Price Anchoring in the Stock Market

UNIVERSITEIT GENT GHENT UNIVERSITY

FACULTEIT ECONOMIE EN BEDRIJFSKUNDE FACULTY OF ECONOMICS AND BUSINESS

ADMINISTRATION

ACADEMIC YEAR 2015 – 2016

Price Anchoring in the Stock Market

Masterproef voorgedragen tot het bekomen van de graad van

Master’s Dissertation submitted to obtain the degree of

Master of Science in Business Administration

Thomas Longeval

Thomas Van Der Vaerent

Under the guidance of

Prof. Koen Inghelbrecht Mr. Hannes Stieperaere

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1. Confidentiality Clause

Ondergetekende verklaart dat de inhoud van deze masterproef mag geraadpleegd en/of

gereproduceerd worden, mits bronvermelding.

Naam studenten: Thomas Longeval & Thomas Van Der Vaerent

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2. Nederlandstalige samenvatting

Deze thesis onderzoekt de behavioral bias “anchoring.” Anchoring is het toekennen van een

bepaalde mate van gewichtigheid aan nietszeggende informatie bij het waarderen van een goed,

ervaring of, in het kader van deze thesis, een aandelenprijs. De aandelenprijs is an sich niet

informatief, omdat deze relatief gemakkelijk te beïnvloeden is door het aantal aandelen aan te

passen. Dat is waarom wij onderzoeken of beleggers hun beleggersbereidheid (deels) laten

afhangen van deze aandelenprijs. Als dit het geval zou zijn, zou dit een toevoeging kunnen zijn

aan de literatuur die diverse “raadsels” in de aandelenmarkt tracht te verklaren. Via een eigen

experiment dat gericht is op de beleggersbereidheid van de respondenten, vinden we dat er geen

significant effect is in deze bereidheid ten aanzien van een hoger geprijsd aandeel vergeleken met

een lager geprijsd aandeel. Deze conclusie is in het voordeel van de Efficient Market Hypothesis,

maar er zijn wel aanwijzingen dat investeerders een lager geprijsd aandeel aantrekkelijker vinden

dan een aandeel dat hoger geprijsd is. Verder onderzoek is dus nog nodig.

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3. Preface

We would like to thank our promotor Mr. Hannes Stieperaere for the wonderful cooperation and

the support in writing this thesis. Furthermore, we would like also like to thank our families and

friends for the amazing support in the months leading up to our final thesis.

Thomas Longeval & Thomas Van Der Vaerent

Ghent, June 2016

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4. Table of Contents

1. Confidentiality Clause .............................................................................................................. i

2. Nederlandstalige samenvatting ................................................................................................ ii

3. Preface ..................................................................................................................................... iii

4. Table of Contents .................................................................................................................... iv

5. List of used abbreviations ....................................................................................................... vi

6. List of tables & figures .......................................................................................................... vii

6.1. Figures .......................................................................................................................... vii

6.2. Tables ............................................................................................................................ vii

1. Abstract .................................................................................................................................... 1

2. Introduction .............................................................................................................................. 2

3. Literature Review ..................................................................................................................... 4

3.1. Stock Market Puzzles ..................................................................................................... 4

3.2. The Efficient Market Hypothesis .................................................................................... 8

3.3. Behavioral Economics .................................................................................................. 10

4. Methodology .......................................................................................................................... 19

5. Results .................................................................................................................................... 22

5.1 General Overview ......................................................................................................... 22

5.2 Paired Samples T-test ................................................................................................... 23

5.3 Relative OLS Regressions ............................................................................................ 24

5.4 Absolute OLS Regressions ........................................................................................... 26

5.5 Anchoring effect between pairs .................................................................................... 29

6. Conclusion ............................................................................................................................. 30

7. Bibliography .......................................................................................................................... 33

8. ADDENDUM ........................................................................................................................ 36

8.1. Survey ........................................................................................................................... 36

8.2. Descriptive statistics control variables ......................................................................... 54

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8.3. Relative OLS regressions ............................................................................................. 55

8.4. Absolute OLS regressions without control variables ................................................... 59

8.5. Absolute OLS regressions with control variables ........................................................ 62

8.6. Paired samples t-test ..................................................................................................... 66

8.7. ANOVA ........................................................................................................................ 68

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5. List of used abbreviations

AAM Absolute Anchoring Measure

ACAPM Anchoring Adjusted Capital Asset Pricing Model

CAPM Capital Asset Pricing Model

EMH Efficient Market Hypothesis

EPP Equity Premium Puzzle

FEPS Forecasted Earnings Per Share

IPO Initial Public Offering

NSPP Nominal Share Price Puzzle

RAM Relative Anchoring Measure

USSEC United States Securities Exchange Commission

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6. List of tables & figures

6.1 Figures

Figure 1: Average share price with and without stock splits

Figure 2: Real annual return on the S&P 500 index

Figure 3: Real annual return on T-bills

Figure 4: Pricing according to EMH

Figure 5: Pricing according to behavioral economics

Figure 6: Raw data table

Figure 7: Bar graph of average willingness to accept

Figure 8: Graph on the anchoring effect between pairs

6.2 Tables

Table 1: Table concerning significance levels

Table 2: ANOVA of the willingness to accept scores

Table 3: Paired Samples t-test on oddly priced pairs

Table 4: OLS regression on the RAM of the regular pairs with control variables

Table 5: OLS regression on the RAM of the oddly priced pairs with control variables

Table 6: OLS regression on the AAM of the regular pairs without control variables

Table 7: OLS regression on the AAM of the oddly priced pairs without control variables

Table 8: OLS regression on the AAM of the regular pairs with control variables


Table 10: Graph on the anchoring effect between pairs

Table 11: ANOVA on the anchoring effect between pairs

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Price Anchoring in the Stock Market

1. Abstract

This scientific paper has the ambition to investigate whether the behavioral bias known as “price

anchoring” can be found in the stock market. Anchoring is a behavioral bias that can be defined

as the attributing of explanatory power to uninformative pieces of information to value a certain

good or experience. That is why we explore the notion of investors giving explanatory power to

the absolute price level of a stock. The price of a stock is inherently uninformative and can be

manipulated relatively easy through e.g. (reverse) stock splits. This is especially relevant as

anchoring could explain several stock market puzzles. We find that investors do anchor on stock

prices, but as they do this in different directions, the stock price remains unaffected. However,

there are indications that investors tend to anchor negatively, meaning they are more willing to

invest in shares with a low absolute price than in shares with a high absolute price.

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2. Introduction

“The purely economic man is indeed close to being a social moron. Economic theory has been

much preoccupied with this rational fool.”

(Thaler, 2015)

Economic agents are prone to a variety of behavioral biases and heuristics. This paper discusses

“anchoring” and the “price anchoring” bias in particular. In short, anchoring implies that

individuals use irrelevant information when evaluating certain goods, experiences or in this case,

stocks (Chapman & Johnson, 1999). We hypothesize that the absolute price of a stock significantly

influences the value investors attribute to this stock. This value is acquired by assessing the

investor’s difference in willingness to invest in a higher priced stock compared to a lower priced

one. Consequently, this could also yield information about the future movement of that stock.

To situate this research the background needs to be described. In particular the pricing/valuation

of stocks will be discussed. A great deal has been written on this topic, and we concentrate on a

few key concepts and theories. This paper therefore discusses the Nominal Share Price Puzzle, the

Equity Premium Puzzle, the Efficient Market Hypothesis and the fundamental valuation of stocks.

Special attention goes to behavioral economics/finance and in extension to “anchoring” itself.

The Nominal Share Price Puzzle discusses why share prices appear to have averaged around a

nominal price of $30 per share in the past decennia. If not for external intervention by managers

of stock-quoted companies, these would have risen to $400-$500 (Benartzi, Michaely, & Thaler,

2006). The Equity Premium Puzzle states that stocks have had too high returns as compared to

“risk-free” assets when accounted for the normative risk premium (Mehra & Prescott, 1985). The

EMH is a widely known financial theory, that states that the price of a stock comprises all public

information, and as such analysis of this public information cannot lead to a better assessment of

the right value than the stock market; nor is their informational value in the past evolution of the

stock prices. Most investors are rational (some are irrational, but their behavior is random and has

therefore no durable impact on pricing) and a “free lunch” is immediately neutralized by rational

arbitrageurs (Fama, 1970). Investors reverting to fundamental valuation techniques in order to

come to their own estimate of a stock’s value, argue against the EMH that “superior” fundamental

analysis can lead to a better estimate value than the stock market. As such, active management

would be able to obtain sustainable risk-adjusted performance (Abarbenell & Bushee, 1997). The

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technique of fundamental valuation and the philosophy of behavioral economics declare, both in

their own way that share prices are not always rightfully reflected in the stock market.

The research of this paper is placed within the field of behavioral economics, more specifically

behavioral finance. This is a more recent field in the economic sciences, and has proven useful in

filling in several gaps in financial theory. Several biases and heuristics lay at the basis of the

anchoring effect or are closely related to it, e.g. coherent arbitrariness, availability heuristic,

representativeness,… and will therefore also be shortly reviewed.

After situating the background for our research, the hypotheses, methodology and research

approach of our experimental setup are expanded upon. Next, the results of this experiment will

be evaluated and are assessed on what they signify for the proposed hypotheses. Finally, we

formulate our conclusions and indicate any possible further research.

Scientifically, anchoring on the real economy has been extensively studied and confirmed.

Research on anchoring in the stock markets, however, has not sufficiently been investigated.

Therefore, it would prove necessary to analyze this phenomenon further and improve on the

already accomplished literature. Besides the improvement on current literature, anchoring could

also prove useful in resolving several stock market puzzles. These puzzles shouldn’t exist from an

Efficient Market Hypothesis and Capital Asset Pricing Model “point of view” (Siddiqi, 2015). Out

of several of these puzzles, two are discussed: the Nominal Share Price Puzzle and the Equity

Premium Puzzle. Combining anchoring with the EMH could reveal new insights on past

unexplained price movements.

In addition to scientific relevance, our research also has societal relevancy. The correct valuation

of a stock entails a more stable share price and comes with several advantages for the current and

future shareholders as well as for the publicly listed company e.g. a lower cost of capital (COC).

This research is also paramount when relating to IPO’s for the reason that an initial mispricing can

lead to increased future volatility and several other negative side effects (Baghestanian & Walker,

2015).

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3. Literature Review

3.1. Stock Market Puzzles

A great amount of research has gone into the forecasting and valuation of stock prices. However

there are some “puzzles” left in financial science that have not been solved through conventional

answers. The behavioral “anchoring” bias might provide an explanation for these puzzles. Two of

these puzzles are believed to be most noteworthy.

The first puzzle to be discussed is the Nominal Share Price Puzzle. In short, nominal share prices

have remained remarkably stable throughout the past decades, even though the value of companies

has undoubtedly gone up and inflation has to be taken into account (Benartzi et al., 2006).

Since the Great Depression, share prices have hovered around $30 through the actively influencing

of these prices by the company management through e.g. stock splits and reverse stock splits

(Benartzi et al., 2006). Thus far economists have not found an irrefutable hypothesis of why

managers would demonstrate this type of behavior. The value of a company should be determined

by its “fundamentals,” not the amount of shares in circulation (or other factors).

Consider the following an example:

The market value of Company A is $10 million and has 1 million shares in circulation. Logically

the price per share is: $10. The expected company market value is $15 million in exactly 1 year

and the price per share: $15. Company B is identical to Company A in all but one characteristic:

Company B has only 100 thousand shares in circulation. Reasonably it can be said that the price

per share for Company B is $100, and will be $150 in one year.

For the managers and other parties examining these shares, the absolute level of the share price

should not matter. A rational investor evaluating these shares will not have a preference over either

one, as they offer the same return and are identical in every aspect. While stock splits and other

corporate actions measures are costly for the company as well as for investors, managers of

publicly listed companies still seem to actively maintain the share price around a certain level

(Benartzi et al., 2006).

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The following graph will demonstrate this in a more comprehensible way:

Figure 1: Average share price with and without stock splits (Dyl & Elliot, 2006)

Company managers apparently assume there is an “optimal trading range” (OTR) of $30 - $60 in

between which a price can fluctuate (ranges may vary depending on the author). Managers act

accordingly to this range and carry out a (reverse) stock split when they see fit (Dyl & Elliot,

2006). Referring to Figure 1, it is undoubtedly shown that if no stock splits existed, the price per

share today would average $450-$500, instead of the $30 mentioned ut supra.

Benartzi, Michaely and Thaler (2006) offer three conventional explanations of previous research

are taken into account as well as the expression of their own explanation. Two of these potential

explanations mention this “OTR hypothesis.”

A first hypothesis states that managers keep prices low to remain attractive to smaller individual

investors, in other words they consider the “marketability” of the share. A second considered

hypothesis attempts to explain this management behavior by emphasizing the bid-ask spread and

brokerage commissions. This hypothesis stems from the rationale that firms set their share prices

low to be more attractive to stock brokers. When a low priced stock is more attractive to brokers,

it increases that stock’s liquidity because of the higher “market making profitability”. Lastly, a

non-“trading range hypothesis” being referred to is the fact that managing one’s stock signals to

investors that the company is doing well. A share that has gone to a too high price and “needs” a

split, suggests that this company is thriving, and will continue to do so in the future (Benartzi,

Michaely, & Thaler, 2006).

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The aforementioned hypotheses are however not supported by sufficiently solidifying evidence,

and Benartzi et al. (2006) come with their own hypothesis. They state that managers exhibit this

kind of behavior based on “norms.” Simply stated, managers do it because it has always been done

this way, irrelevant of the rationality of such an action.

However, it seems plausible that the managers of these companies seem to “anchor” on the lower

and upper price of this trading range of $30 to $60 respectively. The moment a stock price hits the

$60 “frontier”, a manager would consider a stock split and thus artificially neutralize the increase

in price. (Dyl & Elliot, 2006) This occurs counterintuitively from the fact that the stock price

should not influence the valuation of that stock.

But what if the managers are only partially the cause of this puzzle? It has been argued by several

researchers that it is investors that are actually at the root of the NSPP (Birru & Wan, 2016).

Investors could be looking for “cheap bets” i.e. stocks with lottery type characteristics. For a low

price you get the chance of a large possible pay-off, while forgetting the low chance of success.

When applying this logic to the stock market, low-priced stocks are found to be more attractive

than high-priced stocks, even when the risk is higher (Kumar, 2009). However, other research

suggests that investors also perceive low-priced stocks as having more upside potential and that

stocks are categorized based on their price (Green & Hwang, 2009). Investors are led to believe

that a stock is cheaper after a split, and therefore has more “room to grow”, or correspondingly has

“less to lose.” (Baker, Greenwood, & Wurgler, 2009). Next to these hypotheses, it can be argued

that anchoring might prove to be a useful addition to the literature attempting to explain this puzzle.

The second stock market puzzle to be discussed is the “Equity Premium Puzzle.” This puzzle was

first discussed by Mehra and Prescott (1985). These researchers found that historical returns of

stocks are largely higher than the return of risk-free securities. This difference in return is what we

call: the equity premium.

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Figure 2: Real annual return on the S&P 500 index

(Mehra & Prescott, 1985)

Figure 3: Real annual return on T-bills

(Mehra & Prescott, 1985)

From the graphs ut supra it can be argued that there is a substantial difference between stock market

and risk-free asset returns of over 6%. Stocks are riskier than “risk-free” assets and should

therefore indeed produce a risk premium to compensate for this higher risk. However, the

magnitude of the excess returns (realized risk-premium) is such that it is higher than the normative

risk premium i.e. the excess return required to compensate for differences in risk. The phenomenon

of stocks producing abnormally high risk-adjusted returns is called the Equity Premium Puzzle

(Mehra & Prescott, 1985). While the above graphs only consider the S&P500 and the American

Treasury Bills, similar results have been found in other stock markets e.g. Great Britain, Japan,

France,…

Several theories ranging from extreme risk aversion to consumption theories, have not yet been

proven sufficiently robust to provide a satisfying answer. However, there are some economic

researchers that put “anchoring” forward as a justification for the difference in returns. One of

these researchers, Hammad Siddiqi (2015), transformed an existing and widely used model for the

valuation of assets, the Capital Asset Pricing Model (CAPM). By adjusting this model for the

anchoring bias, prices walked a path linked more closely to reality. This model will be further

expanded upon ut infra.

Next to the Equity Premium Puzzle, anchoring is also deemed a valid explanation for various other

economic puzzles:

“…replacing the assumption of an omniscient representative agent with the assumption that

the representative agent is anchoring-prone provides a plausible unified explanation for the

following puzzles: 1) High equity premium, 2) Low risk free rate, 3) Countercyclical equity

premium, 4) High stock price volatility, 5) Size effect, 6) Value effect 7) Momentum effect, 8)

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Abnormal positive returns and high volatility after stock-splits, 9) Abnormal negative returns

and low volatility after reverse stock-splits.”(Siddiqi, 2015)

The CAPM a model based on the principles of the Efficient Market Hypothesis (EMH) (Fama,

1998). The ACAPM takes over certain aspects of this model and the EMH but adds a behavioral

factor. The several aforementioned puzzles also root from this EMH, and before moving on to the

topic of behavioral economics and anchoring, a clarification is in order.

3.2. The Efficient Market Hypothesis

“Nobody - and I don't care if you're Warren Buffet or Jimmy Buffet - nobody knows if a stock is

going up, down or (…) sideways”

(Scorsese, 2013)

The Efficient Market Hypothesis assumes that (most) economic agents are rational and possess

perfect information. Proponents of the EMH, like Eugene Fama (1970) and Burton Malkiel (2003),

believe that stock prices comprise all information available and that future movement of the stock

price is impossible to predict. However, if the EMH were to be true, where do all the

aforementioned stock price puzzles come from?

The researchers introduced ut supra, Fama (1970 and Malkiel (2003), presume that the stock

market and stock prices are efficient in adapting to any new information available. They are

convinced that nor analysis based on historical price movements, nor analysis of the company’s

fundamentals will help investors predict which stocks will outperform in the future. Essentially,

this view implies that share prices follow a “random walk” as they only react to new info that is

by definition unknown beforehand.

Malkiel (2003) will even go so far to state that even though some economic agents are irrational

and fundamental analysis can forecast (partial) movement of share prices, in the end the market

price will always be right. In theory this could mean that in the short term an investor could obtain

above average risk-adjusted returns, but not in the long run. The moment share prices seem to be

predictable on the basis of a given technique or insight, it is already too late. The market will

swiftly absorb this new information and adapt pricing accordingly. Schwert (2003) reasons that

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this occurs because of two reasons. Firstly, investors and researchers will investigate anything that

goes against the EMH to earn an above average return. And secondly, investors and other market

participants adapt so rapidly to an emerging pattern that it nullifies any potential above average

returns.

This is most intriguing for the research scope: even if there would be any market deficiency to be

distinguished, it could shortly disappear after publishing. Nonetheless, if the price comprises all

information then a higher or lower share price should not matter for a company and, again, the

Nominal Share Price Puzzle, the Equity Premium Puzzle and other puzzles mentioned ut supra

should not prevail. When relating this to the Equity Premium Puzzle the following question could

be posed: if investors should only receive returns compensating for risk, do they receive above

risk-adjusted returns for stocks, i.e. a “free” lunch?

One of the models based on the principles of the EMH is the Capital Asset Pricing Model (CAPM)

This model relates risk to expected or required asset returns. (Fama, 1998) It has been adapted in

a variety of ways throughout the years but it does provide a much needed framework. The CAPM

adjusted for several different behavioral biases have surfaced and proven useful in explaining

uncommon stock behavior.

Next to the puzzles there is another concept that is discordant with the EMH, particularly: beating

the market by using superior “fundamental valuation.” Fundamental valuation infers that asset

prices can be linked to their underlying fundamentals (Summers, 1986). Where the EMH states

that researching stocks does not show any merit, fundamental valuation deems a rational approach

to be useful in the assessment of stocks. A rational investor would then go long in fundamentally

undervalued stocks and go short in overvalued ones. Examples of these underlying fundamentals

are financial statement data, estimates of future earnings growth and historical performance

(Abarbenell & Bushee, 1997).

Mike Tarsala, a notable tech stock investor and an adept of the fundamental valuation technique,

even states: “Nothing tells shareholders more about the overall health of a company than a cash

flow statement, (…) Cash flow from a company’s operations holds the key to a company’s true

performance (…) Unlike earnings or revenue, the cash a company creates is just that - cash.”

(Bonner, 2002).

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Other research suggests that analysts and investors should also take macro-economic variables e.g.

inflation, GDP and firm-specific variables e.g. historical earnings growth, expected earnings

growth,… into consideration (Abarbenell & Bushee, 1997).

Financial markets are perceived as one of the most rationalized markets. However, there is no

absolute certainty that even there the level of prices is sensible. When following the logic of the

Efficient Market Hypothesis, the value of a stock should reflect the aggregate of all individual

fundamental valuations, strongly based on that stock’s future cash flow (Fama, 1970). However,

predictions of this future cash flow are highly ambiguous and depend on an extensive amount of

variables. Where impacts on stocks of certain news events can be measured, it is decidedly

challenging to prove that through fundamental valuation, asset prices reflect their true values

(Ariely, Loewenstein, & Prelec, 2003).

Where investors and analysts already seem to take the fundamentals of a company into account,

the reaction time to new information is slow and generally leads to an under reaction in the short

run creating a momentum phenomenon. It is reasoned that where investors under react to new

information, they tend to overreact to old information, with the latter eventually leading to another

phenomenon called “mean reversion.” (De Bondt & Thaler, 1989). These observations ( on e.g.

under reaction) lead to two conclusions: 1. that economic agents are not as efficient as the EMH

suggests, and 2. that further improvement to fundamental analysis can be attained through

additional, perhaps behavioral economic, theory.

3.3. Behavioral Economics

“Wouldn't economics make a lot more sense if it were based on how people actually

behave, instead of how they should behave?”

(Ariely, 2008)

Seeing as there is not always a rational conventional answer, a more unconventional approach

might clarify (part of) the movement of stock prices. Psychology and economics have only come

together recently, but have already proven useful in filling in several gaps of knowledge in

economic theory.

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Behavioral economics and finance have not gained traction until more recently. Frontrunners in

behavioral economics like Ariely, Loewenstein and Nobel prize winner Kahneman believe that

economic agents are not only not rational, they are predictably irrational. Through various

experiments these behavioral researchers find that economic agents are prone to a variety of

behavioral biases and heuristics. Though heuristics and biases, originating from “mental shortcuts”

can be useful, they can also lead to systematic errors (Kahneman, 2011).

The following heuristics and biases have proven to be most relevant to this research: 1. coherent

arbitrariness 2. framing 3. representativeness 4. availability heuristic 5. over – and under reaction.

These provide the basis for anchoring or are closely related to anchoring

Coherent arbitrariness is one irrational behavior linked closely to anchoring, and one cannot be

discussed without the other. Coherent arbitrariness presents itself when people are asked to value

a certain good or experience for a first time. The absolute valuation of these goods or experiences

tends to be largely capricious. The individuals themselves though believe they make a rational

valuation based on the underlying fundamentals of that good or experience. However, where

people for the initial valuation let themselves lead by uninformative pieces of information, the

relative valuation of subsequent similar goods or experiences tended to be accurate (Ariely et al.

2003).

When relating coherent arbitrariness to the stock market, you could ask yourself the same question

as Shiller in 1998: “Who would know what the value of the Dow Jones Industrial Average should

be? Is it really “worth” 6,000 today? Or 5,000 or 7,000? or 2,000 or 10,000? There is no agreed

upon economic theory that would answer these questions.” (Poundstone, 2011) Nevertheless,

where the value of a stock or a market might be unknowable, the impact of certain events can be

more easily recognized on the stock market (Ariely et al. 2003) e.g. The Google stock price is at

$650. Is this the right price? Nobody knows. Google comes with the great news that its new range

of products yielded more earnings than expected. Investors know this is a positive event and the

stock goes up. Where this upward movement is rational, the price itself might not be.

The following bias to be discussed is: framing. This bias can be defined as the influence on rational

decision making by the way in which information is presented. If certain information is presented

in different manners, the ensuing decisions will be different. Kahneman and Tversky (1986) found

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that if test subjects were presented with two questions containing the same information, but one

represented in the form of a “loss” and the other one in the form of a “win”, they would choose in

a different way.

An example should prove clarifying:

An investor has to choose between two stocks with exactly the same characteristics, stock A and

stock B. However, the information on stock A states that: “there is a 70% chance that this stock

will go up.” The information on stock B states that: “there is a 30% that this stock will go down.”

Based on the research by Kahneman & Tversky, test subjects will prefer stock A over stock B,

even though the information given is intrinsically the same.

Representativeness is closely linked to framing, in the sense that the depiction of two intrinsically

same situations, influences how people will make choices. Representativeness, describes the

phenomenon when people intuitively fail to see that a certain number of observations (= a certain

“sample size”) is necessary before a given probability can assumed to be correct (Tversky &

Kahneman, 1974).

Consider the following experiment: two coins are tossed and test subjects have to choose which

one is the “cheating” coin (~the coin that doesn’t give a 50/50 chance). The first coin is tossed five

times and 80% of the time “heads” came up. The other coin is tossed 1000 times and here “heads”

came up 65% of the time. Now which one is the “cheating” coin? Research by Tversky and

Kahneman (1974) suggests that on average people will choose the first coin as the “cheating” coin,

while statisticians will tell you that it is the second coin. Statistically speaking it is highly unlikely

that a fair coin that is tossed a 1000 times diverges so far from its normal probability. However, a

coin that is only tossed five times, can easily deviate from its 50/50 probability.

Another heuristic that people are prone to and which provides the basis for anchoring is the

“availability heuristic.” Where representativeness examines the misinterpretation of given

probabilities, the availability heuristic refers to the heuristic that people will judge a certain good,

experience (and by extension stocks) by recalling previous occurrences of the same phenomena in

their own limited experience. Tversky and Kahneman (1973) reason that by associating this

previous experience to the choice at hand they then make a decision. The more recent a situation

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and the more it has been repeated in the past the easier it will be able to be recalled. It will therefore

have the strongest influence on this decision.

To illustrate this bias, a reference to an experiment carried out by Tversky and Kahneman (1973)

can be considered. They came up with an experiment where test subjects were asked whether

words starting with a K or words with a K in the third place were more frequent in the English

language. A second question was to then estimate the ratio between these two numbers. As words

starting with a K are easier to be recalled than words with a K on the third place, the results should

yield more in favor of the first option. The result ended up being that over 2/3rd of the test subjects

were certain that there were more words starting with a K and the mean ratio was 2:1. However in

reality, words with a K on the third place are much more frequent. The experiment repeated with

different letters, expressed similar results.

The last heuristic to be attended to originates from an essentiality in the Efficient Market

Hypothesis. The EMH states that the adaptation of the market price of a stock to new information

is instantaneous and correct. However, investors tend to underreact to new information and

overreact to older information, consequently mispricing a stock (De Bondt & Thaler, 1989). Let

us take the following two graphs into consideration:

Figure 4: Pricing according to EMH Figure 5: Pricing with over-and underreaction

T-1 is the moment when good news about a firm is made public. There is almost no time between

T-1 and T0 (~”instantaneous”).

The graph to the left represents the change in price according to the EMH: immediate change, and

as long as there is no new information, the price will stay at the same level.

0

10

20

30

40

50

60

T-3 T-2 T-1 T0 T+1 T+2 T+3

0

10

20

30

40

50

60

70

T-3 T-2 T-1 T-0 T+1 T+2 T+3 T+4 T+5

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The graph to the right represents the change in price according to behavioral economics: there

might be an initial underreaction to the good news, leaving the stock under its “true” value. Over

a longer term, there might also follow an overreaction, leading to the stock being overvalued.

Eventually the stock should return to its respective value with an inevitable time delay. This

phenomenon is also referred to as “mean reversion” (De Bondt & Thaler, 1989).

Amir and Ganzach (1998) have linked the over and under reaction in the forecasts of analysts to

the anchoring bias. Analysts use the stock price as an anchor to assess the impact of certain news

events. This forces them to maintain a certain range wherein their consecutive forecast will fall,

diminishing the full effect of the news event and therefore causing the underreaction. The time-

effects of anchoring are less crucial to this research but is nevertheless a notion to take in mind.

Next to the biases and heuristic discussed ut supra, what can be observed in the real economy is

that the price apparently does influence how consumers regard a product or service. Marketeers

have gratefully embraced this phenomenon and have since long used “psychological pricing.” It

appears that consumers give other valuations towards products priced with certain numbers,

specifically the number 9. In short, this means that people will see a product priced as $49.99 as a

lot cheaper than when it would have been priced as $50 (Holdershaw, Gendall, & Garland, 1997).

This type of “psychological pricing” theory is influenced by what is referred to as the “round

numbering effect.” Fraser-Mackenzie, Sung and Johnson (2015), investigated this effect and

established that individuals make their decisions with round numbers as cognitive reference points.

They examined to which extent loss aversion and the prospect theory interacted with psychological

pricing. The prospect theory, originally developed by Kahneman (2011), refers to the fact that

losses are felt stronger than gains. This means consumers regard the $50 as the “reference price”

for that product and that a price of $49,99 would be equal to “winning” $0,01. Additionally Fraser-

Mackenzie, Sung and Johnson (2015) suggested that the consumers anchored on the left digits of

a price. Hereby, consumers tend to only take into consideration 49, meaning that instead of doing

the psychological effort to round the number up to $50, they see the difference between 49.99 and

50 as closer to 1 than to 0.01.

Psychological pricing has an effect in financial markets as well. However, here the opposite

reasoning arises. Prices that break through certain psychological “barriers” will have (in the short

15

term) above average returns (Johnson, Johnson, & Shanthikumar, 2007). A rational investor would

say that the difference between a stock price of $99.99 and a stock price of $100.01 is nihil.

However, in reality players in the financial markets see the price of 100.01 as being “bottomed

out” at 100 and reason that the only possible further movement is up.

Other notable oddly priced stocks include “penny stocks.” The United States Securities Exchange

Commission defines a penny stock as: “a security issued by a very small company that trades at

less than $5 per share. Penny stocks generally are quoted over-the-counter, (…) penny stocks may,

however, also trade on securities exchanges, including foreign securities exchanges.” (USSEC,

2013). Nonetheless, the definition of the USSEC is not a generally accepted rule. Other instances

e.g. Morningstar, an independent investment research and management firm, defines penny stocks

as a “low-priced stock that sells at less than $1.00 per share.” Even though, as mentioned

thoroughly ut supra, share prices should not influence the assessment of stocks, penny stocks are

attributed mostly negative characteristics e.g. small capitalization, high return, high firm-related

volatility, and poor liquidity (Liu, Ree, & Zhang, 2011).

It is previously established that the EMH, to a certain extent, is not as efficient as it makes it out

to be. Next to the heuristics, biases and even psychological pricing mentioned ut supra, there are

several others irrationalities in market participants their behavior. Among these biases and

heuristics, there is a bias that is insufficiently researched: the “anchoring” bias.

Anchoring, or in its complete name: “the anchoring-and-adjustment bias”, is one of the most

important biases discussed in behavioral economics. Anchoring can be described as the use of

irrelevant information when initially evaluating or estimating an unknown value. This bias

presented itself extensively in the “real” market (as opposed to the financial market) in several

experiments by Ariely, Kahneman, and others.

To further discuss “anchoring,” a demonstration with an example is essential:

A certain individual has some money left at the end of the month and decides to give €30 to a

charity. He goes online and tracks down the charity’s website. The website provides the following

five base amounts that can be donated:

- Amount 1: €100

- Amount 2: €150

16

- Amount 3: €200

- Amount 4: €250

- Amount 5: Other (here you can type an amount of your own choosing)

The person finds the base amounts quite high and instead of the €30 he was going to give, he now

decides to give €50.

What happens in the example above is that the person presumes that the base amounts express

some type of information and changes his own amount accordingly. Even though, the base

amounts do not give any information about the amount you should give, the person still changes

his opinion. The charity has actually purposely or non-purposely “manipulated” this person into

giving them more money, by making him anchor on the high provided amounts.

Kahneman (2011) discovered this through his now famous: “Wheel of Fortune”-experiment. Here,

test subjects were asked to state the percentage of African countries in the United Nations. While

the test subjects were thinking about the question, a “Wheel of Fortune” would spin before their

eyes. After assessing the responses, Kahneman found that if the wheel had stopped on a higher

number, the percentage of African states the test subjects conveyed was higher than the percentage

the test subjects gave when the wheel had stopped on a lower number. Again, the test subjects

gave informational value to something which does not, and act accordingly.

Other behavioral researchers like Dan Ariely et al. (2006), who let test subjects anchor on the last

two numbers of their social security number, have come up with similar results and therefore

solidify the theory surrounding “anchoring.”

This phenomenon is strongly associated with the concept of “coherent arbitrariness” introduced ut

supra, meaning that (initial) valuations of goods and experiences are largely random. Economists

therefore observe reactions to incentives and came to the conclusion that individuals make choices

based on fundamental valuation, however they are not mindful of any initial manipulation. This is

why economic agents are able to distinguish the relative value of a good or experience, but not the

absolute value of that same good or experience (Ariely et al., 2003). Simply put, people will value

a 25-year old Châteauneuf-Du-Pape higher than a Bordeaux from 2015. However, they will not be

17

able to distinguish whether the Châteauneuf is worth €500 or €5000, nor will they be able to

distinguish whether the Bordeaux is worth €5 or €50.

Extensive evidence of anchoring has been found in the “real” market, so how does this fare in the

financial market? The financial market is assumed by many economists to be highly rational and

efficient in reflecting the value of a company/stock, so “anchoring” should not exist? Anchoring

has insufficiently been researched, but some insights should be alluded to.

Cen, Hilare and Wei (2011) researched how analyst forecasts behave when encountering a change

in the forecasted earnings per share (FEPS). The forecasts are usually more optimistic when a

firm’s FEPS is higher than the median of the industry. Furthermore, firms with FEPS higher than

the industry median demonstrate abnormally rising stock prices, particularly around ensuing

earnings announcement dates. They came to the conclusion that analysts anchor the FEPS on the

industry median to make their forecast on the stock price.

A pricing model based on the CAPM and anchoring has also recently been theorized by Hammad

Siddiqi (2015): the Anchoring Adjusted Capital Asset Pricing Model (ACAPM). This concept has

previously been introduced along the EMH. The ACAPM model is based on the constatation that

the equity premium is larger than what can be just be clarified by market risk. Therefore, anchoring

could potentially provide an explanation for the aforementioned Equity Premium Puzzle. Both

CAPM and the EPP have been discussed ut supra, therefore Siddiqi’s model that has been adapted

for anchoring can now be fully explained.

Siddiqi (2015) regards anchoring as a potential explanation for the higher than expected returns

and therefore analyzes the effects of stock-splits and reverse stock splits. He makes following

predictions: “1) stock splits generate positive abnormal returns and an increase in return volatility,

2) reverse stock splits generate negative abnormal returns and a fall in return volatility…”

Siddiqi (2015) finds empirical evidence that strongly supports these predictions, and on these

grounds justifies that anchoring could offer an explanation for the Equity Premium Puzzle. What

has to be taken into mind though, is that as of this moment the paper is still a work in progress and

caution is advised when interpreting these results.

18

For this research, additional returns that might or might not occur after stock splits is not the main

focus. In this research it is attempted to verify whether investors anchor on the share price itself

and adapt their willingness to invest accordingly. The share price is inherently irrelevant

information as it can be relatively easily manipulated through the stock splits mentioned ut supra.

Therefore it should not influence a person’s overall willingness to invest.

19

4. Methodology

The hypothesis from which this research originated is the following:

Does anchoring on the price of a share exist in the stock market?

Throughout our research in current literature, it became clear that where anchoring in the real

economy was discussed intensively, little attention was given to anchoring in stock/financial

markets. To that end it was decided to develop our own research/experimental framework. Since

the time span of the data collection is only a few months, it will not be representative for the entire

system of stock markets, but it will provide an opportunity to provide further insight into this

behavioral phenomenon.

In order to obtain significant results a questionnaire was composed. It is completed by 108

recipients with at least basic knowledge of finance and the stock market in particular. This includes

(but is not limited to) students with courses in economics and finance, professors and people

working in the financial sector.

The questionnaire itself consists of sixteen shares and five additional personal questions. For each

share the following fundamental information is given to the respondents:

- Stock price

- Sector in which the company is active

- Number of employees

- Number of years of existence

- Price-Earnings ratio

- Price-Earnings ratio of the sector

- Net profit margin

- Dividend yield

- Price-to-book ratio

- Price-to-book ratio of the sector

- Average return of the company over the last five years

- Graph of the movement of the share price over the past year

20

Many of these factors are considered to be the necessary fundamentals to estimate a share’s value

(H. Summers, 1986). Other ratios mentioned are considered by Morningstar (2010) to be the basic

ratios an investor should take into account when assessing a stock.

For each share, the respondents were requested to provide a value ranging from 0 to 20

representing the extent to which they were willing to invest in the stock. 0 meant that the

respondent is completely not willing to invest in the given share, and 20 meant that he/she would

be completely willing to invest in the share.

However, what is not known to the respondents is that the sixteen shares are actually eight pairs.

Within these pairs the characteristics mentioned ut supra, are exactly the same except for one, the

stock price. Any difference in willingness to invest would then suggest an attribution of

informational value to this stock price. In the first pair the higher priced share is a 10 time multiple

of the lower priced share. The same logic applies to the pairs where the multiples of the higher

priced share are: 8, 6, 4, 2 and 1.5 times the lower priced share.

Most of the lower priced stocks of these pairs are in or close to the NSPP’s “optimal trading range”

of 30 – 60 theorized by Benartzi et al. (2006). All of the higher priced shares are above the upper

barrier of this range. Lastly, there are two pairs with what we call “odd prices,” namely penny

stocks and stocks affected by the “round numbering” bias. The relevance of these odd prices has

already been discussed previously.

Next to their willingness to invest, the respondents were asked to provide their age (AGE), gender

(GENDER), years of experience with financial markets (ACTFIN) and whether they were in the

possession of stocks (POSS). At the very end of the study, the respondents were also inquired if

they understood the concept of anchoring (KNOW) to not influence any previous given scores..

These variables are control variables and will allow for additional research. For example it is

possible that older women anchor more than younger men or vice versa. There is also the

possibility that individuals who claim to understand the notion of anchoring, still fall into the

anchoring trap.

To clarify the application of this questionnaire, there is an example of one pair to be found ut infra.

The full questionnaire can be found in addendum.

19

Questionnaire example: Pair with a multiple of 10

Dit bedrijf bevindt zich in de vastgoedsector en onderstaande gegevens over

dit bedrijf zijn gekend:

Aandelenprijs: €22,86

Aantal personeelsleden: 1050

Bestaat 24 jaar

Koers/Winst-ratio: 55

Koers/Winst-ratio van de sector: 30

Nettowinstmarge: 16%

Dividendrendement: 2%

Koers-Boek ratio: 3

Koers-Boek ratio van de sector: 1,34

Gemiddeld rendement over een periode van 5 jaar: 4%

Dit bedrijf bevindt zich in de vastgoedsector en onderstaande gegevens

over dit bedrijf zijn gekend:

Aandelenprijs: €228,6

Aantal personeelsleden: 1050

Bestaat 24 jaar

Koers/Winst-ratio: 55

Koers/Winst-ratio van de sector: 30

Nettowinstmarge: 16%

Dividendrendement: 2%

Koers-Boek ratio: 3

Koers-Boek ratio van de sector: 1,34

Gemiddeld rendement over een periode van 5 jaar: 4%

20

When attempting to find signs of anchoring in the results, simply comparing the means of the

higher versus the lower priced share does not suffice. Two new variables were created to improve

the analysis of the obtained data: the relative anchoring measure and the absolute anchoring

measure.

The relative anchoring measure (RAM) is calculated by subtracting the value given to the share

with the lower stock price from the value given to the share with the higher stock price. The

absolute anchoring measure (AAM) is obtained by taking the absolute value of the relative

anchoring measure. The reasoning behind this is that one person could give a higher value to higher

priced shares, while another might prefer the lower priced share. Without absolute values, these

figures would compensate each other, thus bringing the illusion that people de facto do not anchor.

E.g. Person 1 gives a score of 10 to share 1 and a score of 15 to share 2 of the pair (RAM1 = 5).

Person 2 gives a score of 15 to share 1 and a score of 10 to share 2 of the pair (RAM2 = -5). The

average RAM would then be 0, while in reality both individuals anchored by 5.

The raw dataset before being processed by analytic software would therefore look like this:

ID GENDER AGE ACT

FIN

POSS ANCH Pair 1-

A

Pair 1-

B

RAM1 AAM1

1 1 36 12 0 1 15 10 -5 5

2 1 25 6 1 0 10 15 5 5

AV. 0 5

Figure 6: Raw data table

The AAM is crucial when attempting to find the mean difference test subjects attribute stocks

within a pair. This provides us with the magnitude of the anchoring. Nonetheless, it does not tell

us anything about the “direction” in which the test subjects anchor. Therefore the RAM is still

necessary. By studying the relative anchoring-measure of a single stock, one can find out whether

on average people prefer the higher priced stock (RAM>0). This is what we label as “positive

anchoring.” When on average people prefer the lower priced one (RAM<0), we regard this as

“negative anchoring.”

We expect there to be a significant anchoring effect, because such extensive evidence has been

found in the real economy. Therefore a second hypothesis has pre-emptively been formulated:

21

Does the anchoring effect persist when the difference in prices decreases?

That is why the next step of the analytical process is to compare the AAM of the different pairs to

one another. Through this process we will be able to review whether the anchoring effect stays the

same, diminishes or even increases when the prices of the pairs come closer. Consider the

following example: Pair 1 with multiple 10 has an average AAM of 5, the following pair with a

multiple of 8: 4, the next pair an average AAM of 3 and the last two pairs have an AAM of 2. In

this example we would find a diminishing anchoring effect.

In order to have a complete understanding of the gathered data, we will run a variety of tests.

Firstly, a simple Analysis Of Variance (ANOVA) as well as a paired samples t-test is run on the

raw scores the respondents attributed to the shares. In first instance this serves to see whether there

is already a significant anchoring effect present. We base ourselves on the table ut infra to assess

this significance.

Level of Significance

(2 tailed)

0,20 0,1 0,05 0,01

Confidence level 80% 90% 95% 99%

Needed t-ratio 1.282i 1.645* 1.96** 2.576***

Table 1: Table concerning significance levels

A confidence level of 90% is the arbitrarily set but commonly accepted level at which a result is

significant. Nevertheless, for this research, results with a confidence level of 80% will also be

considered as important. This confidence level is not unusual and will help assess the results due

to relatively small dataset (The Business Research lab, 2010). These type of results will be marked

with an “i” in the upper right.

A paired samples t-test test will provide us with the direction in which the anchoring happens.

Secondly, there is an OLS regression with the relative anchoring measure (RAM), as well as the

absolute anchoring measure (AAM) as dependent variables. Through this regression we are able

to include the control variables and their effect on anchoring. Lastly, we provide a graph of the

average AAM values per pair, to check for a differing or an equal anchoring effect when prices of

pairs get closer. To analyze this even further, a second ANOVA is run.

22

5. Results

5.1 General Overview

The general profile of the 108 respondents, is distinguished by the following characteristics: The

ratio men to women is 60/40. The average age of the respondents is 31.22 years with the youngest

respondent being 19 and the oldest respondent being 64. The number of years that respondents

have been involved with finance is on average 9.24 years. 35.19% is in the possession of shares

and 37.07% knew what anchoring meant prior to the questionnaire.

To start off the discussion of the results we take a look at the average scores respondents gave to

the respective shares. Figure 7 ut infra indicates that for the pairs (multiples 10 through 1.5) people

are generally more willing to invest in the lower priced share. For the penny stock pair as well as

the pair with the round numbering effect, the effect reverses. Here, the higher priced share is

considered to be more attractive than the lower priced one.

Figure 7: Bar graph of average willingness to accept

This gives us a first indication that investors do actually anchor on the price in the stock market.

Nonetheless, a simple graph is not enough to prove that there is any significant difference between

lower and higher priced shares. Therefore, an ANOVA and a paired samples t-test are necessary.

0

2

4

6

8

10

12

14

10x 8x 6x 4x 2x 1,5x Penny Rnd

Lower priced share

Higher priced share

23

ANOVA Multiple 10 Multiple 8 Multiple 6 Multiple 4 Multiple 2 Multiple 1,5

Between

groups

(Sign.)

0.334 0.188 0.321 0.13 0.974 0.253

Table 2: ANOVA of the willingness to accept scores

From the results of the above ANOVA, we must conclude that there is no significant difference

between a lower and a higher priced share. For the pairs with a multiple of 4 and 8 the difference

is considered important, but only at an 80% significance level. The first indication at anchoring

from Figure 7 seems to be undone. However, there is another test of equal importance to be taken

into account.

5.2 Paired Samples T-test

Table 3: Paired Samples t-test on regular pairs

Whereas the ANOVA deems there is no significant difference between the attributed score, the

paired samples t-test proves otherwise. The six regular pairs seem to be predominantly significant,

except for the pair with a multiple of 2. Next to the significance of the anchoring effect, there is

also the direction of the anchoring that needs to be taken into account. It can be concluded that the

greater part of the pairs anchors negatively. This means that people are more willing to invest in

the lower than in the higher priced share. Again, the pair with multiple 2 is the pair that sticks out.

The anchoring effect, even though small, is in a positive direction.

Penny Round

Mean

(t-value)

1,278

(2,452)**

0,713

(1,828)*

Table 4: Paired Samples t-test on oddly priced pairs

When considering the penny stock pair and the round numbering pair, we find a strongly

significant effect with a confidence level of above 95% and 90% respectively. Here the direction

of the anchoring effect also reverses, with both pairs anchoring positively. This means that people

prefer the higher priced stock over the lower priced one.

Multiple 10 Multiple 8 Multiple 6 Multiple 4 Multiple 2 Multiple 1,5

Mean

(t-value)

-0.657

(-1,47)i

-0,889

(-1,853)*

-0,565

(-1,321)i

-0,889

(-1,868)*

0,019

(0,044)

-0,667

(-1,75)*

24

The first results of the paired samples t-test as well as the conclusions from Figure 7 seem to

confirm our hypothesis that anchoring on the share price exists in the stock market. Therefore, the

philosophy of the EMH where (most) investors are considered rational comes under pressure.

Investors attribute informational value to the stock price, and consequently adjust their willingness

to invest. However, this does provide an explanation for the NSPP. These first results seem to

indicate that average investor’s preference will be more towards the lower priced share. It should

be taken into account that the higher priced shares in this experiment are all above the upper

frontier of the optimal trading range of 60. Managers of publicly listed companies were right,

whether they knew it or not, in catering the price level towards this lower price preference.

Results concerning the penny stock pair and the pair affected by the round numbering effect are in

line with examined literature. Investors apparently attribute negative characteristics to the penny

stock, and are therefore more willing to invest in the “normally” price share. Prices that break

through a certain “barrier” (in this case 100) are considered to be more attractive than shares still

below this barrier.

Notwithstanding the above outcome, there are certain control variables that need to be taken into

account as well. These control variables potentially influence the newly created dependent

variables, and make the model overall more accurate.

5.3 Relative OLS Regressions

The first of our multiple regressions considers the relative anchoring measure (RAM). This can be

considered as a paired samples t-test only with added control variables. An OLS without these

control variables would provide the exact same results as the paired samples t-test.

25

Multiple 10 Multiple 8 Multiple 6 Multiple 4 Multiple 2 Multiple

1,5 constant -1.814

(-1.316)i

-1.849

(-1.246)

-0.0623

(-0.047)

0.129

(0.088)

-1.243

(-0.951)

-1.001

(-0.843) GENDER 0.199

(1.292)i

0.562

(0.5377)

0.464

(0.493)

0.974

(0.946)

0.41491

(0.451)

0.400334

(0.480) AGE 0.771

(0.292)

0.028

(0.487)

−0.0135

(-0.266)

−0.052

(-0.944)

0.070

(1.417)i

0.013

(0.291) ACTFIN 0,779

(0.281)

−0,052

(-0.675)

−0,007

(-0.106)

0,047

(0.616)

−0,060

(-0.885)

−0,006

(-0.093) POSS 0,129

(-1.532)i

1,468

(1.318)i

−0,732

(-0.730)

−1,939

(-1.767)*

−0,690

(-0.74)

−1,196

(-1.343)i

KNOW 0.310

(1.02)

−0.598

(-0.792)

−0.076

(-0.112)

0.645

(0.867)

−0.842

(-1.265)

0.3777

(0.625) Table 5: OLS regression on the RAM of the regular pairs with control variables

In the above table we find that none of our regular pairs have a significant anchoring effect to

them. Only for the pair with multiple there is an important anchoring effect. This could be due to

the fact that it is the pair with the largest difference in price. With regard to the control variables,

only being in possession of shares seems to have an important or significant effect on anchoring.

The direction in which the anchoring effect happens, remains the same as found in the paired

samples t-test. Summarized, the willingness to invest in the lower priced stock is higher than for

the higher priced stock, but the disparity in willingness is no longer significant.

The same multiple regression is done for the penny stock and round numbering pair.

Penny Round

constant −0,757

(-0,478)

0,658

(0,5513) GENDER −0,056

(-0,050)

−0,724

(-0,861) AGE 0,129

(2,139)**

0,041

(0,900) ACTFIN −0,117

(-1,416)i

−0,030

(-0,487) POSS −1,787

(-1,5035)i

−1,523

(-1,7002)* KNOW −0,499

(-0,619)

0,076

(0,125) Table 6: OLS regression on the RAM of the oddly priced pairs with control variables

26

Here the same line of thought applies. The anchoring effect is no longer significant and being in

the possession of shares, reduces the anchoring effect. Another control variable that is strongly

significant here, is age. The significance of this control variable is however negligible, as it does

not appear to be recurring in any other pairs.

While before the results from the paired samples t-test indicated the existence of a significant price

anchoring effect in the stock market, this no longer seems the case. Through the results of the

relative OLS regressions, we no longer detect any significant anchoring. Even for the penny stock,

where the anchoring effect was strongly significant (t=2.452), investors no longer seem to adjust

their willingness to invest to the stock price. This result appears to be in favor of the Efficient

Market Hypothesis. While anchoring is abundantly found in the real economy, the stock market

might be more efficient than originally assumed. However, this also raises questions surrounding

the stock market puzzles. If anchoring is not the answer, perhaps another explanation should be

sought after.

Until now only the direction of the anchoring has been investigated and whether it leads to a

significant difference in willingness to invest. For further analysis we inspect how large the

absolute difference is in this willingness i.e. the magnitude of the anchoring. This result will be

provided by a single and a multiple regression of the absolute anchoring measure (AAM).

5.4 Absolute OLS Regressions

From the relative regressions ut supra, we found that the anchoring effect arises most of the times

as a negative effect, meaning that people prefer the lower priced stock over the higher priced stock.

Nevertheless, this does not tell us anything about the magnitude with which the average person

anchors, as explained in the methodology. The investigation of the single and multiple regression

of the absolute anchoring measure (AAM) will yield the appropriate results.


1,5 constant 3.361

(10.706)***

3.556

(10.294)***

3.120

(10.135)***

3.667

(11.149)***

3.22

(11.223)***

2.852

(10.530)*** Table 7: OLS regression on the AAM of the regular pairs without control variables

27

A simple regression, without taking into account the control variables, suggests an absolute

difference of 3.3 across the pairs. This difference can be interpreted as people according a 3.3

points more/less willingness to invest in the higher/lower priced share. These 3.3 points might not

seem like much but on a scale of 20, this would mean a 16.5% difference in willingness to invest.

Now for the penny stock and round numbering pair, the same line of thought applies.

Penny Round

constant 4.370

(13.282)***

3.065

(11.659)*** Table 8: OLS regression on the AAM of the oddly priced pairs without control variables

The difference for the penny stock is large with a difference of about 4.37 (=21.85%) in

willingness to invest. The difference in willingness for the round numbering effect pair is with a

difference of 3.06 (=15.3%) smaller but large nonetheless.

Even though providing us with this difference, these results should be taken with certain

precaution. The t-ratios of these coefficients are extremely significant (sign.>99%). This occurs

because of the process of making the relative anchoring values absolute. The results will

consequently always be strictly different from zero. The AAM though can, next to the absolute

difference in willingness, also provide us with the effect of the control variables on the overall

absolute anchoring effect.


1.5 constant 3.691

(3.945)***

3.05744

(2.847)***

3.990

(4.2887)***

2.677

(2.7122)***

4.217

(4.8756)***

4.223

(5.0835)*** GENDER −1.195

(-1.814)*

0.445

(0.589)

−0.107

(-0.163)

0.548

(0.788)

0.596

(0.979)

−0.410

(-0.701) AGE 0.038

(1.065)

0.030

(0.740)

−0.025

(-0.670)

0.069

(1.848)*

−0.0222

(-0.677)

−0.031

(-0.982) ACTFIN −0.025

(-0.504)

−0.077

(-1.376)i

0.075

(1.555)i

−0.083

(-1.616)i

−0.031

(-0.700)

0.022

(0.515) POSS −1.430

(-2.036)**

−0.019

(-0.024)

−0.814

(-1.166)

−0.681

(-0.9201)

−1.084

(-1.670)*

−0.791

(-1.269) KNOW −0.153

(-0.321)

0.035

(0.064)

−1.029

(-2.171)**

−1.098

(-2.185)**

0.031

(0.071)

−0.219

(-0.518) Table 9: OLS regression on AAM of the regular pairs with control variables

28

The average difference in willingness increases from 3.3 to 3.6 when adding the control variables,

meaning an 18% difference in willingness to invest. The control variables and the t-ratios going

with them suggest a significant effect amongst several of these control variables. In the pair with

a multiple of 10 both the gender and being in the possession of stocks have a decreasing effect on

anchoring. In this case this would mean that a male will anchor 1.19 points less, and that someone

being in the possession of stocks will anchor 1.43 points less (in absolute terms). We are led to

believe that a male being in the possession of stocks observes the shares more rational than a

female who is not in possession of stocks.

The gender related significance is nevertheless not repeated in the other results. Being in the

possession of stocks does however return as being significant in the pair with a multiple of 2. Other

control variables that are deemed significant are the number of years that one is active on the

financial markets as well as knowing what anchoring is. Where knowledge of anchoring decreases

anchoring, the results for the years of experience with the financial markets are ambiguous. For

multiples 8 and 4, the more years of experience someone has with financial markets the lower the

magnitude of the anchoring effect. However, for multiple 6 the magnitude of the anchoring effect

increases as the years of experience rise.

Penny Round

constant 4.548

(4.620)***

3.456

(4.327)*** GENDER 0.475

(0.687)

−0.536

(-0.954) AGE 0.033

(0.887)

0.007

(0.235) ACTFIN −0.075

(-1.479)i

−0.059

(-1.438)i

POSS −1.466

(-1.985)**

0.047

(0.080) KNOW −0.624

(-1.246)

0.551

(1.354)i


For both the penny stock as well as the round numbering pair the number of years has an important

decreasing effect on anchoring. The possession of stocks has a significant decreasing effect on the

anchoring with penny stocks, but not on round numbering effect stocks.

29

5.5 Anchoring effect between pairs

To end the discussion of the results it is examined whether the anchoring effect stays equal as pairs

come closer to one another, or whether there is a significant difference in anchoring. We use the

absolute anchoring coefficients (without control variables) to this end.

Figure 8: Graph on the anchoring effect between pairs

From the above graph and its corresponding trend line we observe a slightly downward trend,

meaning that as the multiples go down, the anchoring effect goes down with it. To understand

whether this downward trend is of any significance, again an ANOVA is considered.

ANOVA Pairs

Between

groups

(Sign.)

0.467

Figure 19: ANOVA on the anchoring effect between pairs

The ANOVA reveals that, even though there seems to be a downward effect, the difference

between the pairs is not significant. The anchoring effect therefore stays equal even when the

difference in share price decreases. This means that no matter the price, people will anchor with

the same magnitude.

Literature does not provide us with much information about the magnitude of anchoring. It is

therefore interesting to attempt to quantify this magnitude and whether it differs when the values

of uninformative anchors come closer to one another.

y = -0,0857x + 3,5963

2,6

2,8

3

3,2

3,4

3,6

3,8


1,5

AAM

30

6. Conclusion

This paper commenced with the purpose of researching whether the behavioral bias known as

“anchoring” exists not only in the real economy, but also in the stock market. Anchoring is the

phenomenon that occurs when a person takes into consideration irrelevant information to value a

certain good, service, experience or in our case: a stock. As we expected to find this bias, a follow-

up hypothesis was considered: when prices of two stocks of equal fundamental value get closer to

one another, the anchoring effect will decrease as well.

This paper would add to the literature surrounding behavioral economics. This particular field of

economic science goes against the Efficient Market Hypothesis, which considers most economic

agents to be rational and to possess perfect information (Fama, 1970). Anchoring would also

provide an explanation for several stock market “puzzles” of which two have been discussed: the

Nominal Share Price Puzzle and the Equity Premium Puzzle (Siddiqi, 2015).

Through an experiment, the anchoring effect was assessed by reviewing whether the willingness

to invest differed between two exactly the same companies apart from their stock price. The

absolute stock price is a factor which can be easily manipulated by company managers through

stock splits and reverse stock splits and holds inherently no relevant information about the stocks.

Therefore these companies should, based on their respective fundamental values, yield the same

willingness to invest. The amount by which these prices diverge should also not have an influence

on this willingness.

From the results of this experiment we first came to the conclusion that respondents did in fact

anchor. This anchoring effect happened in a negative way, meaning that people are more willing

to invest in stocks with lower prices as opposed to stocks with higher prices. However, when

adding the control variables, the significance of this anchoring effect no longer stands. Even

though we found only the possession of stocks to have some decreasing effect on anchoring, this

overall resulted in the non-significance of the examined bias.

Next to the significance of the anchoring effect, the magnitude of this effect was also investigated.

On an average basis the absolute difference between a lower and a higher priced stock in the model

with the control variables was 3.6. In the experiment, it was asked to give the willingness to invest

31

on a scale of 20. A 3.6 difference therefore means an average 18% difference in willingness to

invest.

At first glance, it seemed as if the magnitude of the anchoring effect decreases as stock prices of

the considered companies came closer. However, it was revealed that there is no significant

difference in the magnitude of anchoring between prices. This means that there is an equal

anchoring effect between a pair of stocks with a small multiple and a pair of stocks with a high

multiple.

Next to pairs with normally priced stocks, we also took into consideration two types of stocks with

“odd” prices. These stocks were 1. a penny stock (= a stock under $5) and 2. a stock that is

supposed to be affected by a round numbering effect. The conclusions for these stocks are similar

to the conclusions for the regular stocks discussed ut supra, except for one. The anchoring effect

for both these type of stocks seems to reverse, meaning that people are more inclined to invest in

a higher priced stock than a lower priced stock. Again, after adding the control variables, the

anchoring affect was no longer significant.

The general conclusion is that people do seem to anchor in the stock market, however this

anchoring affects people in different ways. This signifies that the average willingness to invest in

a lower priced share compared to a higher priced share remains on average at the same level.

Nonetheless we have reason to believe that people will generally prefer a lower priced share as

opposed to a higher priced share. The exception to this is when the lower priced share is a penny

stock or is under a certain price “hurdle.”

Drawing from this conclusion, anchoring could resolve the aforementioned stock market puzzles.

Managers of publicly listed companies who keep the price in an optimal trading range of 30-60

are actually right to do so. Lower-priced stocks make a company more attractive to invest in, bar

stocks that are so lowly priced they define as penny stocks. Investors could be looking for “cheap

bets” (lottery type stocks) and attribute positive characteristics to this low price. They are under

the illusion that such a stock has “more room to grow” or even “less to lose.”

However, as the results of the experiment are ambiguous, a definitive solution cannot be derived.

The same reasoning applies for the Equity Premium Puzzle and the other puzzles. The Efficient

32

Market Hypothesis, which states that (most) investors are mostly rational and that the market price

is always right in the end, cannot be sufficiently disproven. Nevertheless, because there are

indications of price anchoring in the stock market, further research into this matter is necessary.

For any future investigation we propose the following advancements. Firstly, we suggest to

research anchoring in the stock market on a larger scale. A sample of 108 respondents over a

limited time frame cannot comprise the stock market in full. Secondly, it is recommended to also

include a reference pair of identical stocks, where the stock price for both is also the same. This is

to assess whether respondents don not value stocks randomly in general. Lastly, we advise to

include more expanded multiples in to a similar experiment e.g. multiples of 20,50,… This could

provide for a more significant pattern of anchoring.

33

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36

8. ADDENDUM

8.1. Survey

The survey ut infra is the “master version”, meaning that the questions have not been shuffled

and that the companies are paired one after the other. The companies and the pages in the version

for the respondents are also not numbered.

The online version of the survey can be found here:

https://qtrial2015q4az1.az1.qualtrics.com/SE/?SID=SV_29z92yaep2DK7WZ

https://qtrial2015q4az1.az1.qualtrics.com/SE/?SID=SV_29z92yaep2DK7WZ

37

Introductie

Ten aller eerste zou ik u willen bedanken om deel te nemen aan deze enquête in het kader van mijn thesis. In de enquête zal u gevraagd worden het aandeel van verschillende bedrijven te evalueren enkel op basis van de gegevens die u daarbij krijgt. Er is geen juist of fout antwoord, we willen enkel bekijken hoe mensen bepaalde aandelen inschatten. Tussendoor zullen ook enkele persoonsvragen gesteld worden. De bedrijven worden door u geëvalueerd aan de hand van een scoremeter van 0 tot 20 waarbij 0 een aandeel is waar u helemaal niet bereid bent in te willen investeren en 20 een aandeel waar u helemaal bereid bent in te willen investeren. In totaal zijn er 16 verschillende bedrijven te evalueren en neemt de enquête slechts zo'n 10 minuten van uw tijd in.

Persoonsvragen

1) Wat is uw e-mail adres? (enkel in te vullen indien u wenst kans te maken op een duo cinematicket)

2) Welke geslacht heeft u?

3) Hoe oud bent u?

4) Hoeveel jaar bent u al actief bezig met financiële markten? (studies mogen hier ook bij

gerekend worden)

5) Bent u zelf in het bezit van aandelen?

Man Vrouw

Ja Nee

38

PAREN

PAAR 1: Multiplier van 10

Bedrijf 1 Dit bedrijf bevindt zich in de vastgoedsector en onderstaande gegevens over dit bedrijf zijn gekend: Aandelenprijs: €22,86 Aantal personeelsleden: 1050 Bestaat 24 jaar Koers/Winst-ratio: 55 Koers/Winst-ratio van de sector: 30 Nettowinstmarge: 16% Dividendrendement: 2% Koers-Boek ratio: 3 Koers-Boek ratio van de sector: 1,34 Gemiddeld rendement over een periode van 5 jaar: 4%

39

Bedrijf 2 Dit bedrijf bevindt zich in de vastgoedsector en onderstaande gegevens over dit bedrijf zijn gekend: Aandelenprijs: €228,6 Aantal personeelsleden: 1050 Bestaat 24 jaar Koers/Winst-ratio: 55 Koers/Winst-ratio van de sector: 30 Nettowinstmarge: 16% Dividendrendement: 2% Koers-Boek ratio: 3 Koers-Boek ratio van de sector: 1,34 Gemiddeld rendement over een periode van 5 jaar: 4%

40


Bedrijf 3 Dit bedrijf bevindt zich in de biotechnologiesector en onderstaande gegevens over dit bedrijf zijn gekend: Aandelenprijs: €24,38 Aantal personeelsleden: 1200 Bestaat 17 jaar Koers/Winst-ratio: 178 Koers/Winst-ratio van de sector: 165 Nettowinstmarge: 21% Dividendrendement: 2% Koers-Boek ratio: 25 Koers-Boek ratio van de sector: 23,45 Gemiddeld rendement over een periode van 5 jaar: 17%

41

Bedrijf 4 Dit bedrijf bevindt zich in de biotechnologiesector en onderstaande gegevens over dit bedrijf zijn gekend: Aandelenprijs: €195,04 Aantal personeelsleden: 1200 Bestaat 17 jaar Koers/Winst-ratio: 178 Koers/Winst-ratio van de sector: 165 Nettowinstmarge: 21% Dividendrendement: 2% Koers-Boek ratio: 25 Koers-Boek ratio van de sector: 23,45 Gemiddeld rendement over een periode van 5 jaar: 17%

42


Bedrijf 5 Dit bedrijf bevindt zich in de informaticasector en onderstaande gegevens over dit bedrijf zijn gekend: Aandelenprijs: €31,47 Aantal personeelsleden: 800 Bestaat 22 jaar Koers/Winst-ratio: 17 Koers/Winst-ratio van de sector: 22 Nettowinstmarge: 15% Dividendrendement: 2,7% Koers-Boek ratio: 0,93 Koers-Boek ratio van de sector: -11,5 Gemiddeld rendement over een periode van 5 jaar: 6%

43

Bedrijf 6 Dit bedrijf bevindt zich in de informaticasector en onderstaande gegevens over dit bedrijf zijn gekend: Aandelenprijs: €188,82 Aantal personeelsleden: 800 Bestaat 22 jaar Koers/Winst-ratio: 17 Koers/Winst-ratio van de sector: 22 Nettowinstmarge: 15% Dividendrendement: 2,7% Koers-Boek ratio: 0,93 Koers-Boek ratio van de sector: -11,5 Gemiddeld rendement over een periode van 5 jaar: 6%

44

PAAR 4: Multiplicator van 4

Bedrijf 7 Dit bedrijf bevindt zich in de energiesector en onderstaande gegevens over dit bedrijf zijn gekend: Aandelenprijs: €33,84 Aantal personeelsleden: 3800 Bestaat 43 jaar Koers/Winst-ratio: 25 Koers/Winst-ratio van de sector: 23 Nettowinstmarge: 7% Dividendrendement: 4% Koers-Boek ratio: 1,8 Koers-Boek ratio van de sector: 2 Gemiddeld rendement over een periode van 5 jaar: 3%

45

Bedrijf 8 Dit bedrijf bevindt zich in de energiesector en onderstaande gegevens over dit bedrijf zijn gekend: Aandelenprijs: €135,36 Aantal personeelsleden: 3800 Bestaat 43 jaar Koers/Winst-ratio: 25 Koers/Winst-ratio van de sector: 23 Nettowinstmarge: 7% Dividendrendement: 4% Koers-Boek ratio: 1,8 Koers-Boek ratio van de sector: 2 Gemiddeld rendement over een periode van 5 jaar: 3%

46

PAAR 5: Multiplicator van 2

Bedrijf 9 Dit bedrijf bevindt zich in de vastgoedsector en onderstaande gegevens over dit bedrijf zijn gekend: Aandelenprijs: €46,22 Aantal personeelsleden: 650 Bestaat 12 jaar Koers/Winst-ratio: 20 Koers/Winst-ratio van de sector: 30 Nettowinstmarge: 17% Dividendrendement: 3,5% Koers-Boek ratio: 4 Koers-Boek ratio van de sector: 1,34 Gemiddeld rendement over een periode van 5 jaar: 3,5%

47

Bedrijf 10 Dit bedrijf bevindt zich in de vastgoedsector en onderstaande gegevens over dit bedrijf zijn gekend: Aandelenprijs: €92,44 Aantal personeelsleden: 650 Bestaat 12 jaar Koers/Winst-ratio: 20 Koers/Winst-ratio van de sector: 30 Nettowinstmarge: 17% Dividendrendement: 3,5% Koers-Boek ratio: 4 Koers-Boek ratio van de sector: 1,34 Gemiddeld rendement per jaar: 3,5%

48

PAAR 6: Multiplicator van 1,5

Bedrijf 11 Dit bedrijf bevindt zich in de biotechnologiesector en onderstaande gegevens over dit bedrijf zijn gekend: Aandelenprijs: €43,77 Aantal personeelsleden: 8149 Bestaat 43 jaar Koers/Winst-ratio: 164 Koers/Winst-ratio van de sector: 165 Nettowinstmarge: 22% Dividendrendement: 2,5% Koers-Boek ratio: 27 Koers-Boek ratio van de sector: 23,45 Gemiddeld rendement per jaar: 14%

49

Bedrijf 12 Dit bedrijf bevindt zich in de biotechnologiesector en onderstaande gegevens over dit bedrijf zijn gekend: Aandelenprijs: €65,66 Aantal personeelsleden: 8149 Bestaat 43 jaar Koers/Winst-ratio: 164 Koers/Winst-ratio van de sector: 165 Nettowinstmarge: 22% Dividendrendement: 2,5% Koers-Boek ratio: 27 Koers-Boek ratio van de sector: 23,45 Gemiddeld rendement over een periode van 5 jaar: 14%

50

PAAR 7: Penny Stock

Bedrijf 13 Dit bedrijf bevindt zich in de informaticasector en onderstaande gegevens over dit bedrijf zijn gekend: Aandelenprijs: €0,3 Aantal personeelsleden: 120 Bestaat 7 jaar Koers/Winst-ratio: 27 Koers/Winst-ratio van de sector: 22 Nettowinstmarge: 8% Dividendrendement: 3% Koers-Boek ratio: -3 Koers-Boek ratio van de sector: -11,5 Gemiddeld rendement over een periode van 5 jaar: 4%

51

Bedrijf 14 Dit bedrijf bevindt zich in de informaticasector en onderstaande gegevens over dit bedrijf zijn gekend: Aandelenprijs: €60 Aantal personeelsleden: 120 Bestaat 7 jaar Koers/Winst-ratio: 27 Koers/Winst-ratio van de sector: 22 Nettowinstmarge: 8% Dividendrendement: 3% Koers-Boek ratio: -3 Koers-Boek ratio van de sector: -11,5 Gemiddeld rendement over een periode van 5 jaar: 4%

52

Paar 8: Round Number Effect

Bedrijf 15 Dit bedrijf bevindt zich in de energiesector en onderstaande gegevens over dit bedrijf zijn gekend: Aandelenprijs: €99 Aantal personeelsleden: 6697 Bestaat 54 jaar Koers/Winst-ratio: 14 Koers/Winst-ratio van de sector: 23 Nettowinstmarge: 11% Dividendrendement: 4% Koers-Boek ratio: 1,7 Koers-Boek ratio van de sector: 2 Gemiddeld rendement over een periode van 5 jaar: 2%

53

Bedrijf 16 Dit bedrijf bevindt zich in de energiesector en onderstaande gegevens over dit bedrijf zijn gekend: Aandelenprijs: €101 Aantal personeelsleden: 6697 Bestaat 54 jaar Koers/Winst-ratio: 14 Koers/Winst-ratio van de sector: 23 Nettowinstmarge: 11% Dividendrendement: 4% Koers-Boek ratio: 1,7 Koers-Boek ratio van de sector: 2 Gemiddeld rendement over een periode van 5 jaar: 2%

Weet u wat "anchoring" is?

Bedankt voor uw deelname. Deze wordt uitermate geapprecieerd.

Ja Nee

54

8.2. Descriptive statistics control variables

Summary Statistics, using the observations 1 - 108

Variable Mean Median Minimum Maximum

GENDER 0,592593 1,00000 0,000000 1,00000

AGE 31,0185 23,0000 0,000000 64,0000

ACTFIN 9,23611 4,00000 0,000000 46,0000

POSS 0,351852 0,000000 0,000000 1,00000

KNOW 0,435185 0,000000 0,000000 4,00000

Variable Std. Dev. C.V. Skewness Ex. kurtosis

GENDER 0,493643 0,833022 -0,376889 -1,85795

AGE 13,5467 0,436730 0,816317 -0,376335

ACTFIN 10,0346 1,08646 1,48545 1,56399

POSS 0,479774 1,36357 0,620453 -1,61504

KNOW 0,659554 1,51557 2,20340 7,81869

Variable 5% Perc. 95% Perc. IQ range Missing obs.

GENDER 0,000000 1,00000 1,00000 0

AGE 20,0000 57,0000 19,7500 0

ACTFIN 0,000000 30,0000 12,6250 0

POSS 0,000000 1,00000 1,00000 0

KNOW 0,000000 1,00000 1,00000 0

55

8.3. Relative OLS regressions

Multiple 10

Model 1: OLS, using observations 1-108

Dependent variable: ANormal

Coefficient Std. Error t-ratio p-value

const −1,81401 1,3788 -1,3156 0,19124

GENDER 1,25426 0,970581 1,2923 0,19918

AGE 0,0152621 0,0523636 0,2915 0,77129

ACTFIN 0,0201439 0,0717055 0,2809 0,77934

POSS −1,58481 1,03463 -1,5318 0,12868

KNOW 0,715788 0,702019 1,0196 0,31032

Mean dependent var −0,657407 S.D. dependent var 4,648710

Sum squared resid 2220,720 S.E. of regression 4,666023

R-squared 0,039615 Adjusted R-squared -0,007462

F(5, 102) 0,841492 P-value(F) 0,523369

Log-likelihood −316,5120 Akaike criterion 645,0239

Schwarz criterion 661,1167 Hannan-Quinn 651,5490

Multiple 8


Dependent variable: BNormal


const −1,84855 1,48387 -1,2458 0,21571

GENDER 0,561621 1,04454 0,5377 0,59197

AGE 0,0274583 0,0563538 0,4872 0,62713

ACTFIN −0,0520916 0,0771696 -0,6750 0,50119

POSS 1,46797 1,11347 1,3184 0,19033

KNOW −0,598037 0,755514 -0,7916 0,43045




F(5, 102) 0,686910 P-value(F) 0,634423



56

Multiple 6


Dependent variable: CNormal


const −0,0623254 1,33675 -0,0466 0,96290

GENDER 0,463795 0,940975 0,4929 0,62315

AGE −0,0134915 0,0507663 -0,2658 0,79096

ACTFIN −0,00737907 0,0695182 -0,1061 0,91568

POSS −0,731848 1,00307 -0,7296 0,46730

KNOW −0,0762599 0,680605 -0,1120 0,91101




F(5, 102) 0,246670 P-value(F) 0,940601



Multiple 4


Dependent variable: DNormal


const 0,129078 1,46213 0,0883 0,92983

GENDER 0,974112 1,02923 0,9464 0,34616

AGE −0,0524206 0,0555279 -0,9440 0,34738

ACTFIN 0,0468035 0,0760387 0,6155 0,53958

POSS −1,9389 1,09716 -1,7672 0,08019 *

KNOW 0,645042 0,744443 0,8665 0,38826




F(5, 102) 0,975687 P-value(F) 0,436375



57

Multiple 2


Dependent variable: ENormal


const −1,2431 1,30632 -0,9516 0,34355

GENDER 0,41491 0,919555 0,4512 0,65280

AGE 0,0702809 0,0496107 1,4166 0,15963

ACTFIN −0,0601189 0,0679358 -0,8849 0,37827

POSS −0,690033 0,980241 -0,7039 0,48307

KNOW −0,841501 0,665112 -1,2652 0,20868

Mean dependent var 0,018519 S.D. dependent var 4,402594



F(5, 102) 0,824872 P-value(F) 0,534814



Multiple 1.5


Dependent variable: FNormal


const −1,00064 1,18609 -0,8436 0,40084

GENDER 0,400334 0,834926 0,4795 0,63262

AGE 0,0130971 0,0450449 0,2908 0,77183

ACTFIN −0,00576276 0,0616835 -0,0934 0,92575

POSS −1,19553 0,890027 -1,3433 0,18217

KNOW 0,377674 0,6039 0,6254 0,53311




F(5, 102) 0,430305 P-value(F) 0,826559



58

Penny stock


Dependent variable: PENNormal


const −0,756998 1,58367 -0,4780 0,63367

GENDER −0,0561053 1,11479 -0,0503 0,95996

AGE 0,128652 0,0601439 2,1391 0,03482 **

ACTFIN −0,116587 0,0823598 -1,4156 0,15994

POSS −1,78675 1,18836 -1,5035 0,13579

KNOW −0,49883 0,806327 -0,6186 0,53753



R-squared 0,066290 Adjusted R-squared 0,020520

F(5, 102) 1,448326 P-value(F) 0,213465



Round number


Dependent variable: RNDNormal


const 0,658075 1,19375 0,5513 0,58266

GENDER −0,723624 0,840318 -0,8611 0,39119

AGE 0,0408166 0,0453358 0,9003 0,37007

ACTFIN −0,030252 0,0620818 -0,4873 0,62710

POSS −1,52302 0,895775 -1,7002 0,09213 *

KNOW 0,0756468 0,6078 0,1245 0,90120




F(5, 102) 1,145492 P-value(F) 0,341403



59

8.4. Absolute OLS regressions without control variables

Multiple 10


Dependent variable: AAbsolute


const 3,36111 0,313937 10,7063 <0,00001 ***






Multiple 8


Dependent variable: BAbsolute


const 3,55556 0,345403 10,2939 <0,00001 ***






Multiple 6


Dependent variable: CAbsolute


const 3,12037 0,307886 10,1348 <0,00001 ***






60

Multiple 4


Dependent variable: DAbsolute


const 3,66667 0,32889 11,1486 <0,00001 ***






Multiple 2


Dependent variable: EAbsolute


const 3,22222 0,287122 11,2225 <0,00001 ***






Multiple 1.5


Dependent variable: FAbsolute


const 2,85185 0,270832 10,5300 <0,00001 ***






61

Penny stock


Dependent variable: PENAbsolute


const 4,37037 0,329046 13,2819 <0,00001 ***






Round number


Dependent variable: RNDAbsolute


const 3,06481 0,262873 11,6589 <0,00001 ***






62

8.5. Absolute OLS regressions with control variables

Multiple 10


Dependent variable: AAbsolute


const 3,69143 0,935836 3,9445 0,00015 ***

GENDER −1,19488 0,658763 -1,8138 0,07264 *

AGE 0,0378441 0,0355407 1,0648 0,28948

ACTFIN −0,0245109 0,0486687 -0,5036 0,61561

POSS −1,43 0,702238 -2,0363 0,04431 **

KNOW −0,152983 0,476482 -0,3211 0,74882




F(5, 102) 2,310863 P-value(F) 0,049355



Multiple 8


Dependent variable: BAbsolute


const 3,05744 1,07398 2,8468 0,00534 ***

GENDER 0,445348 0,756008 0,5891 0,55711

AGE 0,0301604 0,0407872 0,7395 0,46133

ACTFIN −0,0768633 0,0558531 -1,3762 0,17178

POSS −0,0190275 0,8059 -0,0236 0,98121

KNOW 0,0351275 0,546819 0,0642 0,94891




F(5, 102) 0,474055 P-value(F) 0,794842



63

Multiple 6


Dependent variable: CAbsolute


const 3,98986 0,930321 4,2887 0,00004 ***

GENDER −0,107021 0,65488 -0,1634 0,87051

AGE −0,0247249 0,0353313 -0,6998 0,48564

ACTFIN 0,0752292 0,0483819 1,5549 0,12307

POSS −0,813859 0,698099 -1,1658 0,24641

KNOW −1,02854 0,473673 -2,1714 0,03222 **




F(5, 102) 1,703578 P-value(F) 0,140474



Multiple 4


Dependent variable: DAbsolute


const 2,67664 0,986906 2,7122 0,00785 ***

GENDER 0,547709 0,694713 0,7884 0,43229

AGE 0,0692778 0,0374803 1,8484 0,06744 *

ACTFIN −0,0829143 0,0513246 -1,6155 0,10929

POSS −0,681374 0,74056 -0,9201 0,35970

KNOW −1,09813 0,502484 -2,1854 0,03115 **




F(5, 102) 2,012974 P-value(F) 0,083009



64

Multiple 2


Dependent variable: EAbsolute


const 4,21733 0,864989 4,8756 <0,00001 ***

GENDER 0,595786 0,608892 0,9785 0,33015

AGE −0,0222362 0,0328502 -0,6769 0,50000

ACTFIN −0,0314799 0,0449843 -0,6998 0,48565

POSS −1,08387 0,649075 -1,6699 0,09801 *

KNOW 0,0314304 0,44041 0,0714 0,94325




F(5, 102) 1,836208 P-value(F) 0,112351



Multiple 1.5


Dependent variable: FAbsolute


const 4,22379 0,830879 5,0835 <0,00001 ***

GENDER −0,409797 0,58488 -0,7007 0,48512

AGE −0,0309873 0,0315547 -0,9820 0,32841

ACTFIN 0,0222683 0,0432104 0,5153 0,60743

POSS −0,790879 0,623479 -1,2685 0,20751

KNOW −0,219022 0,423043 -0,5177 0,60577




F(5, 102) 1,042317 P-value(F) 0,397042



65

Penny stock


Dependent variable: PENAbsolute


const 4,54751 0,984298 4,6201 0,00001 ***

GENDER 0,475674 0,692877 0,6865 0,49394

AGE 0,0331403 0,0373812 0,8865 0,37741

ACTFIN −0,0757146 0,051189 -1,4791 0,14219

POSS −1,46638 0,738603 -1,9853 0,04979 **

KNOW −0,624389 0,501156 -1,2459 0,21566




F(5, 102) 2,153274 P-value(F) 0,065067



Round number


Dependent variable: RNDAbsolute


const 3,45647 0,79877 4,3272 0,00004 ***

GENDER −0,536118 0,562278 -0,9535 0,34260

AGE 0,00713154 0,0303353 0,2351 0,81461

ACTFIN −0,0597236 0,0415405 -1,4377 0,15357

POSS 0,0477304 0,599385 0,0796 0,93669

KNOW 0,550688 0,406694 1,3541 0,17871




F(5, 102) 1,457372 P-value(F) 0,210387



66

8.6. Paired samples t-test

Paired Samples Correlations

N Correlation Sig.

Pair 1 A1 & A2 108 ,566 ,000

Pair 2 B1 & B2 108 ,494 ,000

Pair 3 C1 & C2 108 ,435 ,000

Pair 4 D1 & D2 108 ,340 ,000

Pair 5 E1 & E2 108 ,422 ,000

Pair 6 F1 & F2 108 ,571 ,000

Pair 7 G1 & G2 108 ,303 ,001

Pair 8 H1 & H2 108 ,567 ,000

Paired Samples Statistics

Mean N Std. Deviation Std. Error Mean

Pair 1 A1 11,176 108 4,9253 ,4739

A2 10,519 108 5,0557 ,4865

Pair 2 B1 12,019 108 4,7458 ,4567

B2 11,130 108 5,1394 ,4945

Pair 3 C1 11,380 108 4,2989 ,4137

C2 10,815 108 4,0491 ,3896

Pair 4 D1 11,787 108 4,0604 ,3907

D2 10,898 108 4,5240 ,4353

Pair 5 E1 10,769 108 3,9615 ,3812

E2 10,787 108 4,2207 ,4061

Pair 6 F1 12,574 108 4,2913 ,4129

F2 11,907 108 4,2548 ,4094

Pair 7 G1 8,352 108 4,6025 ,4429

G2 9,630 108 4,5705 ,4398

Pair 8 H1 10,213 108 4,3062 ,4144

H2 10,926 108 4,4020 ,4236

67

Paired Samples Test

Paired Differences

t df

Sig. (2-

tailed) Mean

Std.

Deviation

Std. Error

Mean

95% Confidence

Interval of the

Difference

Lower Upper

Pair

1

A1 -

A2 ,6574 4,6487 ,4473 -,2294 1,5442 1,470 108 ,145

Pair

2

B1 -

B2 ,8889 4,9847 ,4797 -,0620 1,8397 1,853 108 ,067

Pair

3

C1 -

C2 ,5648 4,4434 ,4276 -,2828 1,4124 1,321 108 ,189

Pair

4

D1 -

D2 ,8889 4,9452 ,4759 -,0544 1,8322 1,868 108 ,064

Pair

5

E1 -

E2 -,0185 4,4026 ,4236 -,8583 ,8213 -,044 108 ,965

Pair

6

F1 -

F2 ,6667 3,9601 ,3811 -,0887 1,4221 1,750 108 ,083

Pair

7

G1 -

G2

-

1,277

8

5,4152 ,5211 -2,3107 -,2448 -2,452 108 ,016

Pair

8

H1 -

H2 -,7130 4,0535 ,3900 -1,4862 ,0603 -1,828 108 ,070

68

8.7. ANOVA

ANOVA

Sum of

Squares df Mean Square F Sig.

Multiple

10

Between

Groups 23,338 1 23,338 ,937 ,334

Within Groups 5330,620 214 24,909

Total 5353,958 215

Multiple 8 Between

Groups 42,667 1 42,667 1,744 ,188

Within Groups 5236,148 214 24,468

Total 5278,815 215

Multiple 6 Between

Groups 17,227 1 17,227 ,988 ,321

Within Groups 3731,731 214 17,438

Total 3748,958 215

Multiple 4 Between

Groups 42,667 1 42,667 2,309 ,130

Within Groups 3953,981 214 18,477

Total 3996,648 215

Multiple 2 Between

Groups ,019 1 ,019 ,001 ,974

Within Groups 3585,315 214 16,754

Total 3585,333 215

Multiple

1,5

Between

Groups 24,000 1 24,000 1,314 ,253

Within Groups 3907,481 214 18,259

Total 3931,481 215

Penny Between

Groups 88,167 1 88,167 4,191 ,042

Within Groups 4501,815 214 21,037

Total 4589,981 215

Round Between

Groups 27,449 1 27,449 1,448 ,230

Within Groups 4057,509 214 18,960

Total 4084,958 215

69

ANOVA

AAM Pairs

Sum of

Squares df Mean Square F Sig.

Between

Groups 47,796 5 9,559 ,921 ,467

Within Groups 6663,315 642 10,379

Total 6711,111 647

Price Anchoring in the Stock Market

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