge). Again, this top category is very small (N=9) and therefore vulnerable to the few outliers in this category. So, while both groups do show an increasing trend for the rating of charts, saying these groups differ significantly would be too rigid. Concludingly, there are no clear significant differences between those with high and low knowledge about investment, as between the risk-averse and risk-seeking people when it comes to the rating of charts.

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28

5. Discussion and conclusions

Alike the chapter 4, this chapter first starts with discussing the separate regression, before moving on to the multiple regression. Hereafter, the hypotheses are discussed in numerical order. The last section concludes.

5.1 What makes a chart risky?

While all the charts fall within the acceptable regions of skewness as proposed by Bulmer (1979), there is some reason to concern. Eleven charts are marked as being “moderately

skewed” and of those, seven belong to either the top five or top bottom ranked charts. Hence,

the top high (low) rated charts are to some extent due to high (low) ratings for these charts, which skew the data to a reasonable extent to the left (right). A reason for this skewness is partly found in that the majority of these charts had around 60 observations, compared to 70 observations for the normal distributed charts. However, for an explanatory study in which most of the participants are not trained, these levels are acceptable. As a solution, the sample size could be increased in order to mitigate the effect of skewness, with say 100 observations per chart. While most likely the ratings while then covert more to the middle, less question marks can be placed by a presumed “oulier-effect” caused by the moderately skewed charts.

5.2 Separate Regression

A first conclusion that can be drawn from the separate regression is that, with the exception of Endpoint and U_End, every variable has a low adjusted R2_{, indicating that it is not at least one}

factor that determines the perceived riskiness of a chart. The high significance of variable U_End seems odd, but can be explained as follows. Charts that end at 90 have a relatively high number of days performing above their end point, mostly due to the construction of the charts (max. 135 and min. 80). Previous result demonstrated that charts ending at 90 have significantly higher ratings than charts with higher ending points. Likewise, charts ending at 120 have a relatively low number of days performing above their end point. However, these charts are on average rated lower than charts with lower end points. Hence, U_End acts more as a proxy for end point, which is confirmed by the high Pearson’s correlation coefficient between these two variables.

Furthermore, the separate regression provides us another interesting insight, namely the greater explanatory power of StDev_FirstHalf over the insignificant StDev_SecondHalf. A possible indication that investors mainly look at the short-term for determining the perceived riskiness, and not to the whole period. To examine which period matters, future research could

What makes a Chart Risky? An analysis on characteristics of financial charts and perceived risk perception using survey data