IN
DEGREE PROJECT TECHNOLOGY, FIRST CYCLE, 15 CREDITS
STOCKHOLM SWEDEN 2016,
The impact of trade-specific factors on insiders’ excess returns
An evaluation of information asymmetry
dynamics in the modern market environment of the Stockholm Stock Exchange
OSKAR GRENMARK
DANIEL OHLSSON
The impact of trade-specific factors on insiders’ excess returns
An evaluation of information asymmetry dynamics in the modern market environment of the Stockholm Stock Exchange
O S K A R G R E N M A R K D A N I E L O H L S S O N
Degree Project in Applied Mathematics and Industrial Economics (15 credits) Degree Progr. in Industrial Engineering and Management (300 credits)
Royal Institute of Technology year 2016 Supervisors at KTH: Fredrik Armerin, Jonatan Freilich
Examiner: Henrik Hult
TRITA-MAT-K 2016:15 ISRN-KTH/MAT/K--16/15--SE
Royal Institute of Technology SCI School of Engineering Sciences KTH SCI SE-100 44 Stockholm, Sweden URL: www.kth.se/sci
Abstract
“An insider is a person who by his or her position in the company is regarded to have particularly advantageous possibilities to gain confidential information about the company.”
– Finansinspektionen [9]
Replicating investment decisions made by insiders is a frequently discussed and studied investment strategy. The rationale lies in the notion that insiders should have better un- derstanding of the future performance of the company by which they are employed, and therefore replicating their investments seems intuitively as a good strategy for achieving excess returns.
Numerous studies have verified that insiders have managed to achieve excess returns historically. However, what has not been examined as extensively is how insider trades differ in signal value in the modern stock market environment of today. This thesis addresses this very issue by combining qualitative and quantitative finance theories with a data-driven, mathematical analysis of the risk-adjusted return of all insider transactions made on the Stockholm Stock Exchange during the last ten years. The method is based on regression analysis applied to two investment horizons. The result is a mathematical mapping that describes the historical signal value of different insider trade-specific drivers.
Sammanfattning
“En insynsperson ¨ar en person som genom sin st¨allning i bolaget anses ha s¨arskilt goda f¨oruts¨attningar att f˚a tillg˚ang till f¨ortrolig information om bolaget.”
– Finansinspektionen [9]
Att f¨olja insynspersoners investeringsbeslut ¨ar en frekvent diskuterad och studerad in- vesteringsstrategi. Rationalen ligger i id´en att insynspersoner b¨or ha f¨ordelaktig f¨orm˚aga att kunna bed¨oma hur f¨oretaget de arbetar p˚a kommer att prestera i framtiden, och d¨armed ¨ar det intuitivt att det verkar vara en bra strategi att replikera deras investeringar f¨or att uppn˚a ¨overavkastning.
Att insynspersoner har lyckats uppn˚a ¨overavkastning historiskt har fastst¨allts av flertalet studier. Vad som d¨aremot inte har unders¨okts lika ing˚aende ¨ar hur olika insynstransak- tioner skiljer sig i signalv¨arde p˚a dagens moderna aktiemarknadsf¨orh˚allanden. Denna rapport behandlar denna ovisshet genom att kombinera kvalitativ och kvantitativ fi- nansteori med datadriven, matematisk analys av den riskjusterade avkastningen f¨or alla insynstransaktioner genomf¨orda p˚a Stockholmsb¨orsen under de tio senaste ˚aren. Metoden baseras p˚a regressionsanalys applicerad p˚a tv˚a investeringshorisonter. Resultatet ¨ar en matematiskt kartl¨aggning som beskriver karakt¨aren av de faktorer som drivit magnituden av de signalv¨arden som historiska insynstransaktioner har medf¨ort.
Contents
1 Introduction 7
1.1 Background . . . 7
1.2 Purpose and Aim . . . 8
1.3 Research Question . . . 8
1.4 Scope . . . 8
2 Mathematical theory 10 2.1 Multiple regression analysis . . . 10
2.1.1 Covariates . . . 11
2.1.2 Interpreting the β coefficients . . . 11
2.1.3 OLS . . . 12
2.2 Validation and improvement . . . 13
2.2.1 Hypothesis testing . . . 13
2.2.2 R2 . . . 15
2.2.3 Partial eta squared (η2) . . . 15
2.2.4 Akaike Information Criterion (AIC) . . . 16
2.3 Errors . . . 16
2.3.1 Endogeneity . . . 16
2.3.2 Multicollinearity . . . 18
2.3.3 Heteroscedasticity . . . 18
3 Finance theory 20 3.1 Adjusted closing price . . . 20
3.2 Rate of return . . . 20
3.3 Risk . . . 20
3.3.1 Volatility and dispersion - the systematic risk . . . 21
3.3.2 Unsystematic risk . . . 21
3.3.3 The beta ratio . . . 21
3.3.4 Risk-adjusted performance measures . . . 21
3.3.5 Time horizon . . . 22
4 Method 24 4.1 Overall structure and approach . . . 24
4.2 Choice of variables and data collection . . . 24
4.3 Data management . . . 25
5 Model 27 5.1 Variables . . . 27
5.1.1 The dependent variable . . . 27
5.1.2 The independent variables . . . 28
5.2 Initial regression model . . . 35
6 Results 36
6.1 Initial model . . . 36
6.1.1 The short term regression . . . 36
6.1.2 The long term regression . . . 37
6.1.3 Evaluation of the initial model . . . 37
6.1.4 Reducing the initial model . . . 40
6.2 Final model . . . 41
6.2.1 The short term regression . . . 41
6.2.2 The long term regression . . . 41
6.2.3 Evaluation of the final model . . . 42
6.2.4 Final remarks . . . 44
7 Discussion and analysis 45 7.1 The actual behaviour of the excess return . . . 45
7.2 The effect of risk-adjusting . . . 45
7.3 Results analysis . . . 47
8 Conclusions 51 9 Further research 52 10 References 53
List of Tables
1 Initial regression model . . . 352 The short term regression - Results . . . 36
3 The long term initial regression - Results . . . 37
4 Overall model statistics . . . 39
5 Evaluation of significance - Initial model . . . 39
6 Removed covariates from each regression . . . 40
7 The short term final regression - Results . . . 41
8 The long term final regression - Results . . . 41
9 Overall model statistics . . . 43
10 Evaluation of significance - Final models . . . 43
List of Figures
1 Distribution of historical average returns over seasons, [15] . . . 302 The short term regression residuals . . . 38
3 The long term regression residuals . . . 38
4 The short term regression residuals - Final model . . . 42
5 The long term regression residuals - Final model . . . 42
6 Average and median risk-adjusted excess returns . . . 45
7 The effect of risk adjusting . . . 46
8 The effect of risk adjusting trades with β values greater than 1.5 . . . 46
1 Introduction
1.1 Background
One of the most common ways of saving money in Sweden is investing in stocks and mutual funds. In 2015, the median value of private Swedish stock portfolios was 28 000 SEK [63]. This number is growing each year among the Swedish population [57]. Examples of common, passive investment strategies are investing in index funds or allocating a monthly amount to a savings account. A more active investment strategy, that has been frequently discussed in literature, is based on paying regard to the actions of people who have access to special information about the company by which they are employed, information that the market does not have access to. These employees are called insiders. An insider is typically a director, a board member, an executive or a large owner [18]. The rationale is that an insider, if anyone, knows how the company is performing at a certain point in time, and most important of all: how the company will perform in the future.
For an investor to embrace an investment strategy based on insider information, the information about when an insider transaction has been made needs to be available to the investor, and it has to be reported continuously. In Sweden, this information is public and is regularly provided by Finansinspektionen (FI), whose main purpose is to monitor securities markets and ensure that all trading on the markets follow the law of market abuse (Marknadsmissbrukslagen) [11]. The law provides information proliferation and prevents insiders from abusing their power over the market. The purpose of the law is thus to create trust in the market and in financial services. Due to the law, insiders need to report their trades within five days. When FI receives the information, it becomes available to the rest of the market at the end of that day. [7]
However, there are arguments pointing against the usefulness of insider strategies. For example, companies often demand that high-level employees must have a certain amount of stake in the company, with the purpose of creating financial incentives for the employee to perform well [36]. Another example is that stocks, bonds or other financial instruments such as options or futures can be used as compensation to employees, especially to insiders.
In turn, this implies that a strategy based on insider trading may be misleading. Hence, these factors need to be considered by investors pursuing a strategy involving information about insider trading.
Despite the flaws of insider strategies, they have been frequently spoken of in several senses. Numerous studies, both old and relatively contemporary, have obtained the re- sult that insiders generally do manage to create excess returns [41, 58, 68]. An area that however has received less attention is if certain factors of an insider trade have been corre- lated to higher excess returns. A less comprehensive study on this matter was conducted in 2001 [41], but the market environment has changed severely with the emergence of technology and the internet. Hence, there is lack of studies of this sort on the modern market environment. This thesis fills that gap.
1.2 Purpose and Aim
An investor performs trades to generate return on the invested capital. The purpose of this thesis is to clearly outline how an investor should asses the signal value of insider transactions, based on all buy transactions ten years back in time from now. The result presented will be relevant for all types of investors, but perhaps especially for retail investors, as the results and conclusions will be both comprehensible and readily accessible [20]. An analysis of the utility of the results presented in this thesis could therefore be a powerful tool for the everyday person in the pursuit of excess returns.
Numerous studies have been conducted with the purpose to investigate the insider trading universe and how to act on the information as an investor. However, very few or none have been conducted with subject to the modern market environment of the Stockholm Stock Exchange (SSE). By using linear regression as a mathematical model to conduct this investigation, this thesis explores if there are specific factors that are key to consider when following the actions of insiders in the pursuit of excess returns on the Stockholm Stock Exchange.
1.3 Research Question
As mentioned above, previous studies have established that it is possible for retail investor to achieve excess returns by following insiders. The question this thesis serves to answer is: what factors are essential to consider to be successful in embracing an investment strategy of following insiders in the modern market environment of the Stockholm Stock Exchange? How do the impact of the factors differ with time?
This thesis will examine these questions by combining finance theory with mathematical models in the analysis of insider performance on the Stockholm Stock Exchange. A systematic approach will be applied using multiple linear regression on a number of factors to derive what factors of the data presented by Finansinspektionen are key to maximize excess returns.
1.4 Scope
To be able to reach comprehensible conclusions from this investigation, demarcations need to be made. Firstly, this thesis will only consider buy signals from insider trading.
The reason for this is that buy signals are the only signals that can be assured have relevant signal value. If a person actively invests in a company, clearly that person must have reasons to believe that the stock is undervalued, meaning that the price of the stock should increase. As opposed to buy signals, sell signals are not very suitable to use in the type of investigation that this thesis treats. A person could have numerous reasons to why they sell a stock. For example, one reason could be that they need to finance a large purchase of some sort (real estate, car, boat etc.). Another reason could be that they simply do not want to be invested in the stock market anymore, even though they have
reasons to believe the stock price of their company might increase. The same reasoning is used by [41, 58, 68] in their studies. All in all, buy signals are the most valuable signals.
In addition, this thesis will only treat transactions in directly owned stocks. This de- marcation will allow the investigation to remove the majority of data where the insider transaction could be some part of a compensation policy∗.
Furthermore, as mentioned earlier, this thesis will only consider stocks listed on the Stockholm Stock Exchange. The reason for this is that the SSE is more liquid than other Swedish stock exchanges, and is the market where most private investors trade stocks [57]. For the same reason, unusual stock types as preference stocks or equivalent, will not be included. Explained from the other way around, only A, B and C stocks will be included.
∗A common tool for shareholders to increase the incentives of managers to perform well is by offering an ownership stake in the organisation [36].
2 Mathematical theory
To present a describing model of the return that insider trades have created during the past ten years, linear regression analysis will be used. The method estimates the rela- tionship between different variables. More specifically, it investigates how a dependent variable varies when the value of the independent variables are changed one by one. This analysis will result in a model that demonstrates how the information in the data have af- fected the return of an insider investment historically. This section presents the necessary and complete mathematical theory needed to conduct the investigation.
2.1 Multiple regression analysis
Regression analysis is a commonly used tool within mathematical statistics, and is used to describe relationships between a dependent variable and a set of independent variables.
When the regression equation is linear, the tool is called linear regression. The indepen- dent variables are also known as covariates or explanatory variables, and another name for the dependent variable is response variable. When the regression includes two or more covariates, it is entitled multiple linear regression. [39]
The interpretation of the regression can either be structural or predictional. The difference lies in whether the covariates are considered to influence the dependent variable or not. In the predictional interpretation, the covariates need not influence the dependent variable to have a predictive effect. Furthermore, the structural interpretation, which is used in this thesis, grants hypothesis testing. [39]
The multiple regression model is defined by the equation system
yi= β0+ β1xi1+ β2xi2+ ... + βnxin+ ei, i = 1, ..., n
where n is the number of data points, yirepresents data points of the dependent variable, xij the corresponding data points of the covariates and βij the sought coefficients. Since the relationship between the variables seldom is perfectly linear, a linear model will not perfectly describe the response variable. Therefore, an error term ei is included in the model.
The equation system may also be presented with the somewhat more used matrix form
y = Xβ + e
Both forms will be used throughout the thesis.
2.1.1 Covariates
An essential part of multiple linear regression is the choice of covariates. The covariates should explain the outcome of the dependent variable to the greatest extent. However, the world is not perfect. There will be a deviation between the realized outcome of y and the explained part ˆy. The deviation y − ˆy is called the residual, and is denoted e (on vector form) or ei, as in the formulas above. [39]
In this thesis, observational data will be used as values for the covariates. These are what the name indicates: data that have been observed and not created, or in other words, outcomes that cannot be controlled by whom the regression is conducted by. They differ from the other type of data, experimental data, where the data is collected from the outcome of a controlled experiment. [39]
Covariates are deterministic, meaning they are fixed in repeated samples. However, the dependent variable is regarded random, due to the fact that the residual, or error term, is random. Furthermore, the residuals are assumed to be independent between observations.
[39]
2.1.2 Interpreting the β coefficients
Despite linear regression being a commonly used model, it is not obvious how to interpret the estimated coefficients. In basic linear regressions without any logarithms, as the ones that this thesis treats, each βj measures how much the mean of the dependent variable changes on average when changing the independent variable x.j corresponding to the βj, keeping all else equal [39, 61].
Since the intercept β0 does not correspond to a covariate, it cannot be interpreted as explained above. Indeed, the interpretation of the intercept is general and the same for all regressions. A key assumption in residual analysis is that the mean of the residuals should equal zero. Hence, the intercept will be estimated under this assumption, implying that it will collect the bias that is due to omitted covariates, to make the mean of the residuals equal zero. Mathematically, the intercept is calculated as the mean of the response vector when all covariates are set to zero. Thus, the intercept may have an interpretation if it is possible for all covariates to be zero, and if there are data points collected in that all-zero range. [12]
Hence, there is no essential value in trying to interpret the intercept unless it is possible that all covariates could be zero, and that there is data for that possibility. However, it has a crucial meaning: it serves as a coefficient for adjusting where the regression line will cross the y-axis to make the mean of the residuals zero. [12]
2.1.2.1 Quantitative and qualitative covariates
There are two main categories of covariates. These are quantitative and qualitative co- variates. Below are explanations of the two.
Quantitative
The interpretation of quantitative covariates is quite intuitive. It is what the name suggests: a variable that takes on quantitative values. In addition, it is continuous [65].
Qualitative
Qualitative covariates are needed in dealing with qualitative, or categorical, data. For example, if the difference between insider transactions in the summer or winter is to be tested, dummy variables are introduced. These are binary variables, describing whether or not an observation ”belongs” to a qualitative category or attribute. Relating to the example above: if an observation is made in the summer, the covariate could be assigned the value 1. The value 0 would indicate an observation made in the winter. The coefficient of the dummy variable would therefore represent an estimate of the difference in effect of a transaction made in the summer compared to one in the winter. [39, 65]
2.1.3 OLS
OLS, or Ordinary Least Squares, is an estimation method for solving overdetermined equation systems.∗ The method aims to find an estimate ˆβ of the coefficient vector β that minimizes the sum of the squared residuals, that is
ˆ ete =ˆ
n
X
i=1
ˆ e2i =
n
X
i=1
(Y − X ˆβ)2
This is conducted by solving the so called normal equations
Xte = 0ˆ
which yields estimates ˆβ of the true coefficients β [39]. Expanding the normal equations, one obtains
β = (Xˆ tX)−1XtY
which is the explicit formula for obtaining the OLS estimate of β.
∗An equation system is overdetermined if there are more equations than unknowns to solve for.
Despite the fact that OLS is a diligently used model to solve regression problems, in theory some conditions need to be satisfied if OLS is to be BLUE (Best Linear Unbiased Estimator). When the model is homoscedastic, these conditions are satisfied as opposed to when working with heteroscedastic data. However, due to the robustness of OLS, it is still the method used for estimation in the latter case. Instead of changing methods, one strives to represent the data and the regression in a manner that makes the model as close to homoscedastic as possible. [39] The concepts of homoscedasticity and heteroscedasticity will be explained later on in the thesis.
2.2 Validation and improvement
In order to draw conclusions about a linear model, tests for statistical significance and potential errors are needed. Furthermore, methods are needed to choose covariates that explain as much of the variability in the dependent vector as possible. In other words, they are needed for constructing a model that minimizes the information loss relative to the ”true” model (which is unknown). [39] Below are introductions and explanations of methods and tools that are helpful in choosing the best model from the available data.
2.2.1 Hypothesis testing
A hypothesis is an assumption about a certain statistical parameter. Hypothesis testing is the procedure of testing if this assumption can be rejected or not, on a certain significance level [62]. There are two types of statistical hypotheses:
• Null hypothesis, H0: The hypothesis to be tested. In the context of regression analysis, the null hypothesis is often that a subset of the coefficients βk= 0.∗
• Alternative hypothesis, H1: The hypothesis that opposes H0. In the context of regression analysis, the alternative hypothesis is often that βk6= 0.∗∗
2.2.1.1 The F-statistic and the F-test
A hypothesis test used in the context of regression analysis is the F-test. This test serves to investigate whether one or more β coefficients are statistically significant or not. Before embarking on the topic of F-tests, a definition of statistical significance will be made.
A β coefficient is statistically significant if its p-value is less than the chosen significance level. Furthermore, the p-value is the probability of obtaining the data used in the regression, given that the null hypothesis is true. The significance level is the probability that the null hypothesis is rejected given that it is true. [14]
∗A βk= 0 means that covariate k does not influence the dependent variable.
∗∗A βk6= 0 means that covariate k does influence the dependent variable.
The F-test uses an F-statistic to calculate the p-value for the set null hypothesis. This p-value is then compared to the significance level. If the p-value is smaller than the significance level, the null hypothesis is rejected. The general F-statistic in regression on vector form is
F = 1 r
βˆ2tVˆ2
−1βˆ2
which is approximately F (r, n − k − 1)-distributed under the null hypothesis, where r is the number of coefficients tested for, n is the number of data points and k is the number of covariates in the model. Mathematically, the definition of the p-value is the probability defined by
P (X > F ), where X ∼ F (r, n − k − 1)
[39].
The t-test
There is another test that is closely related to the F-test. This test, the t-test, is used for making inferences about a single coefficient in a linear regression, and works in the same way as the F-test. The hypotheses that are tested are specific to a single coefficient βi. The t-statistic used for the hypothesis testing is
t = βˆi
SE( ˆβi)
where the denominator is the standard error of the coefficient to be tested [47], and the statistic is t-distributed.
Note that there is a close relationship between the F-test and the t-test. In fact, they always yield the same p-value when testing one coefficient [46]. The relationship of the statistics (considering βk = βi) is
F = t2
Interpreting a coefficient that is not statistically significant
A common mistake is to make assumptions about a coefficient that is not statistically significant in the same manner as described in section 2.1.2. A coefficient that is not statistically significant ought not to be drawn any conclusions about. [60]
2.2.2 R2
As described earlier, it is in practice not possible for a linear model to perfectly describe a relationship between the dependent variable and the independent variables. However, it is possible to compare models regarding how well they are explaining the variability in the dependent variable. This is commonly done by using R2, which is a measure of goodness of fit. The R2 is defined by
R2= |ˆe∗|2− |ˆe|2
|ˆe∗|2 where
|ˆe∗|2=
n
X
i
(yi− ¯y)2, |ˆe|2=
n
X
i
(X ˆβ − ¯y)2
In words, R2 is the amount of error explained by the model divided by the amount explained by the reduced model, consisting of the intercept only. The result could be seen as a percentage of the error being explained by the model [39]. However, there are some downside with R2 as a tool for choosing models. This measure will increase when increasing the number of covariates, and thus it will often find the biggest model as the best [64, 53].
Adjusted R2
The adjusted R2 is a variation of the regular R2. The benefit of the adjustment is that it penalizes models when adding covariates. It is used in conjunction with the regular R2 to receive a better representation of the true goodness of fit. [64, 53]
2.2.3 Partial eta squared (η2)
Partial eta squared, η2, is a measure of how much one or more covariates are contributing to reducing the error in a regression. It is also known as effect size. The measure is defined as
η2= |ˆe∗|2− |ˆe|2
|ˆe∗|2 =R2− R2∗ 1 − R2∗
Here, the reduced model is the full model shortened only by the covariate(s) tested. [39]
2.2.4 Akaike Information Criterion (AIC)
When deciding which covariates to include in a regression model, a useful tool is the Akaike Information Criterion (AIC). The test suggests that the preferred model is the one that minimizes
AIC = n ln(|ˆe|2) + 2k
where n is the number of observations, k the number of covariates and |ˆe|2 the sum of squared residuals. [39]
Bayesian Information Criterion (BIC)
The Bayesian Information Criterion is another tool used for model selection. It is quite similiar to AIC, but there has been an ongoing discussion about the two and which one is the best. Burnham and Anderson argue that AIC is superior to BIC for several reasons [3, 4]. Yang is in line with their conclusions, and shows that AIC chooses the optimal model in terms of the mean squared error, which BIC does not do [67]. The results of these studies motivate the selection between the two models made in this thesis; AIC will be used due to its superiority over BIC.
2.3 Errors
A number of factors affect the effectiveness of an OLS estimate. This section presents phenomenons that influence the result negatively, and how these may be treated. In this thesis, all presented errors have been considered and assessed throughout the study.
2.3.1 Endogeneity
An assumption for the OLS estimate is that the residual should have conditional mean zero, meaning that
E[|X] = 0
The estimation will otherwise not be valid. Violation of the above is a phenomenon called endogeneity and can be caused by various reasons, some described below. [39]
2.3.1.1 Sample selection bias
In regression analysis, it is often inconvenient or even impossible to use data representing the whole population. The remedy is to use a smaller sample representing the population.
However, if the sample is not selected at random, it will not properly be representative of the larger population. This yields a biased regression result. [39]
2.3.1.2 Simultaneity
Simultaneity is present when there is not a one way causality between the dependent variable and the independent variables. A common example is when trying to estimate a demand for some product using price as a covariate. Naturally, the two factors clearly affect each other both ways. The effect will be described in the error term, causing endogeneity. [39]
2.3.1.3 Missing relevant covariates
If some covariate from the ”true” model is omitted, it will be absorbed by the error term.
Endogeneity will occur if there is a correlation between the omitted variable and one of the included variables, or if the omitted variable separately affects the dependent variable.
[39]
2.3.1.4 Measurement errors
Assume an estimation of the model
yi= α + βX + e
is to be done, where β, α and e are the true coefficients of the relationship in the pop- ulation. However, if there is a measurement error v in the sampling of the independent variables, the covariate matrix X will be biased. Mathematically, the effect on the true X is
X∗= X + v
Inserting the biased X∗ in the regression equation yields
yi= α + βX + (e + βv) = α + βX + ξ
Now, the independent variables and the error term ξ are correlated through v and β, causing endogeneity [39].
2.3.2 Multicollinearity
Multicollinearity occurs when a covariate is highly correlated with another covariate or with a linear combination of multiple covariates. This causes the standard error∗ of some or all covariates to be very large, creating non-accurate estimates. However, since standard errors decrease as the sample size increases, multicollinearity can be seen as a problem only occurring when handling small sample sizes. [39]
2.3.3 Heteroscedasticity
Heteroscedasticity is the concept of unequally distributed error terms ei, as opposed to homoscedasticity, where all error terms are assumed to be equally distributed [39]. In particular, when the model is heteroscedastic, it is assumed that
E[ei] = 0, E[e2i] = σ2i and E[e4i] < ∞
or in the more convenient matrix notation
Y = Xβ + e where E[e] = 0 and E[eet] = D[σi2]
and the n dependent variables are collected in the n × 1 vector y, X is an n × (k + 1) matrix of the intercepts and covariates for each observation, e is an nx1 vector of error terms and D(σi2) is a diagonal matrix with the variances as diagonal elements. As can be seen, what differs in between observations is the variance of the error terms [39].
The ordinary least squares method assumes homoscedasticity, that is
E[ei] = 0, E[e2i] = σ2
In words, the variance of the residuals are equal for all observations [39].
2.3.3.1 Remedies for heteroscedasticity
Reformulate the model
Initially, if experiencing heteroscedasticity, one could try to change or transform the covariates. Common approaches are to use transformations of variables, for example to take the logarithm of y as the dependent variable, instead of the actual values of y. The aim is to reduce the spread of the data used. Adding more explanatory covariates could serve as a remedy as well [39].
∗The standard error of a covariate is the standard deviation of the sampling distribution.
White’s Consistent Variance Estimator
White’s Consistent Variance Estimator is an alternative to the standard covariance matrix for deriving the standard errors of a heteroscedastic regression. The matrix is defined as
Cˆov(ˆβ) = (XtX)−1XtD(ˆe2i)X(XtX)−1
In contrast to the regular covariance matrix, White’s estimator offers a consistent estima- tion of the standard errors despite them being heteroscedastic. Lang suggests that this model always should be used, if possible [39].
3 Finance theory
This section treats the finance theory that is used throughout the thesis. It includes the essential concept of risk, a cornerstone in corporate finance and every investment decision.
3.1 Adjusted closing price
The adjusted closing price of a stock is the regular closing price adjusted for splits, div- idends and other corporate actions that may change the market value of equity of the company. The adjusted closing price gives a fair representation of the equity value of the firm, unlike the market price. The price is useful when examining historical returns, which is why it will be used in this thesis. [21]
3.2 Rate of return
The rate of return, or just return∗, is the gain or loss on an investment for a specified time period in relation to the capital invested in the asset [29]. The gain or loss is comprised of all the cash flows the asset generates during the time period, including capital gains.
The ratio is quoted as a percentage and is calculated according to the formula below.
Rate of return = Final asset value - Initial asset value Initial asset value
Stocks, financial securities or portfolios are commonly evaluated by their historical rate of return in comparison with a benchmark. The benchmark could be assets of a similar type, but it could also be an index∗∗. If the return of an asset class is greater than a comparable index, the difference in return is titled excess return or abnormal return [25].
However, when discussing or comparing returns, the numbers themselves are not of much value without incorporating the concept introduced next, namely risk [6].
3.3 Risk
Risk is a measure of the likelihood that the realized return of an investment will be different than expected [30]. In this section, the concept of risk will be divided into its component parts and they will separately be explained more carefully. This concept is central for obtaining comparable performance values, which is a cornerstone in corporate finance theory as well as in this investigation.
∗In some cases, return alone refers to the absolute number of gain or loss, not the ratio [29].
∗∗Within the confines of financial markets, an index is an imaginary portfolio of a collection of secu- rities. These are selected so that the index represents a specific market or portion of a market [26].
3.3.1 Volatility and dispersion - the systematic risk
Volatility is a measure of dispersion, a term used to describe the degree of uncertainty as- sociated with a particular financial instrument in relation to a benchmark (predominantly an index). The measure used is either the standard deviation or variance related to the particular security. When investing in an asset that replicates a market, for example an index fund, volatility is synonymous with systematic risk, market risk or non-diversifiable risk. This is the common risk every investor assumes when investing in a market [33].
Systematic risk of a financial instrument is mainly measured by the beta (β) of the in- strument, which is explained later in this section.
3.3.2 Unsystematic risk
Unsystematic risk, diversifiable risk or specific risk, is the risk that an individual com- pany or industry is subject to. Hence, when investing in a stock, an investor assumes unsystematic risk in the specific stock and systematic risk in the overall market. [33]
3.3.3 The beta ratio
Beta, β, is a measure for describing the systematic risk of an asset in comparison to a certain benchmark, often an index describing the overall market. Investors use the measure to understand the risk profile of a stock, as it reflects the the behaviour, or volatility, of the stock in relation to the market. [59]
The coefficient is calculated as
β = Cov(Rp, Rb) Var(Rb)
where Rp and Rb are vectors containing historical returns of the asset and respectively, the benchmark [56].
The interpretation of the beta is how much the value of a stock fluctuates in relation to the movements of the benchmark. A beta of 0 therefore indicates that no correlation exists between the two. Stocks with betas high above 1 (or below -1) are considered as high risk stocks, since they fluctuate significantly more than the benchmark does. [27]
3.3.4 Risk-adjusted performance measures
Risk is closely related to rate of return. Higher risk may entail a higher potential rate of return, but also a larger loss. Hence, returns ought not to be compared without paying regard to the risk involved in obtaining the particular return in question.
To be able to measure returns from different securities, a risk-adjusted performance mea- sure can be used, which is a measure of return adjusted for the risk involved. By using a measure of this type, one may compare obtained returns regardless of what risk was involved.
There are numerous amounts of risk-adjusted performance measures. The regression in this thesis was made using the measure introduced below, Jensen’s alpha. It is a common measure frequently used in practice in the finance industry as well as in literature [23, 56, 68].
3.3.4.1 Jensen’s alpha
Jensen’s alpha, α, is a performance measure for an investment, presented in 1969 by Michael Jensen [28]. It measures the abnormal return with respect to a benchmark, often a market index. Hence, it yields a measure of performance relative to an alternative investment, with the risk of the alternative taken into account [56].
The background to alpha is based on modern portfolio theory, saying that investors want the highest possible returns to the lowest possible risk. Assuming excessive risk therefore implies a requirement of higher returns. In turn, this means a comparison of the returns of two investments, without including the risk involved, is misleading.
Alpha is calculated from a market model regression as follows
Rp− Rf = αp+ β(Rm− Rf) + p
where Rp is the realized return of an investment, Rm the market return, Rf the risk-free rate and p the firm-specific component of the risk, the unsystematic risk, fulfilling
E[p] = 0 and Cov[p, Rp] = 0
An alpha of 1 indicates one percentage point better return than expected with regard to the amount of systematic risk borne, described by beta.
Research has concluded that multi-variable versions of alpha reduces the variance of the excess returns. Although, as outlined by MacKinley, the marginal benefit the extra data collection yields is low [42]. Thus, it is not used in this thesis.
3.3.5 Time horizon
Time horizon is the time period of which an investor plans to hold an asset before liquidat- ing it. The time horizon is an essential part of the investment process and risk assessment that an investor goes through when analyzing an investment opportunity. The horizons
are often spoken of as short term or long term. Short term is often considered to be a period of up to one year, whereas long term often is considered three years or longer. [32]
3.3.5.1 Risk and time horizon
A longer time horizon allows for higher risk taking. When the time horizon is short, an investor should not assume much risk. For example, if there has been a downturn in the price of a stock before the time of which the investor plans to liquidate, the investor may have to sell when the rate of return is negative, i.e. with loss. Thus, investors take little risk if they have a short time horizon, and they may take more risk if their time horizon is long. [34]
4 Method
In this section, the overall structure and approach is presented. It is also presented how the data was collected and managed.
4.1 Overall structure and approach
To investigate the regression part of the research question and its underlying issues, the structure was as follows.
Firstly, the variables to include in the model were defined. This included defining the dependent variable, the calculation process of its value and its associated necessary com- ponents. Risk theory and corporate finance theory were central in this process. It also included defining what covariates to incorporate in the model. These selections are thor- oughly explained below. With the variables decided, an initial model was constructed.
Then, hypotheses of the regression results were formulated. The hypotheses were the re- sult of a qualitative study based on a literature study, macro analysis, corporate finance theory and logical reasoning.
Subsequently, data for the variables were collected, followed by data management. Since the result ought to answer what factors are essential to consider to be successful when following insider trading, both short term and long term, one regression for each time horizon was needed. These time horizons were defined as one year and five years respec- tively, in line with two of the periods used by Alles and Athanassakos in their study of the dimensions of time horizons in relation to returns [38]. Given the two horizons, two dependent vectors of data were calculated and used in the regression. Thus, two different regression results were obtained and presented. The results and the model were evaluated using mathematical tools introduced in section 2, followed by a reduction of the model into a final model. New regressions with the final model were conducted and new, im- proved results were obtained. The model and results were evaluated using the same tools as for the initial model. Lastly, conclusions were drawn followed by a discussion of the results in comparison to the hypotheses based on the qualitative study.
4.2 Choice of variables and data collection
There are many factors that could affect how successful insiders are in their trading. In addition, many of the relevant covariates are likely psychological and not measurable.
These would be beneficial to include in the regression, but since they are neither measur- able nor accessible, it is an unreasonable task to attempt to include them. It was decided that the choice of covariates should be based on what information is available from Fi- nansinspektionen (FI), where all data of historical insider transactions are grouped and available in Excel files [10]. From the available data, a qualitative assessment of what fac- tors could possibly affect excess return was done. These were then chosen to be included
in the model. The motivation for not including more measurable data is partly related to simplicity (it would be unreasonable to collect more specific data for each transaction when the sample size is of the magnitude used in this regression), but most importantly:
using only the information given from FI, it gives full resemblance of what information investors are given when taking part of insider trading publications.
The time frame from which to collect data for the covariates was chosen to be 10 years;
from 2006 to 2016. This time frame incorporates both economic downturns and upturns, which was considered favourable for obtaining a more complete investigation, leading to more valuable insights. The chosen time frame also incorporates the environment changes on the Stockholm Stock Exchange that have emerged during the last decade.
The environment changes include cheaper transaction costs and easier accessible company information, conditions which effect not have been tested by previous research [58, 68, 41].
Given the data of insider transactions, the historical stock prices of all companies on the Stockholm Stock Exchange were needed for calculating the rate of return on different time horizons for each transaction. To be able to compare the returns with returns of an index, the prices of the index was also needed. This information was obtained from the built-in Yahoo! Finance function in MATLAB. The stock price chosen was the adjusted closing price, which is suitable when comparing historical returns, as stated earlier. In addition, the risk-free interest rate was needed to calculate the alpha of the transactions.
These time series were collected from Riksbanken’s official website [55].
4.3 Data management
The collected insider data included all transactions in companies listed on the Stockholm Stock Exchange and the Nordic Growth Market∗. The data contained some 115 000 insider transactions, all made during the past 10 years. Clearly, some data management was needed to make the data fit the scope of this thesis. Below are the types of transactions that were removed from the data set.
• Transactions on other stock exchanges than the SSE
• Transactions in non-stock securities (such as options, futures or convertibles)
• Transactions in other than A, B or C stocks
• Sales transactions
• Inherited stocks or gifts
• Trades in stocks not listed on the SSE today, for example bankruptcies and list changes
∗The Nordic Growth Market is a small Swedish company that operates two regulated stock exchanges and one unregulated exchange [45].
• Trades in companies that has not been listed during the period of which beta is estimated on∗
In addition, obvious anomalies and errors have been removed to obtain as relevant data as possible. One important removal of data was the transactions in the Utilities sector, which is one of the sectors defined in the data. The sector contains a small group of companies, in which there were only a few transactions made. The data basis for this sector was thus too little to be of any value.
With all data collected and managed, the initial model could be formulated. The next section presents the initial model, explains the dependent variable and the covariates, and introduces hypotheses regarding the value sign of the coefficients in the model.
∗The reason for this exclusion is related to the calculation of beta, and is explained more thoroughly later. Barber and Lyon argues, however, that these type of exclusions in the data may cause biased abnormal returns if the benchmark is affected by new listings [44]. In this thesis though, the benchmark is represented by the 30 most traded companies on the SSE, and it is unreasonable to assume a potential effect of new listings on OMXS30 (explained thouroghly below) during the relatively short period used for estimating beta.
5 Model
This section presents and defines the two dependent variables and the independent vari- ables that has been used in the regressions. It is explained what data is included in each variable as well as how it is used to conduct the calculations needed. In addition, the qualitative hypotheses are stated. Ultimately, this section presents the complete model of interest.
5.1 Variables
5.1.1 The dependent variable
The dependent variable is the alpha that an investor would receive through a transaction at the publication date of an insider trade, with the OMXS30∗ index as benchmark.
Investing in funds that replicates the performance of the OMXS30 is a common investment alternative in Sweden, which is why it serves as a good benchmark from a retail investor perspective. That is, each element in the dependent vector is the risk-adjusted difference in return of a trade representing an insiders’s compared to the corresponding investment in the benchmark index. The risk-adjustment is done with a beta estimated on monthly returns during a period of three years prior to the publication date. This way of calculating beta emulates the statistic a retail investor would find by various known sources of finance information [8].
In the data management explanation in the preceding section, it was stated that trades in companies that has not been listed during the period of which beta is estimated on were excluded in the regression and that the explanation was beta related. Since the beta is obtained by the calculation stated above, betas for companies that have not been listed during the three years prior to the transaction date cannot be obtained. The beta calculation then becomes uncomparable to the others, resulting in exclusion of these transactions.
Since two different investing horizons are tested, two dependent vectors are needed to sep- arately describe the abnormal returns for each horizon. The resulting dependent variables serving as elements in the dependent vectors are thus
αp= Rp− Rf− β(Rm− Rf)
where Rp is the realized return of an insider investment, Rmthe corresponding return of OMXS30 and Rf the ten year Swedish government bond.
∗OMXS30 is a weighted index representing the 30 largest companies on the Stockholm Stock Exchange in terms of market capitalization.
5.1.2 The independent variables
As described in section 4, the selection of independent variables has been based on the data included in the publications from Finansinspektionen. From the available data, a qualitative assessment of what factors that possibly could affect excess returns culminated in the variables chosen to be included in the model. The factors were then divided into categories that serve as covariates for the regression. Below are explanations of each covariate, and why it was considered reasonable to be included in the model. Furthermore, the hypotheses for each factor are stated and motivated.
Size of transaction
Intuitively it seems reasonable that an insider would make a larger trade if he or she saw a greater potential in the stock. This thought was confirmed respectively by Seyhun and Jeng et al. in their research on insider transactions from the 70’s to the 90’s [58, 68].
They concluded that there was a positive correlation between the size of the an insider trade and its return, suggesting that larger trades exploit more valuable information.
Their research was however conducted almost 20 years ago, and the stock trading en- vironment have since changed substantially. This leads to believe that the result in this thesis might be different. Two main changes of conditions since their research were conducted are as previously mentioned: cheaper transaction costs and easier trading pro- cesses. Firstly, cheaper transaction costs have mainly arisen with the emergence and development of internet banks. The transaction costs of smaller niche banks, for ex- ample Avanza and Nordnet in Sweden, are almost negligible. Actually, in May 2016 Avanza announced that they have removed the transaction costs for smaller investors that have savings less than 50 000 Swedish kronors in an Avanza account [2]. Secondly, the emergence of the internet has made the process of trading stocks considerably easier.
In combination with low transaction costs, this has generally made it less of an effort to trade stocks, not least for insiders and the system of which their transactions are reported to Finansinspektionen. Thus, the insiders may reduce risk by splitting up their purchases into smaller volumes over time, since it comes at almost no cost. It is however worth mentioning that on special occasions, when there are extraordinary reasons for insiders to buy large volumes at one time, a signal value certainly would exist. Despite this, the assessment made here is that it occurs to seldom to be of significance. Cheaper transac- tion costs and easier trading processes should therefore reduce the significant signal value of insiders’ buy transactions, regardless of investing horizons. The conclusion, in contrast to the research of Seyhun and Jeng et al, is that the size of a transaction should not be significantly correlated to the excess return of a trade made by an insider.
Hypothesis 1: Regardless of time horizon, the size of the insider transaction has no significant correlation to the excess return of the investment.
To make the different transaction sizes comparable, and to reduce heteroscedasticity, the transaction size in the regression is defined as a proportion of what the insider’s holding size was before the transaction. Therefore, a value of 0.5 implies that the transaction increased the old holding size by 50%.
Position
Various examples show that when an insider trade gets attention in the news, it is often the case that the CEO of a company has made a large transaction. The rationale is that the CEO is the person with the best insights, and therefore the person with highest potential to predict a good opportunity to buy or sell. In other words, it means that the information asymmetry on the market is greater within the confines of a CEO’s trades.
Seyhun’s research agrees with the above and concludes that insiders who are expected to have more knowledge of the overall business of the organisation are more successful predictors of future abnormal returns than lower hierarchy directors [58]. Jeng et al. are however more careful and state that they cannot draw any conclusions about differences among positions [68]. Common for both is again that they were conducted decades ago.
A thought is that the information asymmetry on the market now may have been reduced by the emergence of the internet and the possibility to easier obtain information. That is, better information availability have made investors more informed and up to date on what is happening on the stock markets as well as in the listed companies, leading to a shrinkage in information asymmetry. Therefore, insiders should not have the same information advantage as they had before, which could cause the estimates to be non- significant.
Another matter arguing for the result of this analysis to be different from Seyhun’s is that his research was made on American stock markets. Since Sweden and America had (and still have) large culture differences, the advantage executives were shown to have over the markets could simply be explained by the American culture to some extent.
It is known that American corporations generally were (and still are) more hierarchical than Swedish corporations, and thus will the top-level information be more exclusive in American corporations, allowing the insiders to have greater information advantage [43, 54]. The above leads to the following hypothesis:
Hypothesis 2: Regardless of horizon, higher level in company hierarchy has no correla- tion to the return of the insider’s investments.
The data from FI contains numerous amounts of titles specified on different insider trans- actions. As this is qualitative data and several of the variations of titles actually describe the same title, but in different words, it is necessary to group them and create dummy variables for the groups. Three groups were ultimately chosen, and hence two dummy variables are used in the model. The third acted as benchmark. The variables are
• CEO
• Board member
• Other (Benchmark)
Season
The season factor is quite interesting. In finance, there is a proverb stating ”Sell in May and go away”. Statistics show that there are season based patterns in returns of stocks [31]. When analyzing historical returns of large indexes like the S&P 500 and OMXS30, it can be seen that returns have been higher during the winter compared to the summer [15]. The Dow Jones Industrial Average, for example, has had an average return of 0.3%
during the period May to October and 7.5% from November to April [22]. Figure 1 shows the distribution of historical average returns over seasons between 1984 and 2014 for the OMXS30 index.
Figure 1: Distribution of historical average returns over seasons, [15]
This questions the efficient market hypothesis∗, since seasonal effects would not be a phenomenon if all stocks always were traded at their fair value. Trying to understand why seasonal effects appear is essential in trying to formulate a hypothesis for the insider matter of this phenomenon. By understanding how they appear, it can be assessed if these reasons are different regarding insiders in relation to the overall market. Hallstr¨om tries to explain the strong seasonality differences by analyzing market psychology and how it affects the decision making of the investor community. His research has found that this could be part of the explanation, since the pricing mechanism on the market is made up of human action. The expectations and hopes of the people are large parts of the overall market investment interest [15].
Then, why would this contribute to seasonal variations in the market? Hallstr¨om argues that a possible explanation could be that the general set of mind tend to change when seasons change. As can be seen in Figure 1, August and September has historically been the months with the worst return. This is also the months where people get back to work from being on vacation. Thus, the general humor in the investment community could be affected by this tediousness, which could be reflected in the will to invest. However,
∗The efficient market hypothesis is a theory suggesting that it is impossible to outperform the market.
It is based on the notion that markets are efficient, meaning that all relevant information continuously is incorporated in share prices [24].
when people have gotten used to the boring weather and to working again, the general set of mind may change, Hallstr¨om continues. This positive mindset change could also be reflected in the will to invest [15]. All in all, this theory suggests that the will to invest is positively correlated with the underlying set of mind possessed by the practitioners in the investment community, and that it thus affects the market performance. Important to emphasize is that this is only one factor that might matter. Other important and more crucial factors are for example the underlying valuation of the stock market, which naturally is different from year to year.
When drawing conclusions about what hypothesis to formulate regarding this subject, it is essential to understand that even if insiders would be good at capitalizing on seasonal trends, that would not be the reason for positive regression results in this thesis. If that would be the case, selling signals would need to be incorporated as well, together with regressions on several time horizons where the the buy and sell transactions are made in different seasons. In this study, however, one possible explanation for an eventual result showing outperformance could be that insiders are good at realizing that their company have its own seasonal effects that are stronger than the market. This is not unreasonable. An interesting aspect which will be essential for this is if the information about a company’s own seasonality available on the market or not, or if insiders possess advantageous information regarding this issue, i.e. if information asymmetry about this exists on the market.
If insiders are able to realize when their company is incorrectly valued due to seasonal effects, the effect should be reduced over time since the uncertainty in the estimate natu- rally should increase as the investing horizon increases. The above leads to the following hypotheses.
Hypothesis 3(a): In the short term, seasons are correlated to the excess return of an insider’s investments. The highest positive correlation is the season of which the largest amount of companies have high seasonal dependence.
Hypothesis 3(b): In the long term, seasons have no significant correlation to the excess return of an insider’s investments.
In the regression, three covariates describing the time of year the transaction was made are introduced and defined as dummy variables, where the fourth season is the benchmark.
The periods are defined as:
• Winter : December - February
• Spring: Mars - May
• Summer : July - August
• Autumn: October - November (Benchmark)
Own holding
This dummy variable informs whether the transaction is made for the insider person’s own account, or if it is a relative or a legal person who has bought the shares. The benchmark, named Other investor, is that the insider is not the one who invests.
A hypothesis for this factor is not easy to support with data. Nevertheless, it could be argued that there should not be a significant difference whether it is the insider or the life partner of the insider who invests, since it is reasonable to believe that the insider is highly involved if a partner or close relative buys stocks in the company in question. At least it is reasonable to believe that there is a dialogue regarding these types of investment opportunities. The thought is supported by the research of Jeng et al. They conclude that the difference in ownership is insignificant [68]. The same argument holds for different time horizons, why it is reasonable to assume no difference in dependence for different investing horizons. Based on this, the hypothesis presented is:
Hypothesis 4: Whether the insider does the transaction for the own account or not, has no significant correlation to the return of the investment. This applies to both short and long term investments.
Sector
The sectors below are defined by Nasdaq∗ [48]. To test whether there is a difference in excess return among sectors, dummy variables corresponding to each sector are included in the regression. Note that Utilities is excluded from the model, as explained earlier.
The variables are
• Basic materials
• Consumer goods
• Financials
• Health care
• Industrials
• Oil & gas
• Technology
• Telecommunications
• Consumer Services (Benchmark)
It is difficult formulating a hypothesis of what sector has been successful to follow or not, and past research have not included this factor. Some reasoning could however be
∗Nasdaq is the company that operates the Stockholm Stock Exchange. The formal name of the exchange is Nasdaq Stockholm.
done to derive a hypothesis. The Health Care sector contains a large amount of biotech companies [50]. The future successes of this type of operations are uncertain since they only get paid for completed pharmaceutical products that can be sold in stores [19]. A similar dependence can be found for companies in the Oil & Gas sector, where future cash flows could be dependent of the potential success of oil or gas prospects. The difference between the two sectors lays in the Oil & Gas sector’s dependence on raw material prices, and as a natural consequence - macroeconomic cycles [52]. That is, the factors of success for the Health care sector are mostly depending on internal factors rather than external, macroeconomic factors. This could enable better conditions for insider investments. The reason is that the timing of the completions is hard to predict, especially for the overall market, which is why insiders should have an extra advantage - they have better insight in when and how the company will reach a milestone in their research. Naturally, this should be most applicable in the short term as the uncertainty of future cash flows will shrink while getting closer to a completion.
By the same reasoning, insiders in companies sensitive to macroeconomic cycles should have less of an advantage over the market since the factors of success are more difficult, or even impossible, to predict or affect. The global asset management company Fidelity Investments classifies Industrials and Basic Materials as sectors highly dependent of eco- nomic cycles [16].
In the long term, the information asymmetry in Health Care and sectors with similar visibility should be reduced as the effect on the total excess return of large, short term stock price increases will decrease over time. Nevertheless, the low signal value for cycle sensitive companies should naturally remain low. That is, the differences among the sectors should level out moderately compared to the short term investing horizon.
Hypothesis 5(a): In the short term, insiders in sectors where the future performance generally is highly dependent of macroeconomic factors will gain less excess return than the average sector. In contrast, insiders in companies in less cycle sensitive sectors should perform better than average.
Hypothesis 5(b): In the long term, the signal value in cycle dependent sectors will be greater than in the short term. Insiders in companies of less cycle sensitive sectors should still perform better than average.
Size of company
Fredrik Tyvand, analyst at Investtech, argues in an interview with Unga Aktiesparare that following insiders in small companies is more successful than following insiders in large companies [1]. He claims that the small companies are not as well covered by journalists and analysts (if covered at all) as larger companies are. This creates a greater information gap between insiders and the overall market. In addition, it is the larger companies that drive the returns of the benchmark index, which gives room for smaller companies to outperform the index if they are particularly successful. A larger information gap allows insiders to buy the shares at lower prices, before the information of value reaches the market (which can, for example, happen in conjunction with a quarterly report)∗. Mats
∗Naturally, these arguments refers to information gaps and time windows linked to quarterly reports
Larsson, small and mid cap analyst at Swedbank, agrees with Tyvand but stresses that insiders’ advantage in smaller companies should shrink as the investing horizon increases.
He argues that the market will rebalance the information gap naturally and therefore reduce the effect in excess return [40]. Previous research by Seyhun, Lakonishok et al.
and Jeng et al. confirms the thoeries of Tyvand and Larsson [58, 68, 41].
However, there are those who disagree. Erik Lid´en, PhD in Finance and Fund Manager at Insiderfonder, argues that the relationship between excess returns and insiders in smaller companies is not that striking. He states that when you adjust for risk, the best insiders are to be found in mid or large cap companies. The simple reason, according to him, is that the majority of the best investors are working in larger companies. [1]
To summarize, the experts do not agree on what company size is the most profitable to follow. To evaluate the question, a hypothesis is stated from the theories of Lakonishok et al. and Jeng et al. as
Hypothesis 6: Regardless of time horizon, the size of a company has a negative corre- lation to the return of an insider trade made in the company.
This factor is included in the regression by defining dummy variables to represent the size of the company. The average daily stock turnover∗ is used as proxy where the turnover is calculated over a period of 365 days prior to the transaction date. The different sizes are grouped in 4 different categories shown below, where the category with the largest turnover acts as benchmark.
• < 100K
• < 1M
• < 10M
• > 10M (Benchmark)
Female
The literature argues that there are differences between genders regarding investment strategies and performance [17]. This could be due to several reasons, and it need not necessarily be that any gender is better at investing than the other. However, what studies have concluded is that male investors generally are more confident than female investors regarding investing. On the other hand, females set clearer goals and trade less than males do [35]. In close relation to this, it has also been found that females are more risk averse than men are, in terms of investments [17]. In line with these findings, the data used in this regression clearly show differences in trading frequency which, possibly, may be closely related to risk. There are approximately eight times more transactions made by males than by females.
within the confines of the law.
∗The daily stock turnover is the number of stocks that has been traded in a specific company during one day.
